Design of control system by root-locus method
Design of control system by root-locus method
(OP)
I am trying to achieve a specific performance criterion of a LTI higher order system approximated to second order system by root locus method. The criteria is 2% Percentage overshoot and minimum settling time. The process transfer function is
(s+2)/s^2(s+9)
and the controller is a PID controller whose transfer function is
kd(s+1-j1)(s+1+j1)/s.
The question is to find the value of gain kd at which that above performance criteria is met.
I tried to find for a more simpler system whose root locus was just a straight line cutting the real axis at a certain point on the left side of s-plane and i was successful, because we can find the angle of line representing the required performance criteria by cos^-1(damping coefficient) and the area under the intersection of that line and the root-locus, can give the value of Kd.
But, if the root locus is more curvy, we cannot determine the exact value of Kd manually by drawing roughly on a piece of paper without matlab?
Please reply with a possible solution of this issue.
(s+2)/s^2(s+9)
and the controller is a PID controller whose transfer function is
kd(s+1-j1)(s+1+j1)/s.
The question is to find the value of gain kd at which that above performance criteria is met.
I tried to find for a more simpler system whose root locus was just a straight line cutting the real axis at a certain point on the left side of s-plane and i was successful, because we can find the angle of line representing the required performance criteria by cos^-1(damping coefficient) and the area under the intersection of that line and the root-locus, can give the value of Kd.
But, if the root locus is more curvy, we cannot determine the exact value of Kd manually by drawing roughly on a piece of paper without matlab?
Please reply with a possible solution of this issue.





RE: Design of control system by root-locus method
Gunnar Englund
www.gke.org
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Half full - Half empty? I don't mind. It's what in it that counts.
RE: Design of control system by root-locus method
But you didn't ask for answer, just for general input, so I don't see a problem.
The open loop transfer function is
K*H(s)*G(s) = kd(s+1-j1)(s+1+j1)/s * (s+2)/s^2(s+9)
For a given s in the complex plane, the angle of the open loop transfer function is sum of angles (s-sp) minus sum of angles (s-sz) where sp and sz are zeroes.
The general approach to analyse pole zero diagram for stability without benefit of computer plotting is to look for places where the angle of the open loop transfer function is -180 +/- n*2*pi and magnitude = 1.
FWIW, my opinion is same as yours... the open loop transfer function looks too complicated to do much without help of computer. If you have matlab, use rlocusplot
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(2B)+(2B)' ?
RE: Design of control system by root-locus method
xnuke
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