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.

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.

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

Composite Nonlinear Feedback Control with Multi-objective Particle Swarm Optimization for Active Front Steering System

2015 ◽  
Vol 72 (2) ◽  
Author(s):  
Liyana Ramli ◽  
Yahaya Md. Sam ◽  
Zaharuddin Mohamed ◽  
M. Khairi Aripin ◽  
M. Fahezal Ismail
Keyword(s):  
Parameter Estimation ◽  
Particle Swarm Optimization ◽  
Nonlinear Feedback ◽  
Nonlinear Gain ◽  
Composite Nonlinear Feedback ◽  
Swarm Optimization ◽  
Vehicle Handling ◽  
Multi Objective ◽  
Yaw Rate ◽  
Active Front Steering

The purpose of controlling the vehicle handling is to ensure that the vehicle is in a safe condition and following its desire path. Vehicle yaw rate is controlled in order to achieve a good vehicle handling. In this paper, the optimal Composite Nonlinear Feedback (CNF) control technique is proposed for an Active Front Steering (AFS) system for improving the vehicle yaw rate response. The model used in order to validate the performance of controller is nonlinear vehicle model with 7 degree-of-freedom (DOF) and a bicycle model is implemented for the purpose of designing the controller. In designing an optimal CNF controller, the parameter estimation of linear and nonlinear gain becomes very important to produce the best output response. An intelligent algorithm is designed to minimize the time consumed to get the best parameter. To design an optimal method, Multi Objective Particle Swarm Optimization (MOPSO) is utilized to optimize the CNF controller performance. As a result, transient performance of the yaw rate has improved with the increased speed of in tracking and searching of the best optimized parameter estimation for the linear and the nonlinear gain of CNF controller.  

scholarly journals Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters

2020 ◽  
Vol 23 (02) ◽  
pp. 124-135
Author(s):  
Muhammad Haris ◽  
Muhammad Shafiq ◽  
Adyda Ibrahim ◽  
Masnita Misiran
Keyword(s):  
Closed Loop ◽  
Lyapunov Stability Theory ◽  
Feedback Controller ◽  
Control Signal ◽  
Stability And Convergence ◽  
Nonlinear Feedback ◽  
Nonlinear Part ◽  
Synchronization Errors ◽  
Novel Structure ◽  
Linear And Nonlinear

This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.

scholarly journals Comparing Combinations of Linear and Nonlinear Feedback Terms for Ship Motion Control

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 193813-193826
Author(s):  
Mikkel Eske Norgaard Sorensen ◽  
Morten Breivik ◽  
Roger Skjetne
Keyword(s):  
Motion Control ◽  
Ship Motion ◽  
Nonlinear Feedback ◽  
Linear And Nonlinear

scholarly journals Rendering a subcritical Hopf bifurcation supercritical

1996 ◽  
Vol 317 ◽  
pp. 91-109 ◽  
Author(s):  
Po Ki Yuen ◽  
Haim H. Bau
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Thermal Convection ◽  
Control Strategy ◽  
Chaotic Motion ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Naturally Occurring ◽  
Subcritical Hopf Bifurcation ◽  
Stable Periodic

It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.

The Motor Active Flexible Suspension and Its Dynamic Effect on the High-Speed Train Bogie

2017 ◽  
Vol 140 (6) ◽  
Author(s):  
Yuan Yao ◽  
Yapeng Yan ◽  
Zhike Hu ◽  
Kang Chen
Keyword(s):  
Control System ◽  
Time Delay ◽  
High Speed ◽  
State Feedback ◽  
State Feedback Control ◽  
System Stability ◽  
High Speed Train ◽  
Suspension Parameters ◽  
Linear And Nonlinear ◽  
Hunting Stability

We put forward the motor active flexible suspension and investigate its dynamic effects on the high-speed train bogie. The linear and nonlinear hunting stability are analyzed using a simplified eight degrees-of-freedom bogie dynamics with partial state feedback control. The active control can improve the function of dynamic vibration absorber of the motor flexible suspension in a wide frequency range, thus increasing the hunting stability of the bogie at high speed. Three different feedback state configurations are compared and the corresponding optimal motor suspension parameters are analyzed with the multi-objective optimal method. In addition, the existence of the time delay in the control system and its impact on the bogie hunting stability are also investigated. The results show that the three control cases can effectively improve the system stability, and the optimal motor suspension parameters in different cases are different. The direct state feedback control can reduce corresponding feed state's vibration amplitude. Suppressing the frame's vibration can significantly improve the running stability of bogie. However, suppressing the motor's displacement and velocity feedback are equivalent to increasing the motor lateral natural vibration frequency and damping, separately. The time delay over 10 ms in control system reduces significantly the system stability. At last, the effect of preset value for getting control gains on the system linear and nonlinear critical speed is studied.

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