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Chapter: Control Systems - Time Response Analysis

P, PI, PD and PID Compensation

Proportional Controller and Integral Controller.

PID Controllers

 

Proportional controllers

– pure gain or attenuation

Integral controllers

– integrate error

 

Derivative controllers

 

– differentiate error

 

Proportional Controller

 

U = Kp e

 

o   Controller input is error (reference output)

 

o   Controller output is control signal

 

o   P controller involves only a proportional gain (or attenuation)

 

Integral Controller

 

o   Integral of error with a constant gain

 

o   Increase system type by 1

 

o   Infinity steady-state gain

 

o   Eliminate steady-state error for a unit step input

 

Integral Controller





Derivative Control


 

o   Differentiation of error with a constant gain

 

o   Reduce overshoot and oscillation

 

o   Do not affect steady-state response

 

o   Sensitive to noise

 

Controller Structure

         

o   Single controller

 

o   P controller, I controller, D controller

 

o   Combination of controllers

 

o   PI controller, PD controller

 

o   PID controller

         

Controller Performance

         

o   P controller

 

o   PI controller

 

o   PD Controller

 

o   PID Controller

         

Design of PID Controllers

         

o   Based on the knowledge of P, I and D

 

       trial and error

 

       manual tuning

 

       simulation

         

Design of PID Controllers

         

o   Time response measurements are particularly simple.

 

o   A step input to a system is simply a suddenly applied input - often just a constant voltage applied through a switch.

 

o   The system output is usually a voltage, or a voltage output from a transducer measuring the output.

 

o   A voltage output can usually be captured in a file using a C program or a Visual Basic program.

 

o   You can use responses in the time domain to help you determine the transfer function of a system.

 

o   First we will examine a simple situation. Here is the step response of a system. This is an example of really "clean" data, better than you might have from measurements. The input to the system is a step of height 0.4. The goal is to determine the transfer function of the system.

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