On the stabilizability of the delayed inverted pendulum controlled by finite spectrum assignment in case of parameter uncertainties

Tamás G. Molnár, T. Insperger

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

1 Citation (Scopus)

Abstract

An application of the Finite Spectrum Assignment (FSA) control technique is presented for an inverted pendulum with feedback delay. The FSA controller predicts the actual state of the system over the delay period using an internal model of the real system. If the internal model is perfectly accurate then the feedback delay can be compensated. However, slight parameter mismatch of the internal model may result in an unstable control process. In this paper, stabilizability of the inverted pendulum for different system and delay parameter mismatches are analyzed. It is shown that, for the same parameter uncertainties, the FSA controller allows stabilization for significantly larger feedback delays than a conventional delayed proportional-derivative controller does. In the analysis, it is assumed that the controller input is piecewise constant (sampled), this way the destabilizing effect of the difference part of the governing neutral functional differential equation is eliminated. The relation of the FSA controller to the Smith predictor is also described in time domain.

Original languageEnglish
Title of host publication9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers
Volume7 B
ISBN (Print)9780791855973
DOIs
Publication statusPublished - 2013
EventASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States
Duration: Aug 4 2013Aug 7 2013

Other

OtherASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013
CountryUnited States
CityPortland, OR
Period8/4/138/7/13

Fingerprint

Stabilizability
Inverted Pendulum
Parameter Uncertainty
Pendulums
Assignment
Feedback Delay
Controller
Controllers
Internal
Feedback
Smith Predictor
Neutral Functional Differential Equation
Process Control
Time Domain
Stabilization
Differential equations
Unstable
Directly proportional
Uncertainty
Model

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation

Cite this

Molnár, T. G., & Insperger, T. (2013). On the stabilizability of the delayed inverted pendulum controlled by finite spectrum assignment in case of parameter uncertainties. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 7 B). [V07BT10A059] American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2013-12316

On the stabilizability of the delayed inverted pendulum controlled by finite spectrum assignment in case of parameter uncertainties. / Molnár, Tamás G.; Insperger, T.

9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B American Society of Mechanical Engineers, 2013. V07BT10A059.

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

Molnár, TG & Insperger, T 2013, On the stabilizability of the delayed inverted pendulum controlled by finite spectrum assignment in case of parameter uncertainties. in 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. vol. 7 B, V07BT10A059, American Society of Mechanical Engineers, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013, Portland, OR, United States, 8/4/13. https://doi.org/10.1115/DETC2013-12316
Molnár TG, Insperger T. On the stabilizability of the delayed inverted pendulum controlled by finite spectrum assignment in case of parameter uncertainties. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B. American Society of Mechanical Engineers. 2013. V07BT10A059 https://doi.org/10.1115/DETC2013-12316
Molnár, Tamás G. ; Insperger, T. / On the stabilizability of the delayed inverted pendulum controlled by finite spectrum assignment in case of parameter uncertainties. 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B American Society of Mechanical Engineers, 2013.
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