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A linear matrix inequality approach to H∞ controller order reduction with stability and performance preservation

Amirifar, R ; Sharif University of Technology | 2003

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  1. Type of Document: Article
  2. DOI: 10.1109/SSST.2003.1194561
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2003
  4. Abstract:
  5. H∞ controller order reduction with stability and performance preservation pose unique challenges to designers. In the paper, an approach for controller order reduction based on minimization of the rank of a matrix variable, subject to linear matrix inequality constraints, is presented. In this approach, the rank of a residue matrix of a high-order controller subject to the error between the loop gain of the closed-loop nominal system and the loop gain of the closed-loop system with the reduced order controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a semidefinite program, so that it can be solved efficiently. It is shown that the reduced order controller preserves the performances and stability of the nominal closed-loop system. The proposed approach is applied to an H∞ high-order controller which is designed for an active suspension system. The performance and stability achieved by the reduced order controller is compared with those achieved by the high-order controller. The comparison is based on experimental results obtained by digital controller implementation. © 2003 IEEE
  6. Keywords:
  7. Control systems ; Equations ; Error correction ; Frequency ; Linear matrix inequalities ; MATLAB ; Minimization methods ; Reduced order systems ; Robust control ; Robust stability
  8. Source: 35th IEEE Southeastern Symposium on System Theory, SSST 2003, 18 March 2003 ; Volume 2003-January , 2003 , Pages 217-221 ; 0780376978 (ISBN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.4590040403