Zero Dynamics Analysis and Adaptive Tracking Control of Underactuated Multibody Systems with Flexible Links

This paper studies the adaptive tracking control problem for underactuated multibody systems with flexible links in the presence of unknown parameters. A four-body system with input signals acting on the first and fourth bodies is chosen as a benchmark model, which can be decomposed into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is Lyapunov stable and is partially input-to-state stable under the condition that the speeds of first and fourth bodies are synchronous. The physical meaning of such partial input-to-state stability is clarified. An adaptive controller is developed to ensure such a needed system stabilization condition and thus the boundedness of the desired closed-loop system signal and asymptotic speed tracking of the control dynamics subsystem. Detailed closed-loop system stability and tracking performance analysis are given, in which the tracking errors satisfy the L^1 performance. Extensions to the other multibody systems with flexible links are derived. The developed adaptive controller is applied to a realistic train dynamic model, and simulation results verify the desired system performance.