Active control of the attitude motion and structural vibration of a flexible satellite by jet thrusters

A Lagrangian formulation is used to obtain the equations of motion of a flexible satellite in a tree-type geometry. The flexible satellite model is the geosynchronous INSAT-II type satellite with a flexible balance beam and a flexible solar panel attached to the rigid main body.; In deriving the equations of motion, the orbital motion, the librational motion, and the structural motion of flexible bodies are involved. The assumed-modes method is used to express the deflections of the flexible structures in the form of a finite series of space-dependent admissible functions multiplied by time-dependent amplitudes. The kinetic energy, potential energy, strain energy, and virtual work of the flexible satellite are evaluated as functions of time in terms of the generalized coordinates. Then, by substituting them into Lagrange's equations for discrete systems, the governing equations of motion of the flexible satellite are obtained as a set of second-order nonlinear ordinary differential equations.; The attitude motion and the structural motion of the flexible satellite are coupled motions with one another. Uncontrolled dynamics show that the librational and structural motions are oscillatory and undamped motions. The stability and performance of the flexible satellite needs to be improved by designing control systems.; A control objective is proposed to improve the stability and performance for pointing accuracy maneuver by controlling the librational motions and flexible modes simultaneously. For the control objective, a control system is synthesized, using feedback linearization control, thrust determination, thrust management, and pulse-width pulse-frequency modulation.; Feedback linearization for second-order nonlinear systems is used to obtain a stable feedback control system for the pointing-accuracy control. A stable feedback control system is obtained by adjusting the diagonal matrices of the linear second-order system.; Jet thrusters are used as the primary actuators. Two types of the jet-thruster systems are developed: a set of six bi-directional jet-thrusters and a set of twelve uni-directional jet-thrusters. Jet-thrust, a nonconservative force acting on the satellite, contributes to generalized forces in Lagrange's equations. The relationship between them can be represented in a linear algebraic matrix equation. Theoretical jet-thrust control is determined in the form of continuous control command by solving the algebraic matrix equation.; For thrust management, the simplex method, the modified minimum vector 2-norm solution, or ad-hoc solutions are used to obtain non-negative jet-thrust input command for uni-directional jet-thrusters.; Continuous-time thrust input control from thrust management are modulated into on-off pulsed-jet thrust control command by pulse-width pulse-frequency (PWPF) modulation. For each thruster, there are five PWPF parameters to be adjusted, based on static and dynamic analysis. The actuation frequency of a jet thruster depends on the five parameters.; It is concluded that by considering the shift in the center of mass of flexible satellites, simultaneous control of the librational motions and flexible modes of flexible satellites are possible with on-off pulsed jet thrusters.