Poincaré map-based design

Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this chapter, Poincaré maps were used, to the best knowledge of the authors, for the first time as a design tool: to find controller parameters that provide the desired amplitude and frequency of the periodic motion of in systems having nonlinear plants, through the use of the TRC. We present application to an underactuated mechanical system via generating a self-excited oscillation of a desired amplitude and frequency of the unactuated position variable. Poincaré map design provides values of the TRC parameters and ensures local orbital stability of the periodic motions, for an arbitrary mechanical plant. The proposed approach is illustrated by the controller design for and experiments on the inertia wheel pendulum.

Original languageBritish English
Title of host publicationSystems and Control
Subtitle of host publicationFoundations and Applications
Number of pages14
StatePublished - 2015

Publication series

NameSystems and Control: Foundations and Applications
ISSN (Print)2324-9749
ISSN (Electronic)2324-9757


  • Controller design
  • Controller parameter
  • Orbital stability
  • Periodic motion
  • Periodic solution


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