Adaptive Control for Nonlinear Time-Varying Rotational Systems

It is common for aerospace systems to exhibit nonlinear, time varying dynamics. This thesis investigates the development of adaptive control laws to stabilize and control a class of nonlinear, time varying systems. Direct adaptive control architectures are implemented in order to compensate for time varying dynamics that could, for example, be caused by varying inertia resulting from fuel slosh or settling in a tank. The direct adaptive controller can also respond to external disturbances and unmodeled or nonlinear dynamics. Simulation results are presented for a prototype system that consists of two rotating tanks with time varying inertia due to the motion of fluid inside the tanks. This system is characterized by highly unstable rotational dynamics which are illustrated through simulation. An adaptive regulator is implemented to control the threedimensional angular velocity to a desired operating point. It is shown that the adaptive controller provides improved performance compared to a baseline linear quadratic regulator designed using a simplified linear dynamics model of the plant. Finally, a direct model reference adaptive controller was implemented to enable the system to track trajectories generated by a reference model. The stability of this control law is investigated via Lyapunov analysis, and simulation results are provided showcasing overall controller performance in the presence of both internal and external disturbances and dynamical effects.