Practical fractional-order terminal sliding-mode control for a class of continuous-time nonlinear systems

Terminal sliding-mode control (TSMC) has been studied and applied extensively in the last few years. This technique gives rise to a robust control with tunable finite-time convergence, providing a fast and accurate response in the presence of parameter uncertainties. In that sense, we present a closed-loop robust controller for a class of nonlinear systems using a terminal sliding-mode controller, with a novel fractional-order sliding surface. The motivation of this work is to consider a time-varying gain for the fractional-order sliding surface that is relatively small at the beginning of the regulation control task to reduce the amplitude of the control input and it increases near the final time to reduce the error in the steady state. Unlike using a constant gain in the conventional terminal sliding surface, the time-varying gain keeps the amplitude of the signal low and enhances the precision simultaneously. An extensive simulation study shows the performance of the proposed design. Finally, the experimental implementation of the fractional-order TSMC in a lightweight (90 g) two-degree-of-freedom manipulator is presented. The implementation used C++ programming language on a Raspberry Pi digital board and a chattering-free modification was presented to address the practical limitation of the actuators.