Consider a plant whose open-loop transfer function is

Chapter , Problem 12.10

(choose chapter or problem)

Consider a plant whose open-loop transfer function is

                                                 \(G(s) H(s)=\frac{1}{s\left[(s+2)^2+9\right]}\)

The complex poles near the origin give only slightly damped oscillations that are considered undesirable. Insert a gain \(K_c\) and a compensator \(G_c(s)\) in series to speed up the closed-loop response of the system. Consider the following for \(G_c(s)\);

a. The lead compensator

b. The lag compensator

c. The so-called reverse-action compensator

                                                 \(G_c(s)=\frac{1-T_1 s}{T_2 s+1}\)

Obtain the root locus plots for the compensated system using each compensator. Use the compensator gain \(K_c\) as the locus parameter. Without computing specific values for the compensator parameters, determine which compensator gives the best response.