This paper presents a robust dynamic sliding mode control for electrically driven robot manipulators. The control law computes the motor voltages based on the voltage control strategy. Uncertainties are estimated using the Fourier series expansion and the truncation error is compensated. The Fourier coefficients are tuned based on the stability analysis. The contribution of this paper is designing a robust controller using a novel adaptive Fourier series expansion. In comparison with previous related works based on the Fourier series expansion, the superiority of this paper is presenting an adaptation law for the fundamental frequency of the Fourier series expansion and, consequently, relaxing the need for trial and error procedure in its tuning. The case study is a SCARA (Selective Compliant Articulated Robot for Assembly) robot manipulator actuated by permanent magnet DC electrical motors. The influence of uncertainty estimation based on the Fourier series expansion instead of using sign function is studied. Simulation results verify robust and satisfactory performance of the proposed controller.

In this work, an adaptive dynamic sliding mode control approach is proposed for robotic systems via uncertainty estimators with exponential convergence rate. The uncertainties are estimated using various uncertainty estimators such as the Fourier series expansion, Legendre polynomials and adaptive fuzzy systems. Also, for each uncertainty estimator, the approximation error is compensated. The adaptation laws are derived using a stability analysis. Moreover, the asymptotic convergence of the tracking error and the boundedness of all closed-loop signals are guaranteed. The novelty of this paper is proposing a positive exponential function for the convergence rate of the adaptation rules to prevent from initial high voltages originated from large initial tracking errors. Another novelty of this paper is presenting a robust control term for the truncation error that improves the accuracy of the control system. Analysis of simulations reveals the effectiveness of the proposed method in terms of fast disturbance rejection and negligible tracking error.