Sliding Mode Control with Estimated Equivalent Control
In this paper Sliding Mode Control (SMC) with estimated equivalent control is presented. A equivalent control in SMC is a continuous control which is introduced to analyze the sliding mode motion on the manifolds. Using a equivalent control as a control input after reaching manifolds is very useful method from a view point of eliminating chattering and analyzing of sliding mode motion on the manifolds. We presents a design method of on-line estimator which estimates a part of equivalent control containing a system's nonlinear term by use of one of a Neural Network's most powerful ability, that is, function approximation. This control algorithm doesn't require abundant information about controlled plant to calculate a equivalent control. The controller is designed to provide sliding mode motion on the selected manifolds in the state space and to satisfy selected Lyapunov function and stability criteria. This resulting control is continuous, so chattering is eliminated. Under the condition of estimation of on-line estimator converging to real value, the motion of sliding mode is equal to that one of SMC with discontinous control.