How to plot the phase margin?
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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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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;
margin(L)
% 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.
L = C*G;
margin(L)
% Bode plot of the compentator
bode(C)
% Closed-loop system
T = L / (1 + L);
bode(T)
step(T)
6 个评论
Bora Eryilmaz
2022-12-22
Please run your code and see yourself if
margin(M)
gives you the desired phase margin.
C= 51/(s+1); % This will give 51 degrees phase margin
How do you know that the controller C above will give you a 51 degree phase margin? Its gain is 51, but that doesn't necessarily give you a 51 degree phase margin.
Looks like it. If the phase margin is better than 50 degrees, then your controller satisties the requirements of your problem. Also take a look at the step response of the closed loop system to make sure it is well behaved:
s = tf('s'); % To enter the transfer function directly
V = 1.5/(s+1); % This will give 61.3 degrees phase margin
G = (s+20)/((s+2)*(s+5));
M = V*G;
margin(M)
step(M/(1+M))
You will see that the steady-state step response value of your closed-loop system is not 1. This was not part of your question, but normally this would not be an acceptable step response... As a small hint, if your controller had an integrator, the steady-state response would have converged to 1, which is more desirable.
Hardik
2022-12-22
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