A Predictive and Sliding Mode Cascade Controller

This paper presents a cascade control structure to determine the open-loop optimal linear surface parameters for the sliding mode control of nonlinear mechanical systems. A discrete-time, nonlinear model predictive controller is used to update the time-invariant parameters of the sliding mode control surfaces in order to achieve some performance objective such as minimum energy or minimum time. The determination of these surface parameters is subject to constraints that arise from the stability conditions imposed by the sliding mode control law and the physical limits on the system such as input saturation. We prove the nominal stability of this cascade control structure and demonstrate its performance using the inverted pendulum on a cart as an illustrative example.