A polynomial perspective on the stability of multivariable predictive controllers
A rigorous method for analyzing the stability of unconstrained multivariable predictive controllers is developed using polynomial operators and coprime matrix factorizations. The technique permits deriving explicit expressions for the closed-loop transfer functions that describe the relevant system dynamics. It is shown that the closed-loop poles can be determined by finding the roots of two characteristic polynomial equations, hence allowing a complete characterization of the asymptotic stability of the system. The controllers require the specification of a large number of tuning parameters, including prediction and control horizons for every input and output signal as well as the elements of input and output weighting matrices. The stability analysis tools proposed tend significant support to the tuning task because sets of parameters that produce unstable poles can be identified and rejected. Further-more, since the location of the poles influences the speed of the closed-loop response, it is also possible to compare the relative merits of alternative sets of stabilizing tuning parameters. Finally, it is shown that the multivariable predictive-control law can be written in standard shift-operator form, facilitating the implementation in a digital control computer using only shift registers, scalar multiplications, and scalar additions. The approach is illustrated in an example involving the control of a multistage gas-liquid absorption column. (C) 2003 Elsevier Science Ltd. All rights reserved.
multivariable predictive controllers polynomial operators closed-loop transfer functions stability of predictive control