following form will give a settling time of no more than 2

Chapter , Problem 12.9

(choose chapter or problem)

The plant transfer function for the angular displacement \(\theta\) of an inertia I subjected to a control torque T is (see Figure P12.8a)

                                                \(G_p(s)=\frac{\Theta(s)}{T(s)}=\frac{1}{I s^2}\)

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 form will give a settling time of no more than 2 sec and an overshoot of no more than 5%.

                                                  \(G_c(s)=K \frac{s+a}{s+b}\)

Obtain suitable values of K, a, and b. What happens if we try to "cancel" one of the poles at the origin by placing the zero very close to the origin?