Stability of a designed system

[tisheebird]

I have designed a system which gives a nice response in the simulation. When I checked the poles and zeros plot, it has 1 dominant pole on the real axis and other poles (2nd and 3rd) are exactly with the zero on the real axis. So i have few doubts :

1. Can we call such system 1 pole system.?
2. Such a system is always stable.?

Please guide me give your suggestions.

 

[andre_luis]

1. Can we call such system 1 pole system.?

No, it is a 3-pole system, regardless where poles are located.

2. Such a system is always stable.?

You did not mention where in the real axis is located the remaining pole (RHP?) and how many zeros are present in the transfer function. In general it is not possible to determine stability conditions unless having numeric parameters to evaluate.

 

[tisheebird]

No, it is a 3-pole system, regardless where poles are located.

But in our basics we have studied that if a zero is exactly on top of a pole then the effect of that pole cancel's out..So which mean that pole as no influence right..?

You did not mention where in the real axis is located the remaining pole (RHP?) and how many zeros are present in the transfer function. In general it is not possible to determine stability conditions unless having numeric parameters to evaluate.

I don't have a transfer function. But when I see the s-plane plot in CAD tool, I have all poles and zeros in LHP and lie on real axis. 2nd pole is with 1st zero together and 3rd pole is with 2nd zero together.

What do you think of such a system.?

- - - Updated - - -

But in our basics we have studied that if a zero is exactly on top of a pole then the effect of that pole cancel's out..So which mean that pole as no influence right..?

 

[andre_luis]

I have all poles and zeros in LHP and lie on real axis. 2nd pole is with 1st zero together and 3rd pole is with 2nd zero together.

In this case, if I understood correctly, the transfer function seems to have 2 zeros and 3 poles, 2 zeros canceling 2 poles, so that in theory its system seems stable since the remaining pole is in the left plane; something like that ?

H (s) = ((s*s)/(s*s*(s+a))

if a zero is exactly on top of a pole then the effect of that pole cancel's out..So which mean that pole as no influence right..?

The practical interpretation of this is different; in reality this "cancellation" does not occur if the transfer function is synthesized with analogical electronic components due to their variance. The actual function would be like this:

H(s) = ((s±0,000x)*(s±0,000y))/((s±0,000z)*(s±0,000w)*(s+a))

And the root locus of the above function in the real world would be something like this (with hypotetical values):



It could even be canceled if it were digitally implemented (digital filter), but still its sampling frequency should be well chosen. In short, the system appears to be marginally stable, which in practice means to be unstable. To solve this, you'd have to think about adding a stabilizer to the system (eg lead), but with what little you've gone over so far, it's hard to know if that applies.

 

[tisheebird]

Thank you for your suggestions. Actually I would like to tell you the position of the zeros and poles:

1st pole- 5 MHz
2nd pole- 33 MHz
3rd pole - 550 MHz

Zeros:

1st zero- 33 MHz
2nd zero- 550MHz.

All the poles and zeros are on the real axis on LHP and not like in the above picture.

I varied the temp, process and montecarlo simulations..But still the pole and zero are together(they are cancel out) in all cases.

In my knowledge if all the poles are on real axis in LHP then damping ratio (zeta) is always more than 1 which leads to overdamped system and finally a stable system...

Please tell me if I am wrong.?

 

[andre_luis]

All the poles and zeros are on the real axis on LHP

We're definitely not talking about the same thing. If the poles are located on the real axis - as you said earlier - they are not measured in frequency, but are indicative of a damping factor in the transfer function. For my part, I'm not going to take any more guesswork until I can get more information about this system. By the way, as you are dealing with very high frequencies, I assume that the concepts I am approaching are not applicable, as they are more commonly used for control systems.

 

[tisheebird]

We're definitely not talking about the same thing. If the poles are located on the real axis - as you said earlier - they are not measured in frequency, but are indicative of a damping factor in the transfer function. For my part, I'm not going to take any more guesswork until I can get more information about this system. By the way, as you are dealing with very high frequencies, I assume that the concepts I am approaching are not applicable, as they are more commonly used for control systems.

1st pole: -5 MHz
2nd pole: -33 MHz

Zeros:

1st zero: -33 MHz...

Do you think such a system is stable system..? Can we call it 1 pole system with the locations I have mentioned before.?
I just know the location of the poles and zeros..

When I see the transient response, there is no ripple. But I want to be very sure about the stability..
Please guide me ...