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6. The block diagram of a video tape drive is shown in Figure Q.6. It is important for the quality of the video image that the tape spool is rotated at a particular reference speed, w.. The actual speed of the tape, o, is sensed, and fed back, any error, E(s) being passed to the controller, G(s), which controls the torque motor. The tape is also subject to torque disturbance, D(s) due to frictional and other effects. a) It is proposed to use a simple proportional controller. Assuming there is no disturbance, calculate the necessary proportional gain, K,, if the maximum allowable steady state error is 2% in response to a unit step change in reference speed, o,. b) Derivative action is added to the controller. Calculate the necessary proportional and derivative gains K, and K, if the rise time is to be 0.04s and the peak time is to be 0.1s in response to a unit step change in reference speed, assuming no disturbance. c) Using the controller designed in part b), calculate the steady state error, maximum overshoot, and the settling time which would occur in response to a unit step change in reference speed, again assuming no disturbance. Torque Disturbance D(s) Controller Torque Motor Tape Dynamics o, (s) E(s) 10 Tm(s) T(s) 1 o(s) G(s) 0.5s + 1 0.1s + 1 Figure Q.6

6. The block diagram of a video tape drive is shown in Figure Q.6. It is important for the quality of the video image that the tape spool is rotated at a particular reference speed, w.. The actual speed of the tape, o, is sensed, and fed back, any error, E(s) being passed to the controller, G(s), which controls the torque motor. The tape is also subject to torque disturbance, D(s) due to frictional and other effects. a) It is proposed to use a simple proportional controller. Assuming there is no disturbance, calculate the necessary proportional gain, K,, if the maximum allowable steady state error is 2% in response to a unit step change in reference speed, o,. b) Derivative action is added to the controller. Calculate the necessary proportional and derivative gains K, and K, if the rise time is to be 0.04s and the peak time is to be 0.1s in response to a unit step change in reference speed, assuming no disturbance. c) Using the controller designed in part b), calculate the steady state error, maximum overshoot, and the settling time which would occur in response to a unit step change in reference speed, again assuming no disturbance. Torque Disturbance D(s) Controller Torque Motor Tape Dynamics o, (s) E(s) 10 Tm(s) T(s) 1 o(s) G(s) 0.5s + 1 0.1s + 1 Figure Q.6

Power System Analysis and Design (MindTap Course List)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter11: Transient Stability
Section: Chapter Questions
Problem 11.17P
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6. The block diagram of a video tape drive is shown in Figure Q.6. It is important for the quality of the video image that the tape spool is rotated at a particular reference speed, 0,. The actual speed of the tape, w, is sensed, and fed back, any error, E(s) being passed to the controller, G(s), which controls the torque motor. The tape is also subject to torque disturbance, D(s) due to frictional and other effects. a) It is proposed to use a simple proportional controller. Assuming there is no disturbance, calculate the necessary proportional gain, K,, if the maximum allowable steady state error is 2% in response to a unit step change in reference speed, w,. b) Derivative action is added to the controller. Calculate the necessary proportional and derivative gains K, and K, if the rise time is to be 0.04s and the peak time is to be 0.1s in response to a unit step change in reference speed, assuming no disturbance. c) Using the controller designed in part b), calculate the steady state error, maximum overshoot, and the settling time which would occur in response to a unit step change in reference speed, again assuming no disturbance. Torque Disturbance D(s) Controller Torque Motor Tape Dynamics ", (s) E(s) 10 Tm(s) T(s) 1 w(s) G(s) 0.5s + 1 0.1s + 1 Figure Q.6
Transcribed Image Text:6. The block diagram of a video tape drive is shown in Figure Q.6. It is important for the quality of the video image that the tape spool is rotated at a particular reference speed, 0,. The actual speed of the tape, w, is sensed, and fed back, any error, E(s) being passed to the controller, G(s), which controls the torque motor. The tape is also subject to torque disturbance, D(s) due to frictional and other effects. a) It is proposed to use a simple proportional controller. Assuming there is no disturbance, calculate the necessary proportional gain, K,, if the maximum allowable steady state error is 2% in response to a unit step change in reference speed, w,. b) Derivative action is added to the controller. Calculate the necessary proportional and derivative gains K, and K, if the rise time is to be 0.04s and the peak time is to be 0.1s in response to a unit step change in reference speed, assuming no disturbance. c) Using the controller designed in part b), calculate the steady state error, maximum overshoot, and the settling time which would occur in response to a unit step change in reference speed, again assuming no disturbance. Torque Disturbance D(s) Controller Torque Motor Tape Dynamics ", (s) E(s) 10 Tm(s) T(s) 1 w(s) G(s) 0.5s + 1 0.1s + 1 Figure Q.6
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