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Research Papers

Oscillatory Tracking Control of a Class of Nonlinear Systems

[+] Author and Article Information
Zheng Wang

Department of Electrical and Computer Engineering,  Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030zwang4@stevens.edu

Yi Guo1

Department of Electrical and Computer Engineering,  Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030yguo1@stevens.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(3), 031011 (Apr 04, 2012) (6 pages) doi:10.1115/1.4005495 History: Received August 24, 2009; Accepted November 11, 2011; Published April 03, 2012; Online April 04, 2012

Vibration control is an effective alternative to conventional feedback and feedforward control. Motivated by its important application in physical systems and few results on general oscillatory tracking control, we consider tracking control of a class of nonlinear systems using oscillation in the paper. We propose a new oscillatory control design using general averaging analysis for the tracking problem. Based on the oscillation functions associated with accessible vibrating components of the system, oscillatory control is designed to track a desired trajectory. Comparing to existing oscillatory tracking control, our approach is robust to initial conditions. We show the effectiveness of the proposed method by two simulation examples, which include a second-order nonholonomic integrator and the inverted pendulum system. For the inverted pendulum system, we show that our designed oscillatory control does not need state feedback to track a desired trajectory, which is desirable for systems where state measurement is not feasible.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

State response of the nonholonomic integrator with the controls [Eq. 29]

Grahic Jump Location
Figure 2

Tracking errors of the nonholonomic integrator with the controls [Eq. 29]

Grahic Jump Location
Figure 3

State response of an inverted pendulum system with the oscillation control [Eq. 40]

Grahic Jump Location
Figure 4

Tracking errors of an inverted pendulum system with the oscillation control [Eq. 40]

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