Retarded, neutral and advanced differential equation models for balancing using an accelerometer

Balazs A. Kovacs, Tamas Insperger

Research output: Contribution to journalArticle

4 Citations (Scopus)


Stabilization of a pinned pendulum about its upright position via a reaction wheel is considered, where the pendulum’s angular position is measured by a single accelerometer attached directly to the pendulum. The control policy is modeled as a simple PD controller and different feedback mechanisms are investigated. It is shown that depending on the modeling concepts, the governing equations can be a retarded functional differential equation or neutral functional differential equation or even advanced functional differential equation. These types of equations have radically different stability properties. In the retarded and the neutral case the system can be stabilized, but the advanced equations are always unstable with infinitely many unstable characteristic roots. It is shown that slight modeling differences lead to significant qualitative change in the behavior of the system, which is demonstrated by means of the stability diagrams for the different models. It is concluded that digital effects, such as sampling, stabilizes the system independently on the modeling details.

Original languageEnglish
Pages (from-to)694-706
Number of pages13
JournalInternational Journal of Dynamics and Control
Issue number2
Publication statusPublished - Jun 1 2018


  • Accelerometer
  • D-subdivision method
  • Feedback delay
  • Functional differential equations
  • Semi-discretization
  • Stabilization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Civil and Structural Engineering
  • Modelling and Simulation
  • Mechanical Engineering
  • Control and Optimization
  • Electrical and Electronic Engineering

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