Chapter 7 - Control of Multivariable Processes

Abstract

The control of multivariable processes uses multiple input multiple output (MIMO) process models. These models are based on the state space and matrix fractional description (MFD) formulations. The MFDs contain matrix polynomials which can be easily used for control and modeling purposes. The Youla parameterization can be extended for MIMO processes and these regulators are very compact formulation of the necessary matrix polynomial manipulations. Besides the general MIMO forms, the “naïve,” and the inverse stable representations are also discussed for process models. An important task of the control of MIMO processes is “decoupling,” when each reference signal influences only the corresponding output signal, and the regulator design is a scalar problem. The different decoupling methods are discussed for general cases and for Youla-parameterized MIMO regulators, too. It is shown how a MIMO process model linear in parameter matrices can be derived. The different MIMO predictive regulators are also shown. The derivation of the MIMO minimum variance regulator is presented and compared to the MIMO Youla-parameterized regulators. The computation of decoupling MIMO regulators is shown for simple examples and for a complex aircraft process model.