A motor and load with negligible friction and a voltage- to-current amplifier Ka is used in the feedback control system, shown in Figure P12.7. A designer selects a PID controller

where KP = 5, Kt = 500, and KD = 0.0475.
(a) Determine the appropriate value of Ku so that the phase margin of the system is 30°. (b) For the gain Ka, plot the root locus of the system and determine the roots of the system for the Ka of part (a), (c) Determine the maximum value of y(t) when T{i(s) = 1/s and R(s) = 0 for the Ka of part (a), (d) Determine the response to a step input r(t), with and without a prefilter.

Transcribed Image Text:

K, + Kps, G(8) = Kp +