A pragmatic approach for selecting weight matrix coefficients in model predictive control algorithm and its application

Selecting appropriate coefficients often requires large expensive computation duty, manual designating the coefficients in weight matrix in model predictive control (MPC) algorithm often leads infeasible control results. In this paper, a pragmatic method used to efficiently select weight matrix coefficients in MPC objective function is proposed. The controllability and the observability Gramians of a stable controlled system are needed to calculate, the controllability and observability Gramians are singular value decomposed, and the controllability and observability Gramians singular value matrices are calculated. Then, Gramians singular values of the system are used as a benchmark to select the weight coefficients corresponding to different variable in the objective function of MPC. Meanwhile, a simple theoretical justification of the method based on a energy analysis is provided. The proposed methodology is validated and estimated by two different industrial application examples and the simulation results show a better agreement comparing to manual selection weight values method.