无轴承异步电机非线性滤波器自适应逆解耦控制
|
摘要
针对无轴承异步电机(bearingless induction motor,BIM)多变量、非线性、强耦合的问题,提出了基于非线性自适应滤波器的无轴承异步电机自适应逆解耦控制策略。在分析了无轴承异步电机工作原理的基础上,推导出无轴承异步电机的数学模型,基于自适应逆控制原理,利用非线性自适应滤波器,分别建立转矩系统和悬浮系统的模型和逆模型。复制逆模型,将其串联在对应系统之前作为逆控制器,并采用变步长最小均方(least mean square,LMS)算法在线调整权值。相比于传统的磁场定向控制方法,此方法不必依靠转矩系统来传递磁链信息,从而避免了各自的控制策略之间的相互制约问题。基于MATLAB/Simulink仿真平台,对无轴承异步电机的转子磁链、转速、转矩、悬浮响应进行了仿真分析。仿真结果证明了该方法的有效性,实现了无轴承异步电机旋转力与悬浮力之间的解耦,而且能够实现两自由度径向悬浮力之间、转速与转子磁链之间的动态解耦。该研究可为基于无轴承异步电机的农业生产设备的研发提供参考。
For agricultural motor drive applications, reliability and stability are very significant, and even under disturbance condition, stable drive operation is essential. In view of the characteristics of the bearingless induction motor, which includes multi-variables, nonlinearity and high coupling, an adaptive inverse decoupling control strategy for the bearingless induction motor based on the nonlinear adaptive filter was proposed to improve the efficiency and reliability of the motor drives. First, the mathematical model of a bearingless induction motor was deduced through analyzing the generation mechanism of a bearingless induction motor's radial levitation force. By adopting the control theory of an adaptive inverse control system and the principle of a nonlinear adaptive filter, the model and inverse model of the torque system and levitation system were established respectively, including the option of the structure of nonlinear adaptive filter and the adaptive algorithm. Based on the inverse model, the adaptive inverse controller which cascaded in front of the corresponding system was designed by making use of the algorithm of variable step size least mean square(LMS) to adjust the weighting factors online. The difference between the given input signal and the system output signal was used as the error signal of the adaptive algorithm of variable step size LMS. In addition, compared to the traditional field oriented control method, this method did not need to rely on torque system to transfer flux information, which avoided the mutual restriction among the control strategies, and solved the coupling problem between the variables in the modeling process. Then, aiming at the performances of rotor flux, speed, torque and levitation response, the simulation and analysis of the adaptive inverse control system for the bearingless induction motor wew carried out on the basis of MATLAB/Simulink simulation platform. Moreover, the initial given value of motor speed was set to 2 000 r/min, the initial value of rotor flux-linkage was 0.65 Wb, the initial radial displacement in horizontal direction was 0.1 mm, and the initial radial displacement in vertical direction was-0.15 mm. The simulation results showed that the stable levitation of the bearingless induction motor could be quickly achieved by this control strategy. Through the comparison with inverse system control, the speed response was faster, and the speed overshooting was smaller in the adaptive inverse control. Further, when the rotor speed suddenly changed from 2 000 to 4 000 r/min at the time of 0.3 s, the speed response of the control system could track the given speed well with a very small steady state error. The magnitude of the error was about 50 r/min. The levitation performance of the rotor was not affected by the sudden change in the load torque. When the radial displacement in horizontal direction changed from 0.1 to 0.01 mm at the time of 0.45 s, the speed response and the radial displacement in vertical direction were nearly unchanged. The simulation results also proved the correctness and effectiveness of the proposed adaptive inverse control method, which achieved the decoupling between rotating force and levitation force of the bearingless induction motor, the dynamic decoupling between the two freedom degrees of the radial levitation force, and the dynamic decoupling between rotational speed and rotor flux linkage. The control system has a fine dynamic and static performance. This research provides the reference for the development of agricultural equipment with the bearingless induction motor.
For agricultural motor drive applications, reliability and stability are very significant, and even under disturbance condition, stable drive operation is essential. In view of the characteristics of the bearingless induction motor, which includes multi-variables, nonlinearity and high coupling, an adaptive inverse decoupling control strategy for the bearingless induction motor based on the nonlinear adaptive filter was proposed to improve the efficiency and reliability of the motor drives. First, the mathematical model of a bearingless induction motor was deduced through analyzing the generation mechanism of a bearingless induction motor's radial levitation force. By adopting the control theory of an adaptive inverse control system and the principle of a nonlinear adaptive filter, the model and inverse model of the torque system and levitation system were established respectively, including the option of the structure of nonlinear adaptive filter and the adaptive algorithm. Based on the inverse model, the adaptive inverse controller which cascaded in front of the corresponding system was designed by making use of the algorithm of variable step size least mean square(LMS) to adjust the weighting factors online. The difference between the given input signal and the system output signal was used as the error signal of the adaptive algorithm of variable step size LMS. In addition, compared to the traditional field oriented control method, this method did not need to rely on torque system to transfer flux information, which avoided the mutual restriction among the control strategies, and solved the coupling problem between the variables in the modeling process. Then, aiming at the performances of rotor flux, speed, torque and levitation response, the simulation and analysis of the adaptive inverse control system for the bearingless induction motor wew carried out on the basis of MATLAB/Simulink simulation platform. Moreover, the initial given value of motor speed was set to 2 000 r/min, the initial value of rotor flux-linkage was 0.65 Wb, the initial radial displacement in horizontal direction was 0.1 mm, and the initial radial displacement in vertical direction was-0.15 mm. The simulation results showed that the stable levitation of the bearingless induction motor could be quickly achieved by this control strategy. Through the comparison with inverse system control, the speed response was faster, and the speed overshooting was smaller in the adaptive inverse control. Further, when the rotor speed suddenly changed from 2 000 to 4 000 r/min at the time of 0.3 s, the speed response of the control system could track the given speed well with a very small steady state error. The magnitude of the error was about 50 r/min. The levitation performance of the rotor was not affected by the sudden change in the load torque. When the radial displacement in horizontal direction changed from 0.1 to 0.01 mm at the time of 0.45 s, the speed response and the radial displacement in vertical direction were nearly unchanged. The simulation results also proved the correctness and effectiveness of the proposed adaptive inverse control method, which achieved the decoupling between rotating force and levitation force of the bearingless induction motor, the dynamic decoupling between the two freedom degrees of the radial levitation force, and the dynamic decoupling between rotational speed and rotor flux linkage. The control system has a fine dynamic and static performance. This research provides the reference for the development of agricultural equipment with the bearingless induction motor.
引文
[1]Hiromi T,Katou T,Chiba A,et al.Anovel magnetic suspension-force compensation in bearingless inductionmotor drive with squirrel-cage rotor[J].IEEE Transactions on Industry Applications,2007,43(1):66-76.
[2]Henzel M,Falkowski K,Zokowski M.The analysis of the control system for the bearingless induction electric motor[J].Journal of Vibroengineering,2012,14(1):16-21.
[3]Victor V F,Quintaes F O,Lopes J S B,et al.Analysis and study of a bearingless AC motor type divided winding,based on a conventional squirrel cage induction motor[J].IEEETransactions on Magnetics,2012,48(11):3571-3574.
[4]Chiba A,Asama J.Influence of rotor skew in induction type bearingless motor[J].IEEE Transactions on Magnetics,2012,48(11):4646-4649.
[5]Schuhmann T,Hofmann W,Werner R.Improving operational performance of active magnetic bearings using Kalman filter and state feedback control[J].IEEE Transactions on Industrial Electronics,2012,59(2):821-829.
[6]诸德宏.交流磁轴承支承电主轴系统设计与控制研究[D].镇江:江苏大学,2009.Zhu Dehong.Design and control research for electric spindle supported by AC active magnetic bearings[D].Zhenjiang:Jiangsu University,2009.(in Chinese with English abstract)
[7]邓智泉,何礼高,严仰光.无轴承交流电机的原理及应用[J].机械科学与技术,2002,21(5):730-733.Deng Zhiquan,He Ligao,Yan Yangguang.The principle and applications of bearingless AC motors[J].Mechanical Science and Technology,2002,21(5):730-733.(in Chinese with English abstract)
[8]李大兴,夏革非,张华东,等.基于混合转子结构和悬浮力控制的新型飞轮储能用无轴承电机[J].电工技术学报,2015,30(1):48-52.Li Daxing,Xia Gefei,Zhang Huadong,et al.A novel bearingless motor with hybrid rotor structure and levitation force control for flywheel energy storage supporting system[J].Transactions of China Electrotechnical Society,2015,30(1):48-52.(in Chinese with English abstract)
[9]Kobayashi S,Ooshima M,Uddin M.N.A radial position control of bearingless motor based on d-q-axis current control[J].IEEE Transactions on Industry Applications,2013,49(4):1827-1835.
[10]邓智泉,王晓琳,张宏荃,等.无轴承异步电机的转子磁场定向控制[J].中国电机工程学报,2003,23(3):89-92.Deng Zhiquan,Wang Xiaolin,Zhang Hongquan,et al.The nonlinear control of bearingless induction motors based on the motor rotor flux orientation[J].Proceedings of the CSEE,2003,23(3):89-92.(in Chinese with English abstract)
[11]王少杰,卜文绍,翟利利,等.无轴承异步电机的定子电流矢量定向转子磁链估计[J].微电机,2012,45(8):14-17.Wang Shaojie,Bu Wenshao,Zhai Lili,et al.Rotor flux estimation of stator current vector orientation of bearingless induction motor[J].Micromotors,2012,45(8):14-17.(in Chinese with English abstract)
[12]Bu Wenshao,Wang Shaojie,Zu Conglin,et al.Rotor flux estimation method of bearingless induction motor based on stator current vector orientation[C]//IEEE International Conference on Automation and Logistics.Zhengzhou,China,2012:437-441.
[13]卜文绍,乔岩珂,祖从林,等.三相无轴承异步电机的磁场定向控制[J].电机与控制学报,2012,16(7):52-57.Bu Wenshao,Qiao Yanke,Zu Conglin,et al.Flux orientation control of three-phase bearingless induction motor[J].Electric Machines and Control,2012,16(7):52-57.(in Chinese with English abstract)
[14]郑静文,刘贤兴.无轴承异步电机气隙磁场定向的优化控制[J].电机与控制应用,2011,38(6):15-20.Zheng Jingwen,Liu Xianxing.Air-gap-flux orientated optimized control of bearingless asynchronous motor[J].Electric Machines&Control Application,2011,38(6):15-20.(in Chinese with English abstract)
[15]Zhu Huangqiu,Zhou Yang,Li Tianbo,et al.Decoupling control of 5 degrees of freedom bearingless induction motors usingα-th order inverse system[J].Acta Automatica Sinica,2007,33(3):273-278.
[16]Bu Wenshao,Lu Chunxiao,Zu Conglin,et al.Research on dynamic decoupling control method of three-phase bearingless induction motor[J].International Journal of Control and Automation,2014,7(5):77-86.
[17]尹忠刚,刘静,钟彦,等.基于双参数模型参考自适应的感应电机无速度传感器矢量控制低速性能[J].电工技术学报,2012,27(7):124-130.Yin Zhonggang,Liu Jing,Zhong Yan,et al.Low-speed performance for induction motor sensorless vector control based on Two-Parameter model reference adaptation[J].Transactions of China Electrotechnical Society,2012,27(7):124-130.(in Chinese with English abstract)
[18]陈波,吴政球.基于约束因子限幅控制的双馈感应发电机有功功率平滑控制[J].中国电机工程学报,2011,31(27):131-137.Chen Bo,Wu Zhengqiu.Power smoothing control strategy of doubly-fed induction generator based on constraint factor extent-limit control[J].Proceedings of the CSEE,2011,31(27):131-137.(in Chinese with English abstract)
[19]杨泽斌,汪明涛,孙晓东.基于自适应模糊神经网络的无轴承异步电机控制[J].农业工程学报,2014,30(2):78-86.Yang Zebin,Wang Mingtao,Sun Xiaodong.Control system of bearingless induction motors based on adaptive neuro-fuzzy inference system[J].Transactions of the Chinese Society of Agricultural Engineering,2014,30(2):78-86.(in Chinese with English abstract)
[20]王正齐,刘贤兴.基于神经网络逆系统的无轴承异步电机非线性内模控制[J].自动化学报,2013,39(4):433-439.Wang Zhengqi,Liu Xianxing.Nonlinear internal model control for bearingless induction motor based on neural network inversion[J].Acta Automatica Sinica,2013,39(4):433-439.(in Chinese with English abstract)
[21]Sun Xiaodong,Zhu Huangqiu.Artificial neural networks inverse control of 5 degrees of freedom bearingless induction motor[J].International Journal of Modeling,Identification and Control,2012,15(3):156-163.
[22]杨泽斌,孙晓东,张新华,等.无轴承异步电机最小二乘支持向量机逆解耦控制[J].江苏大学学报(自然科学版),2013,34(2):184-189.
[23]汪明涛,杨泽斌.基于二基波法的无轴承异步电机径向悬浮力研究[J].微电机,2013,46(7):6-10.Wang Mingtao,Yang Zebin.Study on radial force of bearingless induction motor based on two fundamental[J].Micromotors,2013,46(7):6-10.(in Chinese with English abstract)
[24]Widrow B,Walach E.Adaptive Inverse Control[M].New Jersey:Prentice Hall,1996.
[25]Sun Xiaodong,Zhu Huangqiu,Pan Wei.Decoupling control of bearingless permanent magnet-type synchronous motor using artificial neural networks-based inverse system method[J].International Journal of Modelling,Identification and Control,2009,8(2):114-121.
[26]吴国辉,曾伟,代冀阳.适于变步长LMS自适应滤波的遗传算法[J].自动化仪表,2012,33(12):17-20.Wu Guohui,Zeng Wei,Dai Jiyang.Variable step size LMSalgorithm optimized by using genetic algorithm[J].Process Automation Instrumentation,2012,33(12):17-20.(in Chinese with English abstract)
[27]赵宏飞,马宏忠,陈楷,等.用于变电站噪声有源控制的一种算法研究[J].电工电能新技术,2014,33(10):70-74.Zhao Hongfei,Ma Hongzhong,Chen Kai,et al.Study on algorithm for active noise control in substation[J].Advanced Technology of Electrical Engineering and Energy,2014,33(10):70-74.(in Chinese with English abstract)
[28]张晶晶,周菲菲,许帅.改进的变步长LMS改进算法[J].现代电子技术,2014,37(1):11-13.Zhang Jingjing,Zhou Feifei,Xu Shuai.Improved variable step size LMS improved algorithm[J].Modern Electronics Technique,2014,37(1):11-13.(in Chinese with English abstract)
[29]沈大伟,贺思,李正宙,等.一种改进的变步长变更新速率LMS自适应滤波算法及仿真[J].电子质量,2010(12):11-15.Shen Dawei,He Si,Li Zhengzhou,et al.A modified variable step size and multi-rate updated LMS adaptive filtering algorithm and its simulation[J].Electronics Quality,2010(12):11-15.(in Chinese with English abstract)
[30]Li L,Park I M,Brockmeier A,et al.Adaptive inverse control of neural spatiotemporal spike patterns with a reproducing kernel hilbert space(RKHS)framework[J].IEEETransactions on Neural System and Rehabilitation Engineering,2013,21(4):532-543.
[31]Wang Tiechao,Tong Shaocheng,Yi Jianqiang,et al.Adaptive inverse control of cable-driven parallel system based on type-2 fuzzy logic systems[J].IEEE Transactions on Fuzzy Systems,2015,23(5):1803-1816.
[32]Li Peng,Wang Xubin,Lee W J,et al.Dynamic power conditioning method of microgrid via adaptive inverse control[J].IEEE Transactions on Power Delivery,2015,30(2):906-913.
[33]耿洁,陈振,刘向东,等.永磁同步电机的自适应逆控制[J].电工技术学报,2011,26(6):51-55.Geng Jie,Chen Zhen,Liu Xiangdong,et al.Adaptive inverse control of permanent magnet synchronous motor[J].Transactions of China Electrotechnical Society,2011,26(6):51-55.(in Chinese with English abstract)
[2]Henzel M,Falkowski K,Zokowski M.The analysis of the control system for the bearingless induction electric motor[J].Journal of Vibroengineering,2012,14(1):16-21.
[3]Victor V F,Quintaes F O,Lopes J S B,et al.Analysis and study of a bearingless AC motor type divided winding,based on a conventional squirrel cage induction motor[J].IEEETransactions on Magnetics,2012,48(11):3571-3574.
[4]Chiba A,Asama J.Influence of rotor skew in induction type bearingless motor[J].IEEE Transactions on Magnetics,2012,48(11):4646-4649.
[5]Schuhmann T,Hofmann W,Werner R.Improving operational performance of active magnetic bearings using Kalman filter and state feedback control[J].IEEE Transactions on Industrial Electronics,2012,59(2):821-829.
[6]诸德宏.交流磁轴承支承电主轴系统设计与控制研究[D].镇江:江苏大学,2009.Zhu Dehong.Design and control research for electric spindle supported by AC active magnetic bearings[D].Zhenjiang:Jiangsu University,2009.(in Chinese with English abstract)
[7]邓智泉,何礼高,严仰光.无轴承交流电机的原理及应用[J].机械科学与技术,2002,21(5):730-733.Deng Zhiquan,He Ligao,Yan Yangguang.The principle and applications of bearingless AC motors[J].Mechanical Science and Technology,2002,21(5):730-733.(in Chinese with English abstract)
[8]李大兴,夏革非,张华东,等.基于混合转子结构和悬浮力控制的新型飞轮储能用无轴承电机[J].电工技术学报,2015,30(1):48-52.Li Daxing,Xia Gefei,Zhang Huadong,et al.A novel bearingless motor with hybrid rotor structure and levitation force control for flywheel energy storage supporting system[J].Transactions of China Electrotechnical Society,2015,30(1):48-52.(in Chinese with English abstract)
[9]Kobayashi S,Ooshima M,Uddin M.N.A radial position control of bearingless motor based on d-q-axis current control[J].IEEE Transactions on Industry Applications,2013,49(4):1827-1835.
[10]邓智泉,王晓琳,张宏荃,等.无轴承异步电机的转子磁场定向控制[J].中国电机工程学报,2003,23(3):89-92.Deng Zhiquan,Wang Xiaolin,Zhang Hongquan,et al.The nonlinear control of bearingless induction motors based on the motor rotor flux orientation[J].Proceedings of the CSEE,2003,23(3):89-92.(in Chinese with English abstract)
[11]王少杰,卜文绍,翟利利,等.无轴承异步电机的定子电流矢量定向转子磁链估计[J].微电机,2012,45(8):14-17.Wang Shaojie,Bu Wenshao,Zhai Lili,et al.Rotor flux estimation of stator current vector orientation of bearingless induction motor[J].Micromotors,2012,45(8):14-17.(in Chinese with English abstract)
[12]Bu Wenshao,Wang Shaojie,Zu Conglin,et al.Rotor flux estimation method of bearingless induction motor based on stator current vector orientation[C]//IEEE International Conference on Automation and Logistics.Zhengzhou,China,2012:437-441.
[13]卜文绍,乔岩珂,祖从林,等.三相无轴承异步电机的磁场定向控制[J].电机与控制学报,2012,16(7):52-57.Bu Wenshao,Qiao Yanke,Zu Conglin,et al.Flux orientation control of three-phase bearingless induction motor[J].Electric Machines and Control,2012,16(7):52-57.(in Chinese with English abstract)
[14]郑静文,刘贤兴.无轴承异步电机气隙磁场定向的优化控制[J].电机与控制应用,2011,38(6):15-20.Zheng Jingwen,Liu Xianxing.Air-gap-flux orientated optimized control of bearingless asynchronous motor[J].Electric Machines&Control Application,2011,38(6):15-20.(in Chinese with English abstract)
[15]Zhu Huangqiu,Zhou Yang,Li Tianbo,et al.Decoupling control of 5 degrees of freedom bearingless induction motors usingα-th order inverse system[J].Acta Automatica Sinica,2007,33(3):273-278.
[16]Bu Wenshao,Lu Chunxiao,Zu Conglin,et al.Research on dynamic decoupling control method of three-phase bearingless induction motor[J].International Journal of Control and Automation,2014,7(5):77-86.
[17]尹忠刚,刘静,钟彦,等.基于双参数模型参考自适应的感应电机无速度传感器矢量控制低速性能[J].电工技术学报,2012,27(7):124-130.Yin Zhonggang,Liu Jing,Zhong Yan,et al.Low-speed performance for induction motor sensorless vector control based on Two-Parameter model reference adaptation[J].Transactions of China Electrotechnical Society,2012,27(7):124-130.(in Chinese with English abstract)
[18]陈波,吴政球.基于约束因子限幅控制的双馈感应发电机有功功率平滑控制[J].中国电机工程学报,2011,31(27):131-137.Chen Bo,Wu Zhengqiu.Power smoothing control strategy of doubly-fed induction generator based on constraint factor extent-limit control[J].Proceedings of the CSEE,2011,31(27):131-137.(in Chinese with English abstract)
[19]杨泽斌,汪明涛,孙晓东.基于自适应模糊神经网络的无轴承异步电机控制[J].农业工程学报,2014,30(2):78-86.Yang Zebin,Wang Mingtao,Sun Xiaodong.Control system of bearingless induction motors based on adaptive neuro-fuzzy inference system[J].Transactions of the Chinese Society of Agricultural Engineering,2014,30(2):78-86.(in Chinese with English abstract)
[20]王正齐,刘贤兴.基于神经网络逆系统的无轴承异步电机非线性内模控制[J].自动化学报,2013,39(4):433-439.Wang Zhengqi,Liu Xianxing.Nonlinear internal model control for bearingless induction motor based on neural network inversion[J].Acta Automatica Sinica,2013,39(4):433-439.(in Chinese with English abstract)
[21]Sun Xiaodong,Zhu Huangqiu.Artificial neural networks inverse control of 5 degrees of freedom bearingless induction motor[J].International Journal of Modeling,Identification and Control,2012,15(3):156-163.
[22]杨泽斌,孙晓东,张新华,等.无轴承异步电机最小二乘支持向量机逆解耦控制[J].江苏大学学报(自然科学版),2013,34(2):184-189.
[23]汪明涛,杨泽斌.基于二基波法的无轴承异步电机径向悬浮力研究[J].微电机,2013,46(7):6-10.Wang Mingtao,Yang Zebin.Study on radial force of bearingless induction motor based on two fundamental[J].Micromotors,2013,46(7):6-10.(in Chinese with English abstract)
[24]Widrow B,Walach E.Adaptive Inverse Control[M].New Jersey:Prentice Hall,1996.
[25]Sun Xiaodong,Zhu Huangqiu,Pan Wei.Decoupling control of bearingless permanent magnet-type synchronous motor using artificial neural networks-based inverse system method[J].International Journal of Modelling,Identification and Control,2009,8(2):114-121.
[26]吴国辉,曾伟,代冀阳.适于变步长LMS自适应滤波的遗传算法[J].自动化仪表,2012,33(12):17-20.Wu Guohui,Zeng Wei,Dai Jiyang.Variable step size LMSalgorithm optimized by using genetic algorithm[J].Process Automation Instrumentation,2012,33(12):17-20.(in Chinese with English abstract)
[27]赵宏飞,马宏忠,陈楷,等.用于变电站噪声有源控制的一种算法研究[J].电工电能新技术,2014,33(10):70-74.Zhao Hongfei,Ma Hongzhong,Chen Kai,et al.Study on algorithm for active noise control in substation[J].Advanced Technology of Electrical Engineering and Energy,2014,33(10):70-74.(in Chinese with English abstract)
[28]张晶晶,周菲菲,许帅.改进的变步长LMS改进算法[J].现代电子技术,2014,37(1):11-13.Zhang Jingjing,Zhou Feifei,Xu Shuai.Improved variable step size LMS improved algorithm[J].Modern Electronics Technique,2014,37(1):11-13.(in Chinese with English abstract)
[29]沈大伟,贺思,李正宙,等.一种改进的变步长变更新速率LMS自适应滤波算法及仿真[J].电子质量,2010(12):11-15.Shen Dawei,He Si,Li Zhengzhou,et al.A modified variable step size and multi-rate updated LMS adaptive filtering algorithm and its simulation[J].Electronics Quality,2010(12):11-15.(in Chinese with English abstract)
[30]Li L,Park I M,Brockmeier A,et al.Adaptive inverse control of neural spatiotemporal spike patterns with a reproducing kernel hilbert space(RKHS)framework[J].IEEETransactions on Neural System and Rehabilitation Engineering,2013,21(4):532-543.
[31]Wang Tiechao,Tong Shaocheng,Yi Jianqiang,et al.Adaptive inverse control of cable-driven parallel system based on type-2 fuzzy logic systems[J].IEEE Transactions on Fuzzy Systems,2015,23(5):1803-1816.
[32]Li Peng,Wang Xubin,Lee W J,et al.Dynamic power conditioning method of microgrid via adaptive inverse control[J].IEEE Transactions on Power Delivery,2015,30(2):906-913.
[33]耿洁,陈振,刘向东,等.永磁同步电机的自适应逆控制[J].电工技术学报,2011,26(6):51-55.Geng Jie,Chen Zhen,Liu Xiangdong,et al.Adaptive inverse control of permanent magnet synchronous motor[J].Transactions of China Electrotechnical Society,2011,26(6):51-55.(in Chinese with English abstract)