# 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

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

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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