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Effective Use of PID
                         Controllers
                         ISA New Orleans 3-7-2013




Standards
Certification
Education & Training
Publishing
Conferences & Exhibits
                                                    1
Presenter
  – Greg is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow.
    Greg was an adjunct professor in the Washington University Saint Louis
    Chemical Engineering Department 2001-2004. Presently, Greg contracts as a
    consultant in DeltaV R&D via CDI Process & Industrial and is a part time
    employee of Experitec and MYNAH. Greg received the ISA “Kermit Fischer
    Environmental” Award for pH control in 1991, the Control Magazine “Engineer
    of the Year” Award for the Process Industry in 1994, was inducted into the
    Control “Process Automation Hall of Fame” in 2001, was honored by InTech
    Magazine in 2003 as one of the most influential innovators in automation, and
    received the ISA Life Achievement Award in 2010. Greg is the author of 20
    books on process control, his most recent being Advanced Temperature
    Measurement and Control. Greg has been the monthly “Control Talk”
    columnist for Control magazine since 2002 and has started a Control Talk
    Blog. Greg’s expertise is available on the Control Global and Emerson
    modeling and control web sites:
    http://community.controlglobal.com/controltalkblog
    http://modelingandcontrol.com/author/Greg-McMillan/




                                                                                    2
Resources




            3
Top Ten Ways to Impress Management with Trends

 •   (10) Make large setpoint changes that zip past valve dead band and nonlinearities.
 •   (9) Change the setpoint to operate on the flat part of the titration curve.
 •   (8) Select the tray with minimum process sensitivity for column temperature control.
 •   (7) Pick periods when the unit was down.
 •   (6) Decrease the time span so that just a couple data points are trended.
 •   (5) Increase the reporting interval so that just a couple data points are trended.
 •   (4) Use really thick line sizes.
 •   (3) Add huge signal filters.
 •   (2) Increase the process variable scale span so it is at least 10x control region
 •   (1) Increase the historian's data compression so changes are screened out




                                                                                            4
Contribution of Each PID Mode
•   Proportional (P mode) - increase in gain increases P mode contribution
     –   Provides an immediate reaction to magnitude of measurement change to minimize
         peak error and integrated error for a disturbance
     –   Too much gain action causes fast oscillations (close to ultimate period) and can make
         noise and interactions worse
     –   Provides an immediate reaction to magnitude of setpoint change for P action on Error
         to minimize rise time (time to reach setpoint)
     –   Too much gain causes falter in approach to setpoint
•   Integral (I mode) - increase in reset time decreases I mode contribution
     –   Provides a ramping reaction to error (SP-PV) to minimize integrated error if stable (since
         error is hardly ever exactly zero, integral action is always ramping the controller output)
     –   Too much integral action causes slow oscillations (slower than ultimate period)
     –   Too much integral action causes an overshoot of setpoint (no sense of direction)
•   Derivative (D mode) - increase in rate time increases D mode contribution
     –   Provides an immediate reaction to rate of change of measurement change to minimize
         peak error and integrated error for a disturbance
     –   Too much rate action causes fast oscillations (faster than ultimate period) and can make
         noise and interactions worse
     –   Provides an immediate reaction to rate of change of setpoint change for D action on
         Error to minimize rise time (time to reach setpoint)
     –   Too much rate causes fast oscillation in approach to setpoint
Contribution of Each PID Mode


                   kick from filtered
                   derivative mode


    Signal     ∆%CO1
      (%)     step from
              proportional                               ∆%CO2 = ∆%CO1
              mode
                                                         repeat from
                              seconds/repeat             Integral mode


               ∆%SP


               PID structure with proportional, integral, and derivative action on error


                                                                              Time
                                                                            (seconds)

             Contribution of Each PID Mode for a Step Change in the Set Point
                          Structure of PID on error (β=1 and γ=1)
Effect of Gain on P-Only Controller
Red is 150% of maximum, Green is 100% of maximum, Purple is 50% of maximum of Gain Setting
Effect of Reset Time on PI Controller
Red is 150% of maximum, Green is 100% of maximum, Purple is 50% of maximum Reset Time
Effect of Rate Time on PD Controller
Red is 200% of maximum, Green is 100% of maximum, Purple is 0% of maximum Rate Time
Proportional Mode Basics
Note that many analog controllers used proportional band instead of gain for the proportional mode tuning
setting. Proportional band is the % change in the process variable (∆%PV) needed to cause a 100% change
in controller output (∆%CO). A 100% proportional band means a 100% ∆%PV would cause a 100 % ∆%CO
(a gain of 1). It is critical that users know the units of their controller gain setting and convert accordingly.

Gain = 100 % / Proportional Band


•   Proportional Mode Advantages

•   Minimize dead time from stiction and backlash
•   Minimize rise time
•   Minimize peak error
•   Minimize integrated error

•   Proportional Mode Disadvantages

•   Abrupt changes in output upset operators
•   Abrupt changes in output upset other loops
•   Amplification of noise


                                                                                                                    10
Integral Mode Basics
Note that many analog controllers used reset settings in repeats per minute instead of reset time
for the integral mode tuning setting. Repeats per minute indicate the number of repeats of the
proportional mode contribution in a minute. Today’s reset time settings are minutes per repeat or
seconds per repeat which gives the time to repeat the proportional mode contribution. Often the
“per repeat” term is dropped giving a reset time setting in minutes or seconds.

Seconds per repeat = 60 / repeats per minute

Integral Mode Advantages

•   Eliminate offset
•   Minimize integrated error
•   Smooth movement of output

•   Integral Mode Disadvantages

•   Limit cycles
•   Overshoot
•   Runaway of open loop unstable reactors


                                                                                                    11
Derivative Mode Basics
Nearly all derivative tuning settings are given as a rate time in seconds or minutes. The effective
rate time setting must never be greater than the effective reset time setting. The effective settings
are for an ISA Standard Form. The advantages and disadvantages of the derivative mode are
similar to that of the proportional mode except the relative advantages is less and the relative
disadvantages are greater for the derivative mode.

Seconds = 60 ∗ minutes

•   Derivative Mode Advantages

•   Minimize dead time from stiction and backlash
•   Minimize rise time
•   Minimize peak error
•   Minimize integrated error

•   Derivative Mode Disadvantages

•   Abrupt changes in output upset operators
•   Abrupt changes in output upset other loops
•   Amplification of noise

                                                                                                        12
Reset Gives Operations What They Want

  Should steam or water valve be open ?

                      TC-100
                Reactor Temperature

                 CO     PV    SP
                                      temperature


        steam
        valve
        opens
                                                            SP
  50%                                               PV

        water
        valve
        opens




                  ?     48    52                         time
Open Loop Time Constant (controller in manual)

      Signal
        (%)


                       %CO
                                                                      Controller is in Manual




  Open Loop
  Error Eo (%)
                                         %PV
                        0.63∗Eo                                     %SP




                 0                  θo         τo                                   Time
                                                                                  (seconds)
                      Dead Time                       Open Loop
                     (Time Delay)                      (process)
                                                    Time Constant
                                                      (Time Lag)
Closed Loop Time Constant (controller in auto)

    Signal
      (%)


                  %CO                                       Controller is in Automatic
                                                        %SP




    ∆%SP

                 0.63∗∆%SP           %PV




             0                  θo     τc                                    Time
                                                                           (seconds)
                  Dead Time                  Closed Loop
                 (Time Delay)               Time Constant
                                              (Time Lag)
                                             Lambda (λ)
Top Ten Signs Loops Need to be Tuned
•   (10) Lots of trials and errors.
•   (9) When asked what the controller gain setting is, the answer is given in %.
•   (8) When asked what the controller reset time setting is, the answer is in repeats/min.
•   (7) The data historian compression setting is 25%.
•   (6) There is more recycle than product.
•   (5) Valves are wearing out.
•   (4) Tempers are wearing thin.
•   (3) Operators are placing bets on what loop will cause the next shutdown.
•   (2) The output limits are set to keep the valve from moving.
•   (1) Preferred mode is manual.




                                                                                              16
Conversion of Signals for PID Algorithm

                                                                        Final Control Element




                    %          %           %
             SCLR       SUB                                                   Control              Process
                                     PID         SCLR              AO
      SP                                                OUT                    Valve              Equipment
                               %           %CO                                            MV
                     %PV                                (e.u.)                           (e.u.)
                        SCLR
                                                 PID
                     PV
                    (e.u.)
                                                                              Smart          Sensing
                                                                   AI
                                                                           Transmitter PV    Element
                                   PV - Primary Variable
                                   SV - Second Variable*                              (e.u.)
                                   TV - Third Variable*
           DCS                     FV - Fourth Variable*                          Measurement
                                   * - additional HART variables


   The scaler block (SCLR) that convert between engineering units of application and % of scale
 used in PID algorithm is embedded hidden part of the Proportional-Integral-Derivative block (PID)

       To compute controller tuning settings, the process variable and controller output
       must be converted to % of scale and time units of dead times and time constants
               must be same as time units of reset time and rate time settings!
Series Form

    Form in analog controllers and early DCS – available as a choice in most modern DCS
                 β                 Gain



                ∗       ∆             ∗                                        proportional
                                                Inverse
%SP                                              Reset All signals are % of scale in PID algorithm but
                                                  Time inputs and outputs are in engineering units


filter                  ∆             ∗             ∗                            integral                Σ   %CO
                                                             Filter Time =
                 γ                                           α ∗ Rate Time
                                                 Rate
                                                 Time


                 ∗      ∆             ∗             ∗             filter        derivative


         %PV   filter                                                                                    Σ
                              Switch position for no derivative action




                                                                                                                   18
Parallel Form

                Form in a few early DCS and PLC and in many control theory textbooks
                                       Proportional
                       β               Gain Setting



                      ∗       ∆             ∗                                 proportional

 %SP                                     Integral
                                                      All signals are % of scale in PID algorithm but
                                       Gain Setting
                                                       inputs and outputs are in engineering units


 filter                       ∆             ∗                                   integral                Σ   %CO

                       γ
                                        Derivative
                                       Gain Setting


                       ∗      ∆             ∗                                  derivative


          %PV        filter




                                                                                                                  19
ISA Standard Form

                             Default Form in most modern DCS
                  β               Gain



                 ∗       ∆         ∗                                    proportional
                                         Inverse
 %SP                                      Reset All signals are % of scale in PID algorithm but
                                           Time inputs and outputs are in engineering units


 filter                  ∆         ∗        ∗                             integral                Σ   %CO
                                                   Filter Time =
                  γ                       Rate     α ∗ Rate Time
                                          Time


                  ∗      ∆         ∗        ∗          filter           derivative


          %PV   filter




                                                                                                            20
Positive Feedback Implementation of Integral

                                        Form for Enhanced PID developed for wireless
                                             Gain   * Back out positive feedback of Feedforward (*FF) and ISA Standard Form of
                                                          Proportional (*P) and Derivative (*D) modes with β and γ factors

                        +                                                    P = (β −1) ∗ Gain ∗ %SP
                ∗               ∆             ∗
                            −
                                                    All signals are % of scale in PID algorithm but
                β                                    inputs and outputs are in engineering units
%SP                                                                                                                     Feedforward
                                                           For zero error
                 For reverse action,
                                                             Out1 = 0                                      P                       FF
                 Error = %SP - %PV
                      +                                    Out1
filter                              ∆         ∗                   Σ                                    Σ                      Σ            %CO
                            −                                                    Filter Time =
                                                     Positive         Out2                                 D
                                                                                 Reset Time
                                                    Feedback
                                                                                                                   *P        *FF
                 γ                                                                                                                        Switch position
                                                    Rate
                                                                                     filter                    ∆         ∆                  for external
                                                    Time                                                                                  reset feedback
                                                                                                                   *D
                            +
                ∗                   ∆         ∗       ∗            filter          derivative
                                −                                                                                                   E-R
                                                                                  Filter Time =                          E-R is external reset
         %PV   filter                                                             Reset Time                            (e.g. secondary %PVs)
                                                                Filter Time =                                            Dynamic Reset Limit
                                                                α ∗ Rate Time



                                                                                                                                                            21
Conversion of Series to ISA Form
To convert from Series to ISA Standard Form controller gain:

      Ti ' + Td'
 Kc =            ∗ K c'
          Ti '                          Interaction factor


To convert from Series to ISA Standard Form reset (integral) time:

       Ti ' + Td'
  Ti =            ∗ Ti ' = Ti ' + Td'
           Ti '
 To convert from Series to ISA Standard Form rate time:

         Ti '
  Td = '       ∗ Td'
      Ti + Td'
                            Primed tuning settings are Series Form
 Note that if the rate time is zero, the ISA Standard and Series Form settings are identical.
  When using the ISA Standard Form, if the rate time is greater than ¼ the reset time the
response can become oscillatory. If the rate time exceeds the reset time, the response can
 become unstable from a reversal of action form these modes. The Series Form inherently
prevents this instability by increasing the effective reset time as the rate time is increased.
                                                                                                  22
Anti Reset Windup (ARW) and Output Limits
  • For digital positioners and precise throttling valves
     – ARW & Out Lo Lim = 0%, ARW & Out Hi Lim = 100%
  • For pneumatic positioners & on-off heritage valves
     – Lo Lim = -5%, Hi Lim = 105%
     – ARW set inside output limits to get thru zone of ineffective valve
       response (stick-slip, shaft windup, & poor sensitivity)
  • For primary PID in cascade control, limits are set to match
    secondary setpoint limits in engineering units
Checklist for PID Migration - 1
 There are many features and parameters that vary with the DCS supplier. It is imperative the DCS
   documentation and supplier expertise be fully utilized and all migrations tested by a real time
   simulation for stability. Note the default of 0% low and 100% high output and ARW limits do not
   change to match changes made in output scale or engineering units.
 For cascade control did you set the output scale of the primary PID in engineering units of the PV
   scale of the secondary loop?
 For cascade control did you set the primary PID low and high output limits in engineering units to
match setpoint limits of secondary PID?
 Did you set the anti-reset windup (ARW) limits to match the output limits using same units as
output limits unless there is some special need for ARW limits to be set otherwise?
 Did you convert controller gain setting units (being especially aware of the inverse relationship
between proportional band and gain)?
 Did you convert reset units setting (being especially aware of the inverse relationship between
repeats per minute and seconds per repeat)?
 Did you convert rate units setting and make the alpha setting the same for the rate filter?
 If rate time is not zero and ISA Standard Form is used, did you convert Series Form gain, reset,
and rate settings to corresponding ISA Standard Form settings?


                                                                                                       24
Checklist for PID Migration - 2

 For override control if the positive feedback implementation of integral mode is used, did you
remove the filter on external reset signal used to prevent walk-off since this filter is already there?
 For cascade control, id you turn on external reset feedback (dynamic reset limit) and use PV of
secondary loop for external reset feedback to automatically prevent burst of oscillations from violation
of cascade rule that secondary loop must be 5x faster than primary loop?
 For slow or sticky valve, did you turn on external reset feedback (dynamic reset limit) and use a fast
PV readback for external reset feedback to automatically prevent burst of oscillations from violation of
cascade rule that positioner feedback loop must be 5x faster than primary loop and to prevent limit
cycles from stick-slip? Did you realize the PV readback must normally be faster than a secondary HART
variable update time?
 For wireless control and at-line or on-line analyzer, did you use an enhanced PID developed for
wireless that suspends integral action between updates (PIDPlus option) and uses elapsed time in the
derivative action. The external-reset option should automatically be turned on?
 Did you make sure the BKCAL signals are connected properly paying particular attention to the
propagation of the BKCAL settings for intervening blocks for split range, signal characterization, and
override control?


                                                                                                           25
Top 10 Things You Shouldn't Say
When You Enter a Control Room
•   (10) Does this hard hat make my butt look big?
•   (9) At the last plant I was in we always did it this way.
•   (8) I added alarms to each loop.
•   (7) Does that flare out there always shoot up that high?
•   (6) Ooooh! Did you mean to do that?
•   (5) Can't somebody do something about all those alarms?
•   (4) We just downloaded the version released yesterday
•   (3) Here, I will show you how to operate this plant.
•   (2) Are you ready to put all your loops in Remote Cascade?
•   (1) We want a "lights out" plant!




                                                                 26
Triple Cascade Loop Block Diagram


       Process Primary Controller – Secondary Flow Controller – Digital Valve Controller


                      DCS                                      Valve Positioner
 Process          Flow                                    Drive Signal
   SP              SP                   CO                                                 Control   Flow
           PID               PID                 AO    PID*         I/P       Relay                          Process
                 External             External                                              Valve    Meter
                  Reset                Reset
                 BKCAL                BKCAL                      Position (Valve Travel)
       PV                   PV
                                                              Position Loop Feedback                         Process
            AI                   AI                                                                          Sensor
                                                      * most positioners use proportional only
                                                        Secondary (Inner) Loop Feedback




                                                          Primary (Outer) Loop Feedback
Effect of Slow Secondary Tuning (cascade control)



                                     Secondary loop slowed down by a factor of 5


                                                Secondary CO




                       Primary PV




                          Secondary SP


                                                     Secondary SP
                      Secondary CO
                                                Primary PV
External Reset Feedback (Dynamic Reset Limit)

  •   Prevents PID output changing faster
      than a valve, VFD, or secondary
      loop can respond
       – Secondary PID slow tuning
       – Secondary PID SP Filter Time
       – Secondary PID SP Rate Limit
       – AO, DVC, VFD SP Rate Limit
       – Slow Valve or VFD
       – Use PV for BKCAL_OUT
       – Position used as PV if valve is very
         slow and readback is fast
       – Enables Enhanced PID for Wireless
  •   Stops Limit cycles from deadband,
      backlash, stiction, and threshold
      sensitivity or resolution limits
  •   Key enabling feature that simplifies
      tuning and creates more advanced
      opportunities for PID control
PID Structure Options

(1)   PID action on error (β = 1 and γ = 1)
(2)   PI action on error, D action on PV (β = 1 and γ = 0)
(3)   I action on error, PD action on PV (β = 0 and γ = 0)
(4)   PD action on error, no I action (β = 1 and γ = 1)
(5)   P action on error, D action on PV, no I action (β = 1 and γ = 0)
(6)   ID action on error, no P action (γ = 1)
(7)   I action on error, D action on PV, no P action (γ = 0)
(8)   Two degrees of freedom controller (β and γ adjustable 0 to 1)
(1) PID action on error

• Fastest response to rapid (e.g. step) SP change by
    – Step in output from proportional mode
    – Spike in output from derivative mode can be made more like a kick by
      decreasing gamma factor (γ <1)
    – Zero dead time from deadband, resolution limit, & stiction
•   Burst of flow may affect other uses of fluid
•   Operations do not like sudden changes in output
•   Fast approach to SP more likely to cause overshoot
•   Setpoint filter & rate limits eliminate step & overshoot
(2) PI action on error, D action on PV

  • Slightly slower SP response than structure (1)
     – Still have step from proportional mode
     – Spike or bump from derivative mode eliminated
  • Decrease in SP response speed is negligible if
     – Output hits output limit due to large SP change or PID gain
     – Rate time is less than total loop dead time
     – Alpha factor is increased (α > 0.125) (rate filter increased)
  • Setpoint filter & rate limits eliminate step & overshoot
  • Most popular structure choice
(3) I action on error, PD action on PV

• Provides gradual change in output for SP change
• Slows down SP response dramatically
• Eliminates overshoot for SP changes
• Used for bioreactor temperature and pH SP changes
  (overshoot is much more important than cycle time)
• Used for temperature startup to warm up equipment
• Generally not recommended for secondary loops
(4 - 5) No Integral action
 •   Used if integral action adversely affects process
 •   Used if batch response is only in one direction
 •   Must set bias (output when PV = SP)
 •   Highly exothermic reactors use structure 4 because
     integral action and overshoot can cause a runaway
     – 10x reset time (Ti > 40x dead time) to prevent runaway
 • Traditionally used on Total Dissolved Solids (TDS) drum
   and surge tank level control because of slow integrating
   response and permissibility of SP offset.
     – Low controller gain (Kc) cause slow rolling oscillations due to
       violation of inequality for integrating process. The inequality is
       commonly violated since Ki (integrating process gain) is extremely
       small on most vessels (Ki < 0.000001 %/sec/%).
  Most common problem is use of too small of a reset time for vessel batch
   composition and temperature, level, and gas pressure control causing
                       violation of following rule
                                          2
                               K c * Ti >
                                          Ki
(6 -7) No Proportional Action

  • Predominantly used for valve position control (VPC)
     – Parallel valve control (VPC SP & PV are small valve desired & actual
       position, respectively, & VPC out positions large valve)
     – Optimization (VPC SP & PV are limiting valve desired & actual
       position, respectively, & VPC out optimizes process PID SP)
     – VPC reset time > 10x residence time to reduce interaction
     – VPC reset time > Kc∗Ti of process PID to reduce interaction
     – VPC tuning is difficult & too slow for fast & large disturbances
  • Better solution is external reset feedback & SP rate limits
Improvement in Batch Temperature by
Elimination of Integral action

                      Batch temperature response in a single ended temperature
                      control. Integral action causes overshoot.
                                           Typical Batch Temperature
                      80
                      70
                      60
          degrees C

                      50
                      40
                      30
                      20
                      10
                       0
                           1       51     101    151         201         251     301   351   401
                                                        Time (min)

                                                  Setpoint          PV         CO%



                      Batch temperature response in a single ended temperature
                      control. PD on error. No I action.
                                         Batch Temperature (new tuning)
                      45.0
                      40.0
                      35.0
          degrees C




                      30.0
                      25.0
                      20.0
                      15.0
                      10.0
                       5.0
                       0.0
                               1    51     101    151         201        251     301   351   401
                                                         Time (min)

                                                   Setpoint         PV         CO%


                                                                                                   36
(8) Two Degrees of Freedom

• β and γ SP weighting factors are adjusted to balance fast
  approach & minimal overshoot for SP response
• Alternative is using SP lead-lag with lag = reset time and lead =
  20% of lag to achieve fast SP response with minimal overshoot
Effect of Options on SP Response
Top Ten Reasons to Use a DCS for Your BBQ

•   (10) Automated recipes
•   (9) Predicted BBQ times
•   (8) Five-course meal no problem
•   (7) Don't have to watch cooking shows
•   (6) Feed-forward control
•   (5) Process control comes home
•   (4) Children want to become automation engineers
•   (3) Spouse finally appreciates your expertise
•   (2) Griller not grilled
•   (1) More time to drink beer




                                                       39
Fed-Batch and Startup Time Reduction - 1
•   PID on Error Structure
    –   Maximizes the step and kick of the controller output for a setpoint change.
    –   Overdrive (driving of output past resting point) is essential for getting slow loops, such
        as vessel temperature and pH, to the optimum setpoint as fast as possible.
    –   The setpoint change must be made with the PID in Auto mode.
    –   “SP track PV” will generally maximize the setpoint change and hence the step and kick
        (retaining SP from last batch or startup minimizes kick and bump)
•   SP Feedforward
    –   For low controller gains (controller gain less than inverse of process gain), a setpoint
        feedforward is particularly useful. For this case, the setpoint feedforward gain is the
        inverse of the dimensionless process gain minus the controller gain.
    –   For slow self-regulating (e.g. continuous) processes and slow integrating (e.g. batch)
        processes, even if the controller gain is high, the additional overdrive can be beneficial
        for small setpoint changes that normally would not cause the PID output to hit a limit.
    –   If the setpoint and controller output are in engineering units the feedforward gain must
        be adjusted accordingly.
    –   The feedforward action is the process action, which is the opposite of the control
        action, taking into account valve action. In other words for a reverse control action, the
        feedforward action is direct provided the valve action is increase-open or the analog
        output block, I/P, or positioner reverses the signal for a increase-close.
Fed-Batch and Startup Time Reduction - 2
•   Full Throttle (Bang-Bang Control) - The controller output is stepped to it output
    limit to maximize the rate of approach to setpoint and when the projected PV
    equals the setpoint less a bias, the controller output is repositioned to the final
    resting value. The output is held at the resting value for one dead time. For more
    details, check out the Control magazine article “Full Throttle Batch and Startup
    Response.” http://www.controlglobal.com/articles/2006/096.html
    –   A dead time (DT) block must be used to compute the rate of change so that new values of
        the PV are seen immediately as a change in the rate of approach.
    –   If the total loop dead time (θo) is used in the DT block, the projected PV is simply the current
        PV minus the output of the DT block (∆PV) plus the current PV.
        –   If the PV rate of change (∆PV/∆t) is useful for other reasons (e.g. near integrator or true integrating
            process tuning), then ∆PV/∆t = ∆PV/θo can be computed.
    –   If the process changes during the setpoint response (e.g. reaction or evaporation), the
        resting value can be captured from the last batch or startup
    –   If the process changes are negligible during the setpoint response, the resting value can be
        estimated as:
        –   the PID output just before the setpoint change for an integrating (e.g. batch) process
        –   the PID output just before the setpoint change plus the setpoint change divided by the process gain
            for a self-regulating (e.g. continuous) process
    –   For self-regulating processes such as flow with the loop dead time (θo) approaching or
        less than the largest process time constant (τp ), the logic is revised to step the PID
        output immediately to the resting value. The PID output is held at the resting value for
        the T98 process response time (T98 = θo + 4∗ τo ).
Fed-Batch and Startup Time Reduction - 3
•   Output Lead-Lag
    –   A lead-lag on the controller output or in the digital positioner can kick the signal though
        the valve deadband and stiction, get past split range points, and make faster
        transitions from heating to cooling and vice versa.
    –   A lead-lag can potentially provide a faster setpoint response with less overshoot when
        analyzers are used for closed loop control of integrating processes When combined
        with the enhanced PID algorithm (PIDPlus) described in:
        –   Deminar #1 http://www.screencast.com/users/JimCahill/folders/Public/media/5acf2135-
            38c9-422e-9eb9-33ee844825d3
        –   White paper http://www.modelingandcontrol.com/DeltaV-v11-PID-Enhancements-for-
            Wireless.pdf
•   Dead Time Compensation
    –   The simple addition of a delay block with the dead time set equal to the total loop dead
        time to the external reset signal for the positive feedback implementation of integral
        action described in Deminar #3 for the dynamic reset limit option
        http://www.screencast.com/users/JimCahill/folders/Public/media/f093eca1-958f-4d9c-
        96b7-9229e4a6b5ba .
    –   The controller reset time can be significantly reduced and the controller gain increased
        if the delay block dead time is equal or slightly less than the process dead time as
        studied in Advanced Application Note 3
        http://www.modelingandcontrol.com/repository/AdvancedApplicationNote003.pdf
Fed-Batch and Startup Time Reduction - 4
•   Feed Maximization
    –   Model Predictive Control described in Application Note 1
        http://www.modelingandcontrol.com/repository/AdvancedApplicationNote001.pdf
    –   Override control is used to maximize feeds to limits of operating constraints via valve
        position control (e.g. maximum vent, overhead condenser, or jacket valve position with
        sufficient sensitivity per installed characteristic).
    –   Alternatively, the limiting valve can be set wide open and the feeds throttled for temperature
        or pressure control. For pressure control of gaseous reactants, this strategy can be quite
        effective.
    –   For temperature control of liquid reactants, the user needs to confirm that inverse response
        from the addition of cold reactants to an exothermic reactor and the lag from the
        concentration response does not cause temperature control problems.
    –   All of these methods require tuning and may not be particularly adept at dealing with fast
        disturbances unless some feedforward is added. Fortunately the prevalent disturbance that
        is a feed concentration change is often slow enough due to raw material storage volume to
        be corrected by temperature feedback.
•   Profile Control
    –   If you have a have batch measurement that should increase to a maximum at the batch end
        point (e.g. maximum reaction temperature or product concentration), the slope of the batch
        profile of this measurement can be maximized to reduce batch cycle time. For application
        examples checkout “Direct Temperature Rate of Change Control Improves Reactor
        Yield” in a Funny Thing Happened on the Way to the Control Room
        http://www.modelingandcontrol.com/FunnyThing/ and the Control magazine article
        “Unlocking the Secret Profiles of Batch Reactors”
        http://www.controlglobal.com/articles/2008/230.html .
Dead Time Compensator Configuration




                      Must enable dynamic reset limit !

                     Insert
                    deadtime
                      block
Dead Time Myths Busted
•    Dead time is eliminated from the loop. The smith predictor, which created a PV without
     dead time, fools the controller into thinking there is no dead time. However, for an
     unmeasured disturbance, the loop dead time still causes a delay in terms of when the loop
     can see the disturbance and when the loop can enact a correction that arrives in the
     process at the same point as the disturbance. The ultimate limit to the peak error and
     integrated error for an unmeasured disturbance are still proportional to the dead time, and
     dead time squared, respectively.
•    Control is faster for existing tuning settings. The addition of dead time compensation
     actually slows down the response for the existing tuning settings. Setpoint metrics, such as
     rise time, and load response metrics, such as peak error, will be adversely affected.
     Assuming the PID was tuned for a smooth stable response, the controller must be retuned
     for a faster response. For a PID already tuned for maximum disturbance rejection, the gain
     can be increased by 250%. For dead time dominant systems where the total loop dead
     time is much greater than the largest loop time constant (hopefully the process time
     constant), the reset time must also be decreased or there will be severe undershoot. If you
     decrease the reset time to its optimum, undershoot and overshoot are about equal. For the
     test case where the total loop dead time to primary process time constant ratio was 10:1,
     you could decrease the reset time by a factor of 10. Further study is needed as to whether
     the minimum reset time is a fraction of the underestimated dead time plus the PID module
     execution time where the fraction depends upon the dead time to time constant ratio


     For access to Deminar 10 ScreenCast Recording or SlideShare Presentation go to
    http://www.modelingandcontrol.com/2010/10/review_of_deminar_10_-_deadtim.html
Dead Time Myths Busted
•   Compensator works better for loops dominated by a large dead time. The reduction in
    rise time is greatest and the sensitivity to per cent dead time modeling error particularly for
    an overestimate of dead time is least for the loop that was dominated by the process time
    constant. You could have a dead time estimate that was 100% high before you would see
    a significant jagged response when the process time constant was much larger than the
    process dead time. For a dead time estimate that was 50% too low, some rounded
    oscillations developed for this loop. The loop simply degrades to the response that would
    occur from the high PID gain as the compensator dead time is decreased to zero. While
    the magnitude of the error in dead time seems small, you have to remember that for an
    industrial temperature control application, the loop dead time and process time constant
    would be often at least 100 times larger. For a 400 second dead time and 10,000 second
    process time constant, a compensator dead time 200 seconds smaller or 400 seconds
    larger than actual would start to cause a problem. In contrast, the dead time dominant loop
    developed a jagged response for a dead time that was high or low by just 10%. I think this
    requirement is unreasonable in industrial processes. A small filter of 1 second on the input
    to the dead time block in the BKCAL path may have helped.
•    An underestimate of the dead time leads to instability. In tuning calculations for a
    conventional PID, a smaller than actual dead time can cause an excessively oscillatory
    response. Contrary to the effect of dead time on tuning calculations, a compensator dead
    time smaller than actual dead time will only cause instability if the controller is tuned
    aggressively after the dead time compensator is added.
•   An overestimate of the dead time leads to sluggish response and greater stability. In
    tuning calculations for a conventional PID, a larger than actual dead time can cause an
    excessively slow response. Contrary to the effect of dead time on tuning calculations, a
    compensator dead time greater than actual dead time will cause jagged irregular
    oscillations.
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•   (1) Readily tuned
General PID Checklist - 1

 Does the measurement scale cover the entire operating range, including abnormal
 conditions?
 Is the valve action correct (increase-open for fail close and increase-close for fail open)?
 Is the control action correct (direct for reverse process and reverse for direct process if the
 valve action is set)?
 Is the best “Form” selected (ISA standard form)?
 Is the “obey setpoint limits in cascade and remote cascade mode” option selected?
 Are the external reset feedback (BKCAL) signals correctly connected between blocks?
 Is the PV for BKCAL selected in the secondary loop PID?
 Is the best “Structure” selected (PI action on error, D action on PV for most loops)?
 Is the “setpoint track PV in manual” option selected to provide a faster initial setpoint
 response unless the setpoint must be saved in PID?




                                                                                                    48
General PID Checklist - 2
 Are setpoint limits set to match process, equipment, and valve constraints?
 Are output limits set to match process, equipment, and valve constraints?
 Are anti-reset windup (ARW) limits set to match output limits?
 Is the module scan rate (PID execution time) less than 10% of minimum reset time?
 Is the signal filter time less than 10% of minimum reset time?
 Is the PID tuned with a proven tuning method or by an auto-tuner or adaptive tuner?
 Is the rate time less than ½ the dead time (the rate is typically zero except for temperature)
 Is external-reset feedback (dynamic reset limit) enabled for cascade control, analog output
  (AO) setpoint rate limits, and slow control valves or variable speed drives?
 Are AO setpoint rate limits set for blending, valve position control, and surge valves?
 Is integral deadband greater than limit cycle PV amplitude?
 Can an enhanced PID be used for loops with wireless instruments or analyzers?




                                                                                                   49
Feedforward Applications
•    Feedforward is the most common advanced control technique used - often the
     feedforward signal is a flow or speed for ratio control that is corrected by a feedback
     process controller (Flow is the predominant process input that is manipulated to set
     production rate and to control process outputs (e.g. temperature and composition))
          –   Blend composition control - additive/feed (flow/flow) ratio
          –   Column temperature control - distillate/feed, reflux/feed, stm/feed, and bttms/feed (flow/flow) ratio
          –   Combustion temperature control - air/fuel (flow/flow) ratio
          –   Drum level control - feedwater/steam (flow/flow) ratio
          –   Extruder quality control - extruder/mixer (power/power) ratio
          –   Heat exchanger temperature control - coolant/feed (flow/flow) ratio
          –   Neutralizer pH control - reagent/feed (flow/flow) ratio
          –   Reactor reaction rate control - catalyst/reactant (speed/flow) ratio
          –   Reactor composition control - reactant/reactant (flow/flow) ratio
          –   Sheet, web, and film line machine direction (MD) gage control - roller/pump (speed/speed) ratio
          –   Slaker conductivity control - lime/liquor (speed/flow) ratio
          –   Spin line fiber diameter gage control - winder/pump (speed/speed) ratio
•    Feedforward is most effective if the loop deadtime is large, disturbance speed is fast
     and size is large, feedforward gain is well known, feedforward measurement and
     dynamic compensation are accurate
•    Setpoint feedforward is most effective if the loop deadtime exceeds the process time
     constant and the process gain is well known

                     For more discussion of Feedforward see May 2008 Control Talk
                          http://www.controlglobal.com/articles/2008/171.html
Feedforward Implementation - 1
•   Feedforward gain can be computed from a material or energy balance ODE * &
    explored for different setpoints and conditions from a plot of the controlled variable
    (e.g. composition, conductivity, pH, temperature, or gage) vs. ratio of manipulated
    variable to independent variable (e.g. feed) but is most often simply based on
    operating experience
     –   * http://www.modelingandcontrol.com/repository/AdvancedApplicationNote004.pdf
     –   Plots are based on an assumed composition, pressure, temperature, and/or quality
           – For concentration and pH control, the flow/flow ratio is valid if the changes in the composition
              of both the manipulated and feed flow are negligible.
           – For column and reactor temperature control, the flow/flow ratio is valid if the changes in the
              composition and temperature of both the manipulated and feed flow are negligible.
           – For reactor reaction rate control, the speed/flow is valid if changes in catalyst quality and void
              fraction and reactant composition are negligible.
           – For heat exchanger control, the flow/flow ratio is valid if changes in temperatures of coolant
              and feed flow are negligible.
           – For reactor temperature control, the flow/flow ratio is valid if changes in temperatures of
              coolant and feed flow are negligible.
           – For slaker conductivity (effective alkali) control, the speed/flow ratio is valid if changes in lime
              quality and void fraction and liquor composition are negligible.
           – For spin or sheet line gage control, the speed/speed ratio is valid only if changes in the pump
              pressure and the polymer melt quality are negligible.
•   Dynamic compensation is used to insure the feedforward signal arrives at same
    point at same time in process as upset
     –   Compensation of a delay in the feedforward path > delay in upset path is not possible
Feedforward Implementation - 2
•   Feedback correction is essential in industrial processes
     –   While technically, the correction should be a multiplier for a change in slope and a bias for a change
         in the intercept in a plot of the manipulated variable versus independent variable (independent from
         this loop but possibly set by another PID or MPC), a multiplier creates scaling problems for the user,
         consequently the correction of most feedforward signal is done via a bias.
     –   The bias correction must have sufficient positive and negative range for worst case.
     –   Model predictive control (MPC) and PID loops get into a severe nonlinearity by creating a controlled
         variable that is the ratio. It is important that the independent variable be multiplied by the ratio and
         the result be corrected by a feedback loop with the process variable (composition, conductivity,
         gage, temperature, or pH) as the controlled variable.
•   Feedforward gain is a ratio for most load upsets.
•   Feedforward gain is the inverse of the process gain for setpoint feedforward.
     –   Process gain is the open loop gain seen by the PID (product of manipulated variable, process
         variable, and measurement variable gain) that is dimensionless.
•   Feedforward action must be in the same direction as feedback action for upset.
•   Feedforward action is the opposite of the control action for setpoint feedforward.
•   Feedforward delay and lag adjusted to match any additional delay and lag,
    respectively in path of upset so feedforward correction does not arrive too soon.
•   Feedforward lead is adjusted to compensate for any additional lag in the path of the
    manipulated variable so the feedforward correction does not arrive too late.
•   The actual and desired feedforward ratio should be displayed along with the bias
    correction by the process controller. This is often best done by the use of a ratio block
    and a bias/gain block instead of the internal PID feedforward calculation.
Linear Reagent Demand Control
(PV is X axis of Titration Curve)
•   Signal characterizer converts PV and SP from pH to % Reagent Demand
     –   PV is abscissa of the titration curve scaled 0 to 100% reagent demand
     –   Piecewise segment fit normally used to go from ordinate to abscissa of curve
     –   Fieldbus block offers 21 custom space X,Y pairs (X is pH and Y is % demand)
     –   Closer spacing of X,Y pairs in control region provides most needed compensation
     –   If neural network or polynomial fit used, beware of bumps and wild extrapolation
•   Special configuration is needed to provide operations with interface to:
     – See loop PV in pH and signal to final element
     – Enter loop SP in pH
     – Change mode to manual and change manual output
•   Set point on steep part of curve shows biggest improvements from:
     –   Reduction in limit cycle amplitude seen from pH nonlinearity
     –   Decrease in limit cycle frequency from final element resolution (e.g. stick-slip)
     –   Decrease in crossing of split range point
     –   Reduced reaction to measurement noise
     –   Shorter startup time (loop sees real distance to set point and is not detuned)
     –   Simplified tuning (process gain no longer depends upon titration curve slope)
     –   Restored process time constant (slower pH excursion from disturbance)



                                                                                             53
Output Tracking for SP Response

 •   “Head-Start” logic for startup & batch SP changes:
     –   For SP change PID tracks best/last startup or batch final settling
         value for best/last rise time less total loop deadtime
     –   Closed loop time constant is open loop time constant (λf =1)
     –   Not as fast as Bang-Bang (PID OUT is not at output limit)
 •   “Bang-Bang” logic for startup & batch SP changes:
     –   For SP change PID tracks output limit until the predicted PV one
         deadtime into future gets within a deadband of setpoint, the output is
         then set at best/last startup or batch final settling value for one
         deadtime
     –   Implementation uses simple DT block (loop deadtime) to create an
         old PV subtracted from the new PV to give a delta PV that is added to
         old PV to create a PV one deadtime into future
     –   Works best on slow batch and integrating processes
Output Tracking for Protection - 1

 •   “Open Loop Backup” to prevent compressor surge:
     –   Once a compressor gets into surge, cycles are so fast & large that
         feedback control can not get compressor out of surge
     –   When compressor flow drops below surge SP or a precipitous drop
         occurs in flow, PID tracks an output that provides a flow large enough
         to compensate for the loss in downstream flow for a time larger than
         the loop dead time plus the surge period.
 •   “Open Loop Backup” to prevent RCRA violation:
     –   An excursion < 2 pH or > 12 pH for even a few sec can be a
         recordable RCRA violation regardless of downstream volume
     –   When an inline pH system PV approaches the RCRA pH limit the PID
         tracks an incremental output (e.g. 0.25% per sec) opening the
         reagent valve until the pH sufficiently backs away
 •   “Open Loop Backup” for evaporator conductivity
Open Loop Backup Configuration - 2
  SP_Rate_DN and SP_RATE_UP used to insure fast getaway and slow approach




                  Open Loop Backup Configuration




                           Open loop backup used for prevention of
                           compressor surge and RCRA pH violation
Output Tracking for Protection - 3




                            Feedback Action
Output Tracking for Protection - 4




                            Open Loop Backup
RCRA pH Kicker

  Optimization of pH filter and kicker increment saved $50K in reagent costs



                                                                               MPC-1
                                                                                                                                           MPC-2



                                                      Waste
                                                                                                                           middle selector
                                    RCAS                                                 RCAS


                                                                                                                      Kicker
                                                                                                      ROUT
                                         AC-1                                                 AC-2           AY                              AY

             splitter                                              splitter                                                           AT     AT    AT
       AY                                                     AY                                             AY
                          middle selector                                      middle selector               Filter
        FT                                                    FT
                                            AY                                                   AY                   Attenuation
                                                                                                                         Tank
                    Stage 1         AT      AT   AT                       Stage 2        AT      AT   AT
                        Mixer                                                 Mixer                          FT
Evaporator Conductivity Kicker



                                 Conductivity spike


               WBL Flow Kicker
Setpoint Filter

• PID SP filter reduces overshoot enabling fast tuning
   – Setpoint filter time set equal reset time
• PID SP filter coordinates timing of flow ratio control
   – Simultaneous changes in feeds for blending and reactions
   – Consistent closed loop response for model predictive control
• PID SP filter sets closed loop time constant
• PID SP filter in secondary loop slows down cascade control
  system rejection of primary loop disturbances
   – Secondary loop must be > 4x faster than primary loop
• Primary PID must have dynamic reset limit enabled
• Setpoint Lead-Lag minimizes overshoot and rise time
   – Lag time = reset time
   – Lead time = 20% lag time
Setpoint Rate Limits

• AO & PID SP rate limits minimize disruption while protecting
  equipment and optimizing processes
   – Offers directional moves suppression
   – Enables fast opening and slow closing surge valve
   – VPC fast recovery for upset and slow approach to optimum
• AO SP rate limits minimize interaction between loops
   – Less important loops are made 10x slower than critical loops
• PID driving AO SP or secondary PID SP rate limit must have
  dynamic reset limit enabled so no retuning is needed
• PID faceplate should display PV of AO to show rate limiting
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•   (10) Can immediately implement an inspiration.
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•   (8) Get to wear shorts and sandals.
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•   (6) Lose weight from not eating doughnuts.
•   (5) Can BBQ while solving control problem.
•   (4) No more lonely nights and meals.
•   (3) Your kids start to recognize you.
•   (2) Your kids want to become automation engineers.
•   (1) Your spouse starts to offer you advanced process control.




                                                                    63
Enhanced PID for Wireless Features
•   Positive feedback implementation of reset with external-reset
    feedback (dynamic reset limit)
•   Immediate response to a setpoint change or feedforward signal or
    mode change
•   Suspension of integral action until change in PV
•   Integral action is the exponential response of the positive feedback
    filter to the change in controller output in elapsed time (the time
    interval since last update)
•   Derivative action is the PV or error change divided by elapsed time
    rather than PID execution
Flow Setpoint Response




                   Enhanced PID
                     Sensor PV




                            Traditional PID
                              Sensor PV
Flow Load Response




                     Enhanced PID
                       Sensor PV
                            Traditional PID
                              Sensor PV
Flow Signal Failure Response




                   Enhanced PID
                     Sensor PV




              Traditional PID
                Sensor PV
pH Setpoint Response




           Enhanced PID
             Sensor PV




                          Traditional PID
                            Sensor PV
pH Load Response




                   Enhanced PID
                     Sensor PV Traditional PID
                                 Sensor PV
pH Sensor Failure Response




                  Enhanced PID
                    Sensor PV




              Traditional PID
                Sensor PV
Stop Limit Cycles




                Traditional PID             Enhanced PID



            PID PV


               PID Output


       Limit Cycles from Valve Stick-Slip
Benefits Extend Beyond Wireless - 1

•   The PID enhancement for wireless offers an improvement wherever
    there is an update time in the loop. In the broadest sense, an update
    time can range from seconds (wireless updates and valve or
    measurement sensitivity limits) to hours (failures in communication,
    valve, or measurement). Some of the sources of update time are:
    –   Wireless update time for periodic reporting (default update rate)
    –   Wireless measurement trigger level for exception reporting (trigger level)
    –   Wireless communication failure
    –   Broken pH electrode glass or lead wires (failure point is about 7 pH)
    –   Valve with backlash (deadband) and stick-slip (resolution)
    –   Operating at split range point (no response & abrupt response discontinuity)
    –   Valve with solids, high temperature, or sticky fluid (plugging and seizing)
    –   Plugged impulse lines
    –   Analyzer sample, analysis cycle, and multiplex time
    –   Analyzer resolution and threshold sensitivity limit


        To completely stop a valve limit cycle from backlash or stick-slip,
              measurement updates must not occur due to noise
Benefits Extend Beyond Wireless - 2
•      Enhanced PID executes for a change in setpoint, feedforward, or
       remote output to provide an immediate reaction based on PID structure
•      The improvement in control by the enhanced PID is most noticeable as
       the update time becomes much larger than the 63% process response
       time (defined in the white paper as the sum of the process deadtime
       and time constant). When the update time becomes 4 times larger than
       this 63% process response time ( 98% response time frequently cited in
       the literature), the feedforward and controller gains can be set to
       provide a complete correction for changes in the measurement and
       setpoint.
        –   Helps ignore inverse response and errors in feedforward timing
        –   Helps ignore discontinuity (e.g. steam shock) at split range point
        –   Helps extend packing life by reducing oscillations and hence valve travel
•      Since enhanced PID can be set to execute only upon a significant
       change in user valve position, this PID as a valve position controller
       offers less interaction and cycling for optimization of unit operations by
       increasing reactor feed, column feed or increasing refrigeration unit
       temperature, or decreasing compressor pressure till feed, vent,
       coolant, and/or steam, valves are at maximum good throttle position.
                   Website entries on Enhanced PID Benefits
     http://www.modelingandcontrol.com/2010/08/wireless_pid_benefits_extend_t.html
    http://www.modelingandcontrol.com/2010/10/enhanced_pid_for_wireless_elim.html
           http://www.modelingandcontrol.com/2010/11/a_delay_of_any_sorts.html
Why over 100 PID Tuning Rules?

• Aidan O’Dwyer’s Handbook of PI and PID Controller Tuning
  Rules - 2nd Edition has over 500 pages of rules
• The originators all think their rules are best due to
   –   Gamesmanship
   –   Diverse sources of change
   –   Diverse objectives
   –   Diverse dynamics
   –   Diverse metrics
Convergence of Tuning Rules

• The most popular PID rules converge to the same equations
  for 99% of temperature, composition, level, and gas pressure
  loops despite diversity of metrics, dynamics, objectives, and
  sources of change if the following is used:
   –   Tuning to minimize the effect of unmeasured disturbances
   –   Tuning to maximize absorption of variability (e.g. surge tank level)
   –   Dead time block in identification of process dynamics
   –   Primary PID Setpoint Lag = reset time and Lead = 20% of Lag
   –   Analog output setpoint rate limit and PID external-reset feedback
   –   Enhanced PID developed for wireless with threshold sensitivity
• For the remaining cases:
   – For drastic deceleration from dead time dominance decrease gain,
     reset time, and rate time
   – For severe acceleration from runaway reaction, increase gain,
     reset time, and rate time
Diverse Sources of Change

•   Raw material and recycle composition and impurities
•   Weather (temperature, humidity, snow, rain)
•   Utility temperature and pressure
•   Operators (production rate changes and manual actions)
•   Interactions and Optimization
•   Batch sequences and on-off control
•   Startups, transitions, and shutdowns
•   Measurement and process noise
•   Limit cycles
Diverse Process Objectives


• Maximize safety
   – Prevent activation of relief devices and Safety Instrumented
     Systems (SIS)
• Maximize equipment, environmental, & process protection
• Minimize product variability
   –   Minimize limit cycles
   –   Minimize oscillatory loop response
   –   Minimize interaction between loops
   –   Maximize coordination between loops
• Maximize process capacity and efficiency
   – Increase production rate and decrease raw material and utility use
Diverse Process Objectives
Automated Risk Reduction




            SIS


             PID
Diverse Process Objectives
Maximize Protection

• Eliminate temperature shock and water hammer
   – Slow action of control valve in direction of causing shock
• Eliminate compressor surge
   – Slow closing of surge valves and downstream user valves
   – Fast opening of surge valves
• Eliminate flare stack emissions
   – Fast opening of runaway reactor coolant valves
• Eliminate RCRA pH Violations
   – Fast opening of base reagent valve when approaching 2 pH
   – Fast opening of acid reagent valve when approaching 12 pH
Diverse Process Objectives
Minimize Product Variability

• Minimize cycling from valve discontinuities
   – Suspension of integral action when valve is not moving or for an
     impending unnecessary crossing of the split range point
• Minimize oscillatory response
   – Slow approach to setpoint and suspension of integral action between
     updates from analyzers and wireless transmitters
• Minimize interaction between loops
   – Slow and fast action of less and more critical loop, respectively
• Maximize coordination of loops
   – Identical ratioed rates of change of feeds particularly for plug flow
     reactors, and inline systems, such as blenders and static mixers
Diverse Process Objectives
Maximize Efficiency and Capacity

• Use PID for valve position control (VPC) to increase feed or
  reduce raw material or energy use for valve constraint.
   – Slow approach by VPC to optimum to avoid upsetting loops
   – Fast getaway by VPC for upset to avoid running out of valve
   – Suspension of integral action in VPC for valve that is not moving or
     whose movements are inconsequential
Key PID Features for VPC

       Feature               Function               Advantage 1              Advantage 2



  Direction Velocity     Limit VPC Action       Prevent Running Out      Minimize Disruption
        Limits           Speed Based on               of Valve               to Process
                            Direction

   Dynamic Reset         Limit VPC Action         Direction Velocity       Prevent Burst of
       Limit             Speed to Process               Limits               Oscillations
                            Response

   Adaptive Tuning     Automatically Identify     Eliminate Manual         Compensation of
                       and Schedule Tuning             Tuning                Nonlinearity


    Feedforward        Preemptively Set VPC     Prevent Running Out      Minimize Disruption
                           Out for Upset              of Valve


   Enhanced PID          Suspend Integral       Eliminate Limit Cycles   Minimize Oscillations
     (PIDPlus)         Action until PV Update       from Stiction &      from Interaction & PV
                                                       Backlash              Update Delay
Examples of Optimization by VPC
      Optimization            VPC PID PV             VPC PID SP              VPC PID Out

     Minimize Prime          Reactor Feed        Max Throttle Position   Compressor or Pump
     Mover Energy            Flow PID Out                                   Pressure SP
     Minimize Boiler      Steam Flow PID Out     Max Throttle Position          Boiler
       Fuel Cost                                                             Pressure SP
     Minimize Boiler         Equipment           Max Throttle Position          Boiler
       Fuel Cost         Temperature PID Out                                 Pressure SP
    Minimize Chiller         Equipment           Max Throttle Position       Chiller or CTW
    or CTW Energy        Temperature PID Out                                Temperature SP

  Minimize Purchased     Purchased Reagent or    Min Throttle Position     Waste Reagent
  Reagent or Fuel Cost     Fuel Flow PID Out                               Or Fuel Flow SP
     Minimize Total       Final Neutralization   Min Throttle Position    First Neutralization
     Reagent Use           Stage pH PID Out                                Stage pH PID SP
    Maximize Reactor     Reactor or Condenser    Max Throttle Position   Feed Flow or Reaction
    Production Rate      Temperature PID Out                                Temperature SP

    Maximize Reactor         Reactor Vent        Max Throttle Position   Feed Flow or Reaction
    Production Rate        Pressure PID Out                                 Temperature SP

    Maximize Column      Reboiler or Condenser   Max Throttle Position   Feed Flow or Column
    Production Rate          Flow PID Out                                    Pressure SP

    Maximize Ratio or     Process Feedback               50%                 Flow Ratio or
  Feedforward Accuracy    Correction PID Out       (Zero Correction)       Feedforward Gain
Liquid Reactants (Jacket CTW)
Liquid Product Optimization
     ratio           ZC1-4                                                            ZC1-4 is an enhanced PID VPC
                                  FC              CAS   LC
     calc            OUT
                                  1-1                   1-8
                                                              PT                PC                   FC 1-1       ZC
     FY                                                                                              CAS
     1-6                                                      1-5               1-5                               1-4
                     reactant A   FT                                      FT                            vent
                                  1-1                                     1-5
              LY     residence
              1-8    time calc                          LT          TT                                  TC
                                                        1-8         1-3                                 1-3
                          CAS     FC
                                  1-2


                                                                                TT                      TC
                     reactant B   FT                                            1-4                     1-4
                                  1-2
                                                                                                       return

 Valve position controller (VPC) setpoint
 is the maximum throttle position. The
 VPC should turn off integral action to
 prevent interaction and limit cycles. The                                               AT             AC
 correction for a valve position less than                                               1-6            1-6
 setpoint should be slow to provide a slow
 approach to optimum. The correction for
 a valve position greater than setpoint must
 be fast to provide a fast getaway from the                                                            makeup
 point of loss of control. Directional velocity                                                         CTW
 limits in AO with dynamic reset limit in an                                                   FC
 enhanced PID that tempers integral action                                                     1-7
 can achieve these optimization objectives.

                                                                                               FT               product
                                                                                               1-7
                                                                                                                          84
Liquid Reactants (Jacket CTW)
Gas & Liquid Products Optimization
   ratio           ZY1-1
                                FC                               PT            PC                                      ZC
   calc            OUT
                                1-1                              1-5           1-5                                     1-5
    FY                                        CAS   LC    TT             FT                        product
    1-6                                             1-8   1-10           1-5
                                                                                                    TC
                  reactant A    FT                                                                  1-10
                                                                                                                       ZY-1




                                                                 W
                                1-1                                                                                    IN1
           LY     residence
           1-8    time calc                                            TT                            TC                ZC
                                                    LT                                                                 1-10
                        CAS     FC                                     1-3                           1-3
                                                    1-8
                                1-2

                                                                                                                       ZY-1
                                                                               TT                    TC
                                                                                                                       IN2
                  reactant B    FT                                             1-4                   1-4
                                1-2
                                                                                                    return

           ZC-5
           OUT
                                                                                                                       ZC
               low signal                                                                                              1-4
                selector                                                               AT            AC
FC1-1                   ZC-10                                                          1-6           1-6
           ZY
CAS        1-1          OUT
                                                                                                                       ZY-1
                                                                                                                       IN3
                                                                                                     makeup
           ZC-4
           OUT                                                                                        CTW
                                                                                     CAS     FC
                                                                                             1-7



  ZC1-4, ZC-5, & ZC-10 are enhanced PID VPC                                                  FT              product
                                                                                             1-7
                                                                                                                              85
Innovative PID System to Optimize
Ethanol Yield and Carbon Footprint
                                Corn
   Production Rate
                                                                     Average Fermentation Time
    Enhanced PID
                                                                           Enhanced PID
setpoint                                                                                                                      Slurry Solids
           AC            SC               AT                                    XC                                           Enhanced PID
           1- 4          1-4                   NIR-T
                                          1- 4                                  1- 4             Feedforward
                                                                                                               DX                 DC     RCAS
                                                                                                               2- 4               2- 4
                                                           Fermentable Starch
                         AY              XY                    Correction
                         1- 4            1- 4


                         FC
                         1- 5


      Dilution Water     FT
                         1- 5

                         FC
                         1- 6

                                                                                                                      DT
     Backset Recycle     FT                                                                                           2- 4   Coriolis
                         1- 6                                                                                                 Meter


                                                           Slurry                                   Slurry
                                                           Tank 1                                   Tank 2

            Lag and Delay
                  DY        Predicted Fermentable Starch
                  2- 4
                                                                                                                                                86
Loop Block Diagram
(First Order Approximation)
                Delay              Lag           Gain

                    θd              τL               Kd
                                                                         ∆DV                       Delay <=> Dead Time
                           Load Upset                                                             Lag <=>Time Constant

                                                            Secondary       Secondary        Primary        Primary
                Delay              Lag           Gain         Delay            Lag            Delay           Lag          Gain

                    θv              τv               Kv          θs              τs             θp             τp           Kp
                                                          ∆Fv
                                Valve                                                      Process                            ∆PV
                                                                      τo is the largest lag in the loop (hopefully τp)
                           Kv = slope of installed
                            flow characteristic                    For self-regulating processes: Ko = Kv ∗ Kp ∗ Km
                                                                For near integrating processes: Ki = Kv ∗ (Kp / τp) ∗ Km




                                 Local
                %        ∆%CO                                                         Km = 100% / span
                                Set Point
                                  %SP
   PID     Kc       Ti     Td
                                    %
                                                                               ½ of Wireless Default Update Rate

                %        ∆%PV
                                 Delay           Lag            Gain            Lag           Delay          Lag

                    τc2            θc            τc1            Km              τm2           θm2            τm1           θm1
                    Lag                                                                                                    Delay
                            Controller                                                Measurement
 First Order Approximation: θο ≅ θv + θs + θp + θm1 + θm2 + θc + Y∗τv + Y∗τs + Y∗τm1 + Y∗τm2 + Y∗τc1 + Y∗τc2
   (set by automation system design for flow, pressure, level, speed, surge, and static mixer pH control)                           87
Open Loop Response of
Self-Regulating Process
                                    Response to change in controller output with controller in manual



                                                                                  %PV
        % Controller Output (%CO)        Ko = ∆%PV / ∆%CO
        % Process Variable (%PV)


                                    Self-regulating process gain (%/%)




                                                            %CO
                    or




                                                      Maximum speed                                    ∆%PV
                                                      in 4 dead times
                                                      is critical speed
                                                                                           0.63∗∆%PV
                                        ∆%CO



        Noise Band




                                     observed
                                                       θo     τo   ideally   τp         Time (seconds)
                                     total loop
                                     dead time      Self-regulating process open loop
                                                     negative feedback time constant
                                                                                                              88
Open Loop Response of
Integrating Process
                                     Response to change in controller output with controller in manual

                                                                                               %PV
                                     Ki = { [ %PV2 / ∆t2 ] − [ %PV1 / ∆t1 ] } / ∆%CO

         % Controller Output (%CO)
         % Process Variable (%PV)
                                        Integrating process gain (%/sec/%)




                                                           %CO
                     or




                                                 Maximum ramp rate
                                               in 4 dead times is used
                                               to estimate integrating
                                                    process gain
                                     ∆%CO




        ramp rate is                                                ramp rate is
        ∆%PV1 / ∆t1                                                 ∆%PV2 / ∆t2




                                                                                       Time (seconds)
                         observed             θo
                         total loop
                         dead time

                                                                                                         89
Open Loop Response of
Runaway Process
                                    Response to change in controller output with controller in manual



                                        Ko = ∆%PV / ∆%CO
                                   Runaway process gain (%/%)        Acceleration
       % Controller Output (%CO)
       % Process Variable (%PV)




                                                    For safety reasons, tests are
                                                   terminated within 4 dead times
                                                   before noticeable acceleration                       1.72∗∆%PV
                   or




                                                                                                 ∆%PV

                                         ∆%CO




        Noise Band




                                      observed
                                                         θo           τ’
                                                                       o   must be   τ’
                                                                                      p
                                                                                                 Time (seconds)
                                      total loop
                                      dead time                  runaway process open loop
                                                               positive feedback time constant
                                                                                                                    90
Diverse Loop Metrics


•   Peak and integrated errors for load disturbances
•   Rise time for setpoint change (time to reach setpoint)
•   Overshoot for setpoint change
•   Settling time for setpoint change
•   Standard deviation of oscillations
Diverse Metrics
Peak and Integrated Error




        The use of a setpoint lead-lag with the lag equal to the reset time and the lead
         20% of the lag will provide a fast setpoint response with minimal overshoot
                         despite tuning for maximum load rejection
Ultimate Limit to Loop Performance
            Peak error is proportional to the ratio of loop dead time to 63% response time
  (Important to prevent SIS trips, relief device activation, surge prevention, and RCRA pH violations)

                           Total loop deadtime
                           that is often set by
                           automation design
                                               θo
                                      Ex =              ∗ Eo
                                           (θ o + τ o )
                                                                Largest lag in loop
                                                                that is ideally set by
                                                                large process volume


        Integrated error is proportional to the ratio of loop dead time squared to 63% response time
         (Important to minimize quantity of product off-spec and total energy and raw material use)


                                                θ o2
                                       Ei =              ∗ Eo
                                            (θ o + τ o )
     For a sensor lag (e.g. electrode or thermowell lag) or signal filter that is much larger
      than the process time constant, the unfiltered actual process variable error can be
                            found from the equation for attenuation
Effect of Disturbance Lag on Integrating Process




                                           Periodic load disturbance time constant
                                                   increased by factor of 10




                      Adaptive loop

                         Baseline loop
                                                     Adaptive loop


                                                      Baseline loop
                      Primary reason why bioreactor control loop tuning
                       and performance for load upsets is a non issue!
Practical Limit to Loop Performance

        Peak error decreases as the controller gain increases but is essentially the
        open loop error for systems when total dead time >> process time constant
                                                                 Open loop error for
                                                                 fastest and largest
                                      1
                           Ex =                  ∗ Eo
                                                                 load disturbance


                                (1 + K o ∗ K c )

   Integrated error decreases as the controller gain increases and reset time decreases
       but is essentially the open loop error multiplied by the reset time plus signal
        delays and lags for systems when total dead time >> process time constant



                                     Ti + ∆t x + τ f
                              Ei =                     ∗ Eo
                                        Ko ∗ Kc
    Peak and integrated errors cannot be better than ultimate limit - The errors predicted
     by these equations for the PIDPlus and deadtime compensators cannot be better
        than the ultimate limit set by the loop deadtime and process time constant
Implied Dead Time from Slow Tuning
      Slow tuning (large Lambda) creates an implied dead time where the loop performs
        about the same as a loop with fast tuning and an actual dead time equal to the
                                    implied dead time (θi)



                                 θ i = 0.5 ∗ (λ + θo )
             For most aggressive tuning Lambda is set equal to observed dead time
                      (implied dead time is equal to observed dead time)


                Money spent on improving measurement and process dynamics
                 (e.g. reducing measurement delays and process dead times)
                   will be wasted if the controller is not tuned faster to take
                               advantage of the faster dynamics



                   You can prove most any point you want to make in a comparison
                       of control system performance, by how you tune the PID.
                       Inventors of special algorithms as alternatives to the PID
            naturally tend to tune the PID to prove their case. For example Ziegler-Nichols
                tuning is often used to show excessive oscillations that could have be
                                    eliminated by cutting gain in half
Disturbance Speed


           Effect of load disturbance lag (τL) on peak error can be estimated by replacing the
       open loop error with the exponential response of the disturbance during the loop dead time


 For Ei (integrated error), use closed loop time constant instead of dead time

                                E L = (1 − e −θo /τ L ) ∗ Eo

       For a load disturbance lag much larger than the dead time, the load error in one dead time
         Is very small, allowing a very large implied dead time from slow tuning. In other words,
    tuning and control loop dynamics are not important in terms of disturbance rejection. The focus
         is then on the effect of tuning and dynamics on rise time (time to reach a new setpoint)
Setpoint Response Rise Time



Rise time (time to reach a new setpoint) is inversely proportional to controller gain


                                     ∆% SP
              Tr =                                                   + θo
                   K i ∗ min ( | %∆COmax |, ( K c + K ff ) ∗ ∆% SP )

Rise time can be decreased by setpoint feedforward and bang-bang logic that
sets and holds an output change at maximum (∆%COmax) for one dead time until
future PV value is projected to reach setpoint. The fastest possible rise time is:


                                          ∆% SP
                              Tr =                   + θo
                                   K i ∗ | %∆COmax |
Basic Lambda Tuning (Self-Regulating Processes)

                Self-Regulation Process Gain:
                                  ∆% PV
                         Ko =
                                 ∆%CO

                           Controller Gain
                                    Ti
                        Kc =
                             K o ∗ (λ + θ o )

   Lambda (Closed Loop Time Constant for Setpoint Response)
                                λ = λ f ∗τ o
                      Controller Integral Time
                                   Ti =τ o
               Lambda tuning excels at coordinating loops for blending,
               fixing lower loop dynamics for model predictive control,
                     and reducing loop interaction and resonance
Fastest Lambda Tuning (Self-Regulating Process)


     For max load rejection set lambda equal to dead time

                            λ = θo
                                    τo
                    K c = 0.5 ∗
                                  Ko ∗ θo

                            Ti =τ o
Basic Lambda Tuning Integrating Processes
         Lambda (closed loop arrest time in load response)
                            λ = λ f / Ki
                   Integrating Process Gain:
                       ∆% PV2 / ∆t 2 − ∆% PV1 / ∆t1
                Ki =
                                  ∆%CO

                          Controller Gain:
                                      Ti
                        Kc =
                               K i ∗ [ λ + θ o ]2
               Controller Integral (Reset) Time:
                           Ti = 2 ∗ λ + θ o
              Controller Derivative (Rate) Time:
                    Td = τ s secondary lag
Fastest Lambda Tuning Integrating Processes
      For max load rejection set lambda equal to dead time
                             λ = θo
                       Controller Gain:
                                  3
                        Kc =
                             Ki ∗ 4 ∗ θo

                 Controller Integral (Reset) Time:
                             Ti = 3 ∗ θ o

                  Controller Derivative (Rate) Time:
                        Td = τ s secondary lag

        Check for prevention of slow rolling oscillations:
                                       2.25
                            K c * Ti =
                                        Ki
Often Violated Criteria for Integrating Processes



           To prevent slow rolling oscillations:

                                  2
                       K c * Ti >
                                  Ki




                                                    103
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013
ISA Effective Use of PID Controllers 3-7-2013

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ISA Effective Use of PID Controllers 3-7-2013

  • 1. Effective Use of PID Controllers ISA New Orleans 3-7-2013 Standards Certification Education & Training Publishing Conferences & Exhibits 1
  • 2. Presenter – Greg is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow. Greg was an adjunct professor in the Washington University Saint Louis Chemical Engineering Department 2001-2004. Presently, Greg contracts as a consultant in DeltaV R&D via CDI Process & Industrial and is a part time employee of Experitec and MYNAH. Greg received the ISA “Kermit Fischer Environmental” Award for pH control in 1991, the Control Magazine “Engineer of the Year” Award for the Process Industry in 1994, was inducted into the Control “Process Automation Hall of Fame” in 2001, was honored by InTech Magazine in 2003 as one of the most influential innovators in automation, and received the ISA Life Achievement Award in 2010. Greg is the author of 20 books on process control, his most recent being Advanced Temperature Measurement and Control. Greg has been the monthly “Control Talk” columnist for Control magazine since 2002 and has started a Control Talk Blog. Greg’s expertise is available on the Control Global and Emerson modeling and control web sites: http://community.controlglobal.com/controltalkblog http://modelingandcontrol.com/author/Greg-McMillan/ 2
  • 4. Top Ten Ways to Impress Management with Trends • (10) Make large setpoint changes that zip past valve dead band and nonlinearities. • (9) Change the setpoint to operate on the flat part of the titration curve. • (8) Select the tray with minimum process sensitivity for column temperature control. • (7) Pick periods when the unit was down. • (6) Decrease the time span so that just a couple data points are trended. • (5) Increase the reporting interval so that just a couple data points are trended. • (4) Use really thick line sizes. • (3) Add huge signal filters. • (2) Increase the process variable scale span so it is at least 10x control region • (1) Increase the historian's data compression so changes are screened out 4
  • 5. Contribution of Each PID Mode • Proportional (P mode) - increase in gain increases P mode contribution – Provides an immediate reaction to magnitude of measurement change to minimize peak error and integrated error for a disturbance – Too much gain action causes fast oscillations (close to ultimate period) and can make noise and interactions worse – Provides an immediate reaction to magnitude of setpoint change for P action on Error to minimize rise time (time to reach setpoint) – Too much gain causes falter in approach to setpoint • Integral (I mode) - increase in reset time decreases I mode contribution – Provides a ramping reaction to error (SP-PV) to minimize integrated error if stable (since error is hardly ever exactly zero, integral action is always ramping the controller output) – Too much integral action causes slow oscillations (slower than ultimate period) – Too much integral action causes an overshoot of setpoint (no sense of direction) • Derivative (D mode) - increase in rate time increases D mode contribution – Provides an immediate reaction to rate of change of measurement change to minimize peak error and integrated error for a disturbance – Too much rate action causes fast oscillations (faster than ultimate period) and can make noise and interactions worse – Provides an immediate reaction to rate of change of setpoint change for D action on Error to minimize rise time (time to reach setpoint) – Too much rate causes fast oscillation in approach to setpoint
  • 6. Contribution of Each PID Mode kick from filtered derivative mode Signal ∆%CO1 (%) step from proportional ∆%CO2 = ∆%CO1 mode repeat from seconds/repeat Integral mode ∆%SP PID structure with proportional, integral, and derivative action on error Time (seconds) Contribution of Each PID Mode for a Step Change in the Set Point Structure of PID on error (β=1 and γ=1)
  • 7. Effect of Gain on P-Only Controller Red is 150% of maximum, Green is 100% of maximum, Purple is 50% of maximum of Gain Setting
  • 8. Effect of Reset Time on PI Controller Red is 150% of maximum, Green is 100% of maximum, Purple is 50% of maximum Reset Time
  • 9. Effect of Rate Time on PD Controller Red is 200% of maximum, Green is 100% of maximum, Purple is 0% of maximum Rate Time
  • 10. Proportional Mode Basics Note that many analog controllers used proportional band instead of gain for the proportional mode tuning setting. Proportional band is the % change in the process variable (∆%PV) needed to cause a 100% change in controller output (∆%CO). A 100% proportional band means a 100% ∆%PV would cause a 100 % ∆%CO (a gain of 1). It is critical that users know the units of their controller gain setting and convert accordingly. Gain = 100 % / Proportional Band • Proportional Mode Advantages • Minimize dead time from stiction and backlash • Minimize rise time • Minimize peak error • Minimize integrated error • Proportional Mode Disadvantages • Abrupt changes in output upset operators • Abrupt changes in output upset other loops • Amplification of noise 10
  • 11. Integral Mode Basics Note that many analog controllers used reset settings in repeats per minute instead of reset time for the integral mode tuning setting. Repeats per minute indicate the number of repeats of the proportional mode contribution in a minute. Today’s reset time settings are minutes per repeat or seconds per repeat which gives the time to repeat the proportional mode contribution. Often the “per repeat” term is dropped giving a reset time setting in minutes or seconds. Seconds per repeat = 60 / repeats per minute Integral Mode Advantages • Eliminate offset • Minimize integrated error • Smooth movement of output • Integral Mode Disadvantages • Limit cycles • Overshoot • Runaway of open loop unstable reactors 11
  • 12. Derivative Mode Basics Nearly all derivative tuning settings are given as a rate time in seconds or minutes. The effective rate time setting must never be greater than the effective reset time setting. The effective settings are for an ISA Standard Form. The advantages and disadvantages of the derivative mode are similar to that of the proportional mode except the relative advantages is less and the relative disadvantages are greater for the derivative mode. Seconds = 60 ∗ minutes • Derivative Mode Advantages • Minimize dead time from stiction and backlash • Minimize rise time • Minimize peak error • Minimize integrated error • Derivative Mode Disadvantages • Abrupt changes in output upset operators • Abrupt changes in output upset other loops • Amplification of noise 12
  • 13. Reset Gives Operations What They Want Should steam or water valve be open ? TC-100 Reactor Temperature CO PV SP temperature steam valve opens SP 50% PV water valve opens ? 48 52 time
  • 14. Open Loop Time Constant (controller in manual) Signal (%) %CO Controller is in Manual Open Loop Error Eo (%) %PV 0.63∗Eo %SP 0 θo τo Time (seconds) Dead Time Open Loop (Time Delay) (process) Time Constant (Time Lag)
  • 15. Closed Loop Time Constant (controller in auto) Signal (%) %CO Controller is in Automatic %SP ∆%SP 0.63∗∆%SP %PV 0 θo τc Time (seconds) Dead Time Closed Loop (Time Delay) Time Constant (Time Lag) Lambda (λ)
  • 16. Top Ten Signs Loops Need to be Tuned • (10) Lots of trials and errors. • (9) When asked what the controller gain setting is, the answer is given in %. • (8) When asked what the controller reset time setting is, the answer is in repeats/min. • (7) The data historian compression setting is 25%. • (6) There is more recycle than product. • (5) Valves are wearing out. • (4) Tempers are wearing thin. • (3) Operators are placing bets on what loop will cause the next shutdown. • (2) The output limits are set to keep the valve from moving. • (1) Preferred mode is manual. 16
  • 17. Conversion of Signals for PID Algorithm Final Control Element % % % SCLR SUB Control Process PID SCLR AO SP OUT Valve Equipment % %CO MV %PV (e.u.) (e.u.) SCLR PID PV (e.u.) Smart Sensing AI Transmitter PV Element PV - Primary Variable SV - Second Variable* (e.u.) TV - Third Variable* DCS FV - Fourth Variable* Measurement * - additional HART variables The scaler block (SCLR) that convert between engineering units of application and % of scale used in PID algorithm is embedded hidden part of the Proportional-Integral-Derivative block (PID) To compute controller tuning settings, the process variable and controller output must be converted to % of scale and time units of dead times and time constants must be same as time units of reset time and rate time settings!
  • 18. Series Form Form in analog controllers and early DCS – available as a choice in most modern DCS β Gain ∗ ∆ ∗ proportional Inverse %SP Reset All signals are % of scale in PID algorithm but Time inputs and outputs are in engineering units filter ∆ ∗ ∗ integral Σ %CO Filter Time = γ α ∗ Rate Time Rate Time ∗ ∆ ∗ ∗ filter derivative %PV filter Σ Switch position for no derivative action 18
  • 19. Parallel Form Form in a few early DCS and PLC and in many control theory textbooks Proportional β Gain Setting ∗ ∆ ∗ proportional %SP Integral All signals are % of scale in PID algorithm but Gain Setting inputs and outputs are in engineering units filter ∆ ∗ integral Σ %CO γ Derivative Gain Setting ∗ ∆ ∗ derivative %PV filter 19
  • 20. ISA Standard Form Default Form in most modern DCS β Gain ∗ ∆ ∗ proportional Inverse %SP Reset All signals are % of scale in PID algorithm but Time inputs and outputs are in engineering units filter ∆ ∗ ∗ integral Σ %CO Filter Time = γ Rate α ∗ Rate Time Time ∗ ∆ ∗ ∗ filter derivative %PV filter 20
  • 21. Positive Feedback Implementation of Integral Form for Enhanced PID developed for wireless Gain * Back out positive feedback of Feedforward (*FF) and ISA Standard Form of Proportional (*P) and Derivative (*D) modes with β and γ factors + P = (β −1) ∗ Gain ∗ %SP ∗ ∆ ∗ − All signals are % of scale in PID algorithm but β inputs and outputs are in engineering units %SP Feedforward For zero error For reverse action, Out1 = 0 P FF Error = %SP - %PV + Out1 filter ∆ ∗ Σ Σ Σ %CO − Filter Time = Positive Out2 D Reset Time Feedback *P *FF γ Switch position Rate filter ∆ ∆ for external Time reset feedback *D + ∗ ∆ ∗ ∗ filter derivative − E-R Filter Time = E-R is external reset %PV filter Reset Time (e.g. secondary %PVs) Filter Time = Dynamic Reset Limit α ∗ Rate Time 21
  • 22. Conversion of Series to ISA Form To convert from Series to ISA Standard Form controller gain: Ti ' + Td' Kc = ∗ K c' Ti ' Interaction factor To convert from Series to ISA Standard Form reset (integral) time: Ti ' + Td' Ti = ∗ Ti ' = Ti ' + Td' Ti ' To convert from Series to ISA Standard Form rate time: Ti ' Td = ' ∗ Td' Ti + Td' Primed tuning settings are Series Form Note that if the rate time is zero, the ISA Standard and Series Form settings are identical. When using the ISA Standard Form, if the rate time is greater than ¼ the reset time the response can become oscillatory. If the rate time exceeds the reset time, the response can become unstable from a reversal of action form these modes. The Series Form inherently prevents this instability by increasing the effective reset time as the rate time is increased. 22
  • 23. Anti Reset Windup (ARW) and Output Limits • For digital positioners and precise throttling valves – ARW & Out Lo Lim = 0%, ARW & Out Hi Lim = 100% • For pneumatic positioners & on-off heritage valves – Lo Lim = -5%, Hi Lim = 105% – ARW set inside output limits to get thru zone of ineffective valve response (stick-slip, shaft windup, & poor sensitivity) • For primary PID in cascade control, limits are set to match secondary setpoint limits in engineering units
  • 24. Checklist for PID Migration - 1  There are many features and parameters that vary with the DCS supplier. It is imperative the DCS documentation and supplier expertise be fully utilized and all migrations tested by a real time simulation for stability. Note the default of 0% low and 100% high output and ARW limits do not change to match changes made in output scale or engineering units.  For cascade control did you set the output scale of the primary PID in engineering units of the PV scale of the secondary loop?  For cascade control did you set the primary PID low and high output limits in engineering units to match setpoint limits of secondary PID?  Did you set the anti-reset windup (ARW) limits to match the output limits using same units as output limits unless there is some special need for ARW limits to be set otherwise?  Did you convert controller gain setting units (being especially aware of the inverse relationship between proportional band and gain)?  Did you convert reset units setting (being especially aware of the inverse relationship between repeats per minute and seconds per repeat)?  Did you convert rate units setting and make the alpha setting the same for the rate filter?  If rate time is not zero and ISA Standard Form is used, did you convert Series Form gain, reset, and rate settings to corresponding ISA Standard Form settings? 24
  • 25. Checklist for PID Migration - 2  For override control if the positive feedback implementation of integral mode is used, did you remove the filter on external reset signal used to prevent walk-off since this filter is already there?  For cascade control, id you turn on external reset feedback (dynamic reset limit) and use PV of secondary loop for external reset feedback to automatically prevent burst of oscillations from violation of cascade rule that secondary loop must be 5x faster than primary loop?  For slow or sticky valve, did you turn on external reset feedback (dynamic reset limit) and use a fast PV readback for external reset feedback to automatically prevent burst of oscillations from violation of cascade rule that positioner feedback loop must be 5x faster than primary loop and to prevent limit cycles from stick-slip? Did you realize the PV readback must normally be faster than a secondary HART variable update time?  For wireless control and at-line or on-line analyzer, did you use an enhanced PID developed for wireless that suspends integral action between updates (PIDPlus option) and uses elapsed time in the derivative action. The external-reset option should automatically be turned on?  Did you make sure the BKCAL signals are connected properly paying particular attention to the propagation of the BKCAL settings for intervening blocks for split range, signal characterization, and override control? 25
  • 26. Top 10 Things You Shouldn't Say When You Enter a Control Room • (10) Does this hard hat make my butt look big? • (9) At the last plant I was in we always did it this way. • (8) I added alarms to each loop. • (7) Does that flare out there always shoot up that high? • (6) Ooooh! Did you mean to do that? • (5) Can't somebody do something about all those alarms? • (4) We just downloaded the version released yesterday • (3) Here, I will show you how to operate this plant. • (2) Are you ready to put all your loops in Remote Cascade? • (1) We want a "lights out" plant! 26
  • 27. Triple Cascade Loop Block Diagram Process Primary Controller – Secondary Flow Controller – Digital Valve Controller DCS Valve Positioner Process Flow Drive Signal SP SP CO Control Flow PID PID AO PID* I/P Relay Process External External Valve Meter Reset Reset BKCAL BKCAL Position (Valve Travel) PV PV Position Loop Feedback Process AI AI Sensor * most positioners use proportional only Secondary (Inner) Loop Feedback Primary (Outer) Loop Feedback
  • 28. Effect of Slow Secondary Tuning (cascade control) Secondary loop slowed down by a factor of 5 Secondary CO Primary PV Secondary SP Secondary SP Secondary CO Primary PV
  • 29. External Reset Feedback (Dynamic Reset Limit) • Prevents PID output changing faster than a valve, VFD, or secondary loop can respond – Secondary PID slow tuning – Secondary PID SP Filter Time – Secondary PID SP Rate Limit – AO, DVC, VFD SP Rate Limit – Slow Valve or VFD – Use PV for BKCAL_OUT – Position used as PV if valve is very slow and readback is fast – Enables Enhanced PID for Wireless • Stops Limit cycles from deadband, backlash, stiction, and threshold sensitivity or resolution limits • Key enabling feature that simplifies tuning and creates more advanced opportunities for PID control
  • 30. PID Structure Options (1) PID action on error (β = 1 and γ = 1) (2) PI action on error, D action on PV (β = 1 and γ = 0) (3) I action on error, PD action on PV (β = 0 and γ = 0) (4) PD action on error, no I action (β = 1 and γ = 1) (5) P action on error, D action on PV, no I action (β = 1 and γ = 0) (6) ID action on error, no P action (γ = 1) (7) I action on error, D action on PV, no P action (γ = 0) (8) Two degrees of freedom controller (β and γ adjustable 0 to 1)
  • 31. (1) PID action on error • Fastest response to rapid (e.g. step) SP change by – Step in output from proportional mode – Spike in output from derivative mode can be made more like a kick by decreasing gamma factor (γ <1) – Zero dead time from deadband, resolution limit, & stiction • Burst of flow may affect other uses of fluid • Operations do not like sudden changes in output • Fast approach to SP more likely to cause overshoot • Setpoint filter & rate limits eliminate step & overshoot
  • 32. (2) PI action on error, D action on PV • Slightly slower SP response than structure (1) – Still have step from proportional mode – Spike or bump from derivative mode eliminated • Decrease in SP response speed is negligible if – Output hits output limit due to large SP change or PID gain – Rate time is less than total loop dead time – Alpha factor is increased (α > 0.125) (rate filter increased) • Setpoint filter & rate limits eliminate step & overshoot • Most popular structure choice
  • 33. (3) I action on error, PD action on PV • Provides gradual change in output for SP change • Slows down SP response dramatically • Eliminates overshoot for SP changes • Used for bioreactor temperature and pH SP changes (overshoot is much more important than cycle time) • Used for temperature startup to warm up equipment • Generally not recommended for secondary loops
  • 34. (4 - 5) No Integral action • Used if integral action adversely affects process • Used if batch response is only in one direction • Must set bias (output when PV = SP) • Highly exothermic reactors use structure 4 because integral action and overshoot can cause a runaway – 10x reset time (Ti > 40x dead time) to prevent runaway • Traditionally used on Total Dissolved Solids (TDS) drum and surge tank level control because of slow integrating response and permissibility of SP offset. – Low controller gain (Kc) cause slow rolling oscillations due to violation of inequality for integrating process. The inequality is commonly violated since Ki (integrating process gain) is extremely small on most vessels (Ki < 0.000001 %/sec/%). Most common problem is use of too small of a reset time for vessel batch composition and temperature, level, and gas pressure control causing violation of following rule 2 K c * Ti > Ki
  • 35. (6 -7) No Proportional Action • Predominantly used for valve position control (VPC) – Parallel valve control (VPC SP & PV are small valve desired & actual position, respectively, & VPC out positions large valve) – Optimization (VPC SP & PV are limiting valve desired & actual position, respectively, & VPC out optimizes process PID SP) – VPC reset time > 10x residence time to reduce interaction – VPC reset time > Kc∗Ti of process PID to reduce interaction – VPC tuning is difficult & too slow for fast & large disturbances • Better solution is external reset feedback & SP rate limits
  • 36. Improvement in Batch Temperature by Elimination of Integral action Batch temperature response in a single ended temperature control. Integral action causes overshoot. Typical Batch Temperature 80 70 60 degrees C 50 40 30 20 10 0 1 51 101 151 201 251 301 351 401 Time (min) Setpoint PV CO% Batch temperature response in a single ended temperature control. PD on error. No I action. Batch Temperature (new tuning) 45.0 40.0 35.0 degrees C 30.0 25.0 20.0 15.0 10.0 5.0 0.0 1 51 101 151 201 251 301 351 401 Time (min) Setpoint PV CO% 36
  • 37. (8) Two Degrees of Freedom • β and γ SP weighting factors are adjusted to balance fast approach & minimal overshoot for SP response • Alternative is using SP lead-lag with lag = reset time and lead = 20% of lag to achieve fast SP response with minimal overshoot
  • 38. Effect of Options on SP Response
  • 39. Top Ten Reasons to Use a DCS for Your BBQ • (10) Automated recipes • (9) Predicted BBQ times • (8) Five-course meal no problem • (7) Don't have to watch cooking shows • (6) Feed-forward control • (5) Process control comes home • (4) Children want to become automation engineers • (3) Spouse finally appreciates your expertise • (2) Griller not grilled • (1) More time to drink beer 39
  • 40. Fed-Batch and Startup Time Reduction - 1 • PID on Error Structure – Maximizes the step and kick of the controller output for a setpoint change. – Overdrive (driving of output past resting point) is essential for getting slow loops, such as vessel temperature and pH, to the optimum setpoint as fast as possible. – The setpoint change must be made with the PID in Auto mode. – “SP track PV” will generally maximize the setpoint change and hence the step and kick (retaining SP from last batch or startup minimizes kick and bump) • SP Feedforward – For low controller gains (controller gain less than inverse of process gain), a setpoint feedforward is particularly useful. For this case, the setpoint feedforward gain is the inverse of the dimensionless process gain minus the controller gain. – For slow self-regulating (e.g. continuous) processes and slow integrating (e.g. batch) processes, even if the controller gain is high, the additional overdrive can be beneficial for small setpoint changes that normally would not cause the PID output to hit a limit. – If the setpoint and controller output are in engineering units the feedforward gain must be adjusted accordingly. – The feedforward action is the process action, which is the opposite of the control action, taking into account valve action. In other words for a reverse control action, the feedforward action is direct provided the valve action is increase-open or the analog output block, I/P, or positioner reverses the signal for a increase-close.
  • 41. Fed-Batch and Startup Time Reduction - 2 • Full Throttle (Bang-Bang Control) - The controller output is stepped to it output limit to maximize the rate of approach to setpoint and when the projected PV equals the setpoint less a bias, the controller output is repositioned to the final resting value. The output is held at the resting value for one dead time. For more details, check out the Control magazine article “Full Throttle Batch and Startup Response.” http://www.controlglobal.com/articles/2006/096.html – A dead time (DT) block must be used to compute the rate of change so that new values of the PV are seen immediately as a change in the rate of approach. – If the total loop dead time (θo) is used in the DT block, the projected PV is simply the current PV minus the output of the DT block (∆PV) plus the current PV. – If the PV rate of change (∆PV/∆t) is useful for other reasons (e.g. near integrator or true integrating process tuning), then ∆PV/∆t = ∆PV/θo can be computed. – If the process changes during the setpoint response (e.g. reaction or evaporation), the resting value can be captured from the last batch or startup – If the process changes are negligible during the setpoint response, the resting value can be estimated as: – the PID output just before the setpoint change for an integrating (e.g. batch) process – the PID output just before the setpoint change plus the setpoint change divided by the process gain for a self-regulating (e.g. continuous) process – For self-regulating processes such as flow with the loop dead time (θo) approaching or less than the largest process time constant (τp ), the logic is revised to step the PID output immediately to the resting value. The PID output is held at the resting value for the T98 process response time (T98 = θo + 4∗ τo ).
  • 42. Fed-Batch and Startup Time Reduction - 3 • Output Lead-Lag – A lead-lag on the controller output or in the digital positioner can kick the signal though the valve deadband and stiction, get past split range points, and make faster transitions from heating to cooling and vice versa. – A lead-lag can potentially provide a faster setpoint response with less overshoot when analyzers are used for closed loop control of integrating processes When combined with the enhanced PID algorithm (PIDPlus) described in: – Deminar #1 http://www.screencast.com/users/JimCahill/folders/Public/media/5acf2135- 38c9-422e-9eb9-33ee844825d3 – White paper http://www.modelingandcontrol.com/DeltaV-v11-PID-Enhancements-for- Wireless.pdf • Dead Time Compensation – The simple addition of a delay block with the dead time set equal to the total loop dead time to the external reset signal for the positive feedback implementation of integral action described in Deminar #3 for the dynamic reset limit option http://www.screencast.com/users/JimCahill/folders/Public/media/f093eca1-958f-4d9c- 96b7-9229e4a6b5ba . – The controller reset time can be significantly reduced and the controller gain increased if the delay block dead time is equal or slightly less than the process dead time as studied in Advanced Application Note 3 http://www.modelingandcontrol.com/repository/AdvancedApplicationNote003.pdf
  • 43. Fed-Batch and Startup Time Reduction - 4 • Feed Maximization – Model Predictive Control described in Application Note 1 http://www.modelingandcontrol.com/repository/AdvancedApplicationNote001.pdf – Override control is used to maximize feeds to limits of operating constraints via valve position control (e.g. maximum vent, overhead condenser, or jacket valve position with sufficient sensitivity per installed characteristic). – Alternatively, the limiting valve can be set wide open and the feeds throttled for temperature or pressure control. For pressure control of gaseous reactants, this strategy can be quite effective. – For temperature control of liquid reactants, the user needs to confirm that inverse response from the addition of cold reactants to an exothermic reactor and the lag from the concentration response does not cause temperature control problems. – All of these methods require tuning and may not be particularly adept at dealing with fast disturbances unless some feedforward is added. Fortunately the prevalent disturbance that is a feed concentration change is often slow enough due to raw material storage volume to be corrected by temperature feedback. • Profile Control – If you have a have batch measurement that should increase to a maximum at the batch end point (e.g. maximum reaction temperature or product concentration), the slope of the batch profile of this measurement can be maximized to reduce batch cycle time. For application examples checkout “Direct Temperature Rate of Change Control Improves Reactor Yield” in a Funny Thing Happened on the Way to the Control Room http://www.modelingandcontrol.com/FunnyThing/ and the Control magazine article “Unlocking the Secret Profiles of Batch Reactors” http://www.controlglobal.com/articles/2008/230.html .
  • 44. Dead Time Compensator Configuration Must enable dynamic reset limit ! Insert deadtime block
  • 45. Dead Time Myths Busted • Dead time is eliminated from the loop. The smith predictor, which created a PV without dead time, fools the controller into thinking there is no dead time. However, for an unmeasured disturbance, the loop dead time still causes a delay in terms of when the loop can see the disturbance and when the loop can enact a correction that arrives in the process at the same point as the disturbance. The ultimate limit to the peak error and integrated error for an unmeasured disturbance are still proportional to the dead time, and dead time squared, respectively. • Control is faster for existing tuning settings. The addition of dead time compensation actually slows down the response for the existing tuning settings. Setpoint metrics, such as rise time, and load response metrics, such as peak error, will be adversely affected. Assuming the PID was tuned for a smooth stable response, the controller must be retuned for a faster response. For a PID already tuned for maximum disturbance rejection, the gain can be increased by 250%. For dead time dominant systems where the total loop dead time is much greater than the largest loop time constant (hopefully the process time constant), the reset time must also be decreased or there will be severe undershoot. If you decrease the reset time to its optimum, undershoot and overshoot are about equal. For the test case where the total loop dead time to primary process time constant ratio was 10:1, you could decrease the reset time by a factor of 10. Further study is needed as to whether the minimum reset time is a fraction of the underestimated dead time plus the PID module execution time where the fraction depends upon the dead time to time constant ratio For access to Deminar 10 ScreenCast Recording or SlideShare Presentation go to http://www.modelingandcontrol.com/2010/10/review_of_deminar_10_-_deadtim.html
  • 46. Dead Time Myths Busted • Compensator works better for loops dominated by a large dead time. The reduction in rise time is greatest and the sensitivity to per cent dead time modeling error particularly for an overestimate of dead time is least for the loop that was dominated by the process time constant. You could have a dead time estimate that was 100% high before you would see a significant jagged response when the process time constant was much larger than the process dead time. For a dead time estimate that was 50% too low, some rounded oscillations developed for this loop. The loop simply degrades to the response that would occur from the high PID gain as the compensator dead time is decreased to zero. While the magnitude of the error in dead time seems small, you have to remember that for an industrial temperature control application, the loop dead time and process time constant would be often at least 100 times larger. For a 400 second dead time and 10,000 second process time constant, a compensator dead time 200 seconds smaller or 400 seconds larger than actual would start to cause a problem. In contrast, the dead time dominant loop developed a jagged response for a dead time that was high or low by just 10%. I think this requirement is unreasonable in industrial processes. A small filter of 1 second on the input to the dead time block in the BKCAL path may have helped. • An underestimate of the dead time leads to instability. In tuning calculations for a conventional PID, a smaller than actual dead time can cause an excessively oscillatory response. Contrary to the effect of dead time on tuning calculations, a compensator dead time smaller than actual dead time will only cause instability if the controller is tuned aggressively after the dead time compensator is added. • An overestimate of the dead time leads to sluggish response and greater stability. In tuning calculations for a conventional PID, a larger than actual dead time can cause an excessively slow response. Contrary to the effect of dead time on tuning calculations, a compensator dead time greater than actual dead time will cause jagged irregular oscillations.
  • 47. Top Ten Reasons Why Automation Engineers Makes Great Spouses or at Least a Wedding Gifts • (10) Reliable from day one • (9) Always on the job • (8) Low maintenance (minimal grooming, clothing, and entertainment costs • (7) Many programmable features • (6) Stable • (5) Short settling time • (4) No frills or extraneous features • (3) Relies on feedback • (2) Good response to commands and amenable to real time optimization • (1) Readily tuned
  • 48. General PID Checklist - 1  Does the measurement scale cover the entire operating range, including abnormal conditions?  Is the valve action correct (increase-open for fail close and increase-close for fail open)?  Is the control action correct (direct for reverse process and reverse for direct process if the valve action is set)?  Is the best “Form” selected (ISA standard form)?  Is the “obey setpoint limits in cascade and remote cascade mode” option selected?  Are the external reset feedback (BKCAL) signals correctly connected between blocks?  Is the PV for BKCAL selected in the secondary loop PID?  Is the best “Structure” selected (PI action on error, D action on PV for most loops)?  Is the “setpoint track PV in manual” option selected to provide a faster initial setpoint response unless the setpoint must be saved in PID? 48
  • 49. General PID Checklist - 2  Are setpoint limits set to match process, equipment, and valve constraints?  Are output limits set to match process, equipment, and valve constraints?  Are anti-reset windup (ARW) limits set to match output limits?  Is the module scan rate (PID execution time) less than 10% of minimum reset time?  Is the signal filter time less than 10% of minimum reset time?  Is the PID tuned with a proven tuning method or by an auto-tuner or adaptive tuner?  Is the rate time less than ½ the dead time (the rate is typically zero except for temperature)  Is external-reset feedback (dynamic reset limit) enabled for cascade control, analog output (AO) setpoint rate limits, and slow control valves or variable speed drives?  Are AO setpoint rate limits set for blending, valve position control, and surge valves?  Is integral deadband greater than limit cycle PV amplitude?  Can an enhanced PID be used for loops with wireless instruments or analyzers? 49
  • 50. Feedforward Applications • Feedforward is the most common advanced control technique used - often the feedforward signal is a flow or speed for ratio control that is corrected by a feedback process controller (Flow is the predominant process input that is manipulated to set production rate and to control process outputs (e.g. temperature and composition)) – Blend composition control - additive/feed (flow/flow) ratio – Column temperature control - distillate/feed, reflux/feed, stm/feed, and bttms/feed (flow/flow) ratio – Combustion temperature control - air/fuel (flow/flow) ratio – Drum level control - feedwater/steam (flow/flow) ratio – Extruder quality control - extruder/mixer (power/power) ratio – Heat exchanger temperature control - coolant/feed (flow/flow) ratio – Neutralizer pH control - reagent/feed (flow/flow) ratio – Reactor reaction rate control - catalyst/reactant (speed/flow) ratio – Reactor composition control - reactant/reactant (flow/flow) ratio – Sheet, web, and film line machine direction (MD) gage control - roller/pump (speed/speed) ratio – Slaker conductivity control - lime/liquor (speed/flow) ratio – Spin line fiber diameter gage control - winder/pump (speed/speed) ratio • Feedforward is most effective if the loop deadtime is large, disturbance speed is fast and size is large, feedforward gain is well known, feedforward measurement and dynamic compensation are accurate • Setpoint feedforward is most effective if the loop deadtime exceeds the process time constant and the process gain is well known For more discussion of Feedforward see May 2008 Control Talk http://www.controlglobal.com/articles/2008/171.html
  • 51. Feedforward Implementation - 1 • Feedforward gain can be computed from a material or energy balance ODE * & explored for different setpoints and conditions from a plot of the controlled variable (e.g. composition, conductivity, pH, temperature, or gage) vs. ratio of manipulated variable to independent variable (e.g. feed) but is most often simply based on operating experience – * http://www.modelingandcontrol.com/repository/AdvancedApplicationNote004.pdf – Plots are based on an assumed composition, pressure, temperature, and/or quality – For concentration and pH control, the flow/flow ratio is valid if the changes in the composition of both the manipulated and feed flow are negligible. – For column and reactor temperature control, the flow/flow ratio is valid if the changes in the composition and temperature of both the manipulated and feed flow are negligible. – For reactor reaction rate control, the speed/flow is valid if changes in catalyst quality and void fraction and reactant composition are negligible. – For heat exchanger control, the flow/flow ratio is valid if changes in temperatures of coolant and feed flow are negligible. – For reactor temperature control, the flow/flow ratio is valid if changes in temperatures of coolant and feed flow are negligible. – For slaker conductivity (effective alkali) control, the speed/flow ratio is valid if changes in lime quality and void fraction and liquor composition are negligible. – For spin or sheet line gage control, the speed/speed ratio is valid only if changes in the pump pressure and the polymer melt quality are negligible. • Dynamic compensation is used to insure the feedforward signal arrives at same point at same time in process as upset – Compensation of a delay in the feedforward path > delay in upset path is not possible
  • 52. Feedforward Implementation - 2 • Feedback correction is essential in industrial processes – While technically, the correction should be a multiplier for a change in slope and a bias for a change in the intercept in a plot of the manipulated variable versus independent variable (independent from this loop but possibly set by another PID or MPC), a multiplier creates scaling problems for the user, consequently the correction of most feedforward signal is done via a bias. – The bias correction must have sufficient positive and negative range for worst case. – Model predictive control (MPC) and PID loops get into a severe nonlinearity by creating a controlled variable that is the ratio. It is important that the independent variable be multiplied by the ratio and the result be corrected by a feedback loop with the process variable (composition, conductivity, gage, temperature, or pH) as the controlled variable. • Feedforward gain is a ratio for most load upsets. • Feedforward gain is the inverse of the process gain for setpoint feedforward. – Process gain is the open loop gain seen by the PID (product of manipulated variable, process variable, and measurement variable gain) that is dimensionless. • Feedforward action must be in the same direction as feedback action for upset. • Feedforward action is the opposite of the control action for setpoint feedforward. • Feedforward delay and lag adjusted to match any additional delay and lag, respectively in path of upset so feedforward correction does not arrive too soon. • Feedforward lead is adjusted to compensate for any additional lag in the path of the manipulated variable so the feedforward correction does not arrive too late. • The actual and desired feedforward ratio should be displayed along with the bias correction by the process controller. This is often best done by the use of a ratio block and a bias/gain block instead of the internal PID feedforward calculation.
  • 53. Linear Reagent Demand Control (PV is X axis of Titration Curve) • Signal characterizer converts PV and SP from pH to % Reagent Demand – PV is abscissa of the titration curve scaled 0 to 100% reagent demand – Piecewise segment fit normally used to go from ordinate to abscissa of curve – Fieldbus block offers 21 custom space X,Y pairs (X is pH and Y is % demand) – Closer spacing of X,Y pairs in control region provides most needed compensation – If neural network or polynomial fit used, beware of bumps and wild extrapolation • Special configuration is needed to provide operations with interface to: – See loop PV in pH and signal to final element – Enter loop SP in pH – Change mode to manual and change manual output • Set point on steep part of curve shows biggest improvements from: – Reduction in limit cycle amplitude seen from pH nonlinearity – Decrease in limit cycle frequency from final element resolution (e.g. stick-slip) – Decrease in crossing of split range point – Reduced reaction to measurement noise – Shorter startup time (loop sees real distance to set point and is not detuned) – Simplified tuning (process gain no longer depends upon titration curve slope) – Restored process time constant (slower pH excursion from disturbance) 53
  • 54. Output Tracking for SP Response • “Head-Start” logic for startup & batch SP changes: – For SP change PID tracks best/last startup or batch final settling value for best/last rise time less total loop deadtime – Closed loop time constant is open loop time constant (λf =1) – Not as fast as Bang-Bang (PID OUT is not at output limit) • “Bang-Bang” logic for startup & batch SP changes: – For SP change PID tracks output limit until the predicted PV one deadtime into future gets within a deadband of setpoint, the output is then set at best/last startup or batch final settling value for one deadtime – Implementation uses simple DT block (loop deadtime) to create an old PV subtracted from the new PV to give a delta PV that is added to old PV to create a PV one deadtime into future – Works best on slow batch and integrating processes
  • 55. Output Tracking for Protection - 1 • “Open Loop Backup” to prevent compressor surge: – Once a compressor gets into surge, cycles are so fast & large that feedback control can not get compressor out of surge – When compressor flow drops below surge SP or a precipitous drop occurs in flow, PID tracks an output that provides a flow large enough to compensate for the loss in downstream flow for a time larger than the loop dead time plus the surge period. • “Open Loop Backup” to prevent RCRA violation: – An excursion < 2 pH or > 12 pH for even a few sec can be a recordable RCRA violation regardless of downstream volume – When an inline pH system PV approaches the RCRA pH limit the PID tracks an incremental output (e.g. 0.25% per sec) opening the reagent valve until the pH sufficiently backs away • “Open Loop Backup” for evaporator conductivity
  • 56. Open Loop Backup Configuration - 2 SP_Rate_DN and SP_RATE_UP used to insure fast getaway and slow approach Open Loop Backup Configuration Open loop backup used for prevention of compressor surge and RCRA pH violation
  • 57. Output Tracking for Protection - 3 Feedback Action
  • 58. Output Tracking for Protection - 4 Open Loop Backup
  • 59. RCRA pH Kicker Optimization of pH filter and kicker increment saved $50K in reagent costs MPC-1 MPC-2 Waste middle selector RCAS RCAS Kicker ROUT AC-1 AC-2 AY AY splitter splitter AT AT AT AY AY AY middle selector middle selector Filter FT FT AY AY Attenuation Tank Stage 1 AT AT AT Stage 2 AT AT AT Mixer Mixer FT
  • 60. Evaporator Conductivity Kicker Conductivity spike WBL Flow Kicker
  • 61. Setpoint Filter • PID SP filter reduces overshoot enabling fast tuning – Setpoint filter time set equal reset time • PID SP filter coordinates timing of flow ratio control – Simultaneous changes in feeds for blending and reactions – Consistent closed loop response for model predictive control • PID SP filter sets closed loop time constant • PID SP filter in secondary loop slows down cascade control system rejection of primary loop disturbances – Secondary loop must be > 4x faster than primary loop • Primary PID must have dynamic reset limit enabled • Setpoint Lead-Lag minimizes overshoot and rise time – Lag time = reset time – Lead time = 20% lag time
  • 62. Setpoint Rate Limits • AO & PID SP rate limits minimize disruption while protecting equipment and optimizing processes – Offers directional moves suppression – Enables fast opening and slow closing surge valve – VPC fast recovery for upset and slow approach to optimum • AO SP rate limits minimize interaction between loops – Less important loops are made 10x slower than critical loops • PID driving AO SP or secondary PID SP rate limit must have dynamic reset limit enabled so no retuning is needed • PID faceplate should display PV of AO to show rate limiting
  • 63. Top Ten Reasons to do APC from your Home • (10) Can immediately implement an inspiration. • (9) Can watch the ball game on one of your screens. • (8) Get to wear shorts and sandals. • (7) Get to listen to music rather than alarms. • (6) Lose weight from not eating doughnuts. • (5) Can BBQ while solving control problem. • (4) No more lonely nights and meals. • (3) Your kids start to recognize you. • (2) Your kids want to become automation engineers. • (1) Your spouse starts to offer you advanced process control. 63
  • 64. Enhanced PID for Wireless Features • Positive feedback implementation of reset with external-reset feedback (dynamic reset limit) • Immediate response to a setpoint change or feedforward signal or mode change • Suspension of integral action until change in PV • Integral action is the exponential response of the positive feedback filter to the change in controller output in elapsed time (the time interval since last update) • Derivative action is the PV or error change divided by elapsed time rather than PID execution
  • 65. Flow Setpoint Response Enhanced PID Sensor PV Traditional PID Sensor PV
  • 66. Flow Load Response Enhanced PID Sensor PV Traditional PID Sensor PV
  • 67. Flow Signal Failure Response Enhanced PID Sensor PV Traditional PID Sensor PV
  • 68. pH Setpoint Response Enhanced PID Sensor PV Traditional PID Sensor PV
  • 69. pH Load Response Enhanced PID Sensor PV Traditional PID Sensor PV
  • 70. pH Sensor Failure Response Enhanced PID Sensor PV Traditional PID Sensor PV
  • 71. Stop Limit Cycles Traditional PID Enhanced PID PID PV PID Output Limit Cycles from Valve Stick-Slip
  • 72. Benefits Extend Beyond Wireless - 1 • The PID enhancement for wireless offers an improvement wherever there is an update time in the loop. In the broadest sense, an update time can range from seconds (wireless updates and valve or measurement sensitivity limits) to hours (failures in communication, valve, or measurement). Some of the sources of update time are: – Wireless update time for periodic reporting (default update rate) – Wireless measurement trigger level for exception reporting (trigger level) – Wireless communication failure – Broken pH electrode glass or lead wires (failure point is about 7 pH) – Valve with backlash (deadband) and stick-slip (resolution) – Operating at split range point (no response & abrupt response discontinuity) – Valve with solids, high temperature, or sticky fluid (plugging and seizing) – Plugged impulse lines – Analyzer sample, analysis cycle, and multiplex time – Analyzer resolution and threshold sensitivity limit To completely stop a valve limit cycle from backlash or stick-slip, measurement updates must not occur due to noise
  • 73. Benefits Extend Beyond Wireless - 2 • Enhanced PID executes for a change in setpoint, feedforward, or remote output to provide an immediate reaction based on PID structure • The improvement in control by the enhanced PID is most noticeable as the update time becomes much larger than the 63% process response time (defined in the white paper as the sum of the process deadtime and time constant). When the update time becomes 4 times larger than this 63% process response time ( 98% response time frequently cited in the literature), the feedforward and controller gains can be set to provide a complete correction for changes in the measurement and setpoint. – Helps ignore inverse response and errors in feedforward timing – Helps ignore discontinuity (e.g. steam shock) at split range point – Helps extend packing life by reducing oscillations and hence valve travel • Since enhanced PID can be set to execute only upon a significant change in user valve position, this PID as a valve position controller offers less interaction and cycling for optimization of unit operations by increasing reactor feed, column feed or increasing refrigeration unit temperature, or decreasing compressor pressure till feed, vent, coolant, and/or steam, valves are at maximum good throttle position. Website entries on Enhanced PID Benefits http://www.modelingandcontrol.com/2010/08/wireless_pid_benefits_extend_t.html http://www.modelingandcontrol.com/2010/10/enhanced_pid_for_wireless_elim.html http://www.modelingandcontrol.com/2010/11/a_delay_of_any_sorts.html
  • 74. Why over 100 PID Tuning Rules? • Aidan O’Dwyer’s Handbook of PI and PID Controller Tuning Rules - 2nd Edition has over 500 pages of rules • The originators all think their rules are best due to – Gamesmanship – Diverse sources of change – Diverse objectives – Diverse dynamics – Diverse metrics
  • 75. Convergence of Tuning Rules • The most popular PID rules converge to the same equations for 99% of temperature, composition, level, and gas pressure loops despite diversity of metrics, dynamics, objectives, and sources of change if the following is used: – Tuning to minimize the effect of unmeasured disturbances – Tuning to maximize absorption of variability (e.g. surge tank level) – Dead time block in identification of process dynamics – Primary PID Setpoint Lag = reset time and Lead = 20% of Lag – Analog output setpoint rate limit and PID external-reset feedback – Enhanced PID developed for wireless with threshold sensitivity • For the remaining cases: – For drastic deceleration from dead time dominance decrease gain, reset time, and rate time – For severe acceleration from runaway reaction, increase gain, reset time, and rate time
  • 76. Diverse Sources of Change • Raw material and recycle composition and impurities • Weather (temperature, humidity, snow, rain) • Utility temperature and pressure • Operators (production rate changes and manual actions) • Interactions and Optimization • Batch sequences and on-off control • Startups, transitions, and shutdowns • Measurement and process noise • Limit cycles
  • 77. Diverse Process Objectives • Maximize safety – Prevent activation of relief devices and Safety Instrumented Systems (SIS) • Maximize equipment, environmental, & process protection • Minimize product variability – Minimize limit cycles – Minimize oscillatory loop response – Minimize interaction between loops – Maximize coordination between loops • Maximize process capacity and efficiency – Increase production rate and decrease raw material and utility use
  • 78. Diverse Process Objectives Automated Risk Reduction SIS PID
  • 79. Diverse Process Objectives Maximize Protection • Eliminate temperature shock and water hammer – Slow action of control valve in direction of causing shock • Eliminate compressor surge – Slow closing of surge valves and downstream user valves – Fast opening of surge valves • Eliminate flare stack emissions – Fast opening of runaway reactor coolant valves • Eliminate RCRA pH Violations – Fast opening of base reagent valve when approaching 2 pH – Fast opening of acid reagent valve when approaching 12 pH
  • 80. Diverse Process Objectives Minimize Product Variability • Minimize cycling from valve discontinuities – Suspension of integral action when valve is not moving or for an impending unnecessary crossing of the split range point • Minimize oscillatory response – Slow approach to setpoint and suspension of integral action between updates from analyzers and wireless transmitters • Minimize interaction between loops – Slow and fast action of less and more critical loop, respectively • Maximize coordination of loops – Identical ratioed rates of change of feeds particularly for plug flow reactors, and inline systems, such as blenders and static mixers
  • 81. Diverse Process Objectives Maximize Efficiency and Capacity • Use PID for valve position control (VPC) to increase feed or reduce raw material or energy use for valve constraint. – Slow approach by VPC to optimum to avoid upsetting loops – Fast getaway by VPC for upset to avoid running out of valve – Suspension of integral action in VPC for valve that is not moving or whose movements are inconsequential
  • 82. Key PID Features for VPC Feature Function Advantage 1 Advantage 2 Direction Velocity Limit VPC Action Prevent Running Out Minimize Disruption Limits Speed Based on of Valve to Process Direction Dynamic Reset Limit VPC Action Direction Velocity Prevent Burst of Limit Speed to Process Limits Oscillations Response Adaptive Tuning Automatically Identify Eliminate Manual Compensation of and Schedule Tuning Tuning Nonlinearity Feedforward Preemptively Set VPC Prevent Running Out Minimize Disruption Out for Upset of Valve Enhanced PID Suspend Integral Eliminate Limit Cycles Minimize Oscillations (PIDPlus) Action until PV Update from Stiction & from Interaction & PV Backlash Update Delay
  • 83. Examples of Optimization by VPC Optimization VPC PID PV VPC PID SP VPC PID Out Minimize Prime Reactor Feed Max Throttle Position Compressor or Pump Mover Energy Flow PID Out Pressure SP Minimize Boiler Steam Flow PID Out Max Throttle Position Boiler Fuel Cost Pressure SP Minimize Boiler Equipment Max Throttle Position Boiler Fuel Cost Temperature PID Out Pressure SP Minimize Chiller Equipment Max Throttle Position Chiller or CTW or CTW Energy Temperature PID Out Temperature SP Minimize Purchased Purchased Reagent or Min Throttle Position Waste Reagent Reagent or Fuel Cost Fuel Flow PID Out Or Fuel Flow SP Minimize Total Final Neutralization Min Throttle Position First Neutralization Reagent Use Stage pH PID Out Stage pH PID SP Maximize Reactor Reactor or Condenser Max Throttle Position Feed Flow or Reaction Production Rate Temperature PID Out Temperature SP Maximize Reactor Reactor Vent Max Throttle Position Feed Flow or Reaction Production Rate Pressure PID Out Temperature SP Maximize Column Reboiler or Condenser Max Throttle Position Feed Flow or Column Production Rate Flow PID Out Pressure SP Maximize Ratio or Process Feedback 50% Flow Ratio or Feedforward Accuracy Correction PID Out (Zero Correction) Feedforward Gain
  • 84. Liquid Reactants (Jacket CTW) Liquid Product Optimization ratio ZC1-4 ZC1-4 is an enhanced PID VPC FC CAS LC calc OUT 1-1 1-8 PT PC FC 1-1 ZC FY CAS 1-6 1-5 1-5 1-4 reactant A FT FT vent 1-1 1-5 LY residence 1-8 time calc LT TT TC 1-8 1-3 1-3 CAS FC 1-2 TT TC reactant B FT 1-4 1-4 1-2 return Valve position controller (VPC) setpoint is the maximum throttle position. The VPC should turn off integral action to prevent interaction and limit cycles. The AT AC correction for a valve position less than 1-6 1-6 setpoint should be slow to provide a slow approach to optimum. The correction for a valve position greater than setpoint must be fast to provide a fast getaway from the makeup point of loss of control. Directional velocity CTW limits in AO with dynamic reset limit in an FC enhanced PID that tempers integral action 1-7 can achieve these optimization objectives. FT product 1-7 84
  • 85. Liquid Reactants (Jacket CTW) Gas & Liquid Products Optimization ratio ZY1-1 FC PT PC ZC calc OUT 1-1 1-5 1-5 1-5 FY CAS LC TT FT product 1-6 1-8 1-10 1-5 TC reactant A FT 1-10 ZY-1 W 1-1 IN1 LY residence 1-8 time calc TT TC ZC LT 1-10 CAS FC 1-3 1-3 1-8 1-2 ZY-1 TT TC IN2 reactant B FT 1-4 1-4 1-2 return ZC-5 OUT ZC low signal 1-4 selector AT AC FC1-1 ZC-10 1-6 1-6 ZY CAS 1-1 OUT ZY-1 IN3 makeup ZC-4 OUT CTW CAS FC 1-7 ZC1-4, ZC-5, & ZC-10 are enhanced PID VPC FT product 1-7 85
  • 86. Innovative PID System to Optimize Ethanol Yield and Carbon Footprint Corn Production Rate Average Fermentation Time Enhanced PID Enhanced PID setpoint Slurry Solids AC SC AT XC Enhanced PID 1- 4 1-4 NIR-T 1- 4 1- 4 Feedforward DX DC RCAS 2- 4 2- 4 Fermentable Starch AY XY Correction 1- 4 1- 4 FC 1- 5 Dilution Water FT 1- 5 FC 1- 6 DT Backset Recycle FT 2- 4 Coriolis 1- 6 Meter Slurry Slurry Tank 1 Tank 2 Lag and Delay DY Predicted Fermentable Starch 2- 4 86
  • 87. Loop Block Diagram (First Order Approximation) Delay Lag Gain θd τL Kd ∆DV Delay <=> Dead Time Load Upset Lag <=>Time Constant Secondary Secondary Primary Primary Delay Lag Gain Delay Lag Delay Lag Gain θv τv Kv θs τs θp τp Kp ∆Fv Valve Process ∆PV τo is the largest lag in the loop (hopefully τp) Kv = slope of installed flow characteristic For self-regulating processes: Ko = Kv ∗ Kp ∗ Km For near integrating processes: Ki = Kv ∗ (Kp / τp) ∗ Km Local % ∆%CO Km = 100% / span Set Point %SP PID Kc Ti Td % ½ of Wireless Default Update Rate % ∆%PV Delay Lag Gain Lag Delay Lag τc2 θc τc1 Km τm2 θm2 τm1 θm1 Lag Delay Controller Measurement First Order Approximation: θο ≅ θv + θs + θp + θm1 + θm2 + θc + Y∗τv + Y∗τs + Y∗τm1 + Y∗τm2 + Y∗τc1 + Y∗τc2 (set by automation system design for flow, pressure, level, speed, surge, and static mixer pH control) 87
  • 88. Open Loop Response of Self-Regulating Process Response to change in controller output with controller in manual %PV % Controller Output (%CO) Ko = ∆%PV / ∆%CO % Process Variable (%PV) Self-regulating process gain (%/%) %CO or Maximum speed ∆%PV in 4 dead times is critical speed 0.63∗∆%PV ∆%CO Noise Band observed θo τo ideally τp Time (seconds) total loop dead time Self-regulating process open loop negative feedback time constant 88
  • 89. Open Loop Response of Integrating Process Response to change in controller output with controller in manual %PV Ki = { [ %PV2 / ∆t2 ] − [ %PV1 / ∆t1 ] } / ∆%CO % Controller Output (%CO) % Process Variable (%PV) Integrating process gain (%/sec/%) %CO or Maximum ramp rate in 4 dead times is used to estimate integrating process gain ∆%CO ramp rate is ramp rate is ∆%PV1 / ∆t1 ∆%PV2 / ∆t2 Time (seconds) observed θo total loop dead time 89
  • 90. Open Loop Response of Runaway Process Response to change in controller output with controller in manual Ko = ∆%PV / ∆%CO Runaway process gain (%/%) Acceleration % Controller Output (%CO) % Process Variable (%PV) For safety reasons, tests are terminated within 4 dead times before noticeable acceleration 1.72∗∆%PV or ∆%PV ∆%CO Noise Band observed θo τ’ o must be τ’ p Time (seconds) total loop dead time runaway process open loop positive feedback time constant 90
  • 91. Diverse Loop Metrics • Peak and integrated errors for load disturbances • Rise time for setpoint change (time to reach setpoint) • Overshoot for setpoint change • Settling time for setpoint change • Standard deviation of oscillations
  • 92. Diverse Metrics Peak and Integrated Error The use of a setpoint lead-lag with the lag equal to the reset time and the lead 20% of the lag will provide a fast setpoint response with minimal overshoot despite tuning for maximum load rejection
  • 93. Ultimate Limit to Loop Performance Peak error is proportional to the ratio of loop dead time to 63% response time (Important to prevent SIS trips, relief device activation, surge prevention, and RCRA pH violations) Total loop deadtime that is often set by automation design θo Ex = ∗ Eo (θ o + τ o ) Largest lag in loop that is ideally set by large process volume Integrated error is proportional to the ratio of loop dead time squared to 63% response time (Important to minimize quantity of product off-spec and total energy and raw material use) θ o2 Ei = ∗ Eo (θ o + τ o ) For a sensor lag (e.g. electrode or thermowell lag) or signal filter that is much larger than the process time constant, the unfiltered actual process variable error can be found from the equation for attenuation
  • 94. Effect of Disturbance Lag on Integrating Process Periodic load disturbance time constant increased by factor of 10 Adaptive loop Baseline loop Adaptive loop Baseline loop Primary reason why bioreactor control loop tuning and performance for load upsets is a non issue!
  • 95. Practical Limit to Loop Performance Peak error decreases as the controller gain increases but is essentially the open loop error for systems when total dead time >> process time constant Open loop error for fastest and largest 1 Ex = ∗ Eo load disturbance (1 + K o ∗ K c ) Integrated error decreases as the controller gain increases and reset time decreases but is essentially the open loop error multiplied by the reset time plus signal delays and lags for systems when total dead time >> process time constant Ti + ∆t x + τ f Ei = ∗ Eo Ko ∗ Kc Peak and integrated errors cannot be better than ultimate limit - The errors predicted by these equations for the PIDPlus and deadtime compensators cannot be better than the ultimate limit set by the loop deadtime and process time constant
  • 96. Implied Dead Time from Slow Tuning Slow tuning (large Lambda) creates an implied dead time where the loop performs about the same as a loop with fast tuning and an actual dead time equal to the implied dead time (θi) θ i = 0.5 ∗ (λ + θo ) For most aggressive tuning Lambda is set equal to observed dead time (implied dead time is equal to observed dead time) Money spent on improving measurement and process dynamics (e.g. reducing measurement delays and process dead times) will be wasted if the controller is not tuned faster to take advantage of the faster dynamics You can prove most any point you want to make in a comparison of control system performance, by how you tune the PID. Inventors of special algorithms as alternatives to the PID naturally tend to tune the PID to prove their case. For example Ziegler-Nichols tuning is often used to show excessive oscillations that could have be eliminated by cutting gain in half
  • 97. Disturbance Speed Effect of load disturbance lag (τL) on peak error can be estimated by replacing the open loop error with the exponential response of the disturbance during the loop dead time For Ei (integrated error), use closed loop time constant instead of dead time E L = (1 − e −θo /τ L ) ∗ Eo For a load disturbance lag much larger than the dead time, the load error in one dead time Is very small, allowing a very large implied dead time from slow tuning. In other words, tuning and control loop dynamics are not important in terms of disturbance rejection. The focus is then on the effect of tuning and dynamics on rise time (time to reach a new setpoint)
  • 98. Setpoint Response Rise Time Rise time (time to reach a new setpoint) is inversely proportional to controller gain ∆% SP Tr = + θo K i ∗ min ( | %∆COmax |, ( K c + K ff ) ∗ ∆% SP ) Rise time can be decreased by setpoint feedforward and bang-bang logic that sets and holds an output change at maximum (∆%COmax) for one dead time until future PV value is projected to reach setpoint. The fastest possible rise time is: ∆% SP Tr = + θo K i ∗ | %∆COmax |
  • 99. Basic Lambda Tuning (Self-Regulating Processes) Self-Regulation Process Gain: ∆% PV Ko = ∆%CO Controller Gain Ti Kc = K o ∗ (λ + θ o ) Lambda (Closed Loop Time Constant for Setpoint Response) λ = λ f ∗τ o Controller Integral Time Ti =τ o Lambda tuning excels at coordinating loops for blending, fixing lower loop dynamics for model predictive control, and reducing loop interaction and resonance
  • 100. Fastest Lambda Tuning (Self-Regulating Process) For max load rejection set lambda equal to dead time λ = θo τo K c = 0.5 ∗ Ko ∗ θo Ti =τ o
  • 101. Basic Lambda Tuning Integrating Processes Lambda (closed loop arrest time in load response) λ = λ f / Ki Integrating Process Gain: ∆% PV2 / ∆t 2 − ∆% PV1 / ∆t1 Ki = ∆%CO Controller Gain: Ti Kc = K i ∗ [ λ + θ o ]2 Controller Integral (Reset) Time: Ti = 2 ∗ λ + θ o Controller Derivative (Rate) Time: Td = τ s secondary lag
  • 102. Fastest Lambda Tuning Integrating Processes For max load rejection set lambda equal to dead time λ = θo Controller Gain: 3 Kc = Ki ∗ 4 ∗ θo Controller Integral (Reset) Time: Ti = 3 ∗ θ o Controller Derivative (Rate) Time: Td = τ s secondary lag Check for prevention of slow rolling oscillations: 2.25 K c * Ti = Ki
  • 103. Often Violated Criteria for Integrating Processes To prevent slow rolling oscillations: 2 K c * Ti > Ki 103