Question

Motor Position Control with Torque Disturbance

The following diagram models a motor position control system with torque disturbance. The motor transfer function from torque to position (when connected to a voltage source) is G(s) = 1/s(0.1s + 1).

Problem 5-1: Motor Position Control with Torque Disturbance The following diagram models a motor position control system with torque disturbance. The motor transfer function from torque to position (when connected to a voltage source) is s(0.1s +1) The gain K in this system is the user-selected servo amplifier gain. d(t) . Determine the transfer function C(s)/R(s). . Determine the transfer function C(s)/D(s). . Determine the transfer function E(s)/R(s). . Determine the transfer function E(s)/D(s). . What is the steady state error for step inputs r(t)? What is the steady state error for step inputs d(t)? . Find K so that the system is critically damped

Answer 1

Given that, A motor position control system with forque disturbance. The motor transfer function from torque to position. (when connected to a voltage source) is G(s) = 1/s (0.1 s + 1) The gain k in this system is the user - selected servo amplifier gain. a) c(s0/R(s) Take D(s) = 0 C(s)/R(s) = K G_p(s)/1 + k G_p(s) (because unity feedback) = K 10/0.1s(s + 10)/1 + 10 k/0.1 s(s + 10) = 100k/s^2 + 10 s + 100 k b) C(s0/D(s) Take R(s) = 0 C(s)/D(s) = G_p(s)/1 + KG_p(s) = 100/s (1 + 100)/1 + 100k/s(1 + 1os) = 100/s^2 + 10s + 100 k c) E(s)/R(s) Take D(s) = 0 E(s) = R(s) - C(s) E(s)/R(s) = 1 - C(s)/R(s) 1 - 100 k/s^2 + 10 s + 100 k E(s)/D(s) Take R(s) = 0 E(s) = D(s) - K C(S) E(S)/D(s) = 1 - k C(s)/D(s) = 1 - (100/s^2 + 10 s + 100k) E(s)/D(s) = s^2 + 10s/s^2 + 10s + 100 k e) steady state error for step input r(t) R(s) =