CN108716471B - Active control method for minimum displacement of rotor of magnetic suspension molecular pump - Google Patents

Abstract

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

A method for active control of minimal displacement of the rotor of a magnetic levitation molecular pump

technical field

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.

Background technique

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.

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 . Method 1 has the advantages of low running noise and small moving base effect, etc., but it cannot suppress the whirl at the same frequency of rotation speed in the rotor displacement signal. The system is unstable; the second scheme can make the rotor rotate with high precision and small whirling radius, but because the same-frequency bearing force reacts on the magnetic bearing, the system noise and the dynamic base effect are more obvious, and the system power consumption increases.

SUMMARY OF THE INVENTION

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.

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) Rotordynamic model of magnetic levitation molecular pump

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:

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;

in:

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.

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:

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) Design a linear active disturbance rejection controller

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:

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.

The expression form of the linear state error feedback control law is:

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.

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.

Compared with the existing control scheme, the advantages of the present invention are:

(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) 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.

Description of drawings

Fig. 1 is the flow chart of the scheme of the present invention;

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;

Fig. 3 is the structural block diagram of the magnetic bearing control system;

Figure 4 is a structural diagram of a single-channel linear active disturbance rejection controller;

5 is a structural diagram of a linear expansion state observer with model assistance;

Figure 6 is a spectrum diagram of the displacement signal of the Ax channel of the linear active disturbance rejection controller;

Fig. 7 is the frequency spectrum diagram of displacement signal of Ax channel of traditional PID controller;

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;

FIG. 9 is a spectrum diagram of the displacement signal of the Ax channel of the traditional PID controller with random noise.

specific implementation

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

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) 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) 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:

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.

in:

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.

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:

Then, the magnetic bearing forces at the magnetic bearings A and B are approximately linearized at the working point by Taylor series expansion:

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.

Finally, the dynamic equation of the magnetic suspension rotor in the magnetic bearing coordinate system is obtained:

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):

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) 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:

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) 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:

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＝b₁k_wk_sw_wk_iax，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.

The expression of the linear state error feedback control law is:

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.

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) 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) The comparative simulation results are as follows:

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.

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.

The parts of the present invention that are not described in detail belong to the well-known technology in the art.

Claims (1)

1. A magnetic suspension molecular pump rotor minimum displacement active control method is characterized in that: the method comprises the following steps:

(1) rotor dynamics model of magnetic suspension molecular pump

The rotor of the magnetic suspension molecular pump is regarded as a rigid rotor, the dynamic unbalance of the magnetic suspension rotor is composed of a static unbalance part and an even unbalance part, wherein the static unbalance is caused by the fact that the rotor has mass eccentricity, namely an inertia shaft and a geometric shaft are not overlapped with each other, so that a static unbalance force is generated; the even unbalance is caused by the fact that an inertia shaft of the rotor is not parallel to a geometric shaft, so that disturbance torque is generated; establishing a generalized coordinate system by taking the mass center of the dynamic unbalance rotor as an origin to obtain a dynamic equation of the magnetic suspension rotor:

in the formula: m is rotor mass, J_x、J_yAnd J_zThe moments of inertia of the rotor about the x, y and z axes, respectively; f_xThe rotor is subjected to a magnetic force in the x-direction, F_yThe rotor being subjected to magnetic forces in the y-direction, M_xThe rotor is subjected to magnetic moment in the x direction, M_yThe rotor is subjected to magnetic moment in the y direction; Ω is the rotor rotational angular velocity; alpha is alpha_G、β_GIs the angular displacement of the rotor around the x-axis and the y-axis under a generalized coordinate system; x is the number of_G、y_GRespectively, the displacement of the rotor under a generalized coordinate system; f. of_xdIs the static unbalance force in the x-direction, f_ydIs a static imbalance force in the y-direction; p is a radical of_xdIs the disturbance torque in the x-direction, p_ydIs the disturbance torque in the y-direction;

wherein:

in the formula: epsilon is static unbalance eccentricity; sigma is an included angle between the rotating shaft and the coordinate axis; theta is the static imbalance angular position;

an angular position that is even unbalanced;

considering that a power amplifier system is a first-order inertia link, a sensor is a proportion link, and combining a kinetic equation of the magnetic suspension rotor, a generalized controlled object mathematical model of four radial channels of the magnetic suspension rotor system is obtained:

in the formula: x is the number of_a、x_b、y_aAnd y_bThe linear displacement of the magnetic suspension rotor in the Ax, Bx, Ay and By directions respectively is measured; f (-) is the total disturbance of the system, where ω is_i(i ═ 1,2,3,4) is the unbalance disturbance variable of the magnetic levitation rotor; b_0i(i-1, 2,3,4) is a control signal u_i(t) (i ═ 1,2,3, 4); the sub-type of four channels of the magnetic suspension rotor system can be regarded as a single channel needing active disturbance rejection controllerThe system carries out linear active disturbance rejection controller design on an Ax channel, and carries out real-time estimation and compensation on total disturbance f (-) including the unbalance amount of a rotor by utilizing a linear extended state observer, so that the active control of the minimum displacement of the magnetic suspension rotor system is realized;

(2) designing a linear active disturbance rejection controller

The four channels of the magnetic suspension rotor system adopt controllers with the same structure, and for an Ax channel, the magnetic suspension rotor system has a model-assisted linear extended state observer expression form:

in the formula: y is the displacement output of the Ax channel sensor, y ═ x_a(ii) a u is a control signal output by the controller; z is a radical of₁Is the tracking signal of y, z₂Is that

Of the tracking signal z₃Is that

Of the tracking signal z₄A tracking signal that is the total disturbance f (·); a is₀Is a coefficient of y, a₁Is that

Coefficient of (a)₂Is thatThe coefficient of (a); b₀Is the Ax channel control signal coefficient b₀₁An estimated value of (d); l ═ beta₁ β₂ β₃ β₄]Linear extended state observer gain;

the expression form of the linear state error feedback control law is as follows:

in the formula: u. of₀Is a linear combination of errors; u is the output of the controller; k_PIs the proportionality coefficient, K_d1Is a first order differential coefficient, K_d2Are second order differential coefficients, all of which are controller adjustment parameters; y is_spIs the set displacement tracking target value.

Images