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Design of an Approximate Control Law Using Input-State Linearization for the Ball on a Plate System

[+] Author Affiliations
Randy C. Hoover, Joe St. Amand

South Dakota School of Mines and Technology, Rapid City, SD

Paper No. IMECE2012-88418, pp. 203-212; 10 pages
doi:10.1115/IMECE2012-88418
From:
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 4: Dynamics, Control and Uncertainty, Parts A and B
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4520-2
  • Copyright © 2012 by ASME

abstract

This paper demonstrates an approximate full state feedback linearizing control law for the nonlinear ball on a plate system. It is shown that true full state feedback is not possible due both to the centrifugal acceleration terms and the nonlinear coupling between both coordinate axis. In an effort to make the system feedback linearizable, the dynamics corresponding to the centrifugal acceleration and the nonlinear coupling are simply treated as nonlinear disturbances to the original dynamics. The derived approximate full state feedback linearizing control law is evaluated via simulation of the original dynamics illustrating that the nonlinear disturbances are indeed small, and that the system controlled by the approximate control law is capable of more effective position and trajectory tracking than the standard Jacobian linearization.

Copyright © 2012 by ASME

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