Abstract This study presents the design of a generalized adaptive variable-gain sliding mode control policy that achieves finite-time convergence of a perturbed first-order sliding mode in the presence of input saturation constraints. An important feature of the proposed scheme is the fractional power nature of the integral term which mitigates the chattering effect and reduces steady-state error associated with the discontinuous integral term of the conventional super-twisting control policies considered in previous studies. Moreover, in contrast with most existing schemes, the perturbation and its derivative are assumed to be bounded by unknown constants in this study, and an adaptive gain update mechanism is incorporated within the proposed scheme to realize global finite-time convergence of the sliding variable to a uniform predefined bound around the origin. In particular, Lyapunov stability analysis is used to demonstrate that the proposed scheme ensures convergence of the sliding variable to a uniform ultimate bound that can be made arbitrarily small through continuous and saturated control action. This strategy also enables the proposed scheme to mitigate the integral windup effect that most existing architectures suffer from when deployed under input saturation constraints. Extensive experimental tests for achieving precise position and speed control of a DC motor are used to illustrate its advantages compared to leading alternative designs.
Kashyap et al. (Mon,) studied this question.