无轴承永磁同步电机无位置传感器及控制研究
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摘要
无轴承电机集旋转与转子自悬浮功能于一体,具有无需润滑、无磨损、无机械噪声、高速高精等特点,在精密数控机床、航空航天、飞轮储能等高科技领域有广泛的应用前景。相比其他类型的无轴承电机,无轴承永磁同步电机具有结构简单、高功率密度、高效率、运行可靠等优点,成为目前无轴承电机技术的研究热点之一。传统机械式传感器的安装与使用不仅使电机体积增大、成本增加,更严重限制了无轴承永磁同步电机优良高速性能的发挥。与普通永磁同步电机相比,无轴承永磁同步电机稳定运行时转子处于自悬浮状态,外界扰动、参数摄动等因素使转子位置、速度及径向位移更容易产生振动和突变。突破机械式传感器约束,实现全速范围内无位置传感器稳定悬浮运行及高性能控制对实现无轴承永磁同步电机超高速、低成本、实用化运行具有重要的意义。基于上述背景,本文在国家863高技术研究发展计划(2007AA04Z13)和国家自然科学基金(60974053)等项目资助下,对无轴承永磁同步电机数学模型、转子磁场定向控制、自适应非奇异终端滑模控制、无位置传感器运行、全数字控制实验平台设计及试验运行进行重点研究,主要研究工作及取得的成果如下：
1.对二自由度表贴式无轴承永磁同步电机中悬浮力产生机理进行深入分析,从麦克斯韦张量法出发,建立转子偏心时悬浮力精确解析模型,从机电能量转换关系推导考虑转子偏心与悬浮绕组电流影响的电磁转矩数学模型。从转子动力学出发,建立转子运动方程及系统运动方程。
2.提出一种自适应非奇异终端滑模控制方法。设计自适应变速指数趋近律,通过引入系统状态变量的一阶范数,根据系统状态距离平衡点位置的远近自适应增大指数趋近速度,缩短趋近时间,在快速趋近的同时,自动减小等速趋近速度,从而保证系统在到达切换面时削弱系统抖振,采用该趋近律设计无轴承永磁同步电机转子速度与径向位移非奇异终端滑模控制器,能够更快速地跟踪速度及径向位移给定值,并对外界扰动及参数摄动有较强的鲁棒性。
3.针对平方根无迹卡尔曼滤波存在对模型参数变化鲁棒性差、收敛速度慢及对突变状态跟踪能力低等缺陷,提出一种改进平方根无迹卡尔曼滤波算法。结合强跟踪滤波原理,通过引入时变渐消因子在线自适应调整增益矩阵和状态预测误差协方差平方根矩阵,实现残差序列正交或近似正交,强迫平方根无迹卡尔曼滤波保持对实际状态的快速跟踪。在滤波过程中采用矩阵QR分解和Cholesky因子更新,以协方差平方根阵代替协方差阵参加迭代运算,有效地避免了滤波器发散,提高滤波算法收敛速度和稳定性。应用该方法设计无轴承永磁同步电机转子位置与速度估计器,可以提高系统对平稳状态、转速突变状态及外界扰动下的估计精度。
4.针对单一转速估计方法难以实现全速范围内转子位置与速度准确估计的缺陷,提出一种转子位置与速度复合估计方法。对于表贴式无轴承永磁同步电机,在零速及低速运行时,采用脉振高频信号注入法估计转子位置与速度,该方法不依赖于电机模型参数而仅依赖于电机本身的凸极特性,可实现零速及低速时转子位置与速度的准确估计；中高速运行时,采用改进平方根无迹卡尔曼滤波进行转子位置与速度估计,利用强跟踪滤波极强的模型失配鲁棒性,独特的强跟踪能力,有效地改善系统对稳态及突变状态的跟踪性能,通过设计两种方法的“软切换”,实现低速到高速的平滑过渡,从而实现全速范围内转子位置与速度的准确估计。
5.针对传统旋转高频信号注入法中信号处理精度低、延时时间长及过程复杂等缺陷,提出一种基于有限冲激响应优化滤波的改进型旋转高频信号注入法。通过离线设计等纹波最佳逼近有限冲激响应滤波器,利用该滤波器提取高频电流信号,实现高频电流信号提取误差更小。通过对高频电流做外差处理,提取转子位置误差信号,省去旋转高频信号注入法中的同步轴系滤波单元。针对有限冲激响应滤波器相位滞后,设计线性相位补偿,缩短系统延时时间。该方法结构简单,估计精度高,易于调试与实现,可实现转子位置与速度的准确估计。
6.构建了无轴承永磁同步电机全数字控制实验平台,对其硬件设计及软件流程进行详细阐述。采用空间电压矢量脉宽调制技术实现转子磁场定向控制,进行电机调速、转速突变状态下的悬浮运行试验,设计无位置传感器自适应非奇异终端滑模控制详细实现方案,为进一步开展无轴承永磁同步电机无位置传感器高性能控制奠定基础。
Bearingless motors not only have the functions of rotation and rotor self suspension, but also have the characteristics of no lubrication, no wear, no mechanical noise, high speed and high precision. With these advantages, bearingless motors have broad application prospect in high speed precision numerical control machine tools, aerospace, flywheel energy storage system and other high-tech fields. Compared with other type of bearingless motors, the bearingless permanent magnet synchronous motor, due to its advantages of simple structure, high power density, high efficiency, reliable operation, has become one of the hot spots in the research field of bearingless motors presently. The installation and use of the traditional mechanical sensors has maken the motor volume increase, cost increase, at the same time, it has seriously limited the excellent performance of high speed to the bearingless permanent magnet synchronous motor. Compared with ordinary permanent magnet synchronous motor, the rotor is self-suspension, when the bearingless permanent magnet synchronous motor work at steady state, rotor position, speed and radial displacement are more prone to vibrate and mutate because of the external disturbance, parameter perturbation and other factors. The stable operation without position sensor and high performance control will meet the requirement of ultra high speed, low cost and practical application of the bearingless permanent magnet synchronous motor. Supported by the National High Technology Research and Development Plan of China (2007AA04Z213) and the National Natural Science Foundation of China under grant(60974053), in order to improve the performance of bearingless permanent magnet synchronous motor, several key theoretical and technological problems, such as the mathematical model, rotor magnetic field orientated control, adaptive nonsingular terminal sliding mode control, position sensorless operation in full speed, and digital control system of bearingless permanent magnet synchronous motor and experimental operation are comprehensively studied. The main researches and the corresponding achievement are as follows:
1. A profound analysis on the generation of magnetic levitation forces for a surface-mounted bearingless permanent magnet synchronous motor with two degree of freedom is presented. From Maxwell tensor method, levitation force analytical model is deduced considering the rotor eccentricity. The mathematical model of electromagnetic torque is derived from the electromechanical energy conversion relationship considering rotor eccentricity and suspension winding current, motion equations of the rotor and systems are established.
2. An adaptive nonsingular terminal sliding mode control is put forward. In order to obtain faster convergence of state variables during the whole process in nonsingular terminal sliding mode control, an adaptive variable-rated exponential reaching law is presented where the L1norm of state variables is introduced. Exponential and constant approach speed can adaptively adjust according to the state variables' distance to the equilibrium position, which can short the reaching time and weak system chattering. The method is applied to the bearingless permanent magnet synchronous motor system, speed and radial displacement controller of adaptive nonsingular terminal sliding mode control are designed, simulation results show that, the proposed adaptive nonsingular terminal sliding mode controller could rapidly track the given values, system overshoot and static error are small, higher robustness can be obtained.
3. Aiming at the defects of low robustness to model parameter variation, slow convergence, and undesirable tracking ability to abrupt state changes in square root unscented Kalman filter algorithm, an improved square root unscented Kalman filter is proposed. Combined with the strong tracking filtering principle, by introducing the time-varying fading factor and the diminishing factor to adjust gain matrices and the state-forecast covariance square root matrix, in order to realize the orthogonality of the residual sequences and force the square root unscented Kalman filter to track the real state rapidly. In the process of filtering, Cholesky and QR decomposition are used. Covariance square root matrix is used instead of covariance in iterative computation, which can effectively avoid the filter divergence and improve the algorithm convergence speed and stability. The vector control system for bearingless permanent magnet synchronous motor without a speed sensor is set up based on this approach. Rotor position and speed estimators designed by this method, can improve the estimate accuracy at stationary state, speed mutation status and the external disturbance.
4. Because of one method cannot obtain precise estimation of rotor speed and position in full speed, a compound method using high frequency signal injection and improved square root unscented Kalman filter algorithm is proposed to estimate the rotor speed and position for a surface-mounted bearingless permanent magnet synchronous motor. When the motor work at state of zero and ultra-low speed, fluctuating high frequency signal injection is used, which does not depend on the motor parameter, only depend on motor space-saliency effect, accurate estimation will be achieved; at the high speed, the improved square root unscented Kalman filter is used. The improved square root unscented Kalman filter has strong robustness of the model mismatch and unique strong tracking ability, which can effectively improve the tracking performance to steady state and mutation status. By designing speed switch, smooth switching is achieved. The proposed method is capable of precisely estimating rotor speed and position in full speed.
5. Aiming at the defects of low precision, long delay and complicated process in the signal processing of traditional rotating high frequency signal injection method, an improved rotation high frequency signal injection method based on finite impulse response filter is proposed. Equiripple and optimal approximating finite impulse response filter is introduced to extract the high frequency current, which can realize minimum extraction error of the high frequency current signal. Using heterodyning processing to the high frequency current, the rotor position error signal can be extracted. This method can eliminate the synchronous shaft filter and reduce the complexity of the system.In order to achieve minimum delay of rotor speed and position estimation, linear phase compensation is used in the finite impulse response filter. The method has the advantages of simple structure, high accuracy, easy realization and debugging, accurate estimation of rotor position and speed can be obtained.
6. The digital control system of bearingless permanent magnet synchronous motor is designed, the corresponding hardware systems and software systems are designed. The space voltage vector pulse width modulation is used to realize the rotor magnetic field orientated control strategy. Stable suspension operation in speed adjustment and speed step are achieved in the platform. Detailed experiment scheme for position sensorless control of bearingless permanent magnet synchronous motor based on adaptive nonsingular terminal sliding mode control is proposed, which establishes a solid foundation for developing the high performance position sensorless control of the bearingless permanent magnet synchronous motor further.
1.对二自由度表贴式无轴承永磁同步电机中悬浮力产生机理进行深入分析,从麦克斯韦张量法出发,建立转子偏心时悬浮力精确解析模型,从机电能量转换关系推导考虑转子偏心与悬浮绕组电流影响的电磁转矩数学模型。从转子动力学出发,建立转子运动方程及系统运动方程。
2.提出一种自适应非奇异终端滑模控制方法。设计自适应变速指数趋近律,通过引入系统状态变量的一阶范数,根据系统状态距离平衡点位置的远近自适应增大指数趋近速度,缩短趋近时间,在快速趋近的同时,自动减小等速趋近速度,从而保证系统在到达切换面时削弱系统抖振,采用该趋近律设计无轴承永磁同步电机转子速度与径向位移非奇异终端滑模控制器,能够更快速地跟踪速度及径向位移给定值,并对外界扰动及参数摄动有较强的鲁棒性。
3.针对平方根无迹卡尔曼滤波存在对模型参数变化鲁棒性差、收敛速度慢及对突变状态跟踪能力低等缺陷,提出一种改进平方根无迹卡尔曼滤波算法。结合强跟踪滤波原理,通过引入时变渐消因子在线自适应调整增益矩阵和状态预测误差协方差平方根矩阵,实现残差序列正交或近似正交,强迫平方根无迹卡尔曼滤波保持对实际状态的快速跟踪。在滤波过程中采用矩阵QR分解和Cholesky因子更新,以协方差平方根阵代替协方差阵参加迭代运算,有效地避免了滤波器发散,提高滤波算法收敛速度和稳定性。应用该方法设计无轴承永磁同步电机转子位置与速度估计器,可以提高系统对平稳状态、转速突变状态及外界扰动下的估计精度。
4.针对单一转速估计方法难以实现全速范围内转子位置与速度准确估计的缺陷,提出一种转子位置与速度复合估计方法。对于表贴式无轴承永磁同步电机,在零速及低速运行时,采用脉振高频信号注入法估计转子位置与速度,该方法不依赖于电机模型参数而仅依赖于电机本身的凸极特性,可实现零速及低速时转子位置与速度的准确估计；中高速运行时,采用改进平方根无迹卡尔曼滤波进行转子位置与速度估计,利用强跟踪滤波极强的模型失配鲁棒性,独特的强跟踪能力,有效地改善系统对稳态及突变状态的跟踪性能,通过设计两种方法的“软切换”,实现低速到高速的平滑过渡,从而实现全速范围内转子位置与速度的准确估计。
5.针对传统旋转高频信号注入法中信号处理精度低、延时时间长及过程复杂等缺陷,提出一种基于有限冲激响应优化滤波的改进型旋转高频信号注入法。通过离线设计等纹波最佳逼近有限冲激响应滤波器,利用该滤波器提取高频电流信号,实现高频电流信号提取误差更小。通过对高频电流做外差处理,提取转子位置误差信号,省去旋转高频信号注入法中的同步轴系滤波单元。针对有限冲激响应滤波器相位滞后,设计线性相位补偿,缩短系统延时时间。该方法结构简单,估计精度高,易于调试与实现,可实现转子位置与速度的准确估计。
6.构建了无轴承永磁同步电机全数字控制实验平台,对其硬件设计及软件流程进行详细阐述。采用空间电压矢量脉宽调制技术实现转子磁场定向控制,进行电机调速、转速突变状态下的悬浮运行试验,设计无位置传感器自适应非奇异终端滑模控制详细实现方案,为进一步开展无轴承永磁同步电机无位置传感器高性能控制奠定基础。
Bearingless motors not only have the functions of rotation and rotor self suspension, but also have the characteristics of no lubrication, no wear, no mechanical noise, high speed and high precision. With these advantages, bearingless motors have broad application prospect in high speed precision numerical control machine tools, aerospace, flywheel energy storage system and other high-tech fields. Compared with other type of bearingless motors, the bearingless permanent magnet synchronous motor, due to its advantages of simple structure, high power density, high efficiency, reliable operation, has become one of the hot spots in the research field of bearingless motors presently. The installation and use of the traditional mechanical sensors has maken the motor volume increase, cost increase, at the same time, it has seriously limited the excellent performance of high speed to the bearingless permanent magnet synchronous motor. Compared with ordinary permanent magnet synchronous motor, the rotor is self-suspension, when the bearingless permanent magnet synchronous motor work at steady state, rotor position, speed and radial displacement are more prone to vibrate and mutate because of the external disturbance, parameter perturbation and other factors. The stable operation without position sensor and high performance control will meet the requirement of ultra high speed, low cost and practical application of the bearingless permanent magnet synchronous motor. Supported by the National High Technology Research and Development Plan of China (2007AA04Z213) and the National Natural Science Foundation of China under grant(60974053), in order to improve the performance of bearingless permanent magnet synchronous motor, several key theoretical and technological problems, such as the mathematical model, rotor magnetic field orientated control, adaptive nonsingular terminal sliding mode control, position sensorless operation in full speed, and digital control system of bearingless permanent magnet synchronous motor and experimental operation are comprehensively studied. The main researches and the corresponding achievement are as follows:
1. A profound analysis on the generation of magnetic levitation forces for a surface-mounted bearingless permanent magnet synchronous motor with two degree of freedom is presented. From Maxwell tensor method, levitation force analytical model is deduced considering the rotor eccentricity. The mathematical model of electromagnetic torque is derived from the electromechanical energy conversion relationship considering rotor eccentricity and suspension winding current, motion equations of the rotor and systems are established.
2. An adaptive nonsingular terminal sliding mode control is put forward. In order to obtain faster convergence of state variables during the whole process in nonsingular terminal sliding mode control, an adaptive variable-rated exponential reaching law is presented where the L1norm of state variables is introduced. Exponential and constant approach speed can adaptively adjust according to the state variables' distance to the equilibrium position, which can short the reaching time and weak system chattering. The method is applied to the bearingless permanent magnet synchronous motor system, speed and radial displacement controller of adaptive nonsingular terminal sliding mode control are designed, simulation results show that, the proposed adaptive nonsingular terminal sliding mode controller could rapidly track the given values, system overshoot and static error are small, higher robustness can be obtained.
3. Aiming at the defects of low robustness to model parameter variation, slow convergence, and undesirable tracking ability to abrupt state changes in square root unscented Kalman filter algorithm, an improved square root unscented Kalman filter is proposed. Combined with the strong tracking filtering principle, by introducing the time-varying fading factor and the diminishing factor to adjust gain matrices and the state-forecast covariance square root matrix, in order to realize the orthogonality of the residual sequences and force the square root unscented Kalman filter to track the real state rapidly. In the process of filtering, Cholesky and QR decomposition are used. Covariance square root matrix is used instead of covariance in iterative computation, which can effectively avoid the filter divergence and improve the algorithm convergence speed and stability. The vector control system for bearingless permanent magnet synchronous motor without a speed sensor is set up based on this approach. Rotor position and speed estimators designed by this method, can improve the estimate accuracy at stationary state, speed mutation status and the external disturbance.
4. Because of one method cannot obtain precise estimation of rotor speed and position in full speed, a compound method using high frequency signal injection and improved square root unscented Kalman filter algorithm is proposed to estimate the rotor speed and position for a surface-mounted bearingless permanent magnet synchronous motor. When the motor work at state of zero and ultra-low speed, fluctuating high frequency signal injection is used, which does not depend on the motor parameter, only depend on motor space-saliency effect, accurate estimation will be achieved; at the high speed, the improved square root unscented Kalman filter is used. The improved square root unscented Kalman filter has strong robustness of the model mismatch and unique strong tracking ability, which can effectively improve the tracking performance to steady state and mutation status. By designing speed switch, smooth switching is achieved. The proposed method is capable of precisely estimating rotor speed and position in full speed.
5. Aiming at the defects of low precision, long delay and complicated process in the signal processing of traditional rotating high frequency signal injection method, an improved rotation high frequency signal injection method based on finite impulse response filter is proposed. Equiripple and optimal approximating finite impulse response filter is introduced to extract the high frequency current, which can realize minimum extraction error of the high frequency current signal. Using heterodyning processing to the high frequency current, the rotor position error signal can be extracted. This method can eliminate the synchronous shaft filter and reduce the complexity of the system.In order to achieve minimum delay of rotor speed and position estimation, linear phase compensation is used in the finite impulse response filter. The method has the advantages of simple structure, high accuracy, easy realization and debugging, accurate estimation of rotor position and speed can be obtained.
6. The digital control system of bearingless permanent magnet synchronous motor is designed, the corresponding hardware systems and software systems are designed. The space voltage vector pulse width modulation is used to realize the rotor magnetic field orientated control strategy. Stable suspension operation in speed adjustment and speed step are achieved in the platform. Detailed experiment scheme for position sensorless control of bearingless permanent magnet synchronous motor based on adaptive nonsingular terminal sliding mode control is proposed, which establishes a solid foundation for developing the high performance position sensorless control of the bearingless permanent magnet synchronous motor further.
引文
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