Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our 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, 2) design of an adaptive disturbance observer and, 3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second order system.
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ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control
October 31–November 2, 2011
Arlington, Virginia, USA
Conference Sponsors:
- Dynamic Systems and Control Division
ISBN:
978-0-7918-5475-4
PROCEEDINGS PAPER
Adaptive Cancelation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback
Halil I˙. Bas¸tu¨rk,
Halil I˙. Bas¸tu¨rk
University of California at San Diego, San Diego, CA
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Miroslav Krstic
Miroslav Krstic
University of California at San Diego, San Diego, CA
Search for other works by this author on:
Halil I˙. Bas¸tu¨rk
University of California at San Diego, San Diego, CA
Miroslav Krstic
University of California at San Diego, San Diego, CA
Paper No:
DSCC2011-5956, pp. 353-360; 8 pages
Published Online:
May 5, 2012
Citation
Bas¸tu¨rk, HI, & Krstic, M. "Adaptive Cancelation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback." Proceedings of the ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1. Arlington, Virginia, USA. October 31–November 2, 2011. pp. 353-360. ASME. https://doi.org/10.1115/DSCC2011-5956
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