Adaptive back-stepping control of robot manipulators using the Fourier series expansion

Abstract

Based on back-stepping design procedure and function approximation by the Fourier series expansion, an adaptive controller for robot manipulators has been developed in this paper. The control law is designed based on estimation of the desired motor currents using orthogonal functions. The adaptation laws for the coefficients of the orthogonal functions are derived based on the stability analysis. In comparison with previous related works, the stability analysis of the proposed method is more comprehensive and complete due to including the motor currents dynamics in the controller design. Moreover, in comparison with other approaches based on the Fourier series, the proposed controller is superior due to the reduced number of required estimators. The approximation error is also compensated. The case study is two-link planar robot manipulator driven by permanent magnet DC motors. Simulation results show robustness of the proposed controller against large external disturbance. The output deviation from its desired value is very small and negligible when external disturbance is applied to the system.