DP7.14 Consider the feedback system shown in Figure DP7.14. The process transfer function is marginally sta

ble. The controller is the proportional-derivative (PD)

controller.

a. 

Determine the characteristic equation of the closed-loop system.

b. Let τ = / K K P D. Write the characteristic equa

tion in the form

c. 

Plot the root locus for 0 ≤ KD ∞ when τ = 6.

d. 

What is the effect on the root locus when 0 1 τ 0 ?

e. 

Design the PD controller to meet the following specifications:

(i) P O. . ≤ 5%

(ii) Ts 1 ≤ s

A(s)=1+Kp(s) d(s)