Synthesis of stabilizing antiwindup controllers using piecewise quadratic Lyapunov functions

Pradeep Y. Tiwari, Eric F. Mulder, Mayuresh V. Kothare

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We consider the problem of antiwindup controller synthesis based on the general antiwindup framework presented in Kothare et al. (Automatica, vol. 30, no. 12, pp. 1869-1883, 1994) applicable to linear time-invariant systems (LTI) subject to a saturating actuator. Our synthesis approach takes advantage of the fact that the antiwindup system is a piecewise affine system and thus, we can utilize piecewise quadratic Lyapunov function theory Johansson and Rantzer (IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 555-559, Apr. 1998), Rantzer and Johansson (IEEE Trans. Autom. Control, vol. 45, no. 4, pp. 629-637, Apr. 2000), and Johansson (Proc. 14th World Congr., Beijing, China, 1999, pp. 521-5260) to determine a stabilizing antiwindup control law. The synthesis problem is expressed in terms of bilinear matrix inequalities (BMIs) and is solved using an iterative approach as well as using commercial software. The performance of the system is optimized by minimizing an upper bound on the induced L2 gain of the system. The proposed approach is demonstrated using examples.

Original languageEnglish (US)
Pages (from-to)2341-2345
Number of pages5
JournalIEEE Transactions on Automatic Control
Volume52
Issue number12
DOIs
StatePublished - Dec 2007
Externally publishedYes

Keywords

  • Actuator saturation
  • Antiwindup
  • Bilinear matrix inequalities(BMI)
  • Constrained control
  • Optimal control
  • Piecewise linear system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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