for example system "A" has
rise time=0.0464 Sec, settling time=1.3609, overshoot= 0.332 , peak time=0.81, steady state error=0.1325
system "A" has: rise time=0.0248, settling time=1.6091, overshoot= 0.626, peak time=0.87, steady state error= 0.6231
which system will be faster and more stable.
The question is rather vague. It depends on concrete application. Steady state error has to do with precision. For some applications, lower settling time is crucial even at the cost of some overshoot. For others, an overshoot might be dangerous. Concerning stability, both of your systems are (asymptotic) stable.
Dear Dr. Pavel Osinenko,
Thanks for your prompt reply. My question is how can we compare the two system in rise time, settling time, overshoot, peak time, steady state error. I mean which one will be faster, more accurate, more stable, etc and why?
I think, the criterion regarding "faster" depends on the definition of "fast" (which do you prefer: rise or settling properties?). However, as far as stability is concerned I would vote for the first system: Settling time and overshoot smaller than for system 2.
I think the first system is better (faster and more stable) than the 2nd one because of the lower settling time and steady state error.
For stability comparison you can follow the standard procedure: start from finding poles and zeros and then sensitivity analysis. But if you ask which one is faster then you have to define what would you consider as faster- a system which has a low rise time or a system which has low settling time which depends on your application demand.
The first thing you must consider is that there is no such measure which says that one system is more stable than the other.
However a linear system which has the real parts of its poles more away from the origin in the left half plane are regarded faster than a system which has real parts of its poles near to the origin. You may find poles for both the systems and then you may conclude which one is faster.
Rise time directly depends upon the wn which is determined how far is the imaginary part of the poles from the real-line.
which system is better? can't be answered without having a concrete knowledge of its application area.
The distance of the rightmost stable pole(s), called "dominant pole(s)" to the Imaginary axis is a measure for stability, called grade of stability. The logic is that "the nearer to the Im axis, the less stable is the system" due to its (their) possible movement to the right side.
the performance of a system is defined by the designer. systems are different generally. it is the designer who should choose what parameter has higher priority.
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