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Nonlinear Dynamics in the Attitude Control System of a Flexible Spacecraft
by
Giulio Avanzini
Polytechnic of Turin
Coauthors: Guido de Matteis (University of Rome ``La Sapienza'')
This paper presents the bifurcation analysis of a bias-momentum, single-axis attitude control system for a flexible spacecraft during station-keeping.
Considerable attention has been devoted, in recent times, to the complex dynamic behavior that appears in attitude spacecraft dynamics when nonlinear elements are present in the control laws. Also, the structural mode interaction with attitude control system is still a matter of concern as many satellites feature large appendages having bending modes that can be excited by control motions.
In this context, Dynamical System Theory appears as a very effective tool for the analysis of spacecraft dynamics because, using bifurcation theory and continuation methods, a more global picture than simulation is provided and regions in the parameter space where changes in dynamic behavior occur due to structural/control loop interaction are revealed.
Hybrid-coordinate modelling is adopted for the considered spacecraft, where a single dominant cantilever mode is included. The pitch attitude control system has a variable structure proportional plus integral regulator incorporating anti-windup reset. Since the dynamic behavior of the controller is characterized by motion dependent discontinuities, the flexible mode can limit-cycle due to the combined effects of motor torque saturation and integrator reset.
The global analysis is carried out using a new technique where, in order to deal with highly nonlinear system that presents non smoothable nonlinearities and non-invertible input/output relations, i.e. the integrator reset, the equilibrium points of a discrete Poincarè map are determined by a numerical continuation method, and the map stability is investigated.
Bifurcation diagrams are presented, where the motor time constant te and the natural frequency fn of the structural mode are the continuation parameters. The results reveal the stability region, in the parameter plane te-fn, of the steady-state in the origin. Periodic attactors as well as more complex solutions, where the flexible dynamics have a relevant influence on the system behavior, are determined and discussed.
Date received: January 5, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadd-11.