# Filters responses

I got a filter and I want to examine whether it is stable or not.

My system has the following TF $$H(s) = \frac{0,0001s^4 + 10s^2}{0,0001s^4+0,05s^3+10s^2+s+1}$$

So after plotting the zpmap (shown below), all poles are in the left part which means the Re(poles)<0. According to theory the system is stable,therefore. Now comes my question, after playing around with Matlab I came across different plots. Can anyone interpret them to me? I know that google has numerous information about those plots but I need a quick answer which will help me to superficially understand whats going on.

• Nichols • Bode • Nyquist • another zpmap • What are you trying to understand that you don't already understand from the pole-zero plot? – Matt Young Apr 29 '15 at 13:45
• I stated clearly that i want an interpretation of the other plots. – sayid jetzenden Apr 29 '15 at 14:08
• Really? In the time it took to save those figures, write the question, and wait for a response, you could have figured that out on your own. – Matt Young Apr 29 '15 at 14:11
• Your contribution to my question is colossal, keep it up ;) – sayid jetzenden Apr 29 '15 at 17:19
• @sayidjetzenden: We still don't know exactly what you are asking. What parts are you having problems with? – Dwayne Reid Apr 30 '15 at 11:31

## 1 Answer

None of the plots tells you as much as a direct computation of the roots of the denominator of the transfer function will tell you. And it is these roots that you need, nothing more. If you use Matlab simply use roots(v), where v is a vector with the coefficients of the denominator polynomial. From this you'll find out that you have two complex conjugate pole pairs, one of them with real part $-249.95$, and the other one with real part $-0.05$. From this the conclusion concerning stability should be obvious.

• My question was actually referring to the other plots, no to the theory which i already know. – sayid jetzenden Apr 29 '15 at 17:21
• @sayidjetzenden: OK, I see, but in this case the first sentence of your question is a bit misleading, because if it were about stability, you shouldn't do anything else but compute the pole locations. – Matt L. Apr 29 '15 at 18:30
• I thought that there's a way to tell whether a system is stable out of the other plots as well. – sayid jetzenden Apr 29 '15 at 18:38