?-Interaction measure for unstable systems. (26th November 2007)

• Record Type: Journal Article
• Authors: Kariwala, Vinay; Forbes, J. Fraser; Skogestad, Sigurd
• Is Part Of: International journal of automation and control. Volume 1:Number 4(2007)
• Page Start: 295
• Page End: 313
• Publication Date: 2007-11-26
• Subjects: decentralised control -- large-scale systems -- &amp -- #956 -- -interaction measure -- structured singular value -- micro-interaction -- unstable systems -- system stabilisation; Automation -- Periodicals; Control theory -- Periodicals; Automatic control -- Periodicals; Robots -- Periodicals; Bionics -- Periodicals; Intelligent control systems -- Periodicals
• Languages: English
• ISSNs: 1740-7516

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 ? interaction measure (?-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 ?-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.