Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Question
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, m,. 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 no change in reference speed, calculate the necessary proportional gain, K„, if the maximum allowable steady state error is 0.01rad/s in response to a step disturbance torque of 1Nm. b) Derivative action is added to the controller. Calculate the necessary proportional and derivative gains K, and K,, if the maximum allowable overshoot in speed is 20%, and the speed must settle to its final value in less than 0.25s 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 which would occur in response to a unit step change in reference speed. Torque Disturbance D(S) Controller Torque Motor Tape Dynamics w, (s) E(s) 10 Tm(s) T(s) o(s) 1 G(s) 0.5s + 1 0.1s + 1 Figure Q.6
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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, m,. 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 no change in reference speed, calculate the necessary proportional gain, K„, if the maximum allowable steady state error is 0.01rad/s in response to a step disturbance torque of 1Nm. b) Derivative action is added to the controller. Calculate the necessary proportional and derivative gains K, and K,, if the maximum allowable overshoot in speed is 20%, and the speed must settle to its final value in less than 0.25s 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 which would occur in response to a unit step change in reference speed. Torque Disturbance D(S) Controller Torque Motor Tape Dynamics w, (s) E(s) 10 Tm(s) T(s) o(s) 1 G(s) 0.5s + 1 0.1s + 1 Figure Q.6
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