Analytic PID Design
2
Analytic PID Design If G(s) is the loop gain, then the characteristic equation can be written as We want to find the value of k p , k d , and k i to place a pole of the characteristic equation at a specified location, s 1 . In other words, we want to find the value of s 1 that satisfies If we consider the controller Equation 1 but s 1 is also a complex number that can be represented by a magnitude and a phase: Rewriting equation 1 gives us Assume we can pick k i based on some other criterion, we can rewrite the equation Equating real and imaginary parts of this last equation gives us a set of two equations in two unknowns (since k i is known). Analytic PID Design file:///C:/Documents and Settings/Win XP/Desktop/Survey_PID/Lectur... 1 de 2 12/3/2012 22:33
description
Analytic PID Design
Transcript of Analytic PID Design
-
Analytic PID DesignIf G(s) is the loop gain, then the characteristic equation can be written as
We want to find the value of kp, kd, and ki to place a pole of the characteristic equation at a specified location, s1. Inother words, we want to find the value of s1 that satisfies
If we consider the controller
Equation 1
but s1 is also a complex number that can be represented by a magnitude and a phase:
Rewriting equation 1 gives us
Assume we can pick ki based on some other criterion, we can rewrite the equation
Equating real and imaginary parts of this last equation gives us a set of two equations in two unknowns (since ki isknown).
Analytic PID Design file:///C:/Documents and Settings/Win XP/Desktop/Survey_PID/Lectur...
1 de 2 12/3/2012 22:33
-
If s1 and ki are known, they can be used to find M, q, B and b, and the equations can be solved for kp and kd. Doinga little algebra yields the general result that
Analytic PID Design file:///C:/Documents and Settings/Win XP/Desktop/Survey_PID/Lectur...
2 de 2 12/3/2012 22:33
![A Genetically Tuned Optimal PID controller - WSEASwseas.us/e-library/conferences/2007corfu/papers/540-121.pdf[6] S. Skogestad, "Simple analytic rules for model reduction and PID controller](https://static.fdocuments.in/doc/165x107/5e94e60e6d432c76c83129b9/a-genetically-tuned-optimal-pid-controller-6-s-skogestad-simple-analytic.jpg)
