Discretization-Chattering-Free Implementation of Arbitrary-Order Sliding Mode Controllers

In this paper an implementation of sliding mode control for disturbed integrator chains that does not suffer from the discretization chattering effect is presented. The method is based on an Euler forward discretization of the sliding mode controller. In a vicinity of the origin, that properly scales with the discretization time, the controller is altered to eliminate discretization chattering which can also improve the control accuracy. Finite-time stability of the origin is proven in the absence of a disturbance. In the disturbed case boundedness of the control error is shown. The control actuation is shown to be locally bounded. Exemplary applications to first- and second-order sliding mode control show the effectiveness of the method.