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P/Pi/Pd/Pid Controller Design: Unit-4

This document discusses PID controller design. It describes three main methods for designing PID controllers: root locus approach, frequency response approach, and direct synthesis. The root locus approach designs controllers by placing poles and zeros on the root locus plot. The frequency response approach designs for a specified gain and phase crossover frequency. Direct synthesis designs controllers directly based on system models, including for low-order systems, higher-order systems, and time-delay systems. The document provides examples of calculating PID parameters using direct synthesis for different system types.

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harish9
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196 views39 pages

P/Pi/Pd/Pid Controller Design: Unit-4

This document discusses PID controller design. It describes three main methods for designing PID controllers: root locus approach, frequency response approach, and direct synthesis. The root locus approach designs controllers by placing poles and zeros on the root locus plot. The frequency response approach designs for a specified gain and phase crossover frequency. Direct synthesis designs controllers directly based on system models, including for low-order systems, higher-order systems, and time-delay systems. The document provides examples of calculating PID parameters using direct synthesis for different system types.

Uploaded by

harish9
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Unit-4

P/PI/PD/PID
Controller Design
Basic Control System
Disturbance

Controlled Manipulated
Set-point Error Signal Variable
or
Reference Actual
input + Output
+ +
+ Controller
Controller Actuator
Actuator + Process
Process
-

Feedback Signal Sensor


Sensor
Controller Tunning

The process of selecting the controller parameters to


meet the given performance specifications are known as
Controller Tuning.
Controller OutPut
Controller OutPut

– Increasing gain approaches setpoint faster


– Can leads to overshoot, and even instability
– Steady-state offset
Controller OutPut
➢How do the PID parameters affect system dynamics?
➢4 major characteristics of the closed-loop step response
are important:
1.Rise Time: the time it takes for the plant output y
to rise beyond 90% of the desired level for the
first time.
2.Overshoot: how much the the peak level is higher
than the steady state, normalized against the
steady state.
3.Settling Time: the time it takes for the system to
converge to its steady state.
4.Steady-state Error: the difference between the
steady-state output and the desired output.
Controller OutPut

Controller Response Overshoot Error


time
On-off Smallest Highest Large
Proportional Small Large Small
Integral Decreases Increases Zero
Derivative Increases Decreases Small change
Controller OutPut
Controller OutPut
Controller Design
Design of PI/PD/PID controller

➢Root Locus Approach
➢Bode Approach
➢Direct Synthesis
●
Controller synthesis for delay free systems
●
Controller synthesis for Time­Delay systems
Controller Design
Controller Design
Controller Design
Controller Design
Controller Design
Controller Design
Controller Design

Equation real and imaginary components:

➢The coefficients KI ,KP and KD are to be determined from equation (15)
and (16).
➢The value of KI is either specified or determined from steady state
error requirement.
➢The coefficient KP and  KD are determined in terms of KI  .
Controller Design

Subtract Eqn. (18) from (17), 
Controller Design
Put value of  KP  in eqn 16,  

We can get value of KD, 
Controller Design

We can get value of KD, 
Controller Design Steps
The coefficients KI ,KP and KD are to be determined as below: 

1.  The value of KI is either specified or determined from steady state
error requirement.

2.  The  coefficient  KP  and    KD  are  determined  in  terms  of  KI,  using 
following equations: 
Controller Design Steps
Root Locus Method
Controller Design Steps
Root Locus Method
Controller Design Steps
Root Locus Method
Controller Design Steps
Frequency Response Method
Having  given  the  specified  phase  and  gain 
crossover  frequency,  the  frequency  response 
approach is followed to design a PID controller.

For desired gain crossover frequency w1
 s1 = jw1
|s1| = |w1|\90o 
β= 90o
With the use of PID controller, at w1
Controller Design Steps
Frequency Response Method
With the use of PID controller, at w1
Controller Design Steps
Frequency Response Method
Controller Design Steps
Frequency Response Method
Controller Design
Direct Synthesis
Controller Design
Direct Synthesis
Controller Design
Direct Synthesis
Controller Design
Direct Synthesis
Direct Synthesis for Low order systems:
Controller Design
Direct Synthesis
Direct Synthesis for Low order systems:
Controller Design
Direct Synthesis
Example:
Controller Design
Direct Synthesis
Direct Synthesis for Higher order systems:
Controller Design
Direct Synthesis
Direct Synthesis for Time Delay systems:
Controller Design
Direct Synthesis
Direct Synthesis for Time Delay systems:
Controller Design
Direct Synthesis
Example:
Controller Design

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