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1

Pole-free vs. stable-pole designs of minimum variance control for nonsquare LTI MIMO systems

Hunek W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2011

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Vol. 59, nr 2

201-211

EN

This paper takes advantage of nonuniqueness of the inverse problem for nonsquare transfer function matrices of multivariable systems in order to select such poles, if any, of a minimum variance control system that can either guarantee its closed-loop stability or provide (a sort of) robustness to the control system. As a result, new pole-free and stable-pole MVC designs are offered for nonsquare LTI MIMO systems, the most general of them utilizing the Smith-factorization approach and the so-called control zeros. The new designs contribute to an illustration and extension of the Davison’s theory of (nonsquare) minimum phase systems, in that the lack or presence of (appropriate) control zeros can provide a required performance to the MVC system. Simulation examples in the Matlab/Simulink environment confirm the potential of the control zeros and their impact on redefinition of the minimum phase property.

2

Control zeros and maximum-accuracy / maximum-speed control of LTI MIMO discrete-time systems

Latawiec K. J.

Control and Cybernetics

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2005

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Vol. 34, no 2

453-475

EN

Based on new definitions of "control zeros" and minimum phase property for possibly nonsquare LTI MIMO discrete-time systems, generalizations of perfect regulation and perfect filtering are presented both for polynomial matrix and state space models. Consequently, general equivalence results are announced for multi-step and single-step optimal controls as well as for maximum-accuracy and maximum-speed controls for LTI MIMO discrete-time systems. The latter is made visible after the introduction of a new-category of time-optimal control, namely infimum-time control. The equivalence conditions refer to the system's right-invertibility and the (newly-defined) minimum phase behavior, which demonstrates the usefulness of the new approach to zeros of multi variable systems.

3

Metody wyznaczania zer liniowych ciągłych stacjonarnych układów wielowymiarowych

Hunek W.

Chemistry-Didactics-Ecology-Metrology

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2003

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R.8, NR 1-2

79--81

PL

Przedstawiono istniejące definicje zer układów wielowymiarowych. Wskazano na nierównoważność tych definicji. W konsekwencji przedstawiono nową definicją zer i związaną z nią definicją minimalnofazowości dla układów niekwadratowych. Udowodniono istnienie ‘zer sterowniczych ’ na podstawie nowo wprowadzonego sterowania minimalnowariancyjnego dla układów ciągłych, wywodzącego sią z emulatora ciągłego predyktora wyjścia obiektu.

EN

The definitions of zeros of multivariable systems were presented. It was shown that these definitions are not equivalent. Consequently were introduced new definitions of ‘control zeros' and minimum phase for possibly nonsquare systems. They definition of control zeros is based on a new Continuous-Time Minimum Variance Control, which is derived from Emulator Based Prediction made by prof. Gawthrop.