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Observer Based Adaptive Estimation/Cancellation of Unmatched Sinusoidal Disturbances in Known LTI Systems by State Derivative Measurement

[+] Author Affiliations
Halil Ibrahim Basturk

Bogazici University, Istanbul, Turkey

Paper No. DSCC2015-9685, pp. V002T23A003; 10 pages
  • ASME 2015 Dynamic Systems and Control Conference
  • Volume 2: Diagnostics and Detection; Drilling; Dynamics and Control of Wind Energy Systems; Energy Harvesting; Estimation and Identification; Flexible and Smart Structure Control; Fuels Cells/Energy Storage; Human Robot Interaction; HVAC Building Energy Management; Industrial Applications; Intelligent Transportation Systems; Manufacturing; Mechatronics; Modelling and Validation; Motion and Vibration Control Applications
  • Columbus, Ohio, USA, October 28–30, 2015
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5725-0
  • Copyright © 2015 by ASME


In this paper, an adaptive observer and backstepping controller are designed to cancel and estimate sinusoidal disturbances forcing a linear time-invariant by using only the measurements of the state-derivatives. The parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters with the necessary filter designs enables to approach the problem as an adaptive control problem. An observer is designed for the unmeasured virtual input to apply a backstepping procedure which handles the unmatched disturbance and input condition. Firstly, it is shown that the disturbance and the unmeasured actuator state are observed perfectly in the open loop case. Secondly, the closed loop case is considered and it is proven that the equilibrium of the closed-loop adaptive system is stable and the state of the considered original system converge to zero as t → ∞ with perfect disturbance estimation. The effectiveness of the controller and the observers are illustrated with a simulation example of a third order system.

Copyright © 2015 by ASME



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