Transient Response Introduction

Cuthbert Nyack

The System assumed here is of the form shown above with closed loop Transfer Function Given by:-

C(s)/R(s) = G(s)/(1 + G(s))

From the transfer function the Transient Response can be found by using Laplace Transforms see Laplace

For Large Systems the Transfer Function can be converted into a set of first order differential equations which can be integrated by Runge-Kutta methods.
Assuming a Transfer function of the form

This can be written as a differential eqn

which can be represented as a series of first order equations

The applets show how the transient response depends on the number of poles and zeros and their locations. The Following images show how some of the applets look when enabled.

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