scholarly journals Stabilizing skateboard speed-wobble with reflex delay

2016 ◽  
Vol 13 (121) ◽  
pp. 20160345 ◽  
Author(s):  
Balazs Varszegi ◽  
Denes Takacs ◽  
Gabor Stepan ◽  
S. John Hogan
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Linear Instability ◽  
Uniform Motion ◽  
Rectilinear Motion ◽  
Neutral Delay ◽  
Human Control ◽  
Control Gain ◽  
Delay Differential ◽  
And Control

A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

Stability of Damped Skateboards Under Human Control

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Balazs Varszegi ◽  
Denes Takacs ◽  
Gabor Stepan
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Mechanical Model ◽  
High Speed ◽  
Nonholonomic System ◽  
Equations Of Motion ◽  
Uniform Motion ◽  
Rectilinear Motion ◽  
Pd Controller ◽  
Human Control

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.

scholarly journals Skateboard: A Human Controlled Non-Holonomic System

2015 ◽  
Author(s):  
Balazs Varszegi ◽  
Denes Takacs ◽  
Gabor Stepan
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Mechanical Model ◽  
High Speed ◽  
Equations Of Motion ◽  
Uniform Motion ◽  
Rectilinear Motion ◽  
Pd Controller ◽  
Holonomic System ◽  
Human Control

A simple mechanical model of the skateboard-skater system is analyzed, in which a linear PD controller with delay is included to mimic the effect of human control. The equations of motion of the non-holonomic system are derived with the help of the Gibbs-Appell method. The linear stability analysis of rectilinear motion is carried out analytically using the D-subdivision method. It is shown 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 a function of the speed and the fore-aft location of the skater on the board. Based on these, an explanation is given for the well-known instability of the skateboard-skater system at high speed.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Design and control of a high-speed direct-drive manipulator

1989 ◽  
Vol 27 (3) ◽  
pp. 375-394 ◽  
Author(s):  
K. YOUCEF-TOUMI ◽  
A. T. Y. KUO
Keyword(s):  
High Speed ◽  
Direct Drive ◽  
And Control
Sign in / Sign up

Export Citation Format

Share Document