How to plot the phase margin?

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Hardik . 2022년 12월 22일
편집: Hardik . 2022년 12월 23일
Hello I have one tricky question where I am struck.I know how to plot the bode diagtam using the margin command but i am not sure how can i implement more than 30% margin part. my system and requirement is below. Please help me to understand how can i do this.

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Bora Eryilmaz
Bora Eryilmaz 2022년 12월 22일
편집: Bora Eryilmaz 님. 2022년 12월 22일
The transfer function 20/(s+1) is your controller. As it is, it does not give you a 50-degree phase margin. You need to modify this controller to achieve the desired phase margin. There are couple ways of doing this:
  • Either reduce the gain of the controller to achieve a larger phase margin, but at a lower frequency.
  • Or add additional phase using controller terms such as lead-lags.
% Initial compensator
C = zpk([], -1, 20);
% The plant
G = zpk(-20, [-2 -5], 1);
% Phase and gain margin of the open-loop transfer function with initial
% compensator
L = C*G;
% Modify the compensator C to obtain the desired phase margin (this part is
% up to you, since this seems like a homework question).
C = zpk([], -2, 10) % This is my trivial change, will not give 50 degrees phase margin.
C = 10 ----- (s+2) Continuous-time zero/pole/gain model.
L = C*G;
% Bode plot of the compentator
% Closed-loop system
T = L / (1 + L);
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Hardik 2022년 12월 22일
편집: Hardik 님. 2022년 12월 22일
Hello Sir, in my next part of problem I have to use the Feedback command in Matlab to find the closed loop transfer function of the compensated system. Provide the overall closed loop transfer function.
I have done the coding part but I am bit confused here that Do i have to use feedback command on original given system or the output TF i get from this part i have to use?
And if i have to use new obtanined TF then do i also have to use the plant value (s+20) and multiply them and then use the feedback command ?

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