Balancing using accelerometers and equations with advanced arguments

Tamas Insperger, Richard Wohlfart, Janos Turi, Gabor Stepan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The stick balancing problem is considered, where the vertical direction is measured using a single accelerometer attached to the stick. It is shown that the output is a linear combination of the angular position and the angular acceleration of the stick. If this output is fed back in a PD controller with feedback delay, then the governing equation of motion is an advanced functional differential equation, since the highest derivative, the jerk, appears with delayed argument through the derivative term. Autonomous equations with advanced arguments are typically non-causal and are unstable with infinitely many unstable poles. However, if the sampling effect of the digital controller is modeled, then the argument of the delayed highest derivative term is piecewise constant. In this case, the non-causality does not arise, and the system can also be stabilized by tuning the control parameters properly. In the paper, different models for stick balancing are considered and discussed by analyzing the corresponding stability diagrams.

Original languageEnglish
Title of host publication9th IFAC Workshop on Time Delay Systems, TDS 2010 - Proceedings
PublisherIFAC Secretariat
Pages103-108
Number of pages6
EditionPART 1
ISBN (Print)9783902661715
DOIs
Publication statusPublished - 2010
Event9th IFAC Workshop on Time Delay Systems, TDS 2010 - Prague, Czech Republic
Duration: Jun 7 2010Jun 9 2010

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670

Other

Other9th IFAC Workshop on Time Delay Systems, TDS 2010
CountryCzech Republic
CityPrague
Period6/7/106/9/10

Keywords

  • Accelerometers
  • Advanced functional differential equations
  • Feedback delay
  • Sampled data
  • Stability domains

ASJC Scopus subject areas

  • Control and Systems Engineering

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  • Cite this

    Insperger, T., Wohlfart, R., Turi, J., & Stepan, G. (2010). Balancing using accelerometers and equations with advanced arguments. In 9th IFAC Workshop on Time Delay Systems, TDS 2010 - Proceedings (PART 1 ed., pp. 103-108). (IFAC Proceedings Volumes (IFAC-PapersOnline); No. PART 1). IFAC Secretariat. https://doi.org/10.3182/20100607-3-cz-4010.00020