What is the reason that when we minimize the dc gain of the asymptotically stable LTI system, the poles of the system is shifted in left-hand side or the transient response of the system is improved effectively?
you have considered only the real poles, but if you include the complex poles too, then the general formula doesnt hold.
DC gain can be lower and as the pole is shifted to the left the DC gain increases.
DC gain=T(s) overall transfer function at s=0 for a unit step input.
so as the closed loop poles are so far on the left HSP from the imaginary axis, the dc gain will be smaller and the transient response will be faster.
DC gain inversely with the CLP
Pravin, it seems the DC gain gets smaller as a CONSEQUENCE of the poles getting shifted towards the left half of the plane and not otherwise. Did u intend to mean it in any other way ?
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