Discrete-time and sampled-data anti-windup synthesis: stability and performance

  • Authors:
  • Guido Herrmann;Matthew C. Turner;Ian Postlethwaite

  • Affiliations:
  • Department of Engineering, University of Leicester, Leicester, UK;Department of Engineering, University of Leicester, Leicester, UK;Department of Engineering, University of Leicester, Leicester, UK

  • Venue:
  • International Journal of Systems Science - Special issue: Anti-windup
  • Year:
  • 2006

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Abstract

The anti-windup (AW) problem is formulated in discrete time using a configuration which effectively decouples the nominal linear and nonlinear parts of a closed loop system with constrained plant inputs. Conditions are divided which ensure an upper bound on the induced l2 norm of a certain mapping which is central to the anti-windup problem. Results are given for the full-order case, where a solution always exists, and for static and low-order cases, where a solution does not necessarily exist, but which is often more appealing from a practical point of view The anti-windup problem is also framed and solved for continous-time systems under sampled-data control. It is proved that the stability of the anti-windup compensator loop is equivalent to a purely discrete-time problem, while a hybrid induced norm is used for performance recovery. The performance problem is solved using linear sampled-data lifting techniques to transpose the problem into the purely discrete domain. The results of the paper are demonstrated on a flight control example.