AAS 99-150

Bifurcation Analysis of Spacecraft Attitude Control Systems

Giulio Avanzini and Guido de Matteis

Polytechnic of Turn, Italy


Bifurcation theory is used to realize a comprehensive analysis of the complex behavior that appears in spacecraft attitude dynamics as a result of nonlinearities contained in the control system. In this respect we would cite the adverse effects of saturation, hysteresis and time delay in the actuator characteristics, as well as the unwanted consequences of nonlinearities contained in control system elements. In the latter situation we refer, for instance, to such subsystems as relays with hysteresis and dead-band, or variable-structure, proportional plus integral (PI) regulators incorporating anti-windup reset. The principal objective of the study is to assess and demonstrate the effectiveness of the bifurcation theory and of a numerical continuation algorithm for the analysis of attitude controllers. The proposed applications, where typical control systems including nonlinear elements are dealt with, show that the qualitative structure of the steady states and periodic solutions is revealed. As a result, the use of numerical simulation can be limited and, more important, focused onto well defined regions of the parameter space.