On the Stability of a Periodic Hamiltonian System with One Degree of Freedom in a Transcendental Case

2018 ◽  
Vol 97 (2) ◽  
pp. 161-163 ◽  
Author(s):  
B. S. Bardin
Keyword(s):  
Hamiltonian System ◽  
Degree Of Freedom ◽  
The Stability ◽  
Periodic Hamiltonian System

scholarly journals New time delay estimation-based virtual decomposition control for n-DoF robot manipulator

2021 ◽  
Vol 10 (3) ◽  
pp. 192
Author(s):  
Hachmia Faqihi ◽  
Khalid Benjelloun ◽  
Maarouf Saad ◽  
Mohammed Benbrahim ◽  
M. Nabil Kabbaj
Keyword(s):  
Time Delay ◽  
Dynamic Model ◽  
Control Strategy ◽  
Robot Manipulator ◽  
Time Delay Estimation ◽  
Lyapunov Theory ◽  
Degree Of Freedom ◽  
Delay Estimation ◽  
The Stability

<p>One of the most efficient approaches to control a multiple degree-of-freedom robot manipulator is the virtual decomposition control (VDC). However, the use of the re- gressor technique in the conventionnal VDC to estimate the unknown and uncertaities parameters present some limitations. In this paper, a new control strategy of n-DoF robot manipulator, refering to reorganizing the equation of the VDC using the time delay estimation (TDE) have been investigated. In the proposed controller, the VDC equations are rearranged using the TDE for unknown dynamic estimations. Hence, the decoupling dynamic model for the manipulator is established. The stability of the overall system is proved based on Lyapunov theory. The effectiveness of the proposed controller is proved via case study performed on 7-DoF robot manipulator and com- pared to the conventionnal Regressor-based VDC according to some evalution criteria. The results carry out the validity and efficiency of the proposed time delay estimation- based virtual decomposition controller (TD-VDC) approach.</p>

Relationship between the Steady-Handling Characteristics of Automobiles and Their Stability

1973 ◽  
Vol 15 (5) ◽  
pp. 326-328 ◽  
Author(s):  
R. S. Sharp
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Degree Of Freedom ◽  
Nonlinear Region ◽  
Handling Characteristics ◽  
Yield Information ◽  
Turning Motion ◽  
The Stability ◽  
Three Degree Of Freedom

Analyses of the steady-state handling behaviour of an automobile and the stability of its steady-turning motion, based on a three degree of freedom mathematical model, are used to show that the steady behaviour and the stability are related similarly in the nonlinear region as in the well documented linear one. It is concluded that analysis and measurement of the steady behaviour will yield information on the stability of automobiles.

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

scholarly journals Photonic Nanojets and Whispering Gallery Modes in Smooth and Corrugated Micro-Cylinders under Point-Source Illumination

Photonics ◽  
2020 ◽  
Vol 7 (3) ◽  
pp. 50
Author(s):  
Ibrahim Mahariq ◽  
Thabet Abdeljawad ◽  
Abdullah S. Karar ◽  
Shadi A. Alboon ◽  
Hamza Kurt ◽  
...  
Keyword(s):  
Point Source ◽  
Source Location ◽  
Degree Of Freedom ◽  
Whispering Gallery Modes ◽  
Additional Degree ◽  
Whispering Gallery ◽  
Source Illumination ◽  
Photonic Nanojets ◽  
The Stability

We numerically investigate the generation of photonic nanojets (PNJs) and the excitation of whispering gallery modes (WGMs) supported by both smooth and corrugated dielectric micro-cylinders under point-source illumination. Results show that the location of the point-source defines the location and properties of PNJs, whereas stability of WGMs exists in smooth micro-cylinders but vanishes in corrugated ones. It is shown that the location of the point-source acts as an additional degree of freedom for controlling the characteristics of the generated PNJs for both smooth and corrugated dielectric micro-cylinders. Furthermore, the influence of the point-source location on the stability of the excited WGMs was diminished for the smooth micro-cylinders, while being fully pronounced for their corrugated counterparts.

Stability Criteria for Nonclassically Damped Systems With Nonlinear Uncertainties

2004 ◽  
Vol 71 (5) ◽  
pp. 632-636 ◽  
Author(s):  
D. Q. Cao ◽  
Y. M. Ge ◽  
Y. R. Yang
Keyword(s):  
Output Feedback Control ◽  
Degree Of Freedom ◽  
Asymptotically Stable ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Lyapunov Approach ◽  
Nonlinear Uncertainties ◽  
The Stability ◽  
Damped Systems ◽  
Stable Linear

The asymptotic stability of nonclassically damped systems with nonlinear uncertainties is addressed using the Lyapunov approach. Bounds on nonlinear perturbations that maintain the stability of an asymptotically stable, linear multi-degree-of-freedom system with nonclassical damping are derived. The explicit nature of the construction permits us to directly express the algebraic criteria in terms of plant parameters. The results are then applied to the symmetric output feedback control of multi-degree-of-freedom systems with nonlinear uncertainties. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.

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