Title: µ-Interaction measure for unstable systems

Authors: Vinay Kariwala, J. Fraser Forbes, Sigurd Skogestad

Addresses: Division of Chemical and Biomolecular Engineering, Nanyang Technological University, Singapore 637722. ' Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6. ' Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

Abstract: In this paper, we present a method for system stabilisation through independent designs of the decentralised controller. The proposed method extends the practical applicability of the conventional µ interaction measure (µ-IM) to unstable systems. The decentralised controller is designed based on a block diagonal approximation that is different from the block diagonal elements, but has the same number of unstable poles as the system. By expressing the µ-IM in terms of the transfer matrix between the disturbances and inputs, we show that the block diagonal approximation can be suboptimally selected by minimising the scaled L_∞ distance between the system and the approximation. We present a numerical method for choosing the block diagonal approximation and a simple method for designing the decentralised controller based on the approximation.

Keywords: decentralised control; large-scale systems; μ-interaction measure; structured singular value; micro-interaction; unstable systems; system stabilisation.

DOI: 10.1504/IJAAC.2007.015845

International Journal of Automation and Control, 2007 Vol.1 No.4, pp.295 - 313

Published online: 25 Nov 2007 *

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