Model Predictive Control of Multivariable Plants Using Interactor and Solving Procedure of Matrix Polynomial Diophantine Equations

Abstract

This paper proposes a design method of model predictive control (MPC) for multi-input multi-output (MIMO) plants with time-delay by using an interactor matrix and a sequential procedure to solve the matrix polynomial Diophantine equations required to be solved in the design. The equations are of matrix polynomials, and matrix calculations are not commutative; hence it is not easy to solve the equations, and it is necessary to obtain a sequential solving procedure. Also, the difficulty in the design of MPC of MIMO plants comes from the fact that a plant transfer function is a matrix, which is not commutative in multiplication. This paper avoids this difficulty by deriving a plant transfer function with a scalar polynomial denominator. And to handle the time-delay in MIMO plants, an interactor matrix is used to shift the outputs by time-delay steps. Then the design problem with time-delay is reduced to a problem without time-delay. There exist designs of MPC for time-delay plants by using a longer horizon than the time-delay steps. In this paper, it is shown by simulations that MPC having a long horizon is sensitive to disturbances and that the proposed MPC is less sensitive.