Forced Sliding Mode Control: Synergetic Approach

Abstract

Various methods and approaches of modern control theory are used by engineers to implement the property of robustness. One of such reference approaches is sliding mode control (SMC) used for design of linear and nonlinear control laws. However, the SMC design presents severe difficulties with: (i) vector synthesis procedure; (ii) chattering reducing or elimination problem; and (iii) closed-loop system stability analysis. To overcome these difficulties, we propose to use the Synergetic Control Theory (SCT) for SMC design. It is possible to accelerate the sliding mode by emerging a new sliding mode along the surface of an even lower dimension, i.e., by organizing a forced sliding mode (FSM). The purpose of this work is to present a design procedure for nonlinear laws of synergetic control with FSM, which is a further evolution of discontinuous control law design procedure based on a consistent set of invariant manifolds of SCT, as well as provides speed-up in sliding processes and overcoming the above mentioned difficulties of SMC design.