A proportional–integral–derivative controller (PID controller) is a control loop feedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an error value as the difference between a measured process variable and a desired setpoint.
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State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, Concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area.
A proportional–integral–derivative controller (PID controller) is a control loop feedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an error value as the difference between a measured process variable and a desired setpoint.
State space analysis, eign values and eign vectorsShilpa Shukla
State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, Concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area.
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THIS PPT IS SO USEFUL FOR THE ENGINEERING STUDENTS FOR CONTROL SYSTEMS STUDENTS AND THIS PPT ALSO CONTAINS A MATLAB CODING FOR THE LEAD COMPENSATOR AND THE RESULTS ARE ALSO PLOTTED IN THAT PPT AND THE PROBLEM CAN ALSO BE SOLVED BY USING THE DATA IN PPT AND IT IS SO USEFUL PPT
The Controller Design For Linear System: A State Space ApproachYang Hong
The controllers have been widely used in many industrial processes. The goal of accomplishing a practical control system design is to meet the functional requirements and achieve a satisfactory system performance. We will introduce the design method of the state feedback controller, the state observer and the servo controller with optimal control law for a linear system in this paper.
This presentation gives complete idea about definitions of stability, BIBO, Absolute and relative stability, Routh-Hurwitz Criterion, Special Cases and numerical examples.
laplace transform and inverse laplace, properties, Inverse Laplace Calculatio...Waqas Afzal
Laplace Transform
-Proof of common function
-properties
-Initial Value and Final Value Problems
Inverse Laplace Calculations
-by identification
-Partial fraction
Solution of Ordinary differential using Laplace and inverse Laplace
CONTROL SYSTEMS PPT ON A LEAD COMPENSATOR CHARACTERISTICS USING BODE DIAGRAM ...sanjay kumar pediredla
A LEAD COMPENSATOR CHARACTERISTICS USING BODE DIAGRAM FOR MAXIMUM OF 50 DEG PHASE ANGLE
THIS PPT IS SO USEFUL FOR THE ENGINEERING STUDENTS FOR CONTROL SYSTEMS STUDENTS AND THIS PPT ALSO CONTAINS A MATLAB CODING FOR THE LEAD COMPENSATOR AND THE RESULTS ARE ALSO PLOTTED IN THAT PPT AND THE PROBLEM CAN ALSO BE SOLVED BY USING THE DATA IN PPT AND IT IS SO USEFUL PPT
The Controller Design For Linear System: A State Space ApproachYang Hong
The controllers have been widely used in many industrial processes. The goal of accomplishing a practical control system design is to meet the functional requirements and achieve a satisfactory system performance. We will introduce the design method of the state feedback controller, the state observer and the servo controller with optimal control law for a linear system in this paper.
This presentation gives complete idea about definitions of stability, BIBO, Absolute and relative stability, Routh-Hurwitz Criterion, Special Cases and numerical examples.
Analysis and Design of PID controller with control parameters in MATLAB and S...MIbrar4
• To learn the need of controller
• Types of Basic Controllers (P, I and D Controllers) and their properties.
• Controller combinations (PI, PD and PID Controllers) and their properties.
• PID tunning by MATLAB.
• Comparative performance analysis of PI, PD and PID Controllers
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
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2. 9.2 PID CONTROLLER
• The proportional–integral–derivative (PID)
controller is often referred to as a ‘three-term’
controller.
• It is one of the most frequently used controllers in
the process industry.
• In a PID controller the control variable is generated
from the sum of a term proportional to the error, a
term which is the integral of the error, and a term
which is the derivative of the error.
2
3. 9.2 PID CONTROLLER
• Proportional: the error is multiplied by a gain Kp. A
very high gain may cause instability, and a very low gain
may cause the system to be very sluggish (slow).
• Integral: the integral of the error is found and
multiplied by a gain. The gain can be adjusted to drive
the error to zero in the required time.
• Derivative: The derivative of the error is multiplied by
a gain. The derivative control is used to improve the
transient response by reducing overshoot.
3
4. • The input–output relationship of a PID controller can be
expressed as
• where u(t) is the output from the controller and e(t) = r (t) −
y(t), in which r (t) is the desired set-point (reference input)
and y(t) is the plant output. Ti and Td are known as the
integral and derivative action time, respectively.
• By taking the Laplace transform of this equation, we can write
the transfer function of a continuous-time PID as
4
6. • To implement the PID controller using a digital computer we have
to convert the equation:
from a continuous to a discrete representation.
• There are several methods for doing this and the simplest is to use
the trapezoidal approximation for the integral and the backward
difference approximation for the derivative:
6
Discrete PID Controller
0
𝑡
𝑒 𝑡 𝑑𝑡 ≈ 𝑘=1
𝑛
𝑇𝑒 𝑘𝑇 ,
𝑑𝑒(𝑡)
𝑑𝑡
≈
𝑒 𝑛𝑇 −𝑒(𝑛𝑇−𝑇)
𝑇
7. • Using these approximations, we can write:
𝑢 𝑛𝑇 = 𝐾𝑝[𝑒 𝑛𝑇 +
1
𝑇𝑖
𝑘=1
𝑛
𝑇𝑒 𝑘𝑇 + 𝑇𝑑
𝑒 𝑛𝑇 −𝑒(𝑛𝑇−𝑇)
𝑇
],
𝑢 𝑛𝑇 − 𝑇 = 𝐾𝑝[𝑒 𝑛𝑇 − 𝑇 +
1
𝑇𝑖
𝑘=1
𝑛−1
𝑇𝑒 𝑘𝑇 + 𝑇𝑑
𝑒 𝑛𝑇−𝑇 −𝑒(𝑛𝑇−2𝑇)
𝑇
].
• Subtracting these two equations, we obtain:
𝑢𝑛 = 𝑢𝑛−1 + 𝐾𝑝 𝑒𝑛 − 𝑒𝑛−1 +
𝐾𝑝𝑇
𝑇𝑖
𝑒𝑛 +
𝐾𝑝𝑇𝑑
𝑇
[𝑒𝑛 − 2𝑒𝑛−1 + 𝑒𝑛−2]
where 𝑢𝑛: = 𝑢(𝑛𝑇) and 𝑢𝑛−1: = 𝑢 𝑛𝑇 − 𝑇 .
• The PID is now in a suitable form which can be implemented on a digital
computer. Here the current control action uses the previous control value
as a reference.
7
8. 9.2.3 PID Tuning
• Tuning the controller involves adjusting the
parameters Kp, Td and Ti in order to obtain a
satisfactory response.
• There are many techniques for tuning a controller,
ranging from the first techniques described by J.G.
Ziegler and N.B. Nichols (known as the Ziegler–
Nichols tuning algorithm), to recent auto-tuning
controllers.
• In this section we shall look at the tuning of PID
controllers using the Ziegler–Nichols tuning
algorithm.
8
9. • Ziegler and Nichols suggested values for the PID
parameters of a plant based on open-loop or closed-
loop tests of the plant.
• According to Ziegler and Nichols, the open-loop
transfer function of a system can be approximated
with a time delay and a single-order system, i.e.
• where TD is the system time delay (i.e.
transportation delay), and T1 is the time constant of
the system.
9
10. • For open-loop tuning, we first find the plant parameters by applying
a step input to the open loop system.
• The plant parameters K, TD and T1 are then found from the result of
the step test as shown.
10
11. • Ziegler and Nichols then suggest using the PID controller settings
given in the Table below when the loop is closed.
• These parameters are based on the concept of minimizing the
integral of the absolute error after applying a step change to the set-
point.
11
12. Example
The open-loop unit step response of a thermal system is shown. Obtain
the transfer function of this system and use the Ziegler–Nichols tuning
algorithm to design:
(a) a proportional controller,
(b) a proportional plus integral (PI) controller, and
(c) a PID controller.
Draw the block diagram of the system in each case.
12
13. Solution
• From the previous Figure, the system
parameters are obtained as K = 40◦C, TD = 5 s
and T1 = 20 s, and, hence, the transfer function
of the plant is
13