# Question 4: Steady-state error (8 marks). Consider the proportional control of a second order system subject to a torque disturbance D. The system parameters are./ = 1 kg • m2and b = 2 N • m/rad/sec. a. For a given gain Ic„ determine the system type, and the associated static position error constant ki„ static velocity error constant k„, and static acceleration error constant ka (when D(s)=0). b. Derive the transfer function between C(s) and D(s) (assuming that the reference input is zero or R(s) = 0). c. When the system has an unit-step input (r(t) = 1 or R(s) = !) and an unit-step disturbance torque D (d(t) = 1 or D(s) = !), the steady-state error of the system is e„ (D) = —0.2, determine the control gain K.

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Question 4: Steady-state error (8 marks). Consider the proportional control of a second order system subject to a torque disturbance D. The system parameters are./ = 1 kg • m2and b = 2 N • m/rad/sec.
a. For a given gain Ic„ determine the system type, and the associated static position error constant ki„ static velocity error constant k„, and static acceleration error constant ka (when D(s)=0).
b. Derive the transfer function between C(s) and D(s) (assuming that the reference input is zero or R(s) = 0). c. When the system has an unit-step input (r(t) = 1 or R(s) = !) and an unit-step disturbance torque D (d(t) = 1 or D(s) = !), the steady-state error of the system is e„ (D) = —0.2, determine the control gain K. 