Robust and nominal stability conditions for a simplified model predictive controller

Abstract

A new condition is derived that guarantees robust stability for a set of stable, linear time-invariant plants controlled by using a simplified model predictive control algorithm (SMPC). Discrete single-input-single-output control systems are considered in this paper. Uncertainty is treated in the time domain by considering the stabilization of a set of pulse response functions. The method presented is suitable for stabilizing a set of plants that are not necessarily related. Central to this method is a bounding function, which is a function of the model and controller parameters. The bounding function is designed to have a larger magnitude than all of the pulse response functions in the set of plants to be stabilized. Using this method, it was found that the bounding function is monotonically decreasing when a first-order plus dead-time model is used to design the controller. This allows the coincidence point used in SMPC to be employed directly as a tuning “knob” for robustness, and also simplifies the analysis for dead-time uncertainty. In addition, a comparison of two nominal stability conditions is provided.