Robust Sliding Mode Control of Robot Manipulators Using the Fourier Series Expansion in the Presence of Uncertainty

In this paper, a robust dynamic slip mode controller for an electrical robot manipulator is presented. The control law calculates the motor voltage based on the voltage control strategy. Uncertainties are estimated using the Fourier series expansion and the cutting error is compensated. Fourier coefficients are adjusted based on stability analysis. Also in this paper is the design of a robust controller using a new adaptive Fourier series extension. Compared to previous related works based on the Fourier series expansion, the advantage of this paper is that it provides a matching law for the main frequency of the Fourier series expansion and thus eliminates the need for trial and error in its regulation. A case study of a Scara robot powered by DC magnet electric motors. The effect of uncertainty estimation based on the Fourier series expansion is studied instead of using the sign function. The proposed method is also compared with Legendre polynomials. The simulation results confirm the robust and satisfactory performance of the proposed controller.