Consider a unity feedback system with the plant Gp(s) and the controller Gc(s). PID control action is

Question:

Consider a unity feedback system with the plant Gp(s) and the controller Gc(s). PID control action is applied to the plant
Gp(s) = s + 10 / (s + 1) (s + 2)
The PID controller has the transfer function
Gc(s) = Kp (1 + 1/TIs + TDs
Use the values TI = 0.2 and TD = 0.5.
Identify the open-loop poles and zeros.
Identify the root locus parameter K in terms of Kp.
Identify the closed-loop poles and zeros for the case Kp = 10.