Abstract:With certain connection randomness and coupling strength, the permanent magnet synchronous motors in Newman-Watts small-world (NWSW) networks fall into chaotic motion and threaten the secure and stable operation of the drive system. To control the undesirable chaos in complex motor networks, an adaptive controller based on pinning method is first presented. And then, the stability of the controlled system is proved by Lyapunov stability theory and the threshold values of parameter conditions for the onset of stability are obtained. Finally, the simulation results show that the proposed control law is correct and effective. Our research results are helpful to maintain the secure operation of drive system.
麦贤慧,韦笃取,罗晓曙. Newman-Watts型小世界电机网络混沌行为的牵制控制[J]. 复杂系统与复杂性科学, 2017, 14(1): 96-102.
MAI Xianhui, WEI Duqu, LUO Xiaoshu. Controlling Chaos in Newman-Watts Small-World Motor Networks by Pinning Method[J]. Complex Systems and Complexity Science, 2017, 14(1): 96-102.
[1] 邹国棠, 王政, 程明. 混沌电机驱动及其应用[M].北京: 科学出版社, 2009. [2] Wei D Q, Zhang B, Qiu D Y, et al. Nonlinear dynamics of permanent-magnet synchronous motor with v/f control[J].Communications in Theoretical Physics, 2013, 59(3): 302-306. [3] 于金鹏,于海生,高军伟,等.基于模糊逼近的永磁同步电机混沌控制[J].复杂系统与复杂性科学, 2013, 10 (4): 86-91. Yu Jinpeng, Yu Haisheng, Gao Junwei, et al. Chaos control of permanent magnet synchronous motors based on fuzzy-approximation[J].Complex Systems and Complexity Science, 2013, 10 (4): 86-91. [4] Blair D D, Jensen D L, Doan D R, et al. Networked intelligent motor-control systems[J].IEEE Industry Applications Magazine, 2001, 7(6): 18-25. [5] Walsh G C, Ye H. Scheduling of networked control systems[J].IEEE Control Systems, 2001, 21(1): 57-65. [6] Wei D Q, Luo X S, Zhang B. Chaos in complex motor networks induced by Newman-Watts small-world connections[J].Chin Phys B, 2011, 20(12): 128903. [7] Mai X H, Wei D Q, Zhang B, et al. Controlling chaos in complex motor networks by environment[J].IEEE Trans Circ Syst-Ⅱ, 2015, 62(6): 603-607. [8] 周涛, 张子柯, 陈关荣,等. 复杂网络研究的机遇与挑战[J].电子科技大学学报, 2014, 43(1): 1-5. Zhou Tao, Zhang Zike, Chen Guanrong, et al. The opportunities and challenges of complex networks research[J].Journal of University of Electronic Science and Technology of China, 2014, 43 (1): 1-5. [9] 陈关荣.漫谈系统与网络[J].复杂系统与复杂性科学, 2010, 7(2): 1-4. Chen Guanrong. A talk about systems and networks[J].Complex Systems and Complexity Science, 2010, 7(2): 1-4. [10] 方锦清,汪小帆,郑志刚. 非线性网络的动力学复杂性的研究[J].复杂系统与复杂性科学, 2010, 7(2/3): 5-9. Fang Jinqing, Wang Xiaofan, Zheng Zhigang. Research of dynamical complexity of nonlinear networks[J].Complex Systems and Complexity Science, 2010, 7(2/3): 5-9. [11] 汪小帆, 李翔, 陈关荣. 网络科学导论[M].北京: 高等教育出版社, 2012. [12] Wei D Q, Zhang B, Qiu D Y, et al. Effects of current time-delayed feedback on the dynamics of a permanent-magnet synchronous motor[J].IEEE Trans Circ Syst II, 2010, 57(6): 456-460. [13] Wei D Q, Zhang B, Qiu D Y, et al. Effects of couplings on the collective dynamics of permanent-magnet synchronous motors[J].IEEE Trans Circ Syst II, 2013, 60(10): 692-696. [14] Chen G, Wang X, Li X, Introduction to complex networks: models, structures and dynamics[M].Beijing: Higher Education Press, 2012. [15] Xiao Y, Tang S, Yang X. Adaptive synchronization of dynamical networks via states of several nodes as target orbit[J].Applied Mathematical Modelling, 2014, 38(15): 4148-4156. [16] Wang X F, Li X, Lu J H. Control and flocking of networked systems via pinning[J].IEEE Circuits and Systems Magazine, 2010, 10(3): 83-91. [17] Zhao J C, Lu J A, Wu X Q. Pinning control of general complex dynamical networks with optimization[J].Science China: Information Sciences, 2010, 53 (4): 813-822. [18] Yu W W, Chen G R, Lu J H, et al. Synchronization via pinning control on general complex networks[J].SIAM J Control Optim, 2013, 51(2): 1395-1416. [19] Song Q, Cao J, Yu W. Second-order leader-following consensus of nonlinear multi-agent systems via pinning control[J].Systems & Control Letters, 2010, 59(9): 553-562. [20] 潘玉剑,李翔, 时效复杂网络结构可控性研究[J].复杂系统与复杂性科学, 2015, 12(2): 23-31. Pan Yujjian, Li Xiang. On the structural controllability of temporal networks[J].Complex Systems and Complexity Science, 2015, 12(2): 23-31. [21] 王树国,姚洪兴, 具有时变拓扑结构的复杂网络的牵制控制[J].复杂系统与复杂性科学, 2012, 9(3): 76-81. Wang Shuguo, Yao Hongxing. Pinning synchronization of complex networks with time-varying topological structure[J].Complex Systems and Complexity Science, 2012, 9(3): 76-81. [22] Mai X H, Zhang B, Luo X S. Controlling chaos in complex motor networks by environment[J].Circuits and Systems II: Express Briefs, IEEE Transactions on, 2015, 62(6): 603-607. [23] Wang X F, Chen G R. Pinning control of scale-free dynamical networks[J].Physica A: Statistical Mechanics and Its Applications, 2002, 310(3/4):521-531. [24] Li X, Wang X F, Chen G R. Pinning a complex dynamical network to its equilibrium[J].IEEE Transactions on Circuits and Systems I: Regular Papers, 2004, 51(10): 2074-2087. [25] Wang X F, Li X, Lu J H. Control and flocking of networked systems via pinning[J].IEEE Circuits and Systems Magazine, 2010,10(3):83-91. [26] Zhou J, Lu J, Lu J H. Pinning adptive synchronization of a general complex dynamical network[J].Automatica, 2008, 44(4): 996-1003.