Performance Recovery of Feedback-Linearization-Based Designs

We consider a tracking problem for a partially feedback linearizable nonlinear system with stable zero dynamics. The system is uncertain and only the output is measured. We use an extended high-gain observer of dimension n +1, where n is the relative degree. The observer estimates n derivatives of t...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2008-11, Vol.53 (10), p.2324-2334
Main Authors: Freidovich, L.B., Khalil, H.K.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control nonlinearities
Control system synthesis
Control systems
Control theory. Systems
Derivatives
Dynamical systems
Estimates
Exact sciences and technology
Feedback control
Feedback linearization
high-gain observers
Linear feedback control systems
Modelling and identification
Nonlinear dynamical systems
Nonlinear dynamics
Nonlinear systems
Observers
output feedback control
Performance gain
performance recovery
Perturbation methods
Signal design
State estimation
Studies
Tracking errors
Uncertainty
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Summary:We consider a tracking problem for a partially feedback linearizable nonlinear system with stable zero dynamics. The system is uncertain and only the output is measured. We use an extended high-gain observer of dimension n +1, where n is the relative degree. The observer estimates n derivatives of the tracking error, of which the first ( n -1) derivatives are states of the plant in the normal form and the n th derivative estimates the perturbation due to model uncertainty and disturbance. The controller cancels the perturbation estimate and implements a feedback control law, designed for the nominal linear model that would have been obtained by feedback linearization had all the nonlinearities been known and the signals been available. We prove that the closed-loop system under the observer-based controller recovers the performance of the nominal linear model as the observer gain becomes sufficiently high. Moreover, we prove that the controller has an integral action property in that it ensures regulation of the tracking error to zero in the presence of constant nonvanishing perturbation.
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2008.2006821