Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method

The main obstacles for application of Sliding Mode Control are two interconnected phenomena: chattering and high activity of control action. It is well known that the amplitude of chattering is proportional to the magnitude of discontinuous control. These two problems can be handled simultaneously if the magnitude is reduced to a minimal admissible level defined by the conditions for the sliding mode to exist. In this paper an adaptation methodology is developed for searching the minimum possible value of control based on evaluations of the, so-called, equivalent control by a low-pass filter. It is based on direct measurements of the, so-called, equivalent control by a first-order low-pass filter. The application of this methodology to the Super-Twist control enables reducing the control action magnitude to the minimum possible value keeping the property of a finite-time convergence.