Soft variable structure controller design for constrained systems based on S-class functions

A soft variable structure control (SVSC) strategy based on S-class functions is addressed in this paper. Firstly, the definition of SVSC strategy is given, the structure of SVSC system under constrained control input is analyzed, and S-class functions with smoothness, strict monotonicity, and saturation are presented. Secondly, the sufficient condition on the stability of SVSC system is obtained by Lyapunov stability theory. A soft variable structure controller based on S-class functions is developed aiming at optimizing the smoothness problem of the SVSC systems based on variable saturations, and the chattering problem of sliding mode control (SMC) systems. Then, the concrete algorithm on SVSC strategy based on sigmoid functions is obtained. Finally, a simulation example is carried out to verify the feasibility and effectiveness of the SVSC strategy, and compared with SMC strategy, high regulation rate is achieved, settling time is shorted, and the system chattering can be reduced by the proposed strategy.