How to plot the movement of system roots(poles) with variations to a free system variable

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Hello everyone,
I would like to observe the stability and progation of poles in my system with variation in parameters.
I can not use the Root Locus because i would like to see how poles change with variation in "free system variable" and not just a feedback gain K.
For instance, if i had a characteristic equation given as this. I would like to see, how the poles move with variation in aoG:
The resulting plot with be such as this:
Greatly appreciate your help.
Thanks.

Answers (1)

Paul
Paul on 11 Aug 2022
Hi Sohail,
Let's let
a2 = 1; a1 = 1;
We can still set up the problem for using root locus
sys = tf(1,[a2 a1 0]); % D(s) = 0 -> 1 + a0/(a2*s^2 + a1*s) = 0
[r,a0] = rlocus(sys);
figure
plot(real(r),imag(r),'r.')
Or use brute force. I'll use the same vlaues for a0 to ensure we get the same plot
a0(end) = []; % delete the last value, which is inf
r1 = nan(numel(a0),2);
for ii = 1:numel(a0)
r1(ii,:) = roots([a2 a1 a0(ii)]);
end
figure
plot(real(r1),imag(r1),'r.')

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