Brief paper: State-space solution to weight optimization problem in H∞ loop-shaping control

  • Authors:

  • M. Osinuga;S. Patra;A. Lanzon

  • Affiliations:

  • Control Systems Centre, School of Electrical and Electronic Engineering, University of Manchester, Sackville Street, Manchester, M13 9PL, United Kingdom;Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, 721302, India;Control Systems Centre, School of Electrical and Electronic Engineering, University of Manchester, Sackville Street, Manchester, M13 9PL, United Kingdom

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2012

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Abstract

This paper proposes a state-space solution to weight optimization problem in @?"~ loop-shaping control. A pointwise-in-frequency weight optimization framework is transformed into convex optimization searches that are independent of frequency. The introduced optimization problem therefore avoids gridding of the frequency space and consequently, the inaccuracies attributed to fitting transfer functions to magnitude data. In this optimization problem, the order of the weight is specified 'a priori', thus facilitating the synthesis of low-order controllers, which is desirable from an implementation perspective. The proposed solution algorithm simultaneously synthesizes a robust stabilizing controller and a loop-shaping weight (pre-compensator) that maximize the robust stability margin subject to constraints on the performance and the singular values of the weight. Three numerical examples are given to illustrate the effectiveness of the technique.