Adaptive control of the TORA system with partial state constraint

Abstract

In this paper, we consider the problem of stabilization of a translational oscillator with a rotational actuator (TORA) system. In practical applications, TORA systems usually suffer from parametric uncertainties. Moreover, existing control methods for TORA systems cannot guarantee the rotational scope of the actuator and often lead to unwanted unwinding behaviour. To handle these issues, we present an adaptive control strategy for TORA systems with uncertain or unknown parameters, which is robust to parameter uncertainties and can guarantee that the rotational actuator rotates in a preset range. Specifically, a Lyapunov function is elegantly constructed on the basis of the nonlinear interaction between the translational oscillator and the eccentric rotational proof mass. Then an adaptive control method, along with an online estimation mechanism, is proposed straightforwardly and the stability of the closed-loop system is proven, invoking Lyapunov techniques and LaSalle’s invariance principle. Simulation results are provided to demonstrate the performance of the presented method.