The transfer functions of speed control for a magnetic tape-drive system an shown in Fig. 4.42....

  

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The transfer functions of speed control for a magnetic tape-drive system an shown in Fig. 4.42. The speed sensor is fast enough that its dynamics can he neglected and the diagram shows the equivalent unity feedback system. Problems 229 (a) Assuming the reference is zero, what is the steady-state error due to a step disturbance torque of 1 N-m? What must the amplifier gain K be in order to make the steady-state error ess <0.01 rad/sec? (b) Plot the roots of the closed-loop system in the complex plane and accu- rately sketch the time response of the output for a step reference input using the gain K computed in part (a). (e) Plot the region in the complex plane of acceptable closed-loop poles cor- responding to the specifications of a 1% settling time of ts 0.1 sec and an overshoot Mp S 5%. (d) Give values for kp and kp for a PD controller, which will meet the specifications. (e) How would the disturbance-induced steady-state error change with the new control scheme in part (d)? How could the steady-state error to a disturbance torque be eliminated entirely? Figure 4.42 Speed-control system for a magnetic tape drive Disturbance torque Torque Tape dynamics motor Amplifier Reference Torque + 3. 10 0.5s+1 K speed, fn, Js+b J=0.10 kg-m b=1.00 N-m-sec The transfer functions of speed control for a magnetic tape-drive system an shown in Fig. 4.42. The speed sensor is fast enough that its dynamics can he neglected and the diagram shows the equivalent unity feedback system. Problems 229 (a) Assuming the reference is zero, what is the steady-state error due to a step disturbance torque of 1 N-m? What must the amplifier gain K be in order to make the steady-state error ess <0.01 rad/sec? (b) Plot the roots of the closed-loop system in the complex plane and accu- rately sketch the time response of the output for a step reference input using the gain K computed in part (a). (e) Plot the region in the complex plane of acceptable closed-loop poles cor- responding to the specifications of a 1% settling time of ts 0.1 sec and an overshoot Mp S 5%. (d) Give values for kp and kp for a PD controller, which will meet the specifications. (e) How would the disturbance-induced steady-state error change with the new control scheme in part (d)? How could the steady-state error to a disturbance torque be eliminated entirely? Figure 4.42 Speed-control system for a magnetic tape drive Disturbance torque Torque Tape dynamics motor Amplifier Reference Torque + 3. 10 0.5s+1 K speed, fn, Js+b J=0.10 kg-m b=1.00 N-m-sec

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