CN108716471B - Active control method for minimum displacement of rotor of magnetic suspension molecular pump - Google Patents
Active control method for minimum displacement of rotor of magnetic suspension molecular pump Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D19/00—Axial-flow pumps
- F04D19/02—Multi-stage pumps
- F04D19/04—Multi-stage pumps specially adapted to the production of a high vacuum, e.g. molecular pumps
- F04D19/042—Turbomolecular vacuum pumps
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D19/00—Axial-flow pumps
- F04D19/02—Multi-stage pumps
- F04D19/04—Multi-stage pumps specially adapted to the production of a high vacuum, e.g. molecular pumps
- F04D19/048—Multi-stage pumps specially adapted to the production of a high vacuum, e.g. molecular pumps comprising magnetic bearings
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D29/00—Details, component parts, or accessories
- F04D29/05—Shafts or bearings, or assemblies thereof, specially adapted for elastic fluid pumps
- F04D29/056—Bearings
- F04D29/058—Bearings magnetic; electromagnetic
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D29/00—Details, component parts, or accessories
- F04D29/66—Combating cavitation, whirls, noise, vibration or the like; Balancing
- F04D29/661—Combating cavitation, whirls, noise, vibration or the like; Balancing especially adapted for elastic fluid pumps
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Abstract
本发明涉及一种磁悬浮分子泵转子极小位移主动控制方法。通过分析磁悬浮转子系统不平衡振动形成机理,建立磁悬浮转子系统的广义被控对象数学模型。基于线性自抗扰控制原理设计各通道控制器,将系统的不平衡振动视为一种外部扰动,利用线性扩展状态观测器对扰动进行实时估计并补偿,使得控制信号中叠加了幅值和相位合适的同频补偿信号以抵消转子不平衡激振力,实现转子绕几何轴高速高精度旋转,从而达到磁悬浮转子系统极小位移主动控制的目的。与传统控制方法相比,该方法参数调理简单,易于实现,能大幅减小位移信号中的转速同频分量,转子涡动半径小,旋转精度高,对提高磁悬浮转子系统性能和可靠性有重要意义。
The invention relates to an active control method for the minimal displacement of the rotor of a magnetic suspension molecular pump. By analyzing the formation mechanism of the unbalanced vibration of the magnetic suspension rotor system, the generalized controlled object mathematical model of the magnetic suspension rotor system is established. Based on the linear active disturbance rejection control principle, each channel controller is designed, and the unbalanced vibration of the system is regarded as an external disturbance. The linear extended state observer is used to estimate and compensate the disturbance in real time, so that the amplitude and phase are superimposed on the control signal. The appropriate co-frequency compensation signal can offset the unbalanced excitation force of the rotor, realize the high-speed and high-precision rotation of the rotor around the geometric axis, and achieve the purpose of active control of the minimal displacement of the magnetic suspension rotor system. Compared with the traditional control method, this method has simple parameter adjustment and easy implementation, and can greatly reduce the co-frequency component of the rotational speed in the displacement signal. significance.
Description
技术领域technical field
本发明涉及一种磁悬浮分子泵转子极小位移主动振动控制方法,可应用于高速磁悬浮转子系统高精度和强鲁棒控制,属于运动控制领域。The invention relates to an active vibration control method for the extremely small displacement of a magnetic suspension molecular pump rotor, which can be applied to high-precision and strong robust control of a high-speed magnetic suspension rotor system, and belongs to the field of motion control.
背景技术Background technique
磁悬浮分子泵是获取高真空的一个重要设备,被广泛应用于各种高真空场合。相较于传统机械轴承,磁悬浮轴承作为一种新型轴承,因其具有非接触、无摩擦、高转速、高精度、长寿命、可对转子动不平衡进行主动控制等特殊优点,具有广阔的应用前景。由于磁悬浮转子系统的控制精度是决定分子泵能否高速长期稳定可靠运行的重要因素,而磁悬浮转子在实际运转过程中存在各种复杂振动问题,其中最主要是由于与转子同频的动不平衡,给系统的高精度和高稳定控制带来巨大挑战。动不平衡产生的根本原因在于转子质量不平衡,由于机械加工精度等原因,转子的质量分布不均匀,几何轴和惯性主轴不重合,产生离心力。由于离心力的大小与转子转速的平方成正比,尤其随着转子在转速升高,不平衡振动力急剧增加,导致转子位移精度下降,严重时转子会与机械保护轴承碰撞,影响系统的稳定运行。磁悬浮转子系统具备实时主动控制能力,为实施不平衡振动控制提供了独特优势,通过对不平衡振动抑制,对提高磁悬浮转子系统控制精度和可靠性均有重要意义。Magnetic levitation molecular pump is an important equipment for obtaining high vacuum, which is widely used in various high vacuum occasions. Compared with traditional mechanical bearings, as a new type of bearing, magnetic bearing has a wide range of applications because of its special advantages such as non-contact, no friction, high speed, high precision, long life, and active control of rotor dynamic imbalance. prospect. Because the control accuracy of the magnetic suspension rotor system is an important factor that determines whether the molecular pump can operate stably and reliably at high speed for a long time, and the magnetic suspension rotor has various complex vibration problems in the actual operation process, the most important of which is the dynamic imbalance of the same frequency as the rotor. , which brings great challenges to the high-precision and high-stability control of the system. The fundamental cause of dynamic unbalance is the unbalanced rotor mass. Due to the machining accuracy and other reasons, the mass distribution of the rotor is uneven, and the geometric axis and the inertial spindle do not coincide, resulting in centrifugal force. Since the centrifugal force is proportional to the square of the rotor speed, especially as the rotor speed increases, the unbalanced vibration force increases sharply, resulting in a decrease in the rotor displacement accuracy. In severe cases, the rotor will collide with the mechanical protection bearing, affecting the stable operation of the system. The magnetic suspension rotor system has real-time active control capability, which provides unique advantages for the implementation of unbalanced vibration control. By suppressing the unbalanced vibration, it is of great significance to improve the control accuracy and reliability of the magnetic suspension rotor system.
目前,针对磁悬浮转子不平衡振动主动控制方法有两种,方法一:自平衡主动振动控制,在反馈通道中通过消除位移传感器输出信号中的转速同频分量,从而消除传递给磁轴承的同步激振力,让转子绕惯性主轴旋转;方法二:自对中主动振动控制,使得线圈产生额外的补偿电磁力来抵消不平衡激振力,抑制转子位移的同频振动,使转子绕几何主轴旋转。方法一具有运行噪声小,动基座效应小等优点,但是无法抑制转子位移信号中的转速同频涡动,随着转速升高,造成转子涡动半径增大,可能与保护轴承碰撞,导致系统失稳;方案二能使转子旋转精度高,涡动半径小,但是由于同频轴承力反作用到磁轴承上,系统噪声和动基座效应较为明显,系统功耗增加。At present, there are two active control methods for the unbalanced vibration of the magnetic suspension rotor. Vibration force, let the rotor rotate around the inertial main axis; Method 2: Self-centering active vibration control, so that the coil generates additional compensation electromagnetic force to offset the unbalanced excitation force, suppress the co-frequency vibration of the rotor displacement, and make the rotor rotate around the geometric main axis .
发明内容SUMMARY OF THE INVENTION
本发明要解决的技术问题是:针对磁悬浮分子泵转子系统受不平衡振动引起位移精度下降的问题,提出一种基于线性自抗扰控制器的转子极小位移主动控制方法。该方法将系统的不平衡振动视为一种外部扰动,通过线性扩展状态观测器对扰动进行实时估计并补偿,实现转子绕几何轴高速高精度旋转,从而达到磁悬浮转子系统极小位移主动控制的目的,为磁悬浮分子泵稳定可靠运行提供了有效的控制方法。The technical problem to be solved by the present invention is: Aiming at the problem that the displacement accuracy of the magnetic suspension molecular pump rotor system is reduced by unbalanced vibration, an active control method of the rotor minimum displacement based on the linear active disturbance rejection controller is proposed. In this method, the unbalanced vibration of the system is regarded as an external disturbance, and the disturbance is estimated and compensated in real time through the linear extended state observer, so as to realize the high-speed and high-precision rotation of the rotor around the geometric axis, so as to achieve the active control of the extremely small displacement of the magnetic suspension rotor system. The purpose is to provide an effective control method for the stable and reliable operation of the magnetic levitation molecular pump.
本发明解决上述技术问题采用的技术方案是:一种磁悬浮分子泵转子极小位移主动控制方法,包括以下步骤:The technical scheme adopted by the present invention to solve the above-mentioned technical problems is: a method for actively controlling the minimal displacement of the rotor of a magnetic levitation molecular pump, comprising the following steps:
(1)磁悬浮分子泵的转子动力学模型(1) Rotordynamic model of magnetic levitation molecular pump
将磁悬浮分子泵转子视为刚性转子,磁悬浮转子的动不平衡是由静不平衡和偶不平衡两部分组成,其中静不平衡是由于转子存在质量偏心,即惯性轴与几何轴互不重合,造成静不平衡力;偶不平衡是由于转子惯性轴与几何轴不平行,造成扰动力矩;以动不平衡转子的质心为原点建立广义坐标系,得到磁悬浮转子的动力学方程:The rotor of the magnetic levitation molecular pump is regarded as a rigid rotor. The dynamic unbalance of the magnetic levitation rotor is composed of two parts: static unbalance and even unbalance. The static unbalance is due to the mass eccentricity of the rotor, that is, the inertia axis and the geometric axis do not coincide with each other. The static unbalanced force is caused; the even unbalance is caused by the rotor inertia axis not parallel to the geometric axis, resulting in a disturbance moment; with the center of mass of the dynamically unbalanced rotor as the origin, a generalized coordinate system is established, and the dynamic equation of the magnetic suspension rotor is obtained:
式中:m为转子质量,Jx、Jy和Jz分别是转子绕x、y和z轴的转动惯量;Fx是转子受到沿x方向的磁力,Fy是转子受到沿y方向的磁力,Mx是转子受到x方向的磁力矩、My是转子受到y方向的磁力矩;Ω是转子旋转角速度;αG、βG是转子在广义坐标系下绕x轴和y轴的角位移;xG、yG分别是转子在广义坐标系下的位移;fxd是沿x方向的静不平衡力,fyd是沿y方向的静不平衡力;pxd是沿x方向的扰动力矩,pyd是沿y方向的扰动力矩;In the formula: m is the mass of the rotor, J x , J y and J z are the moments of inertia of the rotor around the x, y and z axes, respectively; F x is the magnetic force along the x direction by the rotor, and F y is the rotor received along the y direction. Magnetic force, M x is the magnetic moment that the rotor receives in the x direction, M y is the magnetic moment that the rotor receives in the y direction; Ω is the rotational angular velocity of the rotor; α G , β G are the angles of the rotor around the x-axis and the y-axis in the generalized coordinate system Displacement; x G , y G are the displacement of the rotor in the generalized coordinate system respectively; f xd is the static unbalanced force along the x direction, f yd is the static unbalanced force along the y direction; p xd is the disturbance along the x direction moment, p yd is the disturbance moment along the y direction;
其中:in:
式中:ε为静不平衡偏心距;σ为旋转轴与坐标轴夹角;θ为静不平衡角位置;为偶不平衡的角位置。Where: ε is the static unbalance eccentric distance; σ is the angle between the rotation axis and the coordinate axis; θ is the static unbalance angle position; is the angular position of the couple unbalance.
考虑功放系统为一阶惯性环节,传感器为比例环节,结合磁悬浮转子的动力学方程,得到磁悬浮转子系统径向四通道的广义被控对象数学模型:Considering that the power amplifier system is a first-order inertial link, and the sensor is a proportional link, combined with the dynamic equation of the magnetic suspension rotor, the generalized controlled object mathematical model of the radial four-channel magnetic suspension rotor system is obtained:
式中:xa、xb、ya和yb时是磁悬浮转子分别在Ax、Bx、Ay和By方向上的线性位移量;f(·)为系统的总扰动,其中ωi(i=1,2,3,4)是磁悬浮转子的不平衡扰动量;b0i(i=1,2,3,4)是控制信号ui(t)(i=1,2,3,4)的系数。In the formula: x a , x b , y a and y b are the linear displacements of the magnetic suspension rotor in the directions of Ax, Bx, Ay and By, respectively; f( ) is the total disturbance of the system, where ω i (i = 1,2,3,4) is the unbalanced disturbance of the magnetic suspension rotor; b 0i (i=1,2,3,4) is the control signal u i (t) (i=1,2,3,4) coefficient.
(2)设计线性自抗扰控制器(2) Design a linear active disturbance rejection controller
磁悬浮转子系统四通道采用相同结构的控制器,对于Ax通道,具有模型辅助的线性扩张状态观测器表达形式:The four-channel magnetic levitation rotor system adopts the same structure of the controller. For the Ax channel, there is a model-assisted linear expansion state observer expression:
式中:y是Ax通道传感器的位移输出,y=xa;u是控制器输出的控制信号;z1是y的跟踪信号,z2是的跟踪信号,z3是的跟踪信号,z4是总扰动f(·)的跟踪信号;a0是y的系数,a1是的系数,a2是的系数;b0是Ax通道控制信号系数b01的估计值;L=[β1 β2 β3 β4]为线性扩张状态观测器增益。In the formula: y is the displacement output of the Ax channel sensor, y=x a ; u is the control signal output by the controller; z 1 is the tracking signal of y, and z 2 is The tracking signal, z 3 is The tracking signal of , z 4 is the tracking signal of the total disturbance f( ); a 0 is the coefficient of y, and a 1 is The coefficient of , a 2 is The coefficient of ; b 0 is the estimated value of the Ax channel control signal coefficient b 01 ; L=[β 1 β 2 β 3 β 4 ] is the linear expansion state observer gain.
线性状态误差反馈控制律的表达形式为:The expression form of the linear state error feedback control law is:
式中:u0为误差的线性组合;u是控制器的输出;KP是比例系数,Kd1是一阶微分系数,Kd2是二阶微分系数,均是控制器调节参数;ysp是设定的位移跟踪目标值。In the formula: u 0 is the linear combination of errors; u is the output of the controller; K P is the proportional coefficient, K d1 is the first-order differential coefficient, and K d2 is the second-order differential coefficient, all of which are the adjustment parameters of the controller; y sp is the The set displacement tracking target value.
本发明的原理是:根据自抗扰控制器对系统扰动的特殊处理方式,将磁悬浮转子系统受到的不平衡振动视为一种外部扰动,通过具有模型辅助的线性扩展状态观测器对其进行实时估计并补偿,使得控制信号中叠加了幅值和相位合适的同频补偿信号以抵消转子不平衡激振力,实现磁悬浮转子系统极小位移的主动振动控制。本发明在建立磁悬浮转子系统广义被控对象数学模型的基础上,基于线性自抗扰控制原理,设计各子系统的线性自抗扰控制器,最终实现转子系统极小位移的主动控制。The principle of the invention is: according to the special processing method of the active disturbance rejection controller to the system disturbance, the unbalanced vibration received by the magnetic suspension rotor system is regarded as an external disturbance, and the linear extended state observer with model assistance is used for real-time monitoring of it. It is estimated and compensated so that a co-frequency compensation signal with suitable amplitude and phase is superimposed on the control signal to offset the unbalanced excitation force of the rotor, and realize the active vibration control of the extremely small displacement of the magnetic suspension rotor system. The invention designs the linear active disturbance rejection controller of each subsystem on the basis of establishing the generalized controlled object mathematical model of the magnetic suspension rotor system and the linear active disturbance rejection control principle, and finally realizes the active control of the rotor system with minimal displacement.
本发明与现有控制方案相比的优点在于:Compared with the existing control scheme, the advantages of the present invention are:
(1)本发明提出了一种基于线性自抗扰控制器的磁悬浮分子泵转子极小位移主动控制方法,该方法结构简单,参数调理容易,易于实现,可应用于对高速磁悬浮转子位移振动幅度要求较高的场合。(1) The present invention proposes an active control method for the minimal displacement of a magnetic levitation molecular pump rotor based on a linear active disturbance rejection controller. The method has a simple structure, easy parameter adjustment, and easy implementation. occasions with higher requirements.
(2)本发明所提出的方法不需要被控对象的精确模型,而且能对系统模型不确定性和陀螺效应进行估计和补偿,有效提高系统的鲁棒性。(2) The method proposed by the present invention does not require an accurate model of the controlled object, and can estimate and compensate for the uncertainty of the system model and the gyroscopic effect, thereby effectively improving the robustness of the system.
附图说明Description of drawings
图1为本发明方案的流程框图;Fig. 1 is the flow chart of the scheme of the present invention;
图2为磁悬浮转子系统结构图,其中,1代表转子,2代表传感器A,3代表磁轴承A,4代表磁轴承B,5代表传感器B;Figure 2 is a structural diagram of a magnetic suspension rotor system, wherein 1 represents the rotor, 2 represents the sensor A, 3 represents the magnetic bearing A, 4 represents the magnetic bearing B, and 5 represents the sensor B;
图3为磁轴承控制系统结构框图;Fig. 3 is the structural block diagram of the magnetic bearing control system;
图4为单通道线性自抗扰控制器结构图;Figure 4 is a structural diagram of a single-channel linear active disturbance rejection controller;
图5为具有模型辅助的线性扩张状态观测器结构图;5 is a structural diagram of a linear expansion state observer with model assistance;
图6为线性自抗扰控制器Ax通道位移信号频谱图;Figure 6 is a spectrum diagram of the displacement signal of the Ax channel of the linear active disturbance rejection controller;
图7为传统PID控制器Ax通道位移信号频谱图;Fig. 7 is the frequency spectrum diagram of displacement signal of Ax channel of traditional PID controller;
图8为含随机噪声的线性自抗扰控制器Ax通道位移信号频谱图;Fig. 8 is the frequency spectrum diagram of the displacement signal of the Ax channel of the linear active disturbance rejection controller with random noise;
图9为含随机噪声的传统PID控制器Ax通道位移信号频谱图。FIG. 9 is a spectrum diagram of the displacement signal of the Ax channel of the traditional PID controller with random noise.
具体实施方案specific implementation
下面结合附图以及具体实施方式进一步说明本发明。The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
如图1-9所示,本发明一种磁悬浮分子泵转子极小位移主动控制方法的具体步骤如下:As shown in Figures 1-9, the specific steps of a method for actively controlling the minimal displacement of a magnetic levitation molecular pump rotor according to the present invention are as follows:
(1)如图1所示,本发明首先分析磁悬浮转子系统不平衡振动形成机理,建立动不平衡的磁悬浮转子动力学方程,然后考虑功放环节和传感器环节,得到磁悬浮转子系统的广义被控对象数学模型,最后,基于线性自抗扰控制原理和广义被控对象数学模型,设计出具有模型辅助的线性自抗扰控制器,用于磁悬浮转子系统极小位移的主动控制。(1) As shown in Figure 1, the present invention first analyzes the unbalanced vibration formation mechanism of the magnetic suspension rotor system, establishes a dynamic unbalanced magnetic suspension rotor dynamic equation, and then considers the power amplifier link and the sensor link to obtain the generalized controlled object of the magnetic suspension rotor system Mathematical model. Finally, based on the linear active disturbance rejection control principle and the generalized mathematical model of the controlled object, a model-aided linear active disturbance rejection controller is designed for the active control of the extremely small displacement of the magnetic levitation rotor system.
(2)如图2所示,本发明将磁悬浮分子泵转子视为刚性转子,磁悬浮转子的动不平衡是由静不平衡和偶不平衡两部分组成,主要是由于转子质量分布不均匀、加工和安装误差等原因造成。其中静不平衡是由于转子存在质量偏心,即惯性轴与几何轴互不重合,造成静不平衡力;偶不平衡是由于转子惯性轴与几何轴不平行,造成扰动力矩。以动不平衡转子的质心为原点建立广义坐标系,得到磁悬浮转子的动力学方程:(2) As shown in Figure 2, the present invention regards the magnetic levitation molecular pump rotor as a rigid rotor, and the dynamic unbalance of the magnetic levitation rotor is composed of two parts: static unbalance and even unbalance, mainly due to uneven rotor mass distribution, processing and installation errors. The static unbalance is due to the mass eccentricity of the rotor, that is, the inertia axis and the geometric axis do not coincide with each other, resulting in static unbalanced force; the even unbalance is due to the rotor inertia axis and the geometric axis are not parallel, resulting in disturbance torque. The generalized coordinate system is established with the center of mass of the dynamically unbalanced rotor as the origin, and the dynamic equation of the magnetic suspension rotor is obtained:
式中:m为转子质量,Jx、Jy和Jz分别是转子绕x、y和z轴的转动惯量;Fx是转子受到沿x方向的磁力,Fy是转子受到沿y方向的磁力,Mx是转子受到x方向的磁力矩、My是转子受到y方向的磁力矩;Ω是转子旋转角速度;αG、βG是转子在广义坐标系下绕x轴和y轴的角位移;xG、yG分别是转子在广义坐标系下的位移;fxd是沿x方向的静不平衡力,fyd是沿y方向的静不平衡力;pxd是沿x方向的扰动力矩,pyd是沿y方向的扰动力矩。In the formula: m is the mass of the rotor, J x , J y and J z are the moments of inertia of the rotor around the x, y and z axes, respectively; F x is the magnetic force along the x direction by the rotor, and F y is the rotor received along the y direction. Magnetic force, M x is the magnetic moment that the rotor receives in the x direction, M y is the magnetic moment that the rotor receives in the y direction; Ω is the rotational angular velocity of the rotor; α G , β G are the angles of the rotor around the x-axis and the y-axis in the generalized coordinate system Displacement; x G , y G are the displacement of the rotor in the generalized coordinate system respectively; f xd is the static unbalanced force along the x direction, f yd is the static unbalanced force along the y direction; p xd is the disturbance along the x direction moment, p yd is the disturbance moment along the y direction.
其中:in:
式中:ε为静不平衡偏心距;σ为旋转轴与坐标轴夹角;θ为静不平衡角位置;为偶不平衡的角位置。Where: ε is the static unbalance eccentric distance; σ is the angle between the rotation axis and the coordinate axis; θ is the static unbalance angle position; is the angular position of the couple unbalance.
通过坐标转换,将广义坐标系下的广义力向量F=[Fx Mx Fy My]和广义位移向量q=[xG αG yG βG]用磁轴承坐标系下的磁轴力向量f=[fax fbx fay fby]和位移向量qh=[xaxb ya yb]分别表示为:Through coordinate transformation, the generalized force vector F=[F x M x F y My y ] and the generalized displacement vector q=[x G α G y G β G ] in the generalized coordinate system are used as the magnetic axis in the magnetic bearing coordinate system The force vector f = [f ax f bx f ay f by ] and the displacement vector q h = [x a x b y a y b ] are expressed as:
然后,通过泰勒级数展开得到在磁轴承A、B处的磁轴承力在工作点处近似线性化关系:Then, the magnetic bearing forces at the magnetic bearings A and B are approximately linearized at the working point by Taylor series expansion:
式中:ki=[kiax kibx kiay kiby]为磁轴承工作点处的位移刚度,kh=[khax khbx khaykhby]为磁轴承工作点处的电流刚度。In the formula: k i =[ kiax k ibx k iay k iby ] is the displacement stiffness at the working point of the magnetic bearing, and k h =[k hax k hbx k hay k hby ] is the current stiffness at the working point of the magnetic bearing.
最后,得到磁悬浮转子在磁轴承坐标系下的动力学方程:Finally, the dynamic equation of the magnetic suspension rotor in the magnetic bearing coordinate system is obtained:
式中:ωi(i=1,2,3,4)为磁悬浮转子系统不平衡振动量,等效为系统的一种外部扰动。ωi(i=1,2,3,4)的具体表达:In the formula: ω i (i=1, 2, 3, 4) is the unbalanced vibration of the magnetic suspension rotor system, which is equivalent to an external disturbance of the system. The specific expression of ω i (i=1,2,3,4):
(3)如图3所示,然后将功放环节和传感器环节纳入考虑,将功放等效为一节惯性环节传感器等效为比例环节Gs(s)=ks。令 得到磁悬浮转子系统的广义被控对象数学模型:(3) As shown in Figure 3, then the power amplifier and sensor links are taken into account, and the power amplifier is equivalent to an inertial link The sensor is equivalent to the proportional element G s ( s )=ks . make The generalized controlled object mathematical model of the magnetic suspension rotor system is obtained:
(4)如图4所示,为线性自抗扰控制器的基本结构,主要由两部分构成:线性误差组合控制律和线性扩展状态观测器,根据线性自抗扰控制理论,将磁悬浮转子系统的广义被控对象数学模型重写成下式:(4) As shown in Figure 4, it is the basic structure of the linear active disturbance rejection controller, which is mainly composed of two parts: the linear error combined control law and the linear extended state observer. According to the linear active disturbance rejection control theory, the magnetic suspension rotor system is The generalized plant mathematical model of is rewritten into the following formula:
式中:xa、xb、ya和yb时是磁悬浮转子分别在Ax、Bx、Ay和By方向上的线性位移量;f(·)为系统的总扰动,它包含系统模型的不确定性和不平衡扰动量ωi(i=1,2,3,4);b0i(i=1,2,3,4)是控制信号ui(t)(i=1,2,3,4)的系数。磁悬浮转子系统四个通道的各子式可以视为单路需要自抗扰控制子系统,对于Ax通道,进行线性自抗扰控制器设计如下,利用线性扩张状态观测器对包含转子不平衡量的总扰动f(·)进行实时估计和补偿,从而实现磁悬浮转子系统极小位移主动控制。In the formula: x a , x b , y a and y b are the linear displacements of the magnetic suspension rotor in the directions of Ax, Bx, Ay and By, respectively; f( ) is the total disturbance of the system, which includes the differences of the system model. Deterministic and unbalanced disturbances ω i (i=1,2,3,4); b 0i (i=1,2,3,4) is the control signal u i (t) (i=1,2,3 ,4) coefficients. Each sub-form of the four channels of the magnetic levitation rotor system can be regarded as a single channel requiring an active disturbance rejection control subsystem. For the Ax channel, the linear active disturbance rejection controller is designed as follows. The linear expansion state observer is used to control the total amount including the rotor unbalance. The disturbance f(·) is estimated and compensated in real time, so as to realize the active control of the minimal displacement of the magnetic suspension rotor system.
(5)如图5所示,采用具有模型辅助的线性扩张状态观测器,将磁悬浮转子系统数学建模获得的部分已知信息纳入线性扩张状态观测器设计,可以降低观测器计算负荷,或在不降低扩张状态观测器带宽的前提下,提高对扰动的估计精度,从而对转子的高精度控制效果。其具体表达式为:(5) As shown in Figure 5, the linear expansion state observer with model assistance is adopted, and some known information obtained by mathematical modeling of the magnetic suspension rotor system is incorporated into the design of the linear expansion state observer, which can reduce the computational load of the observer, or Under the premise of not reducing the bandwidth of the expanded state observer, the estimation accuracy of the disturbance is improved, so that the high-precision control effect of the rotor is achieved. Its specific expression is:
式中:y是Ax通道传感器的位移输出,y=xa;u是控制器输出的控制信号;z1是y的跟踪信号,z2是的跟踪信号,z3是的跟踪信号,z4是总扰动f(·)的跟踪信号;a0是y的系数,a1是的系数,a2是的系数;b0是Ax通道控制信号系数b01的估计值,由建模可得b0=b1kwkswwkiax,b0越接近b01,则线性扩张观测器对扰动f(·)的估计更准确;L=[β1 β2 β3 β4]为线性扩张状态观测器增益,是待确定的参数,一般取β1=4ω0,β2=6ω0 2,β3=4ω0 3,β4=ω0 4,ω0是线性扩张状态观测器带宽。In the formula: y is the displacement output of the Ax channel sensor, y=x a ; u is the control signal output by the controller; z 1 is the tracking signal of y, and z 2 is The tracking signal, z 3 is The tracking signal of , z 4 is the tracking signal of the total disturbance f( ); a 0 is the coefficient of y, and a 1 is The coefficient of , a 2 is b 0 is the estimated value of the Ax channel control signal coefficient b 01 , which can be obtained by modeling b 0 =b 1 k w k s w w k iax , the closer b 0 is to b 01 , the linear expansion observer will disturb the The estimation of f(·) is more accurate; L=[β 1 β 2 β 3 β 4 ] is the gain of the linear expansion state observer, which is the parameter to be determined. Generally, β 1 =4ω 0 ,β 2 =6ω 0 2 , β 3 =4ω 0 3 , β 4 =ω 0 4 , ω 0 is the linear expansion state observer bandwidth.
线性状态误差反馈控制律的表达式为:The expression of the linear state error feedback control law is:
式中:u0为误差的线性组合;u是控制器的输出;ysp是设定的位移跟踪目标值;KP是比例系数,Kd1是一阶微分系数,Kd2是二阶微分系数,是待确定参数,一般取Kp=ωc 3,Kd1=3ωc 2,Kd2=3ωc,ωc为控制器带宽。Where: u 0 is the linear combination of errors; u is the output of the controller; y sp is the set displacement tracking target value; K P is the proportional coefficient, K d1 is the first-order differential coefficient, and K d2 is the second-order differential coefficient , is the parameter to be determined, generally take K p =ω c 3 , K d1 =3ω c 2 , K d2 =3ω c , and ω c is the controller bandwidth.
本发明方法可以通过建模获得控制参数b0的近似值,又因为ωc与ω0存在经验关系:ω0=5~10ωc,仅需要调节参数ωc即可完成线性自抗扰控制器参数调理,所提出方法具有结构简单,参数调理容易,易于实现的优点。The method of the present invention can obtain the approximate value of the control parameter b 0 through modeling, and because ω c and ω 0 have an empirical relationship: ω 0 =5-10ω c , the linear active disturbance rejection controller parameters can be completed only by adjusting the parameter ω c conditioning, the proposed method has the advantages of simple structure, easy parameter conditioning and easy implementation.
(6)为了验证本发明提出主动控制方法的有效性,搭建Simulink仿真模型,使用本发明方法与传统PID控制器进行对比仿真,仿真参数如下:m=19.6kg,Jx=0.2039,Jy=0.2039,Jz=0.1268,lma=0.0279m,lmb=0.1251m,kia=400N/A,kib=115N/A,kha=1.4N/um,khb=0.4N/um。(6) In order to verify the effectiveness of the active control method proposed by the present invention, build a Simulink simulation model, and use the method of the present invention to compare and simulate the traditional PID controller. The simulation parameters are as follows: m=19.6kg, J x =0.2039, J y = 0.2039, Jz= 0.1268 , lma= 0.0279m , lmb = 0.1251m , kia=400N/A, kib=115N/A, kha = 1.4N /um, khb =0.4N/um.
(7)对比仿真结果如下:(7) The comparative simulation results are as follows:
如图6,图7所示,为磁悬浮分子泵在转速为24000r/min情况下运行,使用本发明方法(图6)和传统PID控制器(图7)的Ax通道位移信号频谱图。对比可得:本发明方法位移同频振动频率幅值为0.06,而传统PID控制器位移同频振动频率幅值为0.18,显然,本发明方法对位移同频振动抑制效果明显优于传统PID控制方法。As shown in Fig. 6 and Fig. 7, the magnetic levitation molecular pump is running at a rotational speed of 24000r/min, using the method of the present invention (Fig. 6) and the traditional PID controller (Fig. 7) Ax channel displacement signal spectrum diagram. The comparison can be obtained: the frequency amplitude of the displacement co-frequency vibration of the method of the present invention is 0.06, while the traditional PID controller displacement co-frequency vibration frequency amplitude is 0.18. Obviously, the method of the present invention is significantly better than the traditional PID control in terms of the suppression effect of the displacement co-frequency vibration. method.
如图8,图9所示,为磁悬浮分子泵在转速为27000r/min情况下运行,并添加大小为1e-5的随机噪声信号,使用本发明方法(图8)和传统PID控制器(图9)的Ax通道位移信号频谱图。对比可得:本发明方法对系统随机噪声的抑制效果明显优于传统PID控制方法;其次,随着转速升高,由于陀螺效应,磁悬浮转子系统出现章动频率,如果不加以控制,会导致系统失稳,相比于传统控PID控制方案,本发明方法抑制章动频率效果显著,能极大提高系统的鲁棒性。As shown in Fig. 8 and Fig. 9, the magnetic levitation molecular pump is operated at a rotational speed of 27000r/min, and a random noise signal of 1e-5 is added, using the method of the present invention (Fig. 8) and the traditional PID controller (Fig. 9) Spectrogram of the displacement signal of the Ax channel. It can be seen from the comparison: the suppression effect of the method of the present invention on the random noise of the system is obviously better than that of the traditional PID control method; secondly, with the increase of the rotating speed, due to the gyro effect, the magnetic suspension rotor system will appear nutation frequency, if not controlled, it will lead to the system Compared with the traditional PID control scheme, the method of the present invention has a remarkable effect of suppressing the nutation frequency, and can greatly improve the robustness of the system.
本发明未详细阐述部分属于本领域公知技术。The parts of the present invention that are not described in detail belong to the well-known technology in the art.
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Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP1895180A2 (en) * | 2006-08-30 | 2008-03-05 | Ebara Corporation | Magnetic bearing device, rotating system therewith and method of identification of the model of the main unit in a rotating system |
CN102425555A (en) * | 2011-11-11 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Method for obtaining radial suspension centers of rotor of magnetic molecular pump |
CN102425554A (en) * | 2011-11-10 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Gain scheduling control method for magnetic suspension molecular pump |
CN102435131A (en) * | 2011-11-11 | 2012-05-02 | 北京中科科仪技术发展有限责任公司 | Radial displacement sensor and rotor radial displacement detection system of magnetically levitated molecular pump |
JP2015132340A (en) * | 2014-01-14 | 2015-07-23 | 株式会社島津製作所 | Magnetic bearing device and vacuum pump |
-
2018
- 2018-04-03 CN CN201810285534.1A patent/CN108716471B/en not_active Expired - Fee Related
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP1895180A2 (en) * | 2006-08-30 | 2008-03-05 | Ebara Corporation | Magnetic bearing device, rotating system therewith and method of identification of the model of the main unit in a rotating system |
CN102425554A (en) * | 2011-11-10 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Gain scheduling control method for magnetic suspension molecular pump |
CN102425555A (en) * | 2011-11-11 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Method for obtaining radial suspension centers of rotor of magnetic molecular pump |
CN102435131A (en) * | 2011-11-11 | 2012-05-02 | 北京中科科仪技术发展有限责任公司 | Radial displacement sensor and rotor radial displacement detection system of magnetically levitated molecular pump |
JP2015132340A (en) * | 2014-01-14 | 2015-07-23 | 株式会社島津製作所 | Magnetic bearing device and vacuum pump |
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