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Nonlinear Dynamics

, Volume 92, Issue 3, pp 885–903 | Cite as

Two-scale command shaping for feedforward control of nonlinear systems

  • J. Justin Wilbanks
  • Christopher J. Adams
  • Michael J. Leamy
Original Paper
  • 163 Downloads

Abstract

This paper presents a critical analysis of the two-scale command shaping (TSCS) feedforward control technique as applied to nonlinear Duffing oscillators. TSCS is an approach for tailoring a flexible system’s applied control input to reduce undesirable residual vibrations using multiple problem scales, command shaping of a linear subproblem, and cancelation of a remaining nonlinear subproblem. As shown herein, TSCS proves to be an effective method for feedforward control of nonlinear systems. The strategy outperforms conventional and nonlinearly informed command shaping strategies in traditional and non-traditional Duffing systems (e.g., Duffing systems with quadratic nonlinearity and Coulomb damping). The TSCS approach is also extended herein to nonlinear systems with uncertain parameters through the implementation of robust command shaping strategies and the extended Kalman filtering parameter estimation technique.

Keywords

Command shaping Perturbation Multiple scale Feedforward control Nonlinear Kalman filtering 

Notes

Acknowledgements

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1148903.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • J. Justin Wilbanks
    • 1
  • Christopher J. Adams
    • 1
  • Michael J. Leamy
    • 1
  1. 1.George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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