0
RESEARCH PAPERS

Development of a Feedback Linearization Technique for Parametrically Excited Nonlinear Systems via Normal Forms

[+] Author and Article Information
Yandong Zhang

Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, Auburn, AL 36849zhangya@auburn.edu

S. C. Sinha

Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, Auburn, AL 36849ssinha@eng.auburn.edu

J. Comput. Nonlinear Dynam 2(2), 124-131 (Dec 08, 2006) (8 pages) doi:10.1115/1.2447190 History: Received April 26, 2006; Revised December 08, 2006

The problem of designing controllers for nonlinear time periodic systems via feedback linearization is addressed. The idea is to find proper coordinate transformations and state feedback under which the original system can be (exactly or approximately) transformed into a linear time periodic control system. Then a controller can be designed to guarantee the stability of the system. Our approach is designed to achieve local control of nonlinear systems with periodic coefficients desired to be driven either to a periodic orbit or to a fixed point. The system equations are represented by a quasi-linear system containing nonlinear monomials with periodic coefficients. Using near identity transformations and normal form theory, the original close loop problem is approximately transformed into a linear time periodic system with unknown gains. Then by using a symbolic computation method, the Floquet multipliers are placed in the desired locations in order to determine the control gains. We also give the sufficient conditions under which the system is feedback linearizable up to the rth order.

FIGURES IN THIS ARTICLE
<>
Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

The uncontrolled system

Grahic Jump Location
Figure 2

The controlled system

Grahic Jump Location
Figure 3

The uncontrolled system

Grahic Jump Location
Figure 4

The controlled system

Grahic Jump Location
Figure 5

The closed loop system with parameter perturbations

Grahic Jump Location
Figure 6

Coupled pendulums

Grahic Jump Location
Figure 7

The uncontrolled system

Grahic Jump Location
Figure 8

The controlled system

Grahic Jump Location
Figure 9

The closed loop system with parameter perturbations

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In