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H mixed sensitivity minimization for stable infinite-dimensional plants subject to convex constraints

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2 Author(s)
Cifdaloz, O. ; Dept. of Electr. Eng., Arizona State Univ., Tempe, AZ, USA ; Rodriguez, A.A.

This paper shows how convex optimization may be used to design near-optimal finite-dimensional compensators for stable linear time invariant (LTI) infinite dimensional plants. The infinite dimensional plant is approximated by a finite dimensional transfer function matrix. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity H optimization that is convex in the Youla Q-parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated optimization problem from an infinite dimensional optimization problem involving a search over stable real-rational transfer function matrices in H to a finite-dimensional optimization problem involving a search over a finite-dimensional space. In addition to solving weighted mixed sensitivity H control system design problems, it is shown how subgradient concepts may be used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems, in short, the approach taken permits a designer to address control system design problems for which no direct method exists, illustrative examples are provided.

Published in:

American Control Conference, 2005. Proceedings of the 2005

Date of Conference:

8-10 June 2005