Adaptive Control of Mechanical Systems With Time-Varying Parameters and Disturbances

A new adaptive control algorithm for mechanical systems with time-varying parameters and/or time-varying disturbances is proposed and investigated. The proposed method does not assume any structure to the time-varying parameter or disturbance. The method is based on the expansion of the time-varying parameter/disturbance using Taylor’s formula. This facilitates expanding a time-varying function as a finite length polynomial and a bounded residue. The coefficients of the finite-length polynomial are estimated in a small time interval so that they can be assumed to be constant within that interval. A gradient projection algorithm is used to estimate the parameters within each time interval. Stability of the proposed adaptive controller is shown and discussed. A novel experiment is designed using a two-link planar mechanical manipulator to investigate the proposed algorithm experimentally. Results of the proposed adaptive controller are compared with an ideal nonadaptive controller that assumes complete knowledge of the parameters and disturbances. A representative sample of the experimental results is shown and discussed.