Stability of Damped Skateboards under Human Control

Balazs Varszegi, Denes Takacs, G. Stépán

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A simple mechanical model of the skateboard-skater system is analyzed, in which a linear proportional-derivative (PD) controller with delay is included to mimic the effect of human control. The equations of motion of the nonholonomic system are derived with the help of the Gibbs-Appell method. The linear stability analysis of the rectilinear motion is carried out analytically in closed form. It is shown that how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as functions of the speed, position of the skater on the board, and damping of the skateboard suspension system. Based on these, an explanation is given for the experimentally observed dynamic behavior of the skateboard-skater system at high speed.

Original languageEnglish
Article number051014
JournalJournal of Computational and Nonlinear Dynamics
Volume12
Issue number5
DOIs
Publication statusPublished - Sep 1 2017

Fingerprint

Damped
Linear stability analysis
Nonholonomic Systems
Motion
Gain control
Linear Stability Analysis
Dynamic Behavior
Equations of motion
Equations of Motion
Damping
Closed-form
High Speed
Directly proportional
Derivatives
Controller
Derivative
Controllers
Human
Model

Keywords

  • human balancing
  • nonholonomic mechanics
  • skateboard
  • time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Stability of Damped Skateboards under Human Control. / Varszegi, Balazs; Takacs, Denes; Stépán, G.

In: Journal of Computational and Nonlinear Dynamics, Vol. 12, No. 5, 051014, 01.09.2017.

Research output: Contribution to journalArticle

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