Adaptive control of time-varying mechanical systems: analysis and experiments

A new adaptive controller for time-varying mechanical systems is proposed based on two assumptions: 1) the dynamics of time-varying mechanical systems is derived under the assumption that the generalized constraints on the system do not depend on time but the system parameters, such as masses and payloads are time-varying; and 2) the time-varying parameters are given by a group of known bounded time functions and unknown constants. It is shown that the proposed adaptive controller results in a stable closed-loop system. Further, if the desired trajectory of the system is periodic, a time-scaling technique of mapping one cycle period of the desired trajectory into a unit interval is proposed to provide robustness to the parameter adaptation algorithm. An experimental platform consisting of a two-link robot with a time-varying payload is developed to test the proposed adaptive controller. Comparative experimental results demonstrate the effectiveness of the proposed design