基于DSP平台的磁悬浮轴承数字控制系统
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摘要
磁悬浮轴承(Magnetic Bearing,简称MB)是利用磁力将转子悬浮于空间,使转子和定子之间实现无接触支承的一种新型高性能轴承。由于磁悬浮轴承转子和定子之间没有机械接触,具有众多优点：转子、定子间无摩擦,正常运转时可不考虑磨耗问题,因而主轴寿命长,易维护；振动噪声小；可实现高速旋转；能耗低；无需润滑,无油污染,可在真空中,无尘室内,高温、低温、特殊气体中,甚至人体内等特殊环境中使用；通过控制器对电磁力予以调节,即支承刚度阻尼可调,因而可对转子实施主动控制,进行不平衡补偿,温升补偿等,有利于提高转子的动态性能。因为磁悬浮轴承具有以上优点,目前被应用于旋转机械、透平设备、心脏泵和转子飞轮等各个领域。
作为电气、控制与机械综合的一项高新技术,磁悬浮轴承中控制系统的设计是一项关键技术。优良的控制系统可使磁悬浮轴承具有强大的功能,但另一方面,控制系统的设计也是一项颇具挑战性的工作。本课题的研究目的是,在高转速、高刚度、高精度的工业磨床上应用磁悬浮轴承,通过建立基于DSP平台的磁悬浮轴承数字控制系统,实现系统的鲁棒稳定和高鲁棒性能,并通过时延补偿控制、位姿误差补偿控制提高磨床电主轴系统的稳定性及精密度。
为完成课题,本文主要进行了以下工作：
首先,为了满足磨削时磁悬浮轴承电主轴各项控制要求,本文设计了基于DSP平台的数字控制系统及监测平台。其中,数字控制系统主要由位移传感器、A/D转换器、DSP数字控制器和FPGA数字功率放大器组成。数字电主轴状态监测系统主要对转子位移、电磁铁线圈电流以及电主轴温度进行实时监控。
然后,本文根据H∞理论以及不稳定结构的鲁棒控制原理,结合了对磁悬浮轴承电主轴系统的数学模型及不确定性的分析,设计了磁悬浮轴承鲁棒控制器。其中,使用自适应神经模糊推理系统对磁悬浮轴承的非参数不确定性进行了智能辨识,设计了相应的H∞控制器,相对于仅考虑参数不确定性的控制器来说,这种方法具有更好的鲁棒性能,在实际应用中取得了良好的效果。
数字控制系统中,数字控制时延对系统性能会造成影响。本文在研究了磁悬浮轴承数字控制时延的组成及其对控制系统性能影响的基础上,提出了一种新的时延补偿算法。该算法通过预测下一采样时刻的系统输出来消除时延对控制系统的影响。预测算法由磁悬浮轴承的离散化模型得到,算法系数可以经由神经网络修正。实验结果表明该算法能够很好地补偿数字控制时延,实现了数字控制磁悬浮轴承的稳定悬浮和高速运转。
为了实现在磨床应用上的高定位精度,本文在检测系统温升的基础上,建立了温升与转子位姿的相关模型,确定了5路位移控制输入设定值与转子位姿的对应关系,并利用数字控制系统实现了系统温升膨胀的位姿误差在线补偿。补偿算法由FPGA硬件实现,实验结果表明该算法可很好地补偿温升造成的位姿误差,保证了磁悬浮轴承电主轴的稳定性和精度。
最后,通过对MK2110型内圆磨床进行改装,搭建了磁悬浮轴承电主轴控制系统实验平台。成功实现了磁悬浮轴承磨床电主轴的五自由度稳定悬浮；进行了旋转实验,转速最高达到30000rpm。在360Hz下进行了磨削实验,磨削出的工件粗糙度和圆度基本满足加工要求,接近工业应用水平。
本文主要进行了以下创新：针对磁悬浮轴承电主轴系统的H∞控制器设计,利用智能辨识方法解决加权矩阵选择问题,得到了磁悬浮轴承电主轴系统中的非参数不确定性描述,将非参数不确定加权函数应用在Hoo控制器设计中,实现了高鲁棒性能；针对磁悬浮轴承系统中数字控制时延对控制系统性能的影响,提出了一种数字控制时延的补偿算法,该算法有效地消除了数字控制时延的影响,实现了磁悬浮轴承系统的稳定工作；针对磁悬浮轴承电主轴的温升问题,在检测系统温升的基础上,建立了温升与转子位姿的相关模型；提出了一种温升补偿算法,并利用数字控制系统实现了磨头位姿的在线调整,完成了系统温升膨胀的在线补偿。实验结果表明该算法可很好地对温升膨胀进行补偿,保证了磁悬浮轴承电主轴的稳定性和精度。基于上述创新研究工作,设计的控制系统在实际应用中取得了良好的效果。
以上工作中,实施主动控制,利用数字控制器实现先进控制算法以达到系统高鲁棒性,并进行在线补偿以抵消时延、温升等因素对系统的不利影响,这是磁悬浮轴承的优势体现,也是本课题研究的重点和难点,需要吸取转子动力学分析、系统辨识、自动控制、传感器、电力电子技术等多项学科的先进知识。首先,磁悬浮轴承是具有强烈非线性且本质不稳定的控制对象,磨床加工又要求主轴同时具有高精度和高刚度,需要精心设计合适的控制器。由于系统模型中存在参数不确定性和动态不确定性,使得采用PID控制或者依赖于确定性模型的控制方法达不到理想的控制效果,因此有必要设计一个鲁棒性能良好的控制器与系统模型不确定性相适应。在H∞控制方法中,加权函数的选择是一个待解决的难题,加权函数的选择是依靠设计者的经验和反复试算。一般来说,取决于控制设计目标的要求、指标的选择等。文中使用智能辨识方法进行非参数不确定性加权函数的选择,满足了设计要求,系统具有较好的控制性能。其次,磁悬浮轴承系统中,温升效应会影响磁悬浮轴承系统的静态精度,恶化轴向轴承的特性,对系统可靠性造成威胁。为了解决温升问题,本文研究了温升对转子位姿的影响,并使用神经网络建立了关键温度点温度值与转子位姿偏移的映射关系,如何用硬件实现神经网络,实现在线实时补偿,是本论文的一个难点。
本文采用主动控制对温升问题进行了补偿,作为下一步研究工作,可以从磁悬浮轴承电主轴结构设计的角度,减少系统的发热源,从源头上控制温升。研究过程中,发现磁悬浮轴承电主轴工作中存在拍振现象,影响磨削效果,也需要进一步的研究并加以抑制。
研究工作表明,论文提出并完成的针对磁悬浮轴承数字鲁棒控制系统的理论分析和实验研究方法是重要和有价值的研究成果,得到的控制器在实际应用中具有良好的效果。本文的研究工作为国内磁悬浮轴承控制系统的深入研究和未来的工业应用打下了基础,具有非常重要的理论价值和实际意义。
Magnetic bearing is a novel high-performance bearings which use magnetic force to make the rotor suspended in space providing a non-contact support between the rotor and stator. As the magnetic bearing between the rotor and stator without mechanical contact, it has the following advantages:without friction. The longer spindle life, and easy to maintain; lower vibration noise; high-speed rotation; low energy consumption; no lubrication, no oil pollution, can be used in the environments of vacuum, clean, heat, cold, specialty gases, and even the body, and other special environments. It is particularly suitable for high-speed, vacuum, clean, low temperature and other special circumstances. In addition to the above advantages, in active magnetic bearings, the electromagnetic force can also be adjusted by the controller, which means that adjustable bearing stiffness and damping, thus the implementation of active control of the rotor, the unbalance compensation, temperature compensation, etc., and it can help to improve the dynamics of the rotor performance. You can also apply a variety of advanced control algorithms, and realize the system monitoring and control. Because the magnetic bearings have the above advantages, so the industrial countries strongly focus on the research and development of the magnetic bearing technology. Currently, the application of magnetic bearings are mainly concentrated in rotating machinery, turbine equipment, the heart pumps and rotor flywheel and other fields.
For the completion of the subjects, This paper mainly do the following work:
Rotating machinery are moving into high speed, high precision and high flexibility and many other directions, and because the magnetic bearing (AMB) has many advantages:high speed, no wear, no lubrication, high reliability and dynamic characteristics of adjustable and other advantages, the past two decades in rotating machinery applied research it is taken seriously. Excellent control system can make a powerful magnetic bearing;on the other hand, the controller design is a challenging task. This paper belonging to the National Natural Science Foundation project "Intelligent inline monitoring system of AMB grinding spindle", mainly studies a robust digital control system which can be applied to the CNC grinding machine spindle and compensate for the position changes caused by the temperature rise.
In order to make the digital control system to meet the grinding spindle control requirements, this platform based on DSP digital control systems and monitoring platform is designed. Among them, the digital control system is mainly composed of the displacement sensors, AD converter, DSP digital controller, FPGA digital power amplifiers; the spindle condition monitoring system mainly monitors the displacement of the rotor, the electromagnet coil current and temperature of the spindle.
According to the Hoo theory and the unstable structure of robust control theory, combined with the analysis of the magnetic bearing spindle systems mathematical models and uncertainty, this paper designs a magnetic bearings robust controller. Among them, the adaptive neuro-fuzzy inference system is used for an intelligent identification of magnetic bearings non-parametric uncertainties, then the corresponding Hoo controller is designed, as opposed to only consider the parameter uncertainty of the controller. This method has better robust performance in practical applications achieved the good result.
Based on studying the composition of the magnetic bearing digital control delay and on the impact on performance of the control system, a new delay compensation algorithm is proposed. The algorithm, by predicting the next sample time delay system output, eliminates the impact of the control system. Prediction algorithm is from the discrete model of magnetic bearings, and the algorithm factors are corrected by the neural network. Experimental results show that the algorithm can compensate the delay of the digital controller very well, to achieve a stable digital control magnetic bearing suspension and high-speed operation.
Based on the detection of temperature rise in system, the model of the temperature rise associated with the spindle position and orientation is established; identifies the correspondence relationship of five displacement control input settings and the spindle position and orientation. According to temperature samples of the system, the5-way displacement control input settings are corrected, to achieve the inline adjustment of grinding wheel pose and complete the inline compensation of the system temperature expansion. Compensation algorithm is realized by FPGA. Experimental results show that the algorithm works well to compensate for temperature expansion, to ensure the stability and accuracy of the magnetic bearing spindle.
MK2110-type grinding machine is altered to build a magnetic bearing spindle control system experimental platform. Implementation of a magnetic bearing spindle grinder stable suspension of the five degrees of freedom is successful; the rotation experiment speed is up to500Hz. At360Hz the grinding experiments are preceded. The roughness and roundness of the resulted workpieces can basically meet the processing requirements, close to the level of industrial applications.
In above work, the active control is implemented by the digital controller to realize advanced control algorithms and achieve high system robustness, and the on-line compensation is employed to offset the adverse effects which is caused by temperature and other factors on the system, which reflects the advantages of magnetic bearings and is also the important and difficult parts of the research. Rotor dynamics analysis, system identification, automatic control, sensor, power electronics technology, advanced knowledge of these subjects are needed. First, the magnetic bearing is a strong non-linear and essentially unstable control object, and in grinding process, the spindle is required to have both high precision and high rigidity, the appropriate controller need to be designed carefully. As the uncertainties of system parameter and dynamic uncertainty in the model, the use of PID control or the control strategy dependent on the deterministic model can not get the ideal control effect. Thus it is necessary to design a robust controller with good performance getting used to the system model uncertainty. In the H∞control method, the choice of weighting function is a difficult problem to be solved, the choice of weighting function is to rely on the experience and repeated test. In general, it depends on the requirements and indicators of the control design objectives. By the use of the intelligent identification method for the choice of non-parametric uncertainty weighting function, to meet the design requirements, the system has good control performance. Second, the magnetic bearing system, temperature effects will affect the accuracy of the static magnetic bearing systems, deteriorate the characteristics of axial bearing, threat the system reliability. In order to solve the temperature problem, we study the temperature effect on the rotor position and posture, and use neural networks to establish a critical temperature point temperature and the rotor position offset mapping. How to use the hardware neural network to make on-line real-time compensation, is a difficult point of this paper.
Mainly do the following innovations:the use of smart identification method in the magnetic bearing spindle systems to describe the non-parametric uncertainty weighting function, and for the parameter uncertainty and non-parametric uncertainty, design the Hoo controller to achieve a high robust performance; analyzes the effect of control system time delay in digitally controlled magnetic bearing system, and on this basis, presents a digital controller delay compensation algorithm. The algorithm effectively removes the impact of digital control time delay to achieve a magnetic bearing system stability; for the magnetic bearing spindle temperature problems, in the detection system based on temperature rise, establishes the model of temperature rise and the position and orientation of the spindle; identifies the correspondence of five displacement control input settings and the spindle position and orientation. Experimental results show that the algorithm works well to compensate for the temperature expansion, the magnetic bearing spindle to ensure the stability and accuracy. Based on the innovative research work, the control system in practical applications obtains good results.
This paper accumulated system design and actual operating experience, has important theoretical and engineering significance.
作为电气、控制与机械综合的一项高新技术,磁悬浮轴承中控制系统的设计是一项关键技术。优良的控制系统可使磁悬浮轴承具有强大的功能,但另一方面,控制系统的设计也是一项颇具挑战性的工作。本课题的研究目的是,在高转速、高刚度、高精度的工业磨床上应用磁悬浮轴承,通过建立基于DSP平台的磁悬浮轴承数字控制系统,实现系统的鲁棒稳定和高鲁棒性能,并通过时延补偿控制、位姿误差补偿控制提高磨床电主轴系统的稳定性及精密度。
为完成课题,本文主要进行了以下工作：
首先,为了满足磨削时磁悬浮轴承电主轴各项控制要求,本文设计了基于DSP平台的数字控制系统及监测平台。其中,数字控制系统主要由位移传感器、A/D转换器、DSP数字控制器和FPGA数字功率放大器组成。数字电主轴状态监测系统主要对转子位移、电磁铁线圈电流以及电主轴温度进行实时监控。
然后,本文根据H∞理论以及不稳定结构的鲁棒控制原理,结合了对磁悬浮轴承电主轴系统的数学模型及不确定性的分析,设计了磁悬浮轴承鲁棒控制器。其中,使用自适应神经模糊推理系统对磁悬浮轴承的非参数不确定性进行了智能辨识,设计了相应的H∞控制器,相对于仅考虑参数不确定性的控制器来说,这种方法具有更好的鲁棒性能,在实际应用中取得了良好的效果。
数字控制系统中,数字控制时延对系统性能会造成影响。本文在研究了磁悬浮轴承数字控制时延的组成及其对控制系统性能影响的基础上,提出了一种新的时延补偿算法。该算法通过预测下一采样时刻的系统输出来消除时延对控制系统的影响。预测算法由磁悬浮轴承的离散化模型得到,算法系数可以经由神经网络修正。实验结果表明该算法能够很好地补偿数字控制时延,实现了数字控制磁悬浮轴承的稳定悬浮和高速运转。
为了实现在磨床应用上的高定位精度,本文在检测系统温升的基础上,建立了温升与转子位姿的相关模型,确定了5路位移控制输入设定值与转子位姿的对应关系,并利用数字控制系统实现了系统温升膨胀的位姿误差在线补偿。补偿算法由FPGA硬件实现,实验结果表明该算法可很好地补偿温升造成的位姿误差,保证了磁悬浮轴承电主轴的稳定性和精度。
最后,通过对MK2110型内圆磨床进行改装,搭建了磁悬浮轴承电主轴控制系统实验平台。成功实现了磁悬浮轴承磨床电主轴的五自由度稳定悬浮；进行了旋转实验,转速最高达到30000rpm。在360Hz下进行了磨削实验,磨削出的工件粗糙度和圆度基本满足加工要求,接近工业应用水平。
本文主要进行了以下创新：针对磁悬浮轴承电主轴系统的H∞控制器设计,利用智能辨识方法解决加权矩阵选择问题,得到了磁悬浮轴承电主轴系统中的非参数不确定性描述,将非参数不确定加权函数应用在Hoo控制器设计中,实现了高鲁棒性能；针对磁悬浮轴承系统中数字控制时延对控制系统性能的影响,提出了一种数字控制时延的补偿算法,该算法有效地消除了数字控制时延的影响,实现了磁悬浮轴承系统的稳定工作；针对磁悬浮轴承电主轴的温升问题,在检测系统温升的基础上,建立了温升与转子位姿的相关模型；提出了一种温升补偿算法,并利用数字控制系统实现了磨头位姿的在线调整,完成了系统温升膨胀的在线补偿。实验结果表明该算法可很好地对温升膨胀进行补偿,保证了磁悬浮轴承电主轴的稳定性和精度。基于上述创新研究工作,设计的控制系统在实际应用中取得了良好的效果。
以上工作中,实施主动控制,利用数字控制器实现先进控制算法以达到系统高鲁棒性,并进行在线补偿以抵消时延、温升等因素对系统的不利影响,这是磁悬浮轴承的优势体现,也是本课题研究的重点和难点,需要吸取转子动力学分析、系统辨识、自动控制、传感器、电力电子技术等多项学科的先进知识。首先,磁悬浮轴承是具有强烈非线性且本质不稳定的控制对象,磨床加工又要求主轴同时具有高精度和高刚度,需要精心设计合适的控制器。由于系统模型中存在参数不确定性和动态不确定性,使得采用PID控制或者依赖于确定性模型的控制方法达不到理想的控制效果,因此有必要设计一个鲁棒性能良好的控制器与系统模型不确定性相适应。在H∞控制方法中,加权函数的选择是一个待解决的难题,加权函数的选择是依靠设计者的经验和反复试算。一般来说,取决于控制设计目标的要求、指标的选择等。文中使用智能辨识方法进行非参数不确定性加权函数的选择,满足了设计要求,系统具有较好的控制性能。其次,磁悬浮轴承系统中,温升效应会影响磁悬浮轴承系统的静态精度,恶化轴向轴承的特性,对系统可靠性造成威胁。为了解决温升问题,本文研究了温升对转子位姿的影响,并使用神经网络建立了关键温度点温度值与转子位姿偏移的映射关系,如何用硬件实现神经网络,实现在线实时补偿,是本论文的一个难点。
本文采用主动控制对温升问题进行了补偿,作为下一步研究工作,可以从磁悬浮轴承电主轴结构设计的角度,减少系统的发热源,从源头上控制温升。研究过程中,发现磁悬浮轴承电主轴工作中存在拍振现象,影响磨削效果,也需要进一步的研究并加以抑制。
研究工作表明,论文提出并完成的针对磁悬浮轴承数字鲁棒控制系统的理论分析和实验研究方法是重要和有价值的研究成果,得到的控制器在实际应用中具有良好的效果。本文的研究工作为国内磁悬浮轴承控制系统的深入研究和未来的工业应用打下了基础,具有非常重要的理论价值和实际意义。
Magnetic bearing is a novel high-performance bearings which use magnetic force to make the rotor suspended in space providing a non-contact support between the rotor and stator. As the magnetic bearing between the rotor and stator without mechanical contact, it has the following advantages:without friction. The longer spindle life, and easy to maintain; lower vibration noise; high-speed rotation; low energy consumption; no lubrication, no oil pollution, can be used in the environments of vacuum, clean, heat, cold, specialty gases, and even the body, and other special environments. It is particularly suitable for high-speed, vacuum, clean, low temperature and other special circumstances. In addition to the above advantages, in active magnetic bearings, the electromagnetic force can also be adjusted by the controller, which means that adjustable bearing stiffness and damping, thus the implementation of active control of the rotor, the unbalance compensation, temperature compensation, etc., and it can help to improve the dynamics of the rotor performance. You can also apply a variety of advanced control algorithms, and realize the system monitoring and control. Because the magnetic bearings have the above advantages, so the industrial countries strongly focus on the research and development of the magnetic bearing technology. Currently, the application of magnetic bearings are mainly concentrated in rotating machinery, turbine equipment, the heart pumps and rotor flywheel and other fields.
For the completion of the subjects, This paper mainly do the following work:
Rotating machinery are moving into high speed, high precision and high flexibility and many other directions, and because the magnetic bearing (AMB) has many advantages:high speed, no wear, no lubrication, high reliability and dynamic characteristics of adjustable and other advantages, the past two decades in rotating machinery applied research it is taken seriously. Excellent control system can make a powerful magnetic bearing;on the other hand, the controller design is a challenging task. This paper belonging to the National Natural Science Foundation project "Intelligent inline monitoring system of AMB grinding spindle", mainly studies a robust digital control system which can be applied to the CNC grinding machine spindle and compensate for the position changes caused by the temperature rise.
In order to make the digital control system to meet the grinding spindle control requirements, this platform based on DSP digital control systems and monitoring platform is designed. Among them, the digital control system is mainly composed of the displacement sensors, AD converter, DSP digital controller, FPGA digital power amplifiers; the spindle condition monitoring system mainly monitors the displacement of the rotor, the electromagnet coil current and temperature of the spindle.
According to the Hoo theory and the unstable structure of robust control theory, combined with the analysis of the magnetic bearing spindle systems mathematical models and uncertainty, this paper designs a magnetic bearings robust controller. Among them, the adaptive neuro-fuzzy inference system is used for an intelligent identification of magnetic bearings non-parametric uncertainties, then the corresponding Hoo controller is designed, as opposed to only consider the parameter uncertainty of the controller. This method has better robust performance in practical applications achieved the good result.
Based on studying the composition of the magnetic bearing digital control delay and on the impact on performance of the control system, a new delay compensation algorithm is proposed. The algorithm, by predicting the next sample time delay system output, eliminates the impact of the control system. Prediction algorithm is from the discrete model of magnetic bearings, and the algorithm factors are corrected by the neural network. Experimental results show that the algorithm can compensate the delay of the digital controller very well, to achieve a stable digital control magnetic bearing suspension and high-speed operation.
Based on the detection of temperature rise in system, the model of the temperature rise associated with the spindle position and orientation is established; identifies the correspondence relationship of five displacement control input settings and the spindle position and orientation. According to temperature samples of the system, the5-way displacement control input settings are corrected, to achieve the inline adjustment of grinding wheel pose and complete the inline compensation of the system temperature expansion. Compensation algorithm is realized by FPGA. Experimental results show that the algorithm works well to compensate for temperature expansion, to ensure the stability and accuracy of the magnetic bearing spindle.
MK2110-type grinding machine is altered to build a magnetic bearing spindle control system experimental platform. Implementation of a magnetic bearing spindle grinder stable suspension of the five degrees of freedom is successful; the rotation experiment speed is up to500Hz. At360Hz the grinding experiments are preceded. The roughness and roundness of the resulted workpieces can basically meet the processing requirements, close to the level of industrial applications.
In above work, the active control is implemented by the digital controller to realize advanced control algorithms and achieve high system robustness, and the on-line compensation is employed to offset the adverse effects which is caused by temperature and other factors on the system, which reflects the advantages of magnetic bearings and is also the important and difficult parts of the research. Rotor dynamics analysis, system identification, automatic control, sensor, power electronics technology, advanced knowledge of these subjects are needed. First, the magnetic bearing is a strong non-linear and essentially unstable control object, and in grinding process, the spindle is required to have both high precision and high rigidity, the appropriate controller need to be designed carefully. As the uncertainties of system parameter and dynamic uncertainty in the model, the use of PID control or the control strategy dependent on the deterministic model can not get the ideal control effect. Thus it is necessary to design a robust controller with good performance getting used to the system model uncertainty. In the H∞control method, the choice of weighting function is a difficult problem to be solved, the choice of weighting function is to rely on the experience and repeated test. In general, it depends on the requirements and indicators of the control design objectives. By the use of the intelligent identification method for the choice of non-parametric uncertainty weighting function, to meet the design requirements, the system has good control performance. Second, the magnetic bearing system, temperature effects will affect the accuracy of the static magnetic bearing systems, deteriorate the characteristics of axial bearing, threat the system reliability. In order to solve the temperature problem, we study the temperature effect on the rotor position and posture, and use neural networks to establish a critical temperature point temperature and the rotor position offset mapping. How to use the hardware neural network to make on-line real-time compensation, is a difficult point of this paper.
Mainly do the following innovations:the use of smart identification method in the magnetic bearing spindle systems to describe the non-parametric uncertainty weighting function, and for the parameter uncertainty and non-parametric uncertainty, design the Hoo controller to achieve a high robust performance; analyzes the effect of control system time delay in digitally controlled magnetic bearing system, and on this basis, presents a digital controller delay compensation algorithm. The algorithm effectively removes the impact of digital control time delay to achieve a magnetic bearing system stability; for the magnetic bearing spindle temperature problems, in the detection system based on temperature rise, establishes the model of temperature rise and the position and orientation of the spindle; identifies the correspondence of five displacement control input settings and the spindle position and orientation. Experimental results show that the algorithm works well to compensate for the temperature expansion, the magnetic bearing spindle to ensure the stability and accuracy. Based on the innovative research work, the control system in practical applications obtains good results.
This paper accumulated system design and actual operating experience, has important theoretical and engineering significance.
引文
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