Behavior of isPassive and hinfnorm.
1 visualizzazione (ultimi 30 giorni)
Mostra commenti meno recenti
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.
load HzPw.mat;
nopt = nyquistoptions;
nopt.XLim = [-5e-3 2e-2];
nyquistplot(HzPw, nopt);
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);
bode(Hscat);
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,
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1020905/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1020910/image.png)
hinfnorm(Hscat)
I am wondering what I am not thinking about correctly.
Thank you.
0 Commenti
Risposta accettata
Jon
il 3 Giu 2022
Modificato: Jon
il 3 Giu 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)
p =
1.0e+02 *
-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.
12 Commenti
Più risposte (1)
Paul
il 3 Giu 2022
Hi Siva,
I'm not able to load the .mat file, so can't really look at the problem.
load('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1020880/HzPw.mat');
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:
pole(HzPw)
zero(HzPw)
pole(Hscat)
So maybe HzPw is not BIBO stable, but has a Nyquist plot all in the RHP, like this
h = zpk(2,1,1)
nyquist(h)
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
7 Commenti
Paul
il 3 Giu 2022
load('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1021010/HzPw.mat');
Hmm, same problem. I'm probably not using load() correctly for a remote file.
Vedere anche
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!