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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

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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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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