The use of a motor to control the rotational displacement of an inertia I is shown in Figure P11.17. The open-loop transfer function of the plant for a specific application is
Gp (s) = 6 / s (2s + 2) (3s + 24)
a. Use the root locus plot to show that it is not possible with proportional control to achieve a dominant time constant of less than 2.07 sec for this plant.
b. Use PD control to improve the response, so that the dominant time constant is 0.5 sec or less and the damping ratio is 0.707 or greater. To do this, first select a suitable value for TD, then plot the locus with Kpas the variable.
Figure P11.17

Transcribed Image Text:

O(s)+ O(s) Gi(s) s(Is c) Ls R Motor Controller Θ(s) Controller Plant Gp(s)