A complete formulation of non-linear model-based stable predictive control strategy

Abstract

This paper reports a complete formulation of a model predictive control strategy having guaranteed nominal asymptotic stability. The formulation includes a successive linearisation procedure to obtain a linear model from a non-linear plant model. It gives a complete state-space derivation including long-range prediction, trajectory tracking and modelling of both measured feedforward disturbances and unmeasured stochastic disturbances. The formulation applies a terminal constraint at the end of finite horizon prediction so that outputs reach their steady values asymptotically. The control problem thus effectively becomes an infinite-horizon LQ type model predictive controller (LQMPC). Although the theoretical results are not entirely new, a complete MPC formulation, which has asymptotic stability properties and accounts for both measured and unmeasured disturbances while being able to track predetermined set-point trajectories, is not readily available in MPC literature. The control strategy has been applied in a simulation of a thermal power plant, which is a complex multivariable system based on a non-linear physical model. It requires a predetermined trajectory tracking while being subjected to several types of known and unknown disturbances. For comparison purposes, a usual finite-horizon prediction based model-based predictive control (MPC) strategy has also been designed and applied in the simulation. A set of simulation results demonstrates the effectiveness of the proposed LQMPC strategy and compares its performance with finite horizon MPC.