Behavior of isPassive and hinfnorm.
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For the transfer function HzPw attached, I am not getting the behavior I expect from the function isPassive and hinfnorm. Any suggestions on what I am interpreting incorrectly would be much appreciated.
nopt = nyquistoptions;
nopt.XLim = [-5e-3 2e-2];
The Nyquist plot of this transfer function is entirely in the right half plane. So, I expect this transfer function to be passive. However,
[pf,R] = isPassive(HzPw)
Then, I look at a scattering function corresponding to this transfer function, and the Bode plot of this scattering function.
Hscat = (1-HzPw)/(1+HzPw);
I expect the norm of this to be 1. Indeed, by my thinking, the transfer function is passive, and so the scattering function norm should be ≤ 1. However,
I am wondering what I am not thinking about correctly.
Jon on 3 Jun 2022
Edited: Jon on 3 Jun 2022
I'm thinking that you may have some numerical issues with poles very close to the jw axis. Your transfer function uses quite high order polynomials. Your numerator is a 9th order polynomial and your denominator is a 10th order polynomial. For such high order polynomials very small changes in the coefficient values may result in large changes in the pole and zero location. They are therefore generally to be avoided in favor of other representations.
In particular I see using MATLAB's pole command
p = pole(HzPw)
-9.0685 + 0.0000i
-0.9015 + 3.3574i
-0.9015 - 3.3574i
-0.3718 + 0.2699i
-0.3718 - 0.2699i
-0.0566 + 0.1218i
-0.0566 - 0.1218i
-0.0031 + 0.0036i
-0.0031 - 0.0036i
0.0036 + 0.0000i
So you in fact have an unstable pole in the right half plane at 0.0036.
I'm not an expert in the relation between stability and passivity, but my intuition is that an unstable system is not passive.
More Answers (1)
Paul on 3 Jun 2022
I'm not able to load the .mat file, so can't really look at the problem.
Can you save in v7.3 format and upload, or, if simple enough, just show what it is otherwise, like displaying the A,B,C,D or zpkdata, or the tfdata?
If not, can you post the output of the following commands:
I'm asking because this doc page states "As a result, passive systems are intrinsically stable."
So maybe HzPw is not BIBO stable, but has a Nyquist plot all in the RHP, like this
h = zpk(2,1,1)
Similary, the H-infinity norm, IIRC, is not defined for unstable systems, so if Hscat is not BIBO stable, then hinfnorm will return inf as stated on hinfnorm