Chapter 11, Problem 1RQ

To determine

The major advantage of compensator design by frequency response over root locus design.

Explanation of Solution

For a system, the total response of the system is the sum of the steady state response and transient response.

  $T=T_s+T_r$

Where,

  $T_s$ is the steady state response.

  $T_r$ is the transient response.

In any system, the input poles generate the steady state response and the poles at the origin generate the step function at the output. The poles of the transfer function generate the natural response or the transient response.

Compensator is a device which can be used to improve the steady and transient response of a system. Gain of compensator is used in series with $G_s$ . So, a modified open loop transfer function is obtained. This is the reason that transient and steady state response of the system gets changed after adding the compensator in the circuit.

The major advantage that compensator design by frequency response has over root locus design is derivative compensation. For example, lead compensation, to speed up the system as well as for desired steady-state error, requirement can be full-filled by lead compensator alone. But this advantage is not possible in design by root locus because in root locus there are an infinite number of possible solutions to the design of a lead compensator and difference between these solutions gives the steady-state error.