# PID (Proportional / Integral / Derivative) Control System

Consider the system shown in Fig.1. (attached file) This is a PID control of a second-order plant G(s). Assume that disturbances D(s) enter the system as shown in the diagram. It is assumed that the reference input R(s) is normally held constant, and the response characteristics to disturbances are a very important consideration in this system.

Design a control system such that the response to any step disturbance will be damped out quickly( in 2 to 3 sec. in terms of the 2% settling time). Choose the configuration of the closed-loop poles such that there is a pair of dominant closed-loop poles. Then obtain the response to the unit-step disturbance input. Also, obtain the response to the unit-step reference input.

Hints:

(i).When considering R(s) as the input to obtain closed-loop transfer function C(s)/R(s), assume that D(s) is zero and vice versa.

(ii).To meet design criterion, take ζ=0.5 and ωn =4 rad/sec for the dominant closed loop poles. Also choose a third pole at s = -10. Then the desired characteristic equation becomes as s^3 + 14s^2 + 56s +160 = 0

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#### Solution Summary

A PID control system is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.