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5. A radio telescope must be accurately positioned to be effective. Once positioned any errors due to disturbances from aerodynamics loadings (from gusts of wind) must be corrected quickly. A control system capable of achieving this is shown in Figure Q5, where R(s) is the desired angular position whilst C(s) is the actual position, Ta(s) is the disturbance produced by the wind, G1(s) the controller transfer function and G(s) is the transfer function of the telescope and drive motor. The transfer functions and system parameters are given as G(s) = s2 + 2(wns + w;' Ka G|(s) = 5 = 0.6, T = 0.2 s Wn = 10 rad/s, TS + 1' a) Derive the transfer function relating the actual position C to the torque disturbance Ta for a zero reference input. b) If a gust provides a sudden torque disturbance which is equivalent to a unit step input in T4, what value of K« gives a steady state oOF of 0.4°. c) What range of values of K. will ensure a stable system? output position

5. A radio telescope must be accurately positioned to be effective. Once positioned any errors due to disturbances from aerodynamics loadings (from gusts of wind) must be corrected quickly. A control system capable of achieving this is shown in Figure Q5, where R(s) is the desired angular position whilst C(s) is the actual position, Ta(s) is the disturbance produced by the wind, G1(s) the controller transfer function and G(s) is the transfer function of the telescope and drive motor. The transfer functions and system parameters are given as G(s) = s2 + 2(wns + w;' Ka G|(s) = 5 = 0.6, T = 0.2 s Wn = 10 rad/s, TS + 1' a) Derive the transfer function relating the actual position C to the torque disturbance Ta for a zero reference input. b) If a gust provides a sudden torque disturbance which is equivalent to a unit step input in T4, what value of K« gives a steady state oOF of 0.4°. c) What range of values of K. will ensure a stable system? output position

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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5. A radio telescope must be accurately positioned to be effective. Once positioned any errors due to disturbances from aerodynamics loadings (from gusts of wind) must be corrected quickly. A control system capable of achieving this is shown in Figure Q5, where R(s) is the desired angular position whilst C(s) is the actual position, Ta(s) is the disturbance produced by the wind, G1(s) the controller transfer function and G(s) is the transfer function of the telescope and drive motor. The transfer functions and system parameters are given as Ka G|(s) = Š = 0.6, T = 0.2 s G(s) = Wn = 10 rad/s, s2 + 25wns + w," TS + 1° a) Derive the transfer function relating the actual position C to the torque disturbance Ta for a zero reference input. b) If a gust provides a sudden torque disturbance which is equivalent to a unit step input in T4, what value of Ka gives a steady state OE of 0.4°. output position c) What range of values of K, will ensure a stable system? Ta(s) Telescope & drive motor Controller R(s) C(s) G|(s) G(s) Figure Q5.
Transcribed Image Text:5. A radio telescope must be accurately positioned to be effective. Once positioned any errors due to disturbances from aerodynamics loadings (from gusts of wind) must be corrected quickly. A control system capable of achieving this is shown in Figure Q5, where R(s) is the desired angular position whilst C(s) is the actual position, Ta(s) is the disturbance produced by the wind, G1(s) the controller transfer function and G(s) is the transfer function of the telescope and drive motor. The transfer functions and system parameters are given as Ka G|(s) = Š = 0.6, T = 0.2 s G(s) = Wn = 10 rad/s, s2 + 25wns + w," TS + 1° a) Derive the transfer function relating the actual position C to the torque disturbance Ta for a zero reference input. b) If a gust provides a sudden torque disturbance which is equivalent to a unit step input in T4, what value of Ka gives a steady state OE of 0.4°. output position c) What range of values of K, will ensure a stable system? Ta(s) Telescope & drive motor Controller R(s) C(s) G|(s) G(s) Figure Q5.
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