Fuzzy smoothing algorithms for variable structure systems

A variable structure system (VSS) is a control system implementing different control laws in different regions of the state space divided by a set of boundary manifolds. The control input switches from one control law to another when the state crosses the boundary manifolds. In general, the control input may not be smooth when switching at these boundary manifolds and may excite high frequency dynamics. This paper proposes two fuzzy rule based algorithms for smoothing the control input. The merits of these fuzzy smoothing control algorithms are illustrated by two examples: a semiactive suspension system based on optimal control and a direct drive robot arm under discrete time sliding mode control. The controller design for these two examples is a blend of traditional control theoretic approaches and fuzzy rule based approaches