Causal characteristic decompositions in the time domain provide a convenient means for the extension of GPC to the multivariable case, and the use of Bicausal Decompositions for the general case of stable and unstable branch points is shown to provide superior results in accuracy and performance.
Key Wat~ls--Multivariable feedback control; discrete time systems; eigenfunctions; polynomial approximations; predictive control.
Al~trset--A change of basis from the standard to an eigenvector set has the effect of decomposing a multivariable problem into a set of characteristic scalar sub-problems.
Conformal mapping arguments can be constructed to show that satisfactory characteristic subsystem performance is a prerequisite for overall satisfactory system performance. With this motivation, earlier work proposed a generalization of the Generalized Predictive Control to the multivariable case. The approach was based on causal characteristic representations and this implied some limitations on the accuracy of the method in the case of plants with unstable branch points. In this paper we show that, under some mild conditions, the characteristic subsystems admit a bicausal representation which can be made as accurate as desired.
Bicausality does not constitute a problem in predictive control and a suitable muitivariable self-tuning algorithm is proposed. The superiority of the derived results is demonstrated by means of a design study. *