6. The attitude of a satellite is maintained at its reference value by thrusters mounted on its outer rim, adistance r from the central axis, Figure Q6. Gravitational forces tend to rotate the satellite out of itscorrect attitude, in effect by the application of a disturbing moment D. The actual attitude 0, is measuredby a sensor which has gain K, and is fed back to be compared with the reference value 0,. The errorin the attitude E is passed to a controller with transfer function G.(s) which then activates the thrusterto produce an appropriate force F. The total moment applied to the satellite is then the torque from thethrusters, plus the disturbance torque. The satellite has a moment of inertia about its axis of rotation ofJ kg m².a) Draw the block diagram of this system.b) Show that the transfer function relating the attitude of the satellite, to a disturbance, D, for the casewhere the reference attitude is zero is given by0(s)1D(s)Js² + KrG.(s)c) Explain why a proportional controller would not be appropriate for this system.d) If a proportional plus derivative controller is used, determine the values of the proportional andderivative gains, K, and Ka respectively, if a system damping of 0.8 is required and the transientresponse is to settle to its steady state within 5 seconds of any disturbance. The system parametersare J = 2000 kg m², r = 2 m, K = 5.e) Derive an expression for the transient response of the satellite to a step change of 20 Nm in thedisturbing moment D(s).FFigure Q6.

Given : The altitude of the satellite is always maintained at reference value by thrusters.

Answered: c) Explain why a proportional…

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c) Explain why a proportional controller would not be appropriate for this system.

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

6. The attitude of a satellite is maintained at its reference value by thrusters mounted on its outer rim, a
distance r from the central axis, Figure Q6. Gravitational forces tend to rotate the satellite out of its
correct attitude, in effect by the application of a disturbing moment D. The actual attitude 0, is measured
by a sensor which has gain K, and is fed back to be compared with the reference value 0,. The error
in the attitude E is passed to a controller with transfer function G.(s) which then activates the thruster
to produce an appropriate force F. The total moment applied to the satellite is then the torque from the
thrusters, plus the disturbance torque. The satellite has a moment of inertia about its axis of rotation of
J kg m².
a) Draw the block diagram of this system.
b) Show that the transfer function relating the attitude of the satellite, to a disturbance, D, for the case
where the reference attitude is zero is given by
0(s)
1
D(s)
Js² + KrG.(s)
c) Explain why a proportional controller would not be appropriate for this system.
d) If a proportional plus derivative controller is used, determine the values of the proportional and
derivative gains, K, and Ka respectively, if a system damping of 0.8 is required and the transient
response is to settle to its steady state within 5 seconds of any disturbance. The system parameters
are J = 2000 kg m², r = 2 m, K = 5.
e) Derive an expression for the transient response of the satellite to a step change of 20 Nm in the
disturbing moment D(s).
F
Figure Q6.

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