ME 352 System Dynamics and Control Homework #6 Due: Monday 04.05.2015 [1]. Parameters for the PID control system shown below are given as I  3, c  1 . The performance specifications require a dominant time constant of   2 and damping ratio of   0.707 . For this system, (a) Compute the required controller gains. (b) Verify your control design by simulation. [2]. Figure below shows a PD control applied to an unstable plant. The gains have been computed so that the dampling ratio is   0.707 and the time constant is 2.5 sec, assuming that the transfer functions of the actuator (   0 ), and the sensor are unity. The actuator transfer function might affect the system’s stability, overshoot or settling time. Determine the effect of the actuator transfer function on system’s stability and performance if: (a)   0.2 sec , (b)   1 sec . (c) Find the steady‐state error for a unit‐step command. 1 804  400s 2 500 s  644 [3]. Figure below shows a PD control applied to an unstable plant. The gains have been computed so that the dampling ratio is   0.707 and the time constant is 2.5 sec, assuming that the transfer functions of the actuator (   0 ), and the sensor are unity. The actuator transfer function might affect the system’s stability, overshoot or settling time. 1 . This time, a more realistic feedback sensor is modeled using a transfer function Gs ( s )   s 1 Determine the effect of the feedback sensor transfer function on system’s stability and performance if: (a)   0.2 sec , (b)   1 sec . 1 804  400s 2 500 s  644