Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay

• Halil I. Basturk ^[1] ; Miroslav Krstic ^[2]
  1. [1] Boğaziçi University

     Boğaziçi University

     Turquía

     
  2. [2] University of California, San Diego

     University of California, San Diego

     Estados Unidos

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 58, 2015, págs. 131-138
• Idioma: inglés
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• Resumen

  • Solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays. In this paper, two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time-invariant system in controllable canonical form despite input delay. The design is based on three steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, (2) representation of the delay as a transport PDE, (3) design of the adaptive controller by using the backstepping boundary control technique for PDEs. It is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t→∞t→∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a second order system.