??Problem Statement
Consider the satellite control system design problem in the Midterm Project. Figure 1 (a) shows a satellite with the instrument package. Figure 1 (b) is an equivalent mechanical system diagram illustrating that two masses are connected by a flexible boom with the sensor package mounted on the disk associated with ?2, and ?1 the angle of the main satellite with respect to the star. A cold gas-jets thruster is considered to deliver required torque, and a star tracker sensor reading ?2 (which is relatively noisy, but very accurate in an average sense) is selected. To avoid feedback control related destabilizing effect (which may arise from differentiating the position signal to get the rate signal), a rate gyro to give a clean reading of ??2 is also selected.
J1 : Satellite Main Body Inertia J2 : Instrument Package Inertia k : Boom Torsional Stiffness b : Boom Torsional Damping
Tc : Cold Gas-Jet Thruster Torque
System Parameters & Variation Range
J1 ?1.0
J2 ? 0.1
0.09 ?k ? 0.4
k k
0.038 ?b? 0.2
10 10
Figure 1 Satellite system and an equivalent mechanical system
The pointing requirement arises when it is necessary to point the unit in another direction. It can be met by dynamics with transient settling time of 20 second, and an overshoot of no more than 15%. The control must also be satisfactory for any parameters that can vary. Physical analysis of the boom performed by Systems Department in your company informs you that the boom torsional stiffness and damping vary as a result of temperature fluctuations but are bounded as specified above. Your job is to carry out a feedback control system design study using the full state-space design via the pole-placement method that meets the specifications given above, and compare it with your previous design based on the classical control method. Deliver a comprehensive design study report.
Deliverables:
1) Control system analysis and design
a. state-space analysis: system modal characteristics, stability, controllability and observability properties of the open-loop plant dynamics
b. state-space design: full state feedback design via the pole placement method (you may consider the optimal pole locations derived from ITAE performance index described in the section 5.9, Modern Control Systems by Bishop & Dorf, the textbook for ME3600)
2) Control system design verification & comparison
a. verify your design via (i) closed-loop time domain simulation, (ii) closed-loop frequency response and bandwidth, (iii) cold gas-jet thruster activities
b. apply your controller to the systems with parameters of all the four corners in Figure 2, and investigate your design if it meets the performance specifications
c. compare the full-state feedback design vs. the classical design result using the results from 2).a & 2).b, describe the difference, pros & cons, etc.;
3) Conclusion & Recommendation
Your report will be graded based on the following criteria.
1 2 4 5 6 7 Total
Organization & Professionalism Solution Approach Solution Accuracy Solution Analysis Code
Accuracy &
Organization Conclusion Suggestion