Consider the feedback system shown in Figure DP7.14. The process transfer function is marginally stable. The controller is the proportional-derivative (PD) controller
Gc(s) = KP + KDs.
(a) Determine the characteristic equation of the closed-loop system.
(b) Let Ñ‚ = KP/KD. Write the characteristic equation in the form

(c) Plot the root locus for 0 ‰¤ KD (d) What is the effect on the root locus when 0 (e) Design the PD controller to meet the following specifications:
(i) P.O. (ii) Ts Figure DP7.14
A marginally stable plant with a PD controller in the loop.

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