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, T«(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) = 5 = 0.6, T = 0.2 s G(s) = Wn = 10 rad/s, s2 + 2(wn$ + 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 K. gives a steady state eorof 0.4°. Qutput position c) What range of values of K will ensure a stable system? Ta(s) Telescope & Controller drive motor R(s) C(s) G|(s) G(s) Figure Q5.

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, T«(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) = 5 = 0.6, T = 0.2 s G(s) = Wn = 10 rad/s, s2 + 2(wn$ + 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 K. gives a steady state eorof 0.4°. Qutput position c) What range of values of K will ensure a stable system? Ta(s) Telescope & Controller drive motor R(s) C(s) G|(s) G(s) Figure Q5.

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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