I don't know what is the appropriate section to post this thread in.
If we have two stable systems but one is more stable than the other, why should we choose the more stable and which benefit we can have.
Is the percent overshoot related to stability?

 

Depends on the application. If we are talking high performance jet fighters, they are inherently unstable for performance reasons, and require fly-by-wire control systems, because a human operator cannot react fast enough in certain maneuvers.

 

The generally is a tradeoff between stability and response time of the system.
So how stable to make the system depends upon the requirements.

 

Homework...

 

If the more stable system meets your performance requirements then use it. Overshoot is an indicator of stability; the more overshoot the less stability.

 

If the more stable system meets your performance requirements then use it. Overshoot is an indicator of stability; the more overshoot the less stability.

Stability is more of a binary thing. If the roots are in the left half plane the system is stable. As a root locus will reveal, the system parameters may allow the system to become unstable. It might be more correct to say that overshoot is an indicator of stability margin. The more overshoot you have the closer you are to instability.

 

Stability is more of a binary thing. If the roots are in the left half plane the system is stable. As a root locus will reveal, the system parameters may allow the system to become unstable. It might be more correct to say that overshoot is an indicator of stability margin. The more overshoot you have the closer you are to instability.

Thanks for clear answer.
I have another question.What indications the root locus can provide?i.e. if given the root locus, what can I know about the system, in addition to the stability of the system?

 

Thanks for clear answer.
I have another question.What indications the root locus can provide?i.e. if given the root locus, what can I know about the system, in addition to the stability of the system?

The root locus provides you with an indication of how close the system might be to instability. More importantly it allows you to propose fixes for stability by the introduction of compensating poles and zeros.

http://parlos.tamu.edu/MEEN651/E28.pdf

 

A somewhat amazing characteristic of a root locus plot is that the plant performance point, being on the locus path, is influenced in a manner that is similar to static electric charges lying on a plane. In a sense, the pole positions repel the locus point, and the zeros attract. The system gain magnitude determines the distance that the plant performance point travels along the locus from its origin at a pole.

Here is a tool that was one of the original instruments used to draw root locus diagrams:
http://www.nzeldes.com/HOC/Spirule.htm