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2. 2 STRUCTURAL CONTROL INTERACTION FOR A LSS ATTITUDE CONTROL SYSTEM USING THRUSTERS AND REACTION WHEELS 1. INTRODUCTION Problems related to LSS: Most of the current research in the field of structural control for mitigation of responses due to environmental loads neglects the effects of control-structure interaction (CSI) in the analysis and design of protective systems. The CSI are associated with structural flexibility and/or any kind of fluid or mobile part as component of the LSS system. The space environment may excite the elastic vibration to such a level that the control system loses efficiency. Conversely the control system actuation may create forces which excite the flexible structure

3. 3 Taking into account that most of spacecraft structure includes some level of flexibility, it is mandatory to access the structural interaction with control systems or, conversely to assess the interaction of the control systems with the structure. If the structure control interaction, CSI, is improperly assessed, the spacecraft performance can be jeopardized, structure components can fail, or, in the worse case, the vehicle may be destroyed. The CSI for a specific design can be anticipated and the potential problems avoided through space vehicle modeling simulations and tests execution. Such task requires a cooperative effort between the structural and control designers. To make those designers work as a team is a difficult mission. The need to overcome this typical problem gives birth to the integrated structural control discipline. The problem still persists and is very difficult to reach a structural configuration that in the first design satisfies both control and structure requirements.

4. 4 One form of assessing the control structure interaction is to develop space structure mathematical models followed by a dynamics analysis, including the space vehicle dynamics computer simulations.

5. 5 Space VehicleProblemCause Explorer IDirectional instability Internal energy dissipation and bending of whip antennas ATS-5Dynamics instability Internal energy dissipation due to fluid motion inside heat pipes attached to cylindrical solar arrays Alouette IDespinThermal bending of satellite booms. RAEUndesirable oscillationsVery long booms vulnerable to large deflections OGO IIILimit-cycle oscillationsControl system interaction with boom flexibility. M2-F2Limit-cycle oscillations and Structural resonance vibrations Lightweight control system gyro mount allowed vibration from control surface motion to be sensed. Some examples - CSI problems

6. 6 ZsZs YsYs XsXs z y x dm LSS Physical Model Problem Formulation - LSS Mathematical Model The problem consists of the computer simulation of a large space structure mathematical model to analyze the control structure interaction phenomenon.

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8. 8 X s  ZsZs YsYs z y x rara rprp rdrd rsrs Mathematical Model

9. 9 Kinetic Energy Reaction Wheels Inertia Matrix Coupling terms (gyroscopic) Elastic

10. 10 Discretization Procedure – Assumed Mode Method

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12. 12 Potential Elastic Energy

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15. 15 can be written as

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19. 19 Then the equations were linearized about the gravity-gradient stabilized orientation and integrated via computer

20. 20 results equations

21. 21 Results

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