Influence of Controller’s Parameters on Static Bifurcation of Magnetic-Liquid Double Suspension Bearing

Magnetic-Liquid Double Suspension Bearing (MLDSB) is composed of an electromagnetic supporting and a hydrostatic supporting system. Due to greater supporting capacity and static stiffness, it is appropriate for occasions of middle speed, overloading, and frequent starting. Because of the complicated structure of the supporting system, the probability and degree of static bifurcation of MLDSB can be increased by the coupling of hydrostatic force and electromagnetism force, and then the supporting capacity and operation stability are reduced. As the key part of MLDSB, the controller makes an important impact on its supporting capacity, operation stability, and reliability. Firstly, the mathematical model of MLDSB is established in the paper. Secondly, the static bifurcation point of MLDSB is determined, and the influence of parameters of the controller on singular point characteristics is analyzed. Finally, the influence of parameters of the controller on phase trajectories and basin of attraction is analyzed. The result showed that the pitchfork bifurcation will occur as proportional feedback coefficient Kp increases, and the static bifurcation point is Kp = −60.55. When Kp < −60.55, the supporting system only has one stable node (0, 0). When Kp > −60.55, the supporting system has one unstable saddle (0, 0) and two stable non-null focuses or nodes. The shape of the basin of attraction changed greatly as Kp increases from −60.55 to 30, while the outline of the basin of attraction is basically fixed as Kp increases from 30 to 80. Differential feedback coefficient Kd has no effect on the static bifurcation of MLDSB. The rotor phase trajectory obtained from theoretical simulation and experimental tests are basically consistent, and the error is due to the leakage and damping effect of the hydrostatic system within the allowable range of the engineering. The research in the paper can provide theoretical reference for static bifurcation analysis of MLDSB.

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Effect of the delay on the boundary of the basin of attraction in a Hopfield neural network system

PsycEXTRA Dataset ◽

10.1037/e429062008-001 ◽

2008 ◽

Keyword(s):

Neural Network ◽

Basin Of Attraction ◽

Hopfield Neural Network ◽

Network System ◽

Neural Network System ◽

The Basin Of Attraction

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Double Closed-Loop Compound Control Strategy for Magnetic Liquid Double Suspension Bearing

Processes ◽

10.3390/pr9071195 ◽

2021 ◽

Vol 9 (7) ◽

pp. 1195

Author(s):

Jianhua Zhao ◽

Yongqiang Wang ◽

Xuchao Ma ◽

Sheng Li ◽

Dianrong Gao ◽

...

Keyword(s):

Control Strategy ◽

Electromagnetic Force ◽

Closed Loop ◽

Static Characteristic ◽

Magnetic Liquid ◽

Initial Current ◽

Electromagnetic System ◽

Initial Flow ◽

Hydrostatic Force ◽

Position Feedback

As a new type of suspension bearing, the magnetic liquid double suspension bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic support. At present, the MLDSB adopts the regulation strategy of “electromagnetic-position feedback closed-loop, hydrostatic constant-flow supply” (referred to as CFC mode). In the equilibrium position, the external load is carried by the electromagnetic system, and the hydrostatic system produces no supporting force. Thus, the carrying capacity and supporting stiffness of the MLDSB can be reduced. To solve this problem, the double closed-loop control strategy of “electromagnetic system-force feedback inner loop and hydrostatic-position feedback outer loop” (referred to as DCL mode) was proposed to improve the bearing performance and operation stability of the MLDSB. First, the mathematical models of CFC mode and DCL mode of the single DOF supporting system were established. Second, the real-time variation laws of rotor displacement, flow/hydrostatic force, and regulating current/electromagnetic force in the two control modes were plotted, compared, and analyzed. Finally, the influence law of initial current, flow, and controller parameters on the dynamic and static characteristic index were analyzed in detail. The results show that compared with that in CFC mode, the displacement in DCL mode is smaller, and the adjustment time is shorter. The hydrostatic force is equal to the electromagnetic force in DCL mode when the rotor returns to the balance position. Moreover, the system in DCL mode has better robustness, and the initial flow has a more obvious influence on the dynamic and static characteristic indexes. This study provides a theoretical basis for stable suspension control and the safe and reliable operation of the MLDSB.

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Optimization and Stability of Heat Engines: The Role of Entropy Evolution

Entropy ◽

10.3390/e20110865 ◽

2018 ◽

Vol 20 (11) ◽

pp. 865 ◽

Cited By ~ 5

Author(s):

Julian Gonzalez-Ayala ◽

Moises Santillán ◽

Maria Santos ◽

Antonio Calvo Hernández ◽

José Mateos Roco

Keyword(s):

Local Stability ◽

Production Efficiency ◽

Basin Of Attraction ◽

Heat Engine ◽

Time Constraints ◽

Thermal Gradients ◽

Heat Engines ◽

Low Dissipation ◽

The Basin Of Attraction

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and power output. This allows considering stability and optimization as connected pieces of a single phenomenon. Trajectories inside the basin of attraction display the smallest entropy drops. Additionally, it was found that time constraints, related with irreversible and endoreversible behaviors, influence the thermodynamic evolution of relaxation trajectories. The behavior of the evolution in terms of the symmetries of the model and the applied thermal gradients was analyzed.

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Time Delay and Feedback Control of an Inverted Pendulum With Stick Slip Friction

Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2007-34904 ◽

2007 ◽

Cited By ~ 2

Author(s):

Sue Ann Campbell ◽

Stephanie Crawford ◽

Kirsten Morris

Keyword(s):

Time Delay ◽

Basin Of Attraction ◽

Critical Time ◽

Viscous Friction ◽

Experimental System ◽

Friction Model ◽

Stable Equilibrium Point ◽

Feedback Controllers ◽

Stick Slip ◽

The Basin Of Attraction

We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart which can move in one dimension. There is stick slip friction between the cart and the track on which it moves. Using two different models for this friction we design feedback controllers to stabilize the pendulum in the upright position. We show that controllers based on either friction model give better performance than one based on a simple viscous friction model. We then study the effect of time delay in this controller, by calculating the critical time delay where the system loses stability and comparing the calculated value with experimental data. Both models lead to controllers with similar robustness with respect to delay. Using numerical simulations, we show that the effective critical time delay of the experiment is much less than the calculated theoretical value because the basin of attraction of the stable equilibrium point is very small.

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Method to Estimate the Basin of Attraction and Speed Switch Control for the Underactuated Biped Robot

Climbing and Walking Robots ◽

10.5772/8824 ◽

2010 ◽

Author(s):

Yantao Tian ◽

Limei Liu ◽

Xiaoliang Huang ◽

Jianfei Li ◽

Zhen Sui

Keyword(s):

Basin Of Attraction ◽

Biped Robot ◽

Switch Control ◽

The Basin Of Attraction

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Global Determination of the Basin of Attraction

Lecture Notes in Mathematics - Construction of Global Lyapunov Functions Using Radial Basis Functions ◽

10.1007/978-3-540-69909-5_5 ◽

2007 ◽

pp. 115-132

Keyword(s):

Basin Of Attraction ◽

The Basin Of Attraction

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CHAOTIC CONTROL OF LOGISTIC MAP

Modern Physics Letters B ◽

10.1142/s0217984908016613 ◽

2008 ◽

Vol 22 (20) ◽

pp. 1941-1949 ◽

Cited By ~ 1

Author(s):

XINGYUAN WANG ◽

MINGJUN WANG

Keyword(s):

Periodic Orbit ◽

Dynamic System ◽

Bifurcation Point ◽

Logistic Map ◽

Bifurcation Control ◽

Chaotic Control ◽

Simulation Results ◽

Feedback Method ◽

Chaotic Logistic Map ◽

Feedback Coefficient

With the occasional feedback method, the chaotic logistic map is stabilized at an unstable low-periodic orbit. In our method, the qualified feedback coefficient can be obtained through calculation instead of through simulation. Besides, the bifurcation control of the logistic map is studied, and a new scheme is proposed to change the parameter value of any one bifurcation point of this dynamic system optionally. Simulation results show the effectiveness of the methods.

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Stable running of a planar underactuated biped robot

Robotica ◽

10.1017/s0263574710000512 ◽

2010 ◽

Vol 29 (5) ◽

pp. 657-665 ◽

Cited By ~ 14

Author(s):

Yong Hu ◽

Gangfeng Yan ◽

Zhiyun Lin

Keyword(s):

Limit Cycle ◽

Stance Phase ◽

Control Strategies ◽

Basin Of Attraction ◽

Biped Robot ◽

State Spaces ◽

Continuous State ◽

Event Based ◽

Telescopic Legs ◽

The Basin Of Attraction

SUMMARYThis paper investigates the stable-running problem of a planar underactuated biped robot, which has two springy telescopic legs and one actuated joint in the hip. After modeling the robot as a hybrid system with multiple continuous state spaces, a natural passive limit cycle, which preserves the system energy at touchdown, is found using the method of Poincaré shooting. It is then checked that the passive limit cycle is not stable. To stabilize the passive limit cycle, an event-based feedback control law is proposed, and also to enlarge the basin of attraction, an additive passivity-based control term is introduced only in the stance phase. The validity of our control strategies is illustrated by a series of numerical simulations.

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Basin of Attraction of the Simplest Walking Model

Volume 6A: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21363 ◽

2001 ◽

Author(s):

A. L. Schwab ◽

M. Wisse

Keyword(s):

Equations Of Motion ◽

Basin Of Attraction ◽

Mapping Method ◽

Walking Robots ◽

Natural Energy ◽

Walking Motion ◽

The Stability ◽

The Basin Of Attraction ◽

General Method ◽

Small Disturbances

Abstract Passive dynamic walking is an important development for walking robots, supplying natural, energy-efficient motions. In practice, the cyclic gait of passive dynamic prototypes appears to be stable, only for small disturbances. Therefore, in this paper we research the basin of attraction of the cyclic walking motion for the simplest walking model. Furthermore, we present a general method for deriving the equations of motion and impact equations for the analysis of multibody systems, as in walking models. Application of the cell mapping method shows the basin of attraction to be a small, thin area. It is shown that the basin of attraction is not directly related to the stability of the cyclic motion.

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