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.

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 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.

Sliding Mode Control in Ziegler’s Pendulum With Tracking Force: Novel Modeling Considerations

2013 ◽  
Author(s):  
Ehsan Sarshari ◽  
Nastaran Vasegh ◽  
Mehran Khaghani ◽  
Saeid Dousti
Keyword(s):  
Stability Analysis ◽  
Sliding Mode Control ◽  
Dynamic System ◽  
Linear Stability Analysis ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Sliding Mode Controller ◽  
Gravity Effect ◽  
Tracking Force

Ziegler’s pendulum is an appropriate model of a non-conservative dynamic system. By considering gravity effect, new equations of motion are extracted from Newton’s motion laws. The instability of equilibriums is determined by linear stability analysis. Chaotic behavior of the model is shown by numerical simulations. Sliding mode controller is used for eliminating chaos and for stabilizing the equilibriums.

Stability Analysis of High-Speed Railway Vehicle Based on Multibody Dynamics Analysis

2013 ◽  
Vol 392 ◽  
pp. 156-160
Author(s):  
Ju Seok Kang
Keyword(s):  
Stability Analysis ◽  
Multibody Dynamics ◽  
High Speed ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Dynamics Analysis ◽  
Contact Points ◽  
The Stability

Multibody dynamics analysis is advantageous in that it uses real dimensions and design parameters. In this study, the stability analysis of a railway vehicle based on multibody dynamics analysis is presented. The equations for the contact points and contact forces between the wheel and the rail are derived using a wheelset model. The dynamics equations of the wheelset are combined with the dynamics equations of the other parts of the railway vehicle, which are obtained by general multibody dynamics analysis. The equations of motion of the railway vehicle are linearized by using the perturbation method. The eigenvalues of these linear dynamics equations are calculated and the critical speed is found.

A 2D Simulation Method for Computing Droplet Size Spectrum During the Atomization of High-Speed Liquid Jets

2004 ◽  
Author(s):  
Gian Marco Bianchi ◽  
Piero Pelloni ◽  
Stefano Toninel ◽  
Davide Paganelli ◽  
Daniele Suzzi
Keyword(s):  
Sensitivity Analysis ◽  
Stability Analysis ◽  
Linear Stability ◽  
Droplet Size ◽  
Linear Stability Analysis ◽  
High Speed ◽  
Simulation Method ◽  
Droplet Formation ◽  
Size Spectrum ◽  
Computational Domain

Based on both experimental observations and available numerical methods, an innovative 2D approach for determining droplet size during the atomization process has been developed. Based on experimental evidences (see [1] and [2]) atomization of turbulent high speed jets is assumed to occur in a two stage process: ligaments detachment and droplets formation. The simulation method here proposed wants to take the advantages typical of the two most effective methods in spray investigation. It joins LES (i.e Large Eddy Simulations) approach and Linear Stability Analysis: the first one is used to solve the liquid-air fluid dynamics interaction and in particular the instabilities leading to ligament formation. The second one is finally adopted to compute the droplet size spectrum from ligament break-up. Therefore dynamics of ligament formation is directly computed while droplet formation is modelled by using a Linear Stability Analysis. The numerical simulation adopts a VOF (i.e. Volume of Fluid) method to track liquid-gas interface. Turbulence effects on liquid surface are accounted for by adding a turbulent flow field at the nozzle exit which represents a part of the boundary condition of the computational domain. A physical criterion is then applied to detach ligaments from liquid jet surface which will reduce in diameter during simulation. The droplet formation is then computed by applying the linear stability analysis to the ligaments, assumed being circular and subject to circulation. An extensive validation and sensitivity analysis has been carried out in order to assess method advantages and limits. The experimental results of Wu et al. [3] and Horoyasu et al. [4] were used as test cases. A sensitivity analysis has been performed under typical HSDI Diesel engine injection conditions. The method proved to exhibit promising attitude in the reconstruction of the droplet size spectrum depending on injection parameter or conditions.

scholarly journals Dynamical properties of forced shear layers in an annular geometry

2000 ◽  
Vol 402 ◽  
pp. 255-289 ◽  
Author(s):  
K. BERGERON ◽  
E. A. COUTSIAS ◽  
J. P. LYNOV ◽  
A. H. NIELSEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Initial Conditions ◽  
Landau Equation ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Radius Of Curvature ◽  
Simulation Code ◽  
Annular Geometry

Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvature, initial conditions, etc.) to characterize. This set of variables is limited after the code has been validated with experimental results (Rabaud & Couder 1983; Chomaz et al. 1988) and with the associated linear stability analysis. As part of the linear stability characterization, the pseudo-spectrum for the associated Orr–Sommerfeld operator for plane, circular Couette flow is calculated, and it is found to be insensitive to perturbations.The numerical simulation code is a highly accurate de-aliased spectral method which utilizes banded operators to increase the computational efficiency. Viscous dissipation terms enter the code directly from the equations of motion. The results from the simulation code at low Reynolds numbers are compared with the results from linear stability analysis and are used to give predictions for the coefficients of the Landau equation describing the saturation behaviour near the critical Reynolds number. Numerical results at higher Reynolds numbers demonstrate the effects of spin-up and spin-down, including the experimentally observed hysteresis. The properties of two- dimensional shears at high Reynolds numbers, at which temporal states are formed, are also addressed.

scholarly journals SIMULASI GERAK DAN ANALISIS KESTABILAN KOPLING INERSIA WAHANA DIRGANTARA DENGAN BENTUK BADAN RAMPING

2012 ◽  
Vol 9 (1) ◽  
Author(s):  
Hari Muhammad ◽  
Hilman Samputra ◽  
Yazdi I. Jenie ◽  
Javensius Sembiring
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Equations Of Motion ◽  
Flight Simulation ◽  
Slender Body ◽  
Fighter Aircraft ◽  
Low Aspect Ratio ◽  
Coupling Equations ◽  
Roll Rate ◽  
The Stability

 Inertia coupling is a motion phenomenon of a high-speed airplane having slender body and low aspect ratio. This inertia coupling happens when the aircraft performs a roll manoeuvre motion with a high roll rate. This paper will discuss the derivation of inertia coupling equations of motion, modelling equations of motion in the Matlab/Simulink software, simulating the dynamics motion, and analyzing the stability of the inertia coupling. Numerical simulation and stability analysis of the inertia coupling for a fighter aircraft will be presented in this paper. Keywords:Inertia coupling, Stability analysis, Flight simulation, Slender body

scholarly journals Optomechanics of a stable diffractive axicon light sail

2020 ◽  
Vol 135 (7) ◽  
Author(s):  
Prateek R. Srivastava ◽  
Grover A. Swartzlander
Keyword(s):  
Stability Analysis ◽  
Numerical Integration ◽  
Linear Stability ◽  
Radiation Pressure ◽  
Linear Stability Analysis ◽  
Diffraction Grating ◽  
Equations Of Motion ◽  
Longitudinal Force ◽  
Longitudinal Acceleration ◽  
Diffractive Axicon

Abstract Beamed propulsion of a light sail based on radiation pressure benefits from a passively self-stabilizing “beam riding” diffractive film. We describe the optomechanics of a rigid non-spinning light sail that mitigates catastrophic sail walk-off and tumbling by use of a flat axicon diffraction grating. A linear stability analysis and numerical integration of the coupled translational and rotational equations of motion are examined. Stability is traded against longitudinal acceleration. The examined system achieves 90% of the theoretical longitudinal force limit and stability against a relative sail translation up to 30% of the sail radius when the payload is attached to a long boom.

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