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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




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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Control Systems : Time Response Analysis : P, PI, PD and PID Compensation |

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