BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 59, Issue 2, June 2011

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pp 201 - 211

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

W.P. HUNEK
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.
Key words:

minimum variance control, multivariable control, inverses of polynomial matrices, control zeros, minimum phase systems


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