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

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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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