so can we say that from above statement that a large resonance peak in frequency response corresponds to a large overshoot in transient response?
Hi Biswajit
Your Observation is acceptable but the statement is not true in all the cases.Overshoot is because of the energy level of the input and the damping factor of the system but the resonance peak is due to the inherent property of system i.e natural frequency. statement can't be generalized as you said.
best regards
vasanth
talking about second order systems with a certain zeta, when zeta is >1, the system is overdamped. At zeta = 1, the system is critically damped, and will have no overshoot for step response. Decrease the zeta to any value less than 1, and you have an overshoot. All second order systems have a resonant frequency but zeta decides whether you will ever see the resonance, and higher gain at that frequency. A study of behavior of butterworth second order filters will indicate that if zeta is 0.707, it can be called Butterworth. That will have an overshoot for step response as zeta is less than 1. The criterion for no overshoot is that zeta be greater than or equal to 1. All second order systems have an wn , a frequency of natural resonance. This is apparent when you look at the transfer functions of second order systems. But they will have an overshoot for step response only if their zeta is less than 1. One can easily simulate second order systems (e.g in circuit maker) with various zeta and study their step response. That will help understand the second order system better.....
The two are not related at all !!
The overshoot has a strong dependence on the type of input. A large resonance peak is a feature of the system.
-Sanjay
the transient response depends on the system model, which could be second, third or higher order. 4th order systems have two resonant frequencies one each for the resonant frequency of the corresponding second order part. each second order has a zeta associated with it. Unless the zeta is taken into account one cannot say anything about the transient response. What is a large resonant peak? try to quantify that in terms of zeta. Lower the zeta [=1/(2Q)]. the higher the resonance effect. SO in order to understand the behavior with step, study the behavior of second order systems, third order, and fourth order. A fourth order system with two widely different resonances can provide a reasonably good transient response with low overshoot if the zeta of the lower resonant frequency is high, say 0.8. one has to split the system behavior in terms of the first order, and second order systems it can be decomposed to. If you have a system which can be considered second order, it is simpler to understand this, and a large resonance peak will mean a low zeta and it will have a large overshoot for step response. It will be beneficial to study how these are related. A graph in Kuo' control system book gives some insight. this graph is between overshoot and zeta.
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