scholarly journals Nonlinear Torsional Vibration Analysis and Nonlinear Feedback Control of Complex Permanent Magnet Semidirect Drive Cutting System in Coal Cutters

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Lianchao Sheng ◽  
Wei Li ◽  
Gaifang Xin ◽  
Yuqiao Wang ◽  
Mengbao Fan ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Permanent Magnet ◽  
Torsional Vibration ◽  
Multiple Scales ◽  
Sufficient Conditions ◽  
Harmonic Balance Method ◽  
System Stability ◽  
Nonlinear Feedback ◽  
Hopf Bifurcation Point ◽  
Coal Cutters

The semidirect drive cutting transmission system of coal cutters is prone to unstable torsional vibration when the resistance values of its driving permanent magnet synchronous motor (PMSM) are affected by changes in temperatures and tough conditions. Besides, the system has the properties of complex electromechanically coupling such as the coupling between electrical parameters and mechanical parameters. Therefore, in this study, the nonlinear torsional vibration equation was established on the basis of the Lagrange-Maxwell theory. Moreover, in light of the nonlinear dynamic bifurcation theory, the system stability was analyzed by taking the resistance value of power motor as the bifurcation parameter. In addition, the influence of subcritical bifurcation on the torsional vibration was studied by investigating the necessary and sufficient conditions for dynamic Hopf bifurcation and classifying the bifurcation types. At last, in order to suppress destabilizing oscillation induced by Hopf bifurcation, the nonlinear feedback controller was constructed, with the introduction of feedback from the motor velocity as well as the selection of voltage value on the q shaft as the controlled variable. Meanwhile, the three-order normal form and controlling parameters of the system were obtained with the aid of the multiple scales method and the harmonic balance method. In this way, the Hopf bifurcation point was transferred to control the stability of Hopf bifurcation and the amplitude of limit cycle, thus guaranteeing reliable and safe operation of the system. The numerical simulation results indicate that the designed controller boosts an ideal controlling effect.

Hopf Bifurcation Control for Rolling Mill Multiple-Mode-Coupling Vibration Under Nonlinear Friction

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Lingqiang Zeng ◽  
Yong Zang ◽  
Zhiying Gao
Keyword(s):  
Hopf Bifurcation ◽  
Rolling Mill ◽  
Gain Coefficient ◽  
Stability Domain ◽  
System Stability ◽  
Nonlinear Friction ◽  
Nonlinear Feedback ◽  
Nonlinear Gain ◽  
System Vibration ◽  
Linear And Nonlinear

Rolling mill system may lose its stability due to the change of lubrication conditions. Based on the rolling mill vertical–torsional–horizontal coupled dynamic model with nonlinear friction considered, the system stability domain is analyzed by Hopf bifurcation algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. In order to restrain the instability oscillation induced by the system Hopf bifurcation, a linear and nonlinear feedback controller is constructed, in which the uncoiling speed of the uncoiler is selected as the control variable, and variations of tensions at entry and exit as well as system vibration responses are chosen as feedback variables. On this basis, the linear control of the controller is studied using the Hopf bifurcation algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. The results show that the system stability domain can be expanded by reducing the linear gain coefficient. Through choosing an appropriate nonlinear gain coefficient, the occurring of the system subcritical bifurcation can be suppressed. And system vibration amplitudes reduce as the increase of the nonlinear gain coefficient. Therefore, introducing the linear and nonlinear feedback controller into the system can improve system dynamic characteristics significantly. The production efficiency and the product quality can be guaranteed as well.

Axial-Delayed Control of Nonlinear Resonance of Nanobeams with Graphene Sensor

2017 ◽  
Vol 17 (10) ◽  
pp. 1750116 ◽  
Author(s):  
Canchang Liu ◽  
Qian Ding ◽  
Qingmei Gong ◽  
Chicheng Ma ◽  
Shuchang Yue ◽  
...  
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Sufficient Conditions ◽  
Nonlinear Resonance ◽  
System Stability ◽  
Feedback Gain ◽  
Optimal Method ◽  
Voltage Signal ◽  
Attenuation Ratio

Nonlinear resonance response of an electrostatic-actuated nanobeam is controlled by using a delayed axial electrostatic force with near-half the natural frequency. A graphene sensor pasted on the surface of the nanobeam is used to extract the vibration voltage signal. An axial-delayed capacitive controller is designed to produce delayed axial force to control the nonlinear vibration of the nanobeam. The vibration voltage signal from the graphene sensor is input to the axial-delayed capacitive controller to attenuate the nonlinear vibration of the nanobeam. The dynamic response of the resonator is investigated by using the method of multiple scales directly. The sufficient conditions of guaranteeing the system stability and the saddle-node bifurcation are studied. The attenuation ratio is defined as the ratio of the peak amplitude of the nonlinear vibration system with control to that without control. A critical feedback gain is given, which can shift the frequency–amplitude curves from the nonlinear vibration to a linear vibration. An optimal method in which the attenuation ratio is taken as objective function and the aforementioned sufficient conditions as the constraint conditions is given to calculate the optimal feedback gains. Numerical simulations are conducted for uniform nanobeams.

scholarly journals Spatiotemporal dynamics for a diffusive mussel–algae model near a Hopf bifurcation point

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shihong Zhong ◽  
Xuehan Cheng ◽  
Biao Liu
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Turing Instability ◽  
Stability Conditions ◽  
Hopf Bifurcation Point ◽  
Bifurcation Theorem ◽  
Kinetic System ◽  
Existence And Stability

AbstractIn this paper, the Hopf bifurcation and Turing instability for a mussel–algae model are investigated. Through analysis of the corresponding kinetic system, the existence and stability conditions of the equilibrium and the type of Hopf bifurcation are studied. Via the center manifold and Hopf bifurcation theorem, sufficient conditions for Turing instability in equilibrium and limit cycles are obtained, respectively. In addition, we find that the strip patterns are mainly induced by Turing instability in equilibrium and spot patterns are mainly induced by Turing instability in limit cycles by numerical simulations. These provide a comprehension on the complex pattern formation of a mussel–algae system.

Research on bifurcation and control of electromechanical coupling torsional vibration for wheel-side direct-driven transmission system

2020 ◽  
Vol 235 (1) ◽  
pp. 93-104
Author(s):  
Jinyong Ju ◽  
Wei Li ◽  
Yufei Liu ◽  
Chunrui Zhang
Keyword(s):  
Torsional Vibration ◽  
Electromechanical Coupling ◽  
Linear Part ◽  
Transmission System ◽  
System Stability ◽  
Control Voltage ◽  
Nonlinear Feedback ◽  
Nonlinear Part ◽  
Wheel Side ◽  
And Control

Aiming to the torsional vibration destabilization phenomenon of the wheel-side transmission system direct-driven by the high-power motor, the system torsional vibration bifurcation characteristics and control strategy are analyzed. Through defining the system electromechanical coupling relationship between the electrical link and the mechanical link, the dynamic model of the wheel-side direct-driven transmission system is constructed. Then, based on the Routh–Hurwitz stability criterion, the system Hopf bifurcation characteristics caused by the change of the wheel-ground friction during driving are revealed. Furthermore, with the nonlinear feedback controller and the Washout filter combined, the system torsional vibration stabilization controller is constructed by introducing the system torsional vibration signals into the motor control voltage. The results show that the linear part of the torsional vibration stabilization controller can effectively change the system stability region, as well as the cubic nonlinear part of the torsional vibration stabilization controller can control the stability of the system bifurcation points and suppress the limit cycle amplitude. The research results can provide theoretical basis and technical support for the performance improvement and integrated application of the wheel-side direct-driven transmission system in the electric bus.

Parametric Resonance of Hopf Bifurcation in a Generalized Beck’s Column

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Achille Paolone ◽  
Francesco Romeo ◽  
Marcello Vasta
Keyword(s):  
Hopf Bifurcation ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Continuous Model ◽  
Follower Force ◽  
Phase Portraits ◽  
Perturbation Approach ◽  
Hopf Bifurcation Point ◽  
Dynamic Components

A generalized damped Beck’s column under pulsating actions is considered. The nonlinear partial integrodifferential equations of motion and the associated boundary conditions, expanded up to cubic terms, are tackled through a perturbation approach. The multiple scales method is applied to the continuous model in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. This codimension-2 bifurcation entails two control variables, namely, the amplitude of the static and dynamic components of the follower force, playing the role of detuning and bifurcation parameters, respectively. In the postcritical analysis bifurcation diagrams and relevant phase portraits are examined. Two bifurcation paths associated with specific values of the follower force static component are discussed and the birth of new stable period-2 subharmonic motion is observed.

scholarly journals Hopf bifurcation of a delayed worm model with two latent periods

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Juan Liu ◽  
Zizhen Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Sensor Network ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Worm Model ◽  
Distribution Of Roots ◽  
Influential Parameters

Abstract We investigate a delayed epidemic model for the propagation of worm in wireless sensor network with two latent periods. We derive sufficient conditions for local stability of the worm-induced equilibrium of the system and the existence of Hopf bifurcation by regarding different combination of two latent time delays as the bifurcation parameter and analyzing the distribution of roots of the associated characteristic equation. In particular, we investigate the direction and stability of the Hopf bifurcation by means of the normal form theory and center manifold theorem. To verify analytical results, we present numerical simulations. Also, the effect of some influential parameters of sensor network is properly executed so that the oscillations can be reduced and removed from the network.

scholarly journals Dynamical analysis of a giving up smoking model with time delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

scholarly journals Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Computer Network ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Form Theory ◽  
Worm Model ◽  
The Stability

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

Modified Hopf bifurcation index for power system stability assessment

2005 ◽  
Vol 152 (6) ◽  
pp. 906 ◽  
Author(s):  
M.A. Tomim ◽  
B.I.L. Lopes ◽  
R.C. Leme ◽  
R. Jovita ◽  
A.C. Zambroni de Souza ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Power System ◽  
Power System Stability ◽  
System Stability ◽  
Stability Assessment

Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Licai Wang ◽  
Yudong Chen ◽  
Chunyan Pei ◽  
Lina Liu ◽  
Suhuan Chen
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Critical Point ◽  
Control Parameter ◽  
Eigenvalue Problems ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
State Matrix ◽  
Aeroelastic System ◽  
Center Manifold Reduction

Abstract The feedback control of Hopf bifurcation of nonlinear aeroelastic systems with asymmetric aerodynamic lift force and nonlinear elastic forces of the airfoil is discussed. For the Hopf bifurcation analysis, the eigenvalue problems of the state matrix and its adjoint matrix are defined. The Puiseux expansion is used to discuss the variations of the non-semi-simple eigenvalues, as the control parameter passes through the critical value to avoid the difficulty for computing the derivatives of the non-semi-simple eigenvalues with respect to the control parameter. The method of multiple scales and center-manifold reduction are used to deal with the feedback control design of a nonlinear system with non-semi-simple eigenvalues at the critical point of the Hopf bifurcation. The first order approximate solutions are developed, which include gain vector and input. The presented methods are based on the Jordan form which is the simplest one. Finally, an example of an airfoil model is given to show the feasibility and for verification of the present method.

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