Equilibrium-torus bifurcation in nonsmooth systems

2008 ◽  
Vol 237 (7) ◽  
pp. 930-936 ◽  
Author(s):  
Zhanybai T. Zhusubaliyev ◽  
Erik Mosekilde
Keyword(s):  
Nonsmooth Systems ◽  
Torus Bifurcation

Torus Bifurcation in Uni-Directional Coupled Gyroscopes

2009 ◽  
pp. 463-468
Author(s):  
Huy Vu ◽  
Antonio Palacios ◽  
Visarath In ◽  
Adi Bulsara ◽  
Joseph Neff ◽  
...  
Keyword(s):  
Torus Bifurcation

Impact Control in Hydraulic Actuators

2004 ◽  
Vol 127 (2) ◽  
pp. 197-205 ◽  
Author(s):  
P. Sekhavat ◽  
Q. Wu ◽  
N. Sepehri
Keyword(s):  
Lyapunov Stability Theory ◽  
Control Law ◽  
Asymptotic Convergence ◽  
Hydraulic Parameters ◽  
Hydraulic Actuators ◽  
Task Control ◽  
Nonsmooth Systems ◽  
Type Contact ◽  
The Stability ◽  
Short Transition

Every manipulator contact task that begins with a transition from free motion to constraint motion may exhibit impacts that could drive the system unstable. Stabilization of manipulators during this transition is, therefore, an important issue in contact task control design. This paper presents a discontinuous controller to regulate the transition mode in hydraulic actuators. The controller, upon sensing a nonzero force, positions the actuator at the location where the force was sensed, thus, exerting minimal force on a nonmoving environment. The scheme does not require force or velocity feedback as they are difficult to measure throughout the short transition phase. Also, no knowledge about the environment or hydraulic parameters is required for control action. Due to the discontinuity of the control law, the control system is nonsmooth. First, the existence, continuation and uniqueness of Filippov’s solution to the system are proven. Next, the extension of Lyapunov stability theory to nonsmooth systems is employed to guarantee the global asymptotic convergence of the entire system’s state towards the equilibrium point. Complete dynamic characteristics of hydraulic functions and Hertz-type contact model are included in the stability analysis. Experiments are conducted to verify the practicality and effectiveness of the proposed controller. They include actuator collisions with hard and soft environments and with various approach velocities.

EXPERIMENTAL INVESTIGATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

2012 ◽  
Vol 22 (05) ◽  
pp. 1250110 ◽  
Author(s):  
GUILIN WEN ◽  
HUIDONG XU ◽  
LU XIAO ◽  
XIAOPING XIE ◽  
ZHONG CHEN ◽  
...  
Keyword(s):  
Dynamical Behavior ◽  
Degree Of Freedom ◽  
Modeling And Analysis ◽  
Strongly Nonlinear ◽  
Impact System ◽  
Dynamical Behaviors ◽  
Nonsmooth Systems ◽  
Experimental Apparatus ◽  
Thick Steel ◽  
Two Degree Of Freedom

Vibro-impact systems with intermittent contacts are strongly nonlinear. The discontinuity of impact can give rise to rich nonlinear dynamic behaviors and bring forth challenges in the modeling and analysis of this type of nonsmooth systems. The dynamical behavior of a two-degree-of-freedom vibro-impact system is investigated experimentally in this paper. The experimental apparatus is composed of two spring-linked oscillators moving on a lead rail. One of the two oscillators connected to an excitation system intermittently impacts with a spherical obstacle fixed on the thick steel wall. With different gap sizes between the impacting oscillator and the obstacle, the dynamical behaviors are investigated by changing the excitation frequencies. The experimental results show periodic, grazing and chaotic dynamical behaviors of the vibro-impact system.

Invariant manifolds for nonsmooth systems

2012 ◽  
Vol 241 (22) ◽  
pp. 1895-1902 ◽  
Author(s):  
D. Weiss ◽  
T. Küpper ◽  
H.A. Hosham
Keyword(s):  
Invariant Manifolds ◽  
Nonsmooth Systems

scholarly journals Averaging of nonsmooth systems using dither

Automatica ◽  
2006 ◽  
Vol 42 (4) ◽  
pp. 669-676 ◽  
Author(s):  
Luigi Iannelli ◽  
Karl Henrik Johansson ◽  
Ulf T. Jönsson ◽  
Francesco Vasca
Keyword(s):  
Nonsmooth Systems
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