Pid 6z3x6k

PID CONTROLLER IMPLEMENTATION USING MATLAB

Introduction 

A proportional-integral-derivative controller (PID controller) is a control loop mechanism (controller) widely used in industrial control systems

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A PID controller calculates an error value as the difference between a measured process variable and a desired setpoint

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P depends on the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on current rate of change

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PROBLEM EXAMPLE

overshoot

Ripple

setpoint

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Increase the quantity until you get to the setpoint 

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Temperature, angle, speed, etc

If too much, reduce the quantity, until the setpoint

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CLOSED LOOP CONTROLLER

error

setpoint

controller

signal

system

output

measured quantity • • • •

closed loop because it has output is measured at a certain frequency signal is generated at a certain frequency which frequency is not smaller?

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PROPORTIONAL CONTROL  

Good alternative to on-off control: more “control”  Signal becomes proportional to the error  

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Need to find out value of constant P   

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P ( setpoint – output ) Example, car speed for cruise control Tuning the controller is a hard job If P is too high, what happens? If P is too low, what happens?

Typically a prop cntrl decreases response time (quickly gets to the setpoint) but increases overshoot 5

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ADDING DERIVATIVE CONTROL 

To avoid (or reduce) overshoot/ripple, take into how fast are you approaching the setpoint 

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If very fast, overshoot may be forthcoming: reduce the signal recommended by the proportional controller If very slow, may never get to setpoint: increase the signal In general: D ( current measure – previous measure)

PD controllers are slower than P, but less oscillation, smaller overshoot/ripple 6

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INTEGRAL CONTROL 

There may still be error in the PD controller 

For example, the output is close to setpoint  

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Take the sum of the errors over time, even if they’re small, they’ll eventually add up 

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P is very small and so is the error, discretization of signal will provide no change in the P controller D controller will not change signal, unless there is change in output

I * sum_over_time (setpoint — output)

Again the main problem is the value of I Can we let sum grow to infinity?

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Simulation Output

Applications 1)Used in Motor drive systems 2)PID forms the basis for higher complex process controllers.

References [1] Stuart Bennett, ’Development of the PID controller’, http://www.ieeecss.org/CSM/library/1993/dec1993/w05HistoricalPerspec tive.pdf, May 2009 [2] Kiam Heong Ang, Gregory Chong, Student Member, IEEE, and Yun Li, Member, IEEE, ’PID Controller System Analysis’, Design and Technology, http://www.ieeexplore.ieee.org/iel5/87/31218/01453566.pdf, Dec 1999 [3] Paul Avery,Yaskawa Electric America, Inc. Waukegan, ’Introduction to PID control’, http://machinedesign.com/sensors/introduction-pidcontrol, June 2014 [4] Gregory K. McMillan, ’Industrial Applications of PID Control’, http://emersonprocessxperts.com/wp-content/s/2011/12/IndustrialApplications-of-PID-Control.pdf, Sept 2014