A Novel Approach to Disturbance Rejection in Constrained Model Predictive Control

TL;DR

This thesis introduces a disturbance rejection method in linear model predictive control that uses the plant's increment model and an optimal disturbance estimate to improve tracking and regulation in discrete-time systems.

Contribution

The paper proposes a novel disturbance rejection technique utilizing the plant's increment model and an H2-based observer, differing from traditional velocity or disturbance observer methods.

Findings

Significantly improved output tracking and regulation.

Effective rejection of time-varying disturbances.

Enhanced disturbance compensation using the proposed cost function.

Abstract

This thesis is concerned with the rejection of time-varying disturbances in linear model predictive control of discrete-time systems. In the literature, disturbances are widely rejected by using velocity models, disturbance model with observer approach or a scheme that combines the compensation of a disturbance observer and the feedback regulation of MPC. Contrary to the widely used methods, the technique proposed in this research utilises the increment model of plants, with the assumption of fast-changing disturbances, to formulate a control law to reject the varying-disturbances. The uniqueness of the method stems from the compensation of the disturbance magnitude and rate of change. By proposing a cost function where the increment form of the system disturbance is taken as an optimisation variable, a control signal that is a function of a computed optimal disturbance increment is formulated to ensure that the plant is driven according to the minimisation of the cost function. The degree of freedom introduced by using the optimal disturbance in the control law was exploited to introduce the estimated disturbance increment into the control signal such that it is always in opposition to the external disturbance increment. Moreover, the proposed cost function provides a weighting matrix that can be used to manipulate the impacts of the exogenous disturbances on the response of the system. To estimate the unmeasurable disturbances, a combined state and disturbance observer is designed based on a convex optimisation stated in terms of an H2-minimisation problem. Simulations of three different systems are used to show the benefits of the proposed algorithm when compared with conventional offset-free MPC techniques. The results demonstrated that the proposed scheme can give significantly improved output tracking and regulation.