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

Oguzhan Cifdaloz, Armando Rodriguez

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

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 mixedsensitivity 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.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
Pages3415-3420
Number of pages6
Volume5
StatePublished - 2005
Event2005 American Control Conference, ACC - Portland, OR, United States
Duration: Jun 8 2005Jun 10 2005

Other

Other2005 American Control Conference, ACC
CountryUnited States
CityPortland, OR
Period6/8/056/10/05

Keywords

  • Convex optimization
  • H mixed sensitivity
  • Infinite dimensional
  • Time domain constraints

ASJC Scopus subject areas

  • Control and Systems Engineering

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    Cifdaloz, O., & Rodriguez, A. (2005). H mixed sensitivity minimization for stable infinite-dimensional plants subject to convex constraints In Proceedings of the American Control Conference (Vol. 5, pp. 3415-3420)