Multivariable Model Predictive Control

Abstract

Most industrial plants have many variables that have to be controlled (outputs) and many manipulated variables or variables used to control the plant (inputs). In certain cases a change in one of the manipulated variables mainly affects the corresponding controlled variable, and each the input-output pair can be considered as a single-input single-output (SISO) plant and controlled by independent loops. In many cases, when one of the manipulated variables is changed, it not only affects the corresponding controlled variable but also upsets the other controlled variables. These interactions between process variables may result in poor performance of the control process or even instability. When the interactions are not negligible, the plant must be considered to be a process with multiple inputs and outputs (MIMO) instead of a set of SISO processes. The control of MIMO processes has been extensively treated in literature; perhaps the most popular way of controlling MIMO processes is by designing decoupling compensators to suppress or diminish the interactions and then designing multiple SISO controllers. This requires first determining how to pair the input and output variables, that is, which manipulated variable will be used to control which output variables, and that the plant have the same number of manipulated and controlled variables. Total decoupling is very difficult to achieve for processes with complex dynamics or exhibiting dead times.One of the advantages of Model Predictive Control is that multivariable processes can be handled in a straightforward manner [191], [204]. This chapter is dedicated to showing how MPC can be implemented on MIMO processes. The controllers that are obtained when transfer function matrices, state space models or convolution models are used are analyzed here. Derivation of Multivariable GPCA CARIMA model for an n-output, m-input multivariable process can be expressed as E. F. Camacho et al., Model Predictive Control © Springer-Verlag London Limited 2007with G i = 0 for i < 0. Equation (6.2) can be rewritten as J = (G N 123 u N 3 + f N 12 − w) T R(G N 123 u N 3 + f N 12 − w) + u T N 3 Qu N 3 132 6 Multivariable Model Predictive Control

Predictive Control of an Omnidirectional Mobile Robot with Friction Compensation

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