A Class of Centrifugal Flywheel’s Chaos Mathematical Model and Its Linear Feedback Control

Abstract

Abstract:

Through the analysis of a class of centrifugal flywheel system,this paper gave its mathematical model.By analysing its complex dynamics, such as Lyapunov exponent spectrum, bifurcation diagram, Poincaré diagram,time-domain waveform diagram and the spectrogram,a chaotic mathematical model was established to describe the dynamic process.Then, the control of the centrifugal flywheel system can be converted into chaotic system control. It controlled the chaotic systems of the centrifugal flywheel system by the adaptive control method, and it achieved the goal through the simulation of MATLAB. The results show that chaotic system can be controlled well by adaptive control, and the system can come to a steady state. The control method can greatly improved dynamic performance and anti-disturbance capacity of the system.

Key words: centrifugal flywheel, chaotic system, linear feedback control, chaos control

摘要：

通过分析一类离心轮系统的非线性特性，在其对应数学模型的基础上进行复杂动力学分析得出其Poincaré映射图、Lyapunov指数图、时域波形图和分岔图，进而证明该模型是混沌数学模型，从而将此类离心轮系统控制转化为对混沌系统的控制，用线性反馈控制方法对此类离心轮的三种运行状态进行控制，利用MATLAB仿真实现了控制离心轮系统的目的。结果表明，利用线性反馈可以很好地消除混沌，使系统达到一个稳定的状态。该控制策略能有效地改善离心轮系统的动态性能，并能增强其鲁棒性与抗干扰能力。



关键词:

离心轮, 混沌系统, 线性反馈控制, 混沌控制

CLC Number:

TH133
TP202

CHEN Di-Yi, DAN,LIN,MA Xiao-Xi, CHEN Hai-Chao.

A Class of Centrifugal Flywheel’s Chaos Mathematical Model and Its Linear Feedback Control

[J]. China Mechanical Engineering, 2010, 21(24): 2932-2936.

陈帝伊, 石, 琳, 马孝义, 陈海涛.

一类离心轮系统的混沌数学模型及其线性反馈控制

[J]. 中国机械工程, 2010, 21(24): 2932-2936.

[1]	AI Shu-Feng. Bearing Fault Diagnosis Based on Multi-scale Hermitian Wavelet Envelope Spectrum [J]. China Mechanical Engineering, 2012, 23(1): 34-38.
[2]	HEI Dai, ZHENG Mei-Ru. Dynamics Analysis of Flexible Rotor System Based on Wilson-θ Method [J]. China Mechanical Engineering, 2011, 22(24): 2918-2922,2965.
[3]	AI Shu-Feng. Research on Bearing Fault Diagnosis Based on Dual-tree Complex Wavelet Transform [J]. China Mechanical Engineering, 2011, 22(20): 2446-2451.
[4]	SONG Shou-Hu, ZHANG Jing-Dong, LIU Zhi-Feng. Crack Initiation Period-based Rest Life Prediction of Typical Parts [J]. China Mechanical Engineering, 2011, 22(20): 2490-2494.
[5]	LI Wei-Wei-1, CHEN Xiao-Yang-1, CHEN Xue-Jin-1, ZHANG Xiao-Ling-2. Contact Pressure Calculation and Analysis of Roller Bearings in Skewing Condition [J]. China Mechanical Engineering, 2011, 22(17): 2034-2039.
[6]	LI Wei-Wei, CHEN Xiao-Yang, CHEN Xue-Jin. Numerical Calculation and Roller Pressure Analysis of Theoretical Logarithm Profile Equation [J]. China Mechanical Engineering, 2011, 22(15): 1788-1792.
[7]	YU Wei, LIN Cheng-Jie, LIU Qing-Chao, WANG Dong-Feng. Predicting Skid and Spin Power Loss in a High Speed Hybrid Ball Bearing [J]. China Mechanical Engineering, 2011, 22(6): 715-719.
[8]	YANG Chao-Jun, ZHENG Wu, LI Zhi-Teng, LI Zhi-Bao, JIANG Sheng-Fa. Performance Parameter Calculation of Adjustable Speed Asynchronous Disk Magnetic Coupling [J]. China Mechanical Engineering, 2011, 22(5): 604-608.
[9]	LI Yan, SHU Liang, XIAO Ji-Meng, LI Chu-Juan. Design of Raceway Groove Structure for Megawatt Wind Power Generator Yaw Bearings and Life Studies [J]. China Mechanical Engineering, 2011, 22(2): 132-137,143.
[10]	XIAO Hong, YANG Xia, CHEN Ze-Jun, WANG Jian. Application of Hertz Contact Theory in Analyzing Load Distribution of Mill Roller Bearing with Boundary Element Method [J]. China Mechanical Engineering, 2010, 21(21): 2532-2535,2540.
[11]	LI Sai-Cheng, CHEN Xiao-Yang, MA Chun-Qing, CHEN Ai-Hua. Contact Stress Analysis of Variable Curvature Arc Spherical Roller Bearings [J]. China Mechanical Engineering, 2010, 21(21): 2545-2550.
[12]	CHEN Xiao-Beng, HE Wei-Xing, MA Dong-Ling, DIAO De-An. Symbol Entropy and SVM Based Rolling Bearing Fault Diagnosis [J]. China Mechanical Engineering, 2010, 21(17): 2079-2082.
[13]	JIANG Ke-Jian, CHU Chang-Sheng. On-line Measurement of Supporting Characteristics of an Active Magnetic Levitations with Unknown Transfer Function [J]. China Mechanical Engineering, 2010, 21(8): 883-888.
[14]	ZHANG Ai, ZHANG Xiao-Zhang. A Review of Unbalance Control Technology of Active Magnetic Bearings  [J]. China Mechanical Engineering, 2010, 21(8): 897-903.
[15]	WANG Hong-Chao, GUO Lei-Lei, MO Li, XU Shuo-Yuan. Critical Speed Calculation of Rigid Rotor Supported by AMB [J]. China Mechanical Engineering, 2010, 21(8): 904-907.