The plant transfer function for the angular displacement ( of an inertia / subjected to a control torque T is (see Figure PI 2.8a)
Gp (s) = ( (s) / T (s) = 1 / Is2
Suppose that I = 5 and that the output of the controller is the torque. T. Use the root locus to investigate whether or not a controller transfer function of the following from will give a settling time of no more than 2 sec an overshoot of no more than 5%.
Gc(s) = K s + a / s + b
Obtain the root locus plots for the compensated system using each compensator. Use the compensator gain Kc as the locus parameter. Without computing specific values for the compensator parameters, determine which compensator gives the best response.