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Research Papers

Transformation of a Mismatched Nonlinear Dynamic System into Strict Feedback Form

[+] Author and Article Information
Johanna L. Mathieu1

Department of Mechanical Engineering, University of California, Berkeley, 6141 Etcheverry Hall, MC 1740, Berkeley, CA 94720jmathieu@berkeley.edu

J. Karl Hedrick

Department of Mechanical Engineering, University of California, Berkeley, 6141 Etcheverry Hall, MC 1740, Berkeley, CA 94720khedrick@me.berkeley.edu

1

Correspoding author.

J. Dyn. Sys., Meas., Control 133(4), 041010 (Apr 11, 2011) (7 pages) doi:10.1115/1.4003795 History: Received July 23, 2010; Revised January 12, 2011; Published April 11, 2011; Online April 11, 2011

Dynamic surface control is a robust nonlinear control technique. It is generally applied to mismatched dynamic systems in strict feedback form. We have developed a new method of defining states and state-dependent disturbances to transform a mismatched dynamic system into strict feedback form. We apply this method to a multi-input multi-output (MIMO) extended-state kinematic model of a bicycle. We show how a dynamic surface controller can be used for position tracking of the bicycle. The performance of the dynamic surface controller is compared with that of a controller designed using feedback linearization. Transformation of the dynamic system into strict feedback form allows us to successfully apply dynamic surface control. Both the dynamic surface controller and the feedback linearization controller perform well in the absence of disturbances. The dynamic surface controller is more robust when disturbances are introduced; however, a large control effort is required to reject the disturbances. Our method of defining new states and state-dependent disturbances to transform mismatched nonlinear dynamic systems into strict feedback form could be used on other systems requiring robust nonlinear control.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of a bicycle

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Figure 2

Tracking error in x1 and x2 when MIMO FL and MIMO DSC are applied to the uncertain system

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Figure 3

Control inputs u2 and u4 and an approximation of u1 (computed from u4) when MIMO FL and MIMO DSC are applied to the uncertain system

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Figure 4

Sliding surfaces for x1 and x2. The stars indicate the point (0,0,0) and the arrows indicate the direction of increasing time. All surfaces converge to approximately zero.

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