Consider a unity feedback system with the plant G p(s) and

Chapter , Problem 11.6

(choose chapter or problem)

Consider a unity feedback system with the plant \(G_p(s)\) and the controller \(G_c(s)\). PID control action is applied to the plant

                                                  \(G_p(s)=\frac{s+10}{(s+1)(s+2)}\)

The PID controller has the transfer function

                                                           \(G_c(s)=K_P\left(1+\frac{1}{T_l s}+T_D s\right)\)

Use the values \(T_I=0.2\) and \(T_D=0.5\).

a. Identify the open-loop poles and zeros.

b. Identify the root locus parameter K in terms of \(K_P\).

c. Identify the closed-loop poles and zeros for the case \(K_P=10\).