Control engineering module 1 part-a 18me71

CONTROL ENGINEERING
Course Code 18ME71 CIE Marks 40
Teaching Hours / Week (L:T:P) 3:0:0 SEE Marks 60
Credits 03 Exam Hours 03
[AS PER CHOICE BASED CREDIT SYSTEM (CBCS) SCHEME]
SEMESTER – VII
Dr. Mohammed Imran
B. E. IN MECHANICAL ENGINEERING

Course Objectives
 To develop comprehensive knowledge and understanding of
modern control theory, industrial automation, and systems
analysis.
 To model mechanical, hydraulic, pneumatic and electrical
systems.
 To represent system elements by blocks and its reduction
 To represent system elements by blocks and its reduction
techniques.
 To understand transient and steady state response analysis
of a system.
 To carry out frequency response analysis using polar plot,
Bode plot.
 To analyse a system using root locus plots.
 To study different system compensators and characteristics
of linear systems.
Dr. Mohammed Imran

Course outcomes
On completion of the course the student will be able to
CO1: Identify the type of control and control actions.
CO2: Develop the mathematical model of the physical systems.
CO3: Estimate the response and error in response of first and
second order systems subjected standard input signals.
second order systems subjected standard input signals.
CO4: Represent the complex physical system using block diagram
and signal flow graph and obtain transfer function.
CO5: Analyse a linear feedback control system for stability using
Hurwitz criterion, Routh‟s criterion an root Locus technique in
complex domain.
CO6: Analyse the stability of linear feedback control systems in
frequency domain using polar plots, Nyquist and Bode plots.
Dr. Mohammed Imran

Module-1
Part-A
 Introduction: Components of a control system, Open
loop and closed loop systems.
 Types of controllers: Proportional, Integral,
 Types of controllers: Proportional, Integral,
Differential, Proportional-Integral, and Proportional-
Integral Differential controllers.
Part-B
 Modelling of Physical Systems: Mathematical
Models of Mechanical, Electrical, Thermal, Hydraulic
Systems.
10 Hours
Dr. Mohammed Imran

Text Books:
 Automatic Control
Systems, Farid G., Kuo
B. C, McGraw Hill
Education, 10th
Edition,2018
Dr. Mohammed Imran
Edition,2018
 Control systems, Manik
D. N, Cengage, 2017

Reference Books:
 Modern control Engineering K. Ogeta Pearson 5th
Edition, 2010
 Control Systems Engineering Norman S Nice Fourth
Edition, 2007
Modern control Systems Richard C Dorf Pearson
Dr. Mohammed Imran
 Modern control Systems Richard C Dorf Pearson
2017
 Control Systems Engineering IjNagrath, M Gopal
New Age International (P) Ltd 2018
 Control Systems Engineering S Palani Tata McGraw
Hill Publishing Co Ltd ISBN-13 9780070671935

MODULE -1
PART-A
PART-A
Dr. Mohammed Imran CONTROL ENGINEERING

Introduction:
 Over the past five decades, control systems have assumed an
increasingly important role in the development and advancement of
modern civilization and technology.
 Practically every aspect of our day-today activities is affected by some
type of control system.
 For instance, in the domestic domain, we need to regulate the
 For instance, in the domestic domain, we need to regulate the
temperature and humidity of homes and buildings for comfortable
living.
 For transportation, various functionalities of the modern automobiles
and airplanes involve control systems.
 Industrially, manufacturing processes contain numerous objectives for
products that will satisfy the precision and cost-effectiveness
requirements.
 A human being is capable of performing a wide range of tasks,
including decision making.
Dr. Mohammed Imran

Introduction:
 Some of these tasks, such as picking up objects and walking from one point to another, are
commonly carried out in a routine fashion. Under certain conditions, some of these tasks are
to be performed in the best possible way.
 For instance, an athlete running a 100- yd dash has the objective of running that distance in
the shortest possible time. A marathon runner, on the other hand, not only must run the
distance as quickly as possible, but, in doing so, he or she must also control the consumption of
energy and devise the best strategy for the race.
Cont………
energy and devise the best strategy for the race.
 The means of achieving these “objectives” usually involve the use of control systems that
implement certain control strategies.
 Control systems are found in abundance in all sectors of industry, such
as quality control of manufactured products, automatic assembly lines, machine-tool control,
space technology, computer control, transportation systems, power systems, robotics, micro-
electro-mechanical systems (MEMS), nanotechnology, and many others.
 Even the control of inventory and social and economic systems may be approached from the
control system theory. More specifically, applications of control systems benefit many areas,
including….
Dr. Mohammed Imran

Introduction:
 Control systems abound in modern civilization.
 Process control. Enable automation and mass production in industrial
setting.
 Machine tools. Improve precision and increase productivity.
 Robotic systems. Enable motion and speed control.
Cont………
Robotic systems. Enable motion and speed control.
 Transportation systems. Various functionalities of the modern automobiles and
airplanes involve control systems.
 MEMS. Enable the manufacturing of very small electromechanical devices
such as microsensors and microactuators.
 Lab-on-a-chip. Enable functionality of several laboratory tasks on a single
chip of only millimeters to a few square centimeters in size for medical
diagnostics or environmental monitoring.
 Biomechanical and biomedical. Artificial muscles, drug delivery systems, and
other assistive technologies.
Dr. Mohammed Imran

Terminology of a control system
Following are the basic terms used in the study of control engineering:
 Control : The meaning control is to regulate, direct or command a system so that a desired
objective is achieved.
 System : A system is an arrangement or a combination of different physical components that are
connected together or related together to form an entire unit to achieve a certain objective. A
system can be both physical and an abstract one. For example - A class room is a physical system
and an abstract system can be dynamic phenomena such as economical, educational or social.
 Input : Input is the applied signal or external excitation signal that is applied to the control system
Cont………
 Input : Input is the applied signal or external excitation signal that is applied to the control system
to get a required output.
 Plant : Plant is the portion of the system which is to be controlled or regulated.
 Process : It is an operation which is to be controlled or regulated to obtain the desired output.
 Controller : It is an element in a control system which generates necessary control action to control
the plant or process
 Manipulated variable : It is an output signal or control action generated by the controller to affect
the value of controlled variable or output from the plant or process.
 Disturbance : It is an undesired signal which tends to affect the output response of the system. If
such disturbances generated outside the system and acts addition to normal input is known as
 external disturbance and if the disturbance generated within a system by it self is known as
internal disturbance.
 Control system : A control system is an arrangement of components interconnected in such a way
so as to regulate, direct or command itself to obtain a certain objective.

1.1 Components of a control system
 The basic ingredients of a control system can be described by
 Objectives of control.
 Control-system components.
 Results or outputs.
 The basic relationship among these three components is illustrated
Figure 1. Basic components of a control system
 The basic relationship among these three components is illustrated
in a block diagram representation, as shown Fig.1.
 The block diagram representation, provides a graphical
approach to describe how components of a control system interact.
 In this case, the objectives can be identified with inputs, or
actuating signals, u, and the results are also called outputs, or
controlled variables, y.
 In general, the objective of the control system is to control the
outputs in some prescribed manner by the inputs through the
elements of the control system.
Dr. Mohammed Imran

1.1.1 Examples of Control-System Applications
 Intelligent Transportation Systems
 Steering Control of an Automobile
 Idle-Speed Control of an Automobile
 Sun-Tracking Control of Solar Collectors
Dr. Mohammed Imran
Figure Idle-speed control system.
Figure Conceptual method of efficient water extraction using solar power.

1.2 Classification Of Control Systems
Type 1 : Generally, control systems can be classified into three
types. They are
 Natural control system : A control system which exists in nature
including biological systems are called natural control system. Ex :
Human being
 Made-made control system : A control system created by human
beings are called man-made control system. Ex : Automobile
 Combinational control system : A control system which is having
combination of both natural and man-made are called
combinational control system. Ex : Man driving an automobile
Type 2 :Based on the operation, control systems can be classified
into
 Manually operated control system
 Automatic control system
Dr. Mohammed Imran

Type 3: From the analysis point of view, control system can be
classified into
1. Linear and Non-linear control systems
A control system which obeys the principle of superposition is
known as liner control system. The principle of superposition is
a combination of an additive property and homogenous property
Cont………
a combination of an additive property and homogenous property
 Additive Property: If 'x' and 'y' belongs to the domain of the function f '
then we can write f (x+y) = f (x) + f (y)
 Homogenous Property: For any..t ' belongs to the domain of the
function f ' and for any scalar constant α , we can write
f (αx) = αf (x)
 For a linear system input/ output relationships may be represented by a
linear differential equation. A control system which does not obey the
pinciple of superposition is known as Non-linear control system.
If function f (x) = x2
Therefore the function f (x) = x2 is Non-linear.
Dr. Mohammed Imran

Type 3: From the analysis point of view, control system can be classified into
2. Time varying and Time invariant control systems
 A control system in which one or more parameters vary as a function of time in
known as time varying control system.
 Thus, a time-variant system is a system described by a differential equation with
variable coefficients and a linear time variant system is described by linear
differential equations with variable coefficients.
Cont………
differential equations with variable coefficients.
 Its derivatives appear as linear combinations, but a coefficient or coefficients of
terms may involve the independent variable.
Example-1: A space shuttle leaving the earth as it mass reduces with time during the
flight. Also, a rocket-burning fuel system is an example of time variant system since the
rocket mass varies during the flight as the fuel is burned. A control system in which all
the parameters are constant with respect to time is known as time in variant control
system. Thus, a time-invariant system is a system described by a differential equation
with constant coefficients and a linear time invariant system is described by linear
differential equations with constant coefficients.
Example-2: Resistance, capacitance and inductance in an electrical network and a single
degree of freedom spring mass viscous damper system is an example of a time-invariant
system provided the characteristics of all the three components do not vary with time.
Dr. Mohammed Imran

3. Deterministic and Stochastic control systems
 A control system in which the response to input is predictable and repeatable
is known as deterministic control system.
 A control system in which the response to input is unpredictable is known as
stochastic control system.
Cont………
4. Continuous - Time and Discrete Time control systems
A control system in which all the system variables are defined for all the time is known as
continuous time control systems.
Example-1: Tacho-generator feedback used in the control of the DC motor. A control
system is which one or more system variables are defined only at certain discrete
intervals of time, generally evenly spaced steps is known as Discrete-time control system.
Example:-2 Micro processor based systems. Lumped-parameter and Distributed
parameter control system
Dr. Mohammed Imran

3. Deterministic and Stochastic control systems
 A control system in which the response to input is predictable and repeatable is
known as deterministic control system.
 A control system in which the response to input is unpredictable is known as
Cont………
4. Continuous - Time and Discrete Time control systems
A control system in which all the system variables are defined for all the time is known as
continuous time control systems.
Example-1: Tacho-generator feedback used in the control of the DC motor. A control system
is which one or more system variables are defined only at certain discrete intervals of time,
generally evenly spaced steps is known as Discrete-time control system.
Example:-2 Micro processor based systems. Lumped-parameter and Distributed parameter
control system.
A control system that can be described by ordinary differential equation is known as lumped-
parameter control system.
A control system that can be described by partial differential equations are known as distributed-
parameter control systems.
Dr. Mohammed Imran

4. Single input - Single Output [SISO] and Multiple Input Multiple-Output
[MIMO] control systems
 A control system in which there is one input and one output is called single
input and single output control system.
A control system in which there are multiple input and multiple output is known
Cont………
 A control system in which there are multiple input and multiple output is known
as multiple input and multiple output control systems.
Type 4 : Based on the presence of feedback
 Open Loop control system - A control system in which control action is
independent of the desired output is known as open loop control system.
(Feedback is absent)
 Closed Loop-control system - A control system in which control action in
dependent on the. desired output is Ic.nowh as closed-loop control system.
(Feedback is present)
Dr. Mohammed Imran

1.3 Two general categories Of Control Systems
Types of control systems
Control systems are classified into two general categories
based upon the control action which is responsible to
activate the system to produce the output viz.
activate the system to produce the output viz.
1) Open loop control system in which the control action is
independent of the out put.
2) Closed loop control system in which the control action is
some how dependent upon the output and are generally
called as feedback control systems.
Dr. Mohammed Imran

1.2 Open loop and closed loop systems
1.2.1 Open loop
 An open loop control system is one in which control action is independent of the
desired output. It means the desired output is neither measured nor compared
with the input.
 The block diagram of the open loop control system is as shown in figure 1.1
 In this system, when input is applied to the controller which generates necessary
control action required to control the plant or process which is to be controlled
to generate desired output.
 The accuracy of these system depends entirely on the accuracy with which the
input-output relationship is designed. If there are any variations in the external
environment or disturbance during operation, desired output will not be
accurate. These systems are to be calibrated frequently to obtain accurate
results and to maintain quality of the output.
Dr. Mohammed Imran
Fig. 1: Open Loop control system

1.2.1 Open loop
 The examples of an open loop control systems are
Traffic control system, Automatic bread toaster, Electric
fan, Electric switch, Automatic washing machine and
many more.
Cont………
 Consider a traffic control system which is used regulate
the flow of traffic at cross roads. In this system, Red,
Yellow, Green lights glow according to the set duration
by the timer mechanism and sequence by the relays,
which are predetermined. which do not dependent on
the traffic.
Dr. Mohammed Imran

1.2.1 Open loop
ADVANTAGES
The advantages of open loop control systems are
1. Simple in construction and ease of maintenance.
2. Lower cost.
3. No stability problem.
4. Convenient to use when output is difficult to measure.
Cont………
4. Convenient to use when output is difficult to measure.
5. Economical because simple is design.
DISADVANTAGES
1. The disadvantages of open loop control systems are
2. Frequent calibration is required to maintain quality of the output.
3. Very sensitive to the disturbance.
4. Not reliable and Not accurate because of their dependent on the
accuracy of the calibration.
5. Requires skilled worker to obtain accurate desired output.
Dr. Mohammed Imran

1.2.2 Closed loop systems
 A closed loop control system is one in which control action is dependent on the desired
output. It means the desired output is measured and compared with input using the feedback
element.
 The block diagram of the closed loop control system is as shown in figure. 3
Figure.3 Closed loop
control system
 In this system, output is measured and fed back for comparison with the reference input at
the summing point and this determines the error based on which control action is generated.
The difference between the input arid corresponding output is known as error.
 This error signal is used by the controller to generate manipulated signal which is used to
control the plant or process so as to reduce the error and to bring the actual output to a
desired value.
 The examples of a closed loop control system are Room heating system, Automobile speed
control system, Automatic tank-level control system, Temperature control system and many
more.
Dr. Mohammed Imran
control system

1.2.2 Closed loop systems
ADVANTAGES
The advantages of closed loop control system are
 Insensitive to disturbances.
 Increased accuracy and band width.
 More flexible in operation and reliable.
Cont………
 More flexible in operation and reliable.
 No skilled workers are required
 Faster system response
DISADVANTAGES
The disadvantages of closed loop control system are
 Less stable
 More complex and expensive
 Tendency to overcorrect the error may cause oscillations due to feed back.
Dr. Mohammed Imran

1.2.3 Comparison
Open loop control system Closed loop control system
1.
Output is neither measured nor
compared with input
Output is measured and compared with input
2. Feed back element is absent Feed back element is present
3. Simple to construct and economical Complex in design and hence not economical
Dr. Mohammed Imran
3. Simple to construct and economical Complex in design and hence not economical
4. More stable Less stable
5.
Accuracy depends on the
calibration and unreliable
More accurate due to feedback and reliable
6. Error detector in absent Error detector is present
7. Optimisation in not possible Optimisation is possible
8. Highly sensitive to disturbances Less sensitive to disturbances
9. Narrow band width Broad band width
10. Skilled worker are required Skilled workers are not required.

1.2.4 Application Of The Closed Loop Control System
1. Automatic Electric Iron
Figure 4 shows block diagram of an automatic electric Iron with
temperature control.
 It works on the principle of feedback.
 In an automatic electric Iron, thermostat acts as a feedback element.
 Thermostat senses the actual temperature of iron, if temperature is
beyond the particular value (desired temperature), Relay switches off
the supply to iron and maintains constant temperature at the output.
 Thus, it is a closed loop control system.
Dr. Mohammed Imran
Fig.4. Automatic electric Iron

2. Voltage Stabilizer
Figure 5 shows voltage stabilizer can be treated as closed loop control system.
Cont………
 Input to the voltage stabilizer is the variable voltage and output is the constant
voltage.
 Working principle of voltage stabilizer is based on the controlling the number
of secondary turns as per requirement to increase or decrease the output
voltage.
 When input decreases, the output switch will be connected above A.
 On the other hand, if input increases, the output switch will be connected below
A.
Dr. Mohammed Imran
Fig.4. Voltage stabilizer

3. Ship Stabilization System using fin
Cont………
 Figure 6(a) shows the block diagram of a ship stabilization system using fin. In
this system roll sensor acts a feedback element.
 Fin actuator acts as a controller and ship acts a plant which is to be
controlled.
 The desired roll position and controlled roll (output) are compared at the
summing point to generated error or deviation (if any) based on which fin
actuator initiates the necessary control action to stabilize the ship
Dr. Mohammed Imran
Fig. 6(a) : Ship stabilization system Fig. 6(b) : Ship stabilization system using fin

4. Room Heating System
Cont………
 The block diagram of a room heating system is as shown in figure 7.
 In this system, thermostat acts as a feedback element, its function is to
sense the actual temperature and compares with the desired
temperature.
 Based on the deviation (error) obtained controlling elements such as
relay and switch are activated to produce necessary signal to the plant
(furnace) so as to obtain the desired output temperature of the room.
Dr. Mohammed Imran
Fig. 7: Room heating system

5. Automobile speed control system
Cont………
 Figure 8 shows a block diagram of an automobile speed control system.
 In this system, speedometer measures the actual speed of the engine
and compares with the desired speed to generates the error (if any).
 Based on the error controlling elements such as eyes and brain takes a
decision and leg muscle and accelerator is actuated to increase or
decrease the speed of the engine.
Dr. Mohammed Imran
Fig. 8: Automobile speed control system

6. Automatic missile launching
Cont………
Dr. Mohammed Imran
Fig. 8.1: Automatic missile launching

6. Automatic missile launching
 The missile launching and guidance system of Fig. 8.1 is a sophisticated example of
military applications of feedback control.
 The target plane is sited by a rotating radar antenna which then locks in and continuously
tracks the target.
 Depending upon the position and velocity of the plane as given by the radar output data,
the launch computer calculates the firing angle in terms of a launch command signal,
Cont………
the launch computer calculates the firing angle in terms of a launch command signal,
which when amplified through a power amplifier drives the launcher (drive motor).
 The launcher angular position is feedback to the launch computer and the missile is
triggered as soon as the error between the launch command signal and the missile firing
angle becomes zero.
 After being fired the missile enters the radar beam which is tracking the target. The
control system contained within the missile now receives a guidance signal from the beam
which automatically adjusts the control surface of the missile such that the missile rides
along the beam, finally homing on to the target.
 It is important to note that the actual missile launching and guidance system is far more
complex requiring control of gun's bearing as well as elevation. The simplified case
discussed above illustrates the principle of feedback control.
Dr. Mohammed Imran

 Feedback control system are the control system in which effect of disturbance is seen as an error after comparing the
output and reference input before controller takes the proper corrective action.
 Thus, in feedback control system controller initiates the proper corrective action for the difference obtained between the
output of the system (controlled variable) and the reference input due to the presence of disturbance.
 Thus error in the control system output is reduced due to feedback.
 But feedback not only reduces the error but also reduces the sensitivity of the system to variation in parameter and
unwanted disturbances (Internal and external).
1.2.5 CONCEPT OF FEEDBACK CONTROL SYSTEM
For example, consider a room heating system as shown in figure 9 in which temperature of room is controlled at the desired
level. This system consists of heating system as a plant which operated by valve as a controller, and a thermal sensor as a
feedback element. In this system, actual temperature of the room (output from the heating system) is sensed by the thermal
sensor and is compared with reference input (desired value) to generate error. For the error, valve mechanism is actuated to
take the proper corrective action so that desired temperature level is maintained.
Dr. Mohammed Imran
Fig. 9: Room heating system

Cont………
1. CONTINUOUS-DATA CONTROL SYSTEMS
A continuous-data system is one in which the signals
at various parts of the system are all functions of
the continuous time variable t.
 The signals in continuous-data systems may be
further classified as ac or dc.
 Unlike the general definitions of ac and dc
Dr. Mohammed Imran
Fig. 9.1: Schematic diagram of a typical
dc closed-loop system.
Unlike the general definitions of ac and dc
signals used in electrical engineering, ac and
dc control systems carry special significance in
control systems terminology. When one refers
to an ac control system, it usually means that
the signals in the system are modulated by
some form of modulation scheme.
 A dc control system, on the other hand, simply
implies that the signals are un-modulated, but
they are still ac signals according to the
conventional definition. The schematic diagram
of a closed-loop dc control system is shown in
Fig. 9.1.
 Typical waveforms of the signals in response to a
step-function input are shown in the figure.
 Typical components of a dc control system are
potentiometers, dc amplifiers, dc motors, dc
tachometers, and so on.

Cont………
2. DISCRETE-DATA CONTROL SYSTEMS
 Discrete-data control systems differ from the continuous-data systems in that the
signals at one or more points of the system are in the form of either a pulse train or a
digital code.
 Usually, discrete-data control systems are subdivided into sampled-data and digital
control systems.
Dr. Mohammed Imran
control systems.
 Sampled-data control systems refer to a more general class of discrete-data systems
in which the signals are in the form of pulse data.
 A digital control system refers to the use of a digital computer or controller in the
system so that the signals are digitally coded, such as in binary code.

Cont………
2.1 Sampled-data
Dr. Mohammed Imran
Fig. 9.2: Sampled-data control system
 Figure 9.2 illustrates how a typical sampled-data system operates.
 A continuous-data input signal r(t) is applied to the system.
 The error signal e(t) is sampled by a sampling device, the sampler, and the output of the
sampler is a sequence of pulses.
 The sampling rate of the sampler may or may not be uniform. There are many advantages to
incorporating sampling into a control system.
 One important advantage is that expensive equipment used in the system may be time-shared
among several control channels. Another advantage is that pulse data are usually less
susceptible to noise.

Cont………
2.2 Digital control
Dr. Mohammed Imran
Fig. 9.3: Digital autopilot system for aircraft attitude control.
 Because digital computers provide many advantages in size and flexibility, computer control
has become increasingly popular in recent years. Many airborne systems contain digital
controllers that can pack thousands of discrete elements into a space no larger than the size
of this subject.
 Figure 9.3 shows the basic elements of a digital autopilot for aircraft attitude control.

 Feedback in control system improves the time response.
 By proper design and application of feedback, stability
of the system can be effectively controlled.
 Gain of the system can be controlled by controlling
1.2.6 EFFECT OF FEEDBACK ON THE CONTROL SYSTEM
 Gain of the system can be controlled by controlling
feedback.
 Feedback in control system reduces the effect of
disturbance (Internal and External) on the system and
reduces the sensitivity of the system to variation in
parameter.
Dr. Mohammed Imran

Various parameters are considered in the design of a control system.
All the control systems are designed to perform specific objectives. To
achieve the required objective, a control systems must satisfy the
following requirements :
 Stability
1.2.6..1 REQUIREMENT OF AN IDEAL CONTROL SYSTEM
(Factor affect for Feedback on Control System)
 Stability
 Sensitivity
 Speed
 Accuracy
 Disturbance or Noise
 Bandwidth
Dr. Mohammed Imran

If a control system satisfy the all requirements the system is known as ideal control
system.
 Stability : Stability in a control system implies that small changes in the system
input, in initial conditions or in system parameters do not result in large changes
in the system behaviour. Stability is the important characteristic of the transient
response of a control system. A ideal control system is one which gives bounded
1.2.7 REQUIREMENT OF AN IDEAL CONTROL SYSTEM
Cont………
response of a control system. A ideal control system is one which gives bounded
output for bounded input. A ideal control system are designed to be stable.
 Sensitivity : An ideal control system should be insensitive to the variations in
parameters of the system but it should be sensitive to the input commands. It is a
important parameter that should be considered in the design of control system.
 Speed : Speed of the control system means how fast the output of the system
approaches to the desired value. This is measured interms of the settling time
and rise time. An ideal control system should have good speed.
Dr. Mohammed Imran

 Accuracy : Accuracy of the control system means how much the output of the
control system is nearer to the input or desired value. An ideal control system
must be highly accurate.
 Disturbance : All control systems are subject to some type of extraneous signals
or noise during operation. External disturbance such as wind gust, thermal noise
voltage are quite common. Therefore, in the design of a control system,
1.2.7 REQUIREMENT OF AN IDEAL CONTROL SYSTEM
Cont………
voltage are quite common. Therefore, in the design of a control system,
Considerations should be given so that the system is insensitive to noise and
disturbances but sensitive to input commands.
 Band width : Band width of the control system means for the range of input, the
output of the control system should be constant. It refers to the frequency
response of the control system. An ideal control system must give satisfactory
output for the input frequency range.
Dr. Mohammed Imran

2. Controllers
 It is generally known as an automatic controllers.
 The controller is a basic element in a control system which compares the
actual value of the plant output with the reference input or desired value to
determine the error or deviation and produces proper corrective action
(control signal) that will reduce the error to a smaller value or to zero.
The measurement of-error is possible due to feedback.
 The measurement of-error is possible due to feedback.
 The feedback allows to compare the plant output with its reference input to
generate error.
 Thus input to the controller is the deviation of the output from its desired
value known as error and output from the controller is the corrective action
known as manipulated signal.
 The manner is which the controller produces output i.e., manipulated control
signal is known as control action.
Dr. Mohammed Imran

2. Controllers
TYPES OF CONTROLLERS
 Based on the control action, controllers are classified as
 On-off or two position controllers
 Proportional controllers
Derivative controller
Cont………
 Derivative controller
 Integral controllers
 Proportional plus integral controllers
 Proportional plus differential controllers
 Proportional plus integral plus differential controllers.
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2.2 Proportional Controller
 Figure 10 shows a simple block diagram
of the proportional controller. In this, the
output of the controller i.e., manipulated
or actuating signal is proportional to the
input of the controller i.e., error signal.
 For a controller with proportional control
 For a controller with proportional control
action the relationship between output of
the controller m(t) and error signal e(t) is
m(t) = k p e(t)
 Taking Laplace transform on both sides,
we get
M(s) = k p E(s)
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Fig.10 Proportional controller
where kp is the proportional gain.
The relation between output of the controller
m(t) and the error signal e(t) for the unit step
input is as shown in figure 11.
Fig.11

2.2 Proportional Controller
 It shows that there exists a linear relation between controller
output m(t) and the error signal e(t). For a zero error the
controller output should be zero otherwise the process will
come to halt. Hence mathematically it can be expressed as
m(t) = Kp e(t)+ mo
Where m is the controller output for zero error.
 Where mo is the controller output for zero error.
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Fig.11
CHARACTERSTICS
A control system with proportional control mode has the following characteristics:
1. The controller output is equal to mo when the error is zero.
2. The system is stable Improves Closed Loop Response.
3. Provides fast response.
4. Improves steady state error and Rise time.
5. But, high gain may lead to instability due to high oscillation.
DISADVANTAGES
1. Provides heavily damped response.
2. Provides large steady state error.
Example: Non-inverting operational Amplifiers.

2.3 Differential Controller
 In this control mode, the output of the controller i.e., manipulated signal m(t) is
directly proportional to the time derivative of the input to the controller i.e., error
signal e(t). Mathematically it can be expressed as
• The main advantage of this control
mode is that it responds to the rate of
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mode is that it responds to the rate of
change of error and can produce
necessary corrective action before the
magnitude of the error becomes too
large.
• Thus derivative controller anticipates the
error and also initiates the early
corrective action for the anticipated
error.

2.3 Differential Controller
 For example, if the error changes at a rate of 2% per minute, and the
derivative time Td = 3 minutes, the predicted error is 6%. If the Controller Gain,
lc = 0.2, then the derivative control mode will add an additional 0.2 x 6% =
1.2% to the controller output.
 The derivative control mode gives a controller additional control action when the
error changes consistently.
 It also makes the loop more stable (up to a point) which allows using a higher
controller gain and a faster integral (shorter integral time or higher integral gain).
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controller gain and a faster integral (shorter integral time or higher integral gain).
 These have the effect of reducing the maximum deviation of process variable from
set point if the process receives and external disturbance
 However Derivative control action can never be used alone as it takes corrective
action on the rate of change of actual error rather than actuating error itself.
 Any noise in the error signal amplifies and gives an erratic behavior.
CHARACTERISTICS
 Produces significant correction before magnitude of actuating error
becomes too large.
 Tends to increase stability of the system.
 Adds damping to the system hence large values of gain which will improve
accuracy can be used

2.4 Integral Controller
 Figure 12 shows a simple block diagram
of the integral controller. In this, output of
the controller
 i.e., manipulated signal is changed at a
rate proportional to the input of the
controller i.e., error signal.
 For a controller with integral control
Cont………
the controller m(t) and error signal e(t) is
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Fig. 12: Integral controller
By integrating, we get
Taking Laplace transform on both sides, we get
The integral controller gives a output which is ramp the
integral control action is also called reset control Integral
control action is used whenever the steady state error is
too large.
CHARACTERISTICS
• Slows down system Response.
• Increases setting and Rise time.
Ex: Integrator using operational Amplifier followed by sign
inverter.

2.5 Proportional plus Differential Controller
This is a combination of proportional and
derivative controller which is used to improve
the steady state behavior of the system. In this
control mode manipulated signal consists of
proportional error signal added with the
derivative error signal. Mathematically it can
derivative error signal. Mathematically it can
be expressed as
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Figure 13 shows the block diagram of the
transfer function of the PD controller
Figure 14 shows response of the PD controller
for the unit step input.
Fig. 13 : PD controller
Fig. 14

2.6 Proportional-Integral Controller
 This is a combination of proportional and
integral controller which is used to improve
the performance of the system. In this, the
manipulated signal consists proportional
error signal added with an integral of the
error signal. It is given by
Fig. 15: PI controller
where k is the proportional gain
error signal. It is given by
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Taking Laplace transform on both sides, we get
where k is the proportional gain
Ti is the integral time.
Fig. 15 shows Block diagram of the transfer
function is given by
The integral time adjusts the integral control
action, while change in proportional gain affects
both proportional and integral action. The
inverse of the integral time is called reset rate.
The reset rate is the number of times per minute
that a proportional part of the control action is
duplicated.

2.7 Proportional- Integral-Differential Controller
It is the combination of proportional,
integral and differential control actions
so as to derive the advantages of all
the control action. General, it is known
as PID controllers. The equation for
the PID controller is given by
Fig. 16: PID controller
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where, kp is the proportional gain, Ti is the integral time and Td is the derivative or differential time
Fig. 16 shows the block diagram of the PID controller for the transfer function.
These controllers are used extensively in industrial processes.. Setting of PIP gain is called as tuning
however tuning should be done carefully as there are three gains.
Taking Laplace transform on both sides,

2.8 ON — OFF CONTROLLER
 On OFF Controller are required to switch ON or
OFF the component at appropriate time.
 Switches relays times unit are used for the purposes.
 The main disadvantage with these ON/OFF
Controller are they consume significant voltage and
Controller are they consume significant voltage and
current during their operation hard wised electronic
logic controller are also used they are cheap
however they are complicated.
 Fluid logic systems are also available to install and
maintain

Control engineering module 1 part-a 18me71

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