CN106026828A - Radial magnetic bearing displacement detection method and system based on cubature Kalman filter - Google Patents

Abstract

The invention relates to a radial magnetic bearing displacement detection method and a system based on a cubature Kalman filter, wherein the radial magnetic bearing displacement detection method comprises the following steps: obtaining radial displacement output signals and rotation speed signals of the rotor in the x and y directions according to the continuous time system, and discretizing the continuous time system to extract displacement information of the rotor by a volume Kalman filter algorithm; the invention avoids the linear treatment of the radial magnetic bearing which is essentially a nonlinear model, realizes the operation without a displacement sensor, has strong interference suppression capability, can accurately detect the displacement of the radial magnetic bearing, and can also detect the displacement of the radial magnetic bearing when the exact property of the system is unknown.

Description

Radial magnetic bearing displacement detection method and system based on cubature Kalman filter

Technical Field

The invention relates to a method for accurately measuring the displacement of a radial magnetic bearing in the field of high-speed and high-precision motor transmission, which is mainly used for modern equipment such as artificial satellites and missiles, high-performance flywheel energy storage, generators, artificial heart pumps and the like, and belongs to the field of electric transmission control equipment.

Background

Compared with mechanical bearings, the magnetic bearings have the advantages of high rotating speed, no abrasion, long service life, no need of lubrication and the like. The magnetic bearing is widely applied to the fields of flywheel energy storage, high-speed and high-precision motors, artificial heart pumps and other electric transmission, and is particularly suitable for severe environments such as high temperature and the like. Magnetic bearings are essentially open-loop unstable nonlinear systems and therefore require closed-loop control systems to be designed to accommodate them. The linear control theory is widely applied to a magnetic bearing control system, and a common linearization method is to perform Taylor expansion on a mathematical model expression of the suspension force of the system near a balance point of a magnetic suspension rotor and omit infinitesimal quantity above the second order, so as to design the control system. The displacement information is an important parameter in the mathematical model of the suspension force, so the accuracy and the real-time performance of the displacement information are directly related to the stability of the magnetic bearing. Although the linear control theory is mature, compared with a nonlinear control method, the displacement detection precision and the real-time performance of the magnetic bearing are poor, and the nonlinear control method of the volume Kalman filter is applied to the magnetic bearing, so that the displacement detection precision and the real-time performance can be effectively improved.

At present, most methods for acquiring radial displacement of a rotor are mechanical eddy current displacement sensors, but the displacement sensors have many defects: on one hand, the maximum rotating speed of the magnetic bearing is restricted; on the other hand, the maintenance is difficult, the reliable operation of the whole control system is influenced, and the application of the control system in the occasions with severe environment is limited. The control system without the displacement sensor does not need detection hardware, so that various troubles brought by the displacement sensor are avoided, the reliability of the system is improved, and the cost of the system is reduced; on the other hand, the system is small in size and light in weight. The invention applies the displacement-free sensor to the magnetic bearing system, reduces the connecting line with the controller and simplifies the maintenance requirement.

The method for detecting the displacement of the magnetic bearing by the displacement-free sensor comprises an extended Kalman filter, an unscented Kalman filter and particle filtering. Compared with the three methods, the cubature Kalman filter has higher filtering precision and better real-time property. Through searching relevant patents and documents at home and abroad, no displacement sensor-free control method and device of the volume Kalman filter applied to the magnetic bearing is available.

Disclosure of Invention

The invention aims to provide a method for constructing a continuous time system for detecting the displacement of a radial magnetic bearing.

In order to solve the technical problem, the invention provides a method for constructing a continuous time system for detecting the displacement of a radial magnetic bearing, which comprises the following steps:

step S1, calculating the suspension force of the rotor in the three magnetic pole directions;

step S2, a continuous time system is established.

Further, the method for calculating the levitation force applied to the rotor in the three magnetic pole directions in step S1 includes:

step S11, calculating the magnetic flux of each magnetic pole air gap, as shown in equation (1):

$\left\{\begin{array}{c}{\mathrm{\Φ}}_A=N_3\frac{(R_B+R_C)i_A-R_C{i}_B-R_B{i}_C}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\\ {\mathrm{\Φ}}_B=N_3\frac{(R_A+R_C)i_B-R_C{i}_A-R_A{i}_C}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\\ {\mathrm{\Φ}}_C=N_3\frac{(R_A+R_B)i_C-R_A{i}_B-R_B{i}_A}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\end{array}\right.---\left(1\right)$

in the formula (1), phi_A、Φ_B、Φ_CMagnetic fluxes corresponding to the three-phase magnetic pole air gaps respectively; n is a radical of₃Equivalent turns in the x and y directions; r_A、R_B、R_CRespectively the magnetic resistance of three magnetic pole air gaps; i.e. i_A、i_B、i_CRespectively, the current flowing through the three magnetic poles;

step S12, for N in formula (1)₃i_A，N₃i_B，N₃i_CAnd (3) converting the three-phase static coordinate system into a two-phase static coordinate system, namely as shown in formula (2):

$\left[\begin{array}{c}{N}_3{i}_A\\ N_3{i}_B\\ N_3{i}_C\end{array}\right]=\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& -\frac{1}{2}\\ 0& 1\\ -\frac{\sqrt{3}}{2}& -\frac{1}{2}\end{array}\right]\left[\begin{array}{c}{N}_2{i}_x\\ N_2{i}_y\end{array}\right]---\left(2\right)$

in the formula (2), N₂Is a three-phase AC coil with ampere turns i_x、i_yActual control currents in x and y directions respectively;

in the step of S13,projecting the suspension force to the x and y directions to obtain two forces respectively_x(t) and f_y(t) represents;

f is_x(t) and f_yThe expression of (t) is as follows:

$\left\{\begin{array}{c}{f}_x\left(t\right)=\frac{\sqrt{3}}{2\mathrm{\μ}S}({\mathrm{\Φ}}_C^2\cos \mathrm{\α}+{\mathrm{\Φ}}_B^2\cos (\mathrm{\α}+\frac{2}{3}\mathrm{\π})+{\mathrm{\Φ}}_A^2\cos (\mathrm{\α}-\frac{2}{3}\mathrm{\π}\left)\right)\\ f_y\left(t\right)=\frac{1}{2\mathrm{\μ}S}({\mathrm{\Φ}}_C^2\sin \mathrm{\α}+{\mathrm{\Φ}}_B^2\sin (\mathrm{\α}+\frac{2}{3}\mathrm{\π})+{\mathrm{\Φ}}_A^2\sin (\mathrm{\α}-\frac{2}{3}\mathrm{\π}\left)\right)\end{array}\right.---\left(3\right)$

in the formula (3), μ is magnetic permeability, S is magnetic pole equivalent area, and α is magnetic pole azimuth.

Further, the continuous-time system is as shown in equation (4):

$\stackrel{\·}{X}\left(t\right)=f_c\left(X\right(t),u(t\left)\right)+v\left(t\right)---\left(4\right)$

in the formula:

$\stackrel{\·}{X}\left(t\right)=\frac{d}{dt}\left(\begin{array}{c}x\left(t\right)\\ V\left(t\right)\\ i_x\left(t\right)\\ f_{zx}\left(t\right)\\ y\left(t\right)\\ V_y\left(t\right)\\ i_y\left(t\right)\\ f_{zy}\left(t\right)\end{array}\right);f_c\left(X\right(t),u(t\left)\right)=\left\{\begin{array}{c}{V}_x\left(t\right)\\ \frac{1}{m}\[f_x\left(t\right)+f_{zx}\left(t\right)\]\\ \frac{K_a}{T_a}{i}_{xref}\left(t\right)-\frac{1}{T_a}{i}_x\left(t\right)\\ 0\\ V_y\left(t\right)\\ \frac{1}{m}\[f_y\left(t\right)+f_{zy}\left(t\right)\]\\ \frac{K_a}{T_a}{i}_{yref}\left(t\right)-\frac{1}{T_a}{i}_y\left(t\right)\\ 0\end{array}\right.;v\left(t\right)=\left\{\begin{array}{c}{v}_x\left(t\right)\\ v_{Vx}\left(t\right)\\ v_{i_x}\left(t\right)\\ v_{f_{zx}}\left(t\right)\\ v_y\left(t\right)\\ v_{V_y}\left(t\right)\\ v_{i_y}\left(t\right)\\ v_{f_{zy}}\left(t\right)\end{array}\right.;$

wherein, V_x，V_yThe rotation speeds of the rotor in the x and y directions respectively; f. of_zxAnd f_zyPerturbation of the rotor in the x and y directions, respectively; t is_a、K_aRespectively an equivalent time constant and a power amplification gain; i.e. i_xrefAnd i_yrefReference currents in the x and y directions, respectively; f. of_x(x,i_x) And f_y(x,i_y) Respectively as a function of the displacement in the x direction, the control current, the displacement in the y direction, and the control current; m is the rotor mass; v. of_xIs the interference amount of the displacement of the rotor in the x direction, v_VxFor the disturbance variable v of the rotor speed in the x direction_ixFor the current disturbance variable, v, of the rotor in the x-direction_fzxDisturbance quantity v of rotor in x direction_yIs the interference amount of the displacement of the rotor in the y direction, v_VyFor the disturbance variable v of the rotor speed in the y direction_iyFor the current disturbance variable, v, of the rotor in the y-direction_fzyIs the disturbance quantity of the rotor in the y direction.

In another aspect, the invention further provides a radial magnetic bearing displacement detection method applying the construction method, so that the radial magnetic bearing displacement detection method has better robustness and anti-interference performance.

The radial magnetic bearing displacement detection method comprises the following steps:

and obtaining radial displacement output signals and rotation speed signals of the rotor in the x and y directions according to the continuous time system, and discretizing the continuous time system to realize the extraction of the displacement information of the rotor by a volume Kalman filter algorithm.

In a third aspect, the invention also provides a displacement detection method for the radial magnetic bearing.

The radial magnetic bearing displacement detection method is characterized in that a feedback loop is constructed through a cubature Kalman filter to adjust the current generated by a voltage source inverter to drive the magnetic bearing to realize closed-loop stable suspension.

Furthermore, a feedback loop is constructed by a cubature Kalman filter, i.e. the cubature Kalman filter generates a current I according to a voltage source inverter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estWith a given reference position signal x_refAnd y_refComparing, processing the obtained result by a first P controller, and respectively comparing with the rotating speed signal v obtained by the observer_xestAnd v_yestGenerating a reference current signal i by comparing the current signals processed by the second P controller_xrefAnd i_yref(ii) a And the adjusting voltage source inverter generates current to drive the magnetic bearing to realize closed-loop stable suspension, namely, the reference current signal i is simultaneously transmitted_xrefAnd i_yrefAfter comparing with the current obtained by the 2/3 converter, the comparison result is processed by a PID controller to obtain a control voltage u_xAnd u_yThen the control voltage u is applied_xAnd u_yGenerating a current I by a voltage source inverter_A，I_B，I_CThe magnetic bearing is driven to realize closed-loop stable suspension.

In a fourth aspect, the invention also provides a radial magnetic bearing displacement detection system.

The radial magnetic bearing displacement detection system comprises: a feedback loop is constructed through a cubature Kalman filter to adjust the current generated by a voltage source inverter to drive the magnetic bearing to realize closed-loop stable suspension.

Further, the feedback loop comprises: the system comprises a volume Kalman filter, an observer, a first P controller and a second P controller; generating a current I from a voltage source inverter by a volumetric Kalman filter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estWith a given reference position signal x_refAnd y_refComparing, processing the obtained result by a first P controller, and respectively comparing with the rotating speed signal v obtained by the observer_xestAnd v_yestGenerating a reference current signal i by comparing the current signals processed by the second P controller_xrefAnd i_yref。

Further, the radial magnetic bearing displacement detection system further comprises: 2/3 converter, PID controller and voltage source inverter; reference current signal i_xrefAnd i_yrefAfter comparing with the current obtained by the 2/3 converter, the comparison result is processed by a PID controller to obtain a control voltage u_xAnd u_yThen the control voltage u is applied_xAnd u_yI generation by a voltage source inverter_A，I_B，I_CThe magnetic bearing is driven to realize closed-loop stable suspension.

The invention has the beneficial effects that:

the volume Kalman filter overcomes the theoretical limitations that an Extended Kalman Filter (EKF) is low in first-order linear approximate precision, a Jacobian matrix needs to be calculated, a nonlinear function is required to be continuous and differentiable, and the like, and in a magnetic bearing model with strong nonlinearity, CKF overcomes the defects of poor EKF filtering precision and poor numerical stability.

The volume Kalman filter (CKF) adopts a spherical radial rule to approximate state posterior distribution in an optimal frame, so that the problem that the Unscented Kalman Filter (UKF) has poor filtering performance and even diverges when solving the problem of nonlinear state estimation of high dimensionality (more than or equal to 20) is avoided.

The calculated amount of Particle Filter (PF) is increased along with the increase of the number of particles, while the calculated amount of the volume Kalman filter is far smaller than the particle filter, and the particle degradation and the depletion of the PF caused by random sampling can not occur, so that the control system of the invention can better meet the real-time requirement of a magnetic bearing model on displacement detection.

Drawings

The invention is further illustrated with reference to the following figures and examples.

FIG. 1 is a system block diagram of the radial magnetic bearing displacement detection system of the present invention.

Detailed Description

The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.

Example 1

As shown in fig. 1, the present embodiment 1 provides a method for constructing a continuous time system for detecting displacement of a radial magnetic bearing, comprising the following steps:

step S1, calculating the suspension force of the rotor in the three magnetic pole directions;

step S2, a continuous time system is established.

Specifically, the method for calculating the levitation force applied to the rotor in the three magnetic pole directions in step S1 includes:

step S11, calculating the magnetic flux of each magnetic pole air gap, as shown in equation (1):

$\left\{\begin{array}{c}{\mathrm{\Φ}}_A=N_3\frac{(R_B+R_C)i_A-R_C{i}_B-R_B{i}_C}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\\ {\mathrm{\Φ}}_B=N_3\frac{(R_A+R_C)i_B-R_C{i}_A-R_A{i}_C}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\\ {\mathrm{\Φ}}_C=N_3\frac{(R_A+R_B)i_C-R_A{i}_B-R_B{i}_A}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\end{array}\right.---\left(1\right)$

in the formula (1), phi_A、Φ_B、Φ_CMagnetic fluxes corresponding to the three-phase magnetic pole air gaps respectively; n is a radical of₃Equivalent turns in the x and y directions; r_A、R_B、R_CRespectively the magnetic resistance of three magnetic pole air gaps; i.e. i_A、i_B、i_CRespectively, the current flowing through the three magnetic poles;

step S12, for N in formula (1)₃i_A，N₃i_B，N₃i_CAnd (3) converting the three-phase static coordinate system into a two-phase static coordinate system, namely as shown in formula (2):

$\left[\begin{array}{c}{N}_3{i}_A\\ N_3{i}_B\\ N_3{i}_C\end{array}\right]=\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& -\frac{1}{2}\\ 0& 1\\ -\frac{\sqrt{3}}{2}& -\frac{1}{2}\end{array}\right]\left[\begin{array}{c}{N}_2{i}_x\\ N_2{i}_y\end{array}\right]---\left(2\right)$

in the formula (2), N₂Is a three-phase AC coil with ampere turns i_x、i_yActual control currents in x and y directions respectively;

step S13, projecting the suspension force to the x and y directions to obtain two forces respectively_x(t) and f_y(t) represents;

f is_x(t) and f_yThe expression of (t) is as follows:

$\left\{\begin{array}{c}{f}_x\left(t\right)=\frac{\sqrt{3}}{2\mathrm{\μ}S}({\mathrm{\Φ}}_C^2\cos \mathrm{\α}+{\mathrm{\Φ}}_B^2\cos (\mathrm{\α}+\frac{2}{3}\mathrm{\π})+{\mathrm{\Φ}}_A^2\cos (\mathrm{\α}-\frac{2}{3}\mathrm{\π}\left)\right)\\ f_y\left(t\right)=\frac{1}{2\mathrm{\μ}S}({\mathrm{\Φ}}_C^2\sin \mathrm{\α}+{\mathrm{\Φ}}_B^2\sin (\mathrm{\α}+\frac{2}{3}\mathrm{\π})+{\mathrm{\Φ}}_A^2\sin (\mathrm{\α}-\frac{2}{3}\mathrm{\π}\left)\right)\end{array}\right.---\left(3\right)$

in the formula (3), μ is magnetic permeability, s is magnetic pole equivalent area, and α is magnetic pole azimuth.

The continuous-time system is shown in equation (4):

$\stackrel{\·}{X}\left(t\right)=f_c\left(X\right(t),u(t\left)\right)+v\left(t\right)---\left(4\right)$

in the formula:

$\stackrel{\·}{X}\left(t\right)=\frac{d}{dt}\left(\begin{array}{c}x\left(t\right)\\ V\left(t\right)\\ i_x\left(t\right)\\ f_{zx}\left(t\right)\\ y\left(t\right)\\ V_y\left(t\right)\\ i_y\left(t\right)\\ f_{zy}\left(t\right)\end{array}\right);f_c\left(X\right(t),u(t\left)\right)=\left\{\begin{array}{c}{V}_x\left(t\right)\\ \frac{1}{m}\[f_x\left(t\right)+f_{zx}\left(t\right)\]\\ \frac{K_a}{T_a}{i}_{xref}\left(t\right)-\frac{1}{T_a}{i}_x\left(t\right)\\ 0\\ V_y\left(t\right)\\ \frac{1}{m}\[f_y\left(t\right)+f_{zy}\left(t\right)\]\\ \frac{K_a}{T_a}{i}_{yref}\left(t\right)-\frac{1}{T_a}{i}_y\left(t\right)\\ 0\end{array}\right.;v\left(t\right)=\left\{\begin{array}{c}{v}_x\left(t\right)\\ v_{Vx}\left(t\right)\\ v_{i_x}\left(t\right)\\ v_{f_{zx}}\left(t\right)\\ v_y\left(t\right)\\ v_{V_y}\left(t\right)\\ v_{i_y}\left(t\right)\\ v_{f_{zy}}\left(t\right)\end{array}\right.;$

wherein, V_x，V_yThe rotation speeds of the rotor in the x and y directions respectively; f. of_zxAnd f_zyPerturbation of the rotor in the x and y directions, respectively; t is_a、K_aRespectively an equivalent time constant and a power amplification gain; i.e. i_xrefAnd i_yrefReference currents in the x and y directions, respectively; f. of_x(x,i_x) And f_y(x,i_y) Respectively as a function of the displacement in the x direction, the control current, the displacement in the y direction, and the control current; m is the rotor mass; v. of_xIs the interference amount of the displacement of the rotor in the x direction, v_VxFor the disturbance variable v of the rotor speed in the x direction_ixFor the current disturbance variable, v, of the rotor in the x-direction_fzxDisturbance quantity v of rotor in x direction_yIs the interference amount of the displacement of the rotor in the y direction, v_VyFor the disturbance variable v of the rotor speed in the y direction_iyFor the current disturbance variable, v, of the rotor in the y-direction_fzyIs the disturbance quantity of the rotor in the y direction.

As can be seen from the formula (4), the method comprises the displacement information and the rotating speed information of the rotor in the x and y directions, so that the sensorless detection method of the displacement of the controlled radial magnetic bearing rotor can be realized, and the specific steps are as follows:

discretizing equation (4) into a nonlinear system state equation and a measurement equation:

$\left\{\begin{array}{c}{x}_k=f(x_{k-1},u_k)+d_k\\ y_k=h(x_k,u_k)+v_k\end{array}\right.---\left(5\right)$

u_kas input at time k of the system, x_k-1And x_kThe state of the system at the time k-1 and k, respectively, d_kAnd v_kAre uncorrelated zero-mean gaussian white noise;

the volume Kalman filter algorithm is divided into time prediction and measurement updating, and the specific flow is as follows:

(1) temporal prediction

Calculating a volume point:

$x_{i,k-1}=\sqrt{p_{k-1}^{+}}{\mathrm{\ξ}}_i+x_{k-1}^{+},i=1,...,2n---\left(6\right)$

x_i,k-1the volume points are a priori at time k-1,as covariance, ξ_iIs a set of volume points, and is,is a volume point posterior test

Volume point propagation:

$x_{i,k-1}^{*}=f(X_{i,k-1},u_{k-1}),i=1,...,2n---\left(7\right)$

is the volume point propagation quantity, u_k-1For input of system k time

The estimated prediction mean and the covariance matrix are respectively:

in order to estimate the mean of the prediction,for volume point propagation at time K, Q_k-1Covariance matrix for dk.Is a prior covariance matrix.

(2) Measurement update

Calculating a volume point:

$x_{i,k}=\sqrt{p_k^{-}}{\mathrm{\ξ}}_i+x_k^{-},i=1,...,2n---\left(10\right)$

x_i，kthe volume points are a priori at time k-1,mean volume point propagation is predicted a priori:

Z_i,k＝h(X_i,k,u_k),i＝1,…,2n (11)

Z_i，kfor updated volume point propagation values, X_i，kAnd the updated K time volume point is prior.

Calculating a measurement prediction value, a new covariance and a covariance matrix:

in order to measure and predict the prior estimated value,for updated volume point propagation values at time K, R_k-1Is v_kThe covariance matrix of (a) is obtained,the measured prediction prior value at the time K is transposed,for new covariance prior values, P_xz，kA covariance matrix;

and (3) calculating measurement updating:

$x_k^{+}=x_k^{-}+K_k\left(z_k-{\hat{z}}_k^{-}\right)---\left(14\right)$

$P_k^{+}=P_k^{-}+K_k{P}_{zz,k}{K}_k^T---\left(13\right)$

wherein,for a priori prediction of the mean estimate, K_kAs a gain amount, z_kIn order to measure the actual value of the measured value,in order to perform the transposition operation of the gain amount,is the covariance of the a priori estimation error,covariance of a posteriori estimation error, P_zz，k-is the covariance actual value.

Example 2

On the basis of embodiment 1, the present embodiment 2 provides a radial magnetic bearing displacement detection method, including:

and obtaining radial displacement output signals and rotation speed signals of the rotor in the x and y directions according to the continuous time system, and discretizing the continuous time system to realize the extraction of the displacement information of the rotor by a volume Kalman filter algorithm.

The method for extracting the displacement information of the rotor by the cubature Kalman filter algorithm comprises the following steps: generating a current I from a voltage source inverter by a volumetric Kalman filter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estWherein the displacement outputs a signal x_estAnd y_estAnd also displacement information of the rotor.

The specific implementation steps of the volume kalman filter algorithm to extract the displacement information of the rotor in the embodiment 2 are shown in the implementation process of the volume kalman filter algorithm in the embodiment 1, which is divided into time prediction and measurement updating.

The invention avoids the linear treatment of the radial magnetic bearing which is essentially a nonlinear model, realizes the operation without a displacement sensor, has strong interference suppression capability, can accurately detect the displacement of the radial magnetic bearing, and can also detect the displacement of the radial magnetic bearing when the exact property of the system is unknown.

Example 3

On the basis of embodiment 1, the present embodiment 3 provides a displacement detection method for a radial magnetic bearing.

The radial magnetic bearing displacement detection method comprises the following steps: a feedback loop is constructed through a cubature Kalman filter to adjust the current generated by a voltage source inverter to drive the magnetic bearing to realize closed-loop stable suspension.

In particular, the feedback loop is constructed by a volumetric Kalman filter, i.e.

Generating a current I from a voltage source inverter by a volumetric Kalman filter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estWith a given reference position signal x_refAnd y_refComparing, processing the obtained result by a first P controller, and respectively comparing with the rotating speed signal v obtained by the observer_xestAnd v_yestGenerating a reference current signal i by comparing the current signals processed by the second P controller_xrefAnd i_yref(ii) a And the adjusting voltage source inverter generates current to drive the magnetic bearing to realize closed-loop stable suspension, namely, the reference current signal i is simultaneously transmitted_xrefAnd i_yrefAfter comparing with the current obtained by the 2/3 converter, the comparison result is processed by a PID controller to obtain a control voltage u_xAnd u_yThen the control voltage u is applied_xAnd u_yGenerating a current I by a voltage source inverter_A，I_B，I_CThe magnetic bearing is driven to realize closed-loop stable suspension.

The 2/3 converter is specifically a 2-phase coordinate system/3-phase coordinate system converter.

Example 4

This embodiment 4 also provides a radial magnetic bearing displacement detection system, including:

a feedback loop is constructed through a cubature Kalman filter to adjust the current generated by a voltage source inverter to drive the magnetic bearing to realize closed-loop stable suspension.

Specifically, the feedback loop includes: the system comprises a volume Kalman filter, an observer, a first P controller and a second P controller;

generating a current I from a voltage source inverter by a volumetric Kalman filter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estAnd is andgiven reference position signal x_refAnd y_refComparing, processing the obtained result by a first P controller, and respectively comparing with the rotating speed signal v obtained by the observer_xestAnd v_yestGenerating a reference current signal i by comparing the current signals processed by the second P controller_xrefAnd i_yref。

The radial magnetic bearing displacement detection system further comprises: 2/3 converter, PID controller and voltage source inverter; reference current signal i_xrefAnd i_yrefAfter comparing with the current obtained by the 2/3 converter, the comparison result is processed by a PID controller to obtain a control voltage u_xAnd u_yThen the control voltage u is applied_xAnd u_yI generation by a voltage source inverter_A，I_B，I_CThe magnetic bearing is driven to realize closed-loop stable suspension.

In example 3 and example 4, the 2/3 converter is specifically a 2-phase coordinate system/3-phase coordinate system converter.

The controller designed by utilizing the cubature Kalman filter has good nonlinear essential characteristics, and particularly adopts the current reference signal i obtained by processing a rotor rotating speed signal extracted by the cubature Kalman filter under an online adjustment observer by a corresponding P controller_xrefAnd i_yrefThe adverse effects caused by uncertain factors such as model parameter change, nonlinearity and the like in the magnetic bearing system can be better overcome, and a better control effect is obtained. The invention adopts the cubature Kalman filter to replace the nonlinear filters of the extended Kalman filter, the unscented Kalman filter and the particle filter, has higher precision, can obviously show the advantages of the cubature Kalman filter for the control object with more prominent nonlinear characteristics such as the magnetic bearing, can effectively realize the stable suspension force control of the radial magnetic bearing system, and has stronger robustness to the external interference.

In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (9)

1. A method for constructing a continuous time system for detecting the displacement of a radial magnetic bearing is characterized by comprising the following steps:

step S1, calculating the suspension force of the rotor in the three magnetic pole directions;

step S2, a continuous time system is established.

2. The construction method according to claim 1,

the method for calculating the levitation force applied to the rotor in the three magnetic pole directions in step S1 includes:

step S11, calculating the magnetic flux of each magnetic pole air gap, as shown in equation (1):

$\left\{\begin{array}{c}{\mathrm{\Φ}}_A=N_3\frac{(R_B+R_C)i_A-R_C{i}_B-R_B{i}_C}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\\ {\mathrm{\Φ}}_B=N_3\frac{(R_A+R_C)i_B-R_C{i}_A-R_A{i}_C}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\\ {\mathrm{\Φ}}_C=N_3\frac{(R_A+R_B)i_C-R_A{i}_B-R_B{i}_A}{R_A{R}_B+R_B{R}_C+R_C{R}_A}\end{array}\right.---\left(1\right)$

in the formula (1), phi_A、Φ_B、Φ_CMagnetic fluxes corresponding to the three-phase magnetic pole air gaps respectively; n is a radical of₃Equivalent turns in the x and y directions; r_A、R_B、R_CRespectively the magnetic resistance of three magnetic pole air gaps; i.e. i_A、i_B、i_CRespectively, the current flowing through the three magnetic poles;

step S12, for N in formula (1)₃i_A，N₃i_B，N₃i_CAnd (3) converting the three-phase static coordinate system into a two-phase static coordinate system, namely as shown in formula (2):

$\left[\begin{array}{c}{N}_3{i}_A\\ N_3{i}_B\\ N_3{i}_C\end{array}\right]=\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& -\frac{1}{2}\\ 0& 1\\ -\frac{\sqrt{3}}{2}& -\frac{1}{2}\end{array}\right]\left[\begin{array}{c}{N}_2{i}_x\\ N_2{i}_y\end{array}\right]---\left(2\right)$

in the formula (2), N₂Is a three-phase AC coil with ampere turns i_x、i_yActual control currents in x and y directions respectively;

step S13, projecting the suspension force to the x and y directions to obtain two forces respectively_x(t) and f_y(t) represents;

f is_x(t) and f_yThe expression of (t) is as follows:

$\left\{\begin{array}{c}{f}_x\left(t\right)=\frac{\sqrt{3}}{2\mathrm{\μ}S}({\mathrm{\Φ}}_C^2\cos \mathrm{\α}+{\mathrm{\Φ}}_B^2\cos (\mathrm{\α}+\frac{2}{3}\mathrm{\π})+{\mathrm{\Φ}}_A^2\cos (\mathrm{\α}-\frac{2}{3}\mathrm{\π}\left)\right)\\ f_y\left(t\right)=\frac{1}{2\mathrm{\μ}S}({\mathrm{\Φ}}_C^2\sin \mathrm{\α}+{\mathrm{\Φ}}_B^2\sin (\mathrm{\α}+\frac{2}{3}\mathrm{\π})+{\mathrm{\Φ}}_A^2\sin (\mathrm{\α}-\frac{2}{3}\mathrm{\π}\left)\right)\end{array}\right.---\left(3\right)$

in the formula (3), μ is magnetic permeability, S is magnetic pole equivalent area, and α is magnetic pole azimuth.

3. The building method according to claim 2, wherein the continuous-time system is as shown in equation (4):

$\stackrel{\·}{X}\left(t\right)=f_c\left(X\right(t),u(t\left)\right)+v\left(t\right)---\left(4\right)$

in the formula:

$\stackrel{\·}{X}\left(t\right)=\frac{d}{dt}\left(\begin{array}{c}x\left(t\right)\\ V\left(t\right)\\ i_x\left(t\right)\\ f_{zx}\left(t\right)\\ y\left(t\right)\\ V_y\left(t\right)\\ i_y\left(t\right)\\ f_{zy}\left(t\right)\end{array}\right);f_c\left(X\right(t),u(t\left)\right)=\left\{\begin{array}{c}{V}_x\left(t\right)\\ \frac{1}{m}\[f_x\left(t\right)+f_{zx}\left(t\right)\]\\ \frac{K_a}{T_a}{i}_{xref}\left(t\right)-\frac{1}{T_a}{i}_x\left(t\right)\\ 0\\ V_y\left(t\right)\\ \frac{1}{m}\[f_y\left(t\right)+f_{zy}\left(t\right)\]\\ \frac{K_a}{T_a}{i}_{yref}\left(t\right)-\frac{1}{T_a}{i}_y\left(t\right)\\ 0\end{array}\right.;v\left(t\right)=\left\{\begin{array}{c}{v}_x\left(t\right)\\ v_{Vx}\left(t\right)\\ v_{i_x}\left(t\right)\\ v_{f_{zx}}\left(t\right)\\ v_y\left(t\right)\\ v_{V_y}\left(t\right)\\ v_{i_y}\left(t\right)\\ v_{f_{zy}}\left(t\right)\end{array}\right.;$

wherein, V_x，V_yThe rotation speeds of the rotor in the x and y directions respectively; f. of_zxAnd f_zyPerturbation of the rotor in the x and y directions, respectively; t is_a、K_aRespectively an equivalent time constant and a power amplification gain; i.e. i_xrefAnd i_yrefReference currents in the x and y directions, respectively; f. of_x(x,i_x) And f_y(x,i_y) Respectively as a function of the displacement in the x direction, the control current, the displacement in the y direction, and the control current; m is the rotor mass; v. of_xIs the interference amount of the displacement of the rotor in the x direction, v_VxFor the disturbance variable v of the rotor speed in the x direction_ixFor the current disturbance variable, v, of the rotor in the x-direction_fzxDisturbance quantity v of rotor in x direction_yIs the interference amount of the displacement of the rotor in the y direction, v_VyFor the disturbance variable v of the rotor speed in the y direction_iyFor the current disturbance variable, v, of the rotor in the y-direction_fzyIs the disturbance quantity of the rotor in the y direction.

4. A radial magnetic bearing displacement detection method applying the construction method as set forth in claim 1, comprising:

and obtaining radial displacement output signals and rotation speed signals of the rotor in the x and y directions according to the continuous time system, and discretizing the continuous time system to realize the extraction of the displacement information of the rotor by a volume Kalman filter algorithm.

5. A displacement detection method of a radial magnetic bearing is characterized in that,

a feedback loop is constructed through a cubature Kalman filter to adjust the current generated by a voltage source inverter to drive the magnetic bearing to realize closed-loop stable suspension.

6. The radial magnetic bearing displacement detection method of claim 5,

the feedback loop being constructed by a volumetric Kalman filter, i.e.

Generating a current I from a voltage source inverter by a volumetric Kalman filter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estWith a given reference position signal x_refAnd y_refComparing, processing the obtained result by a first P controller, and respectively comparing with the rotating speed signal v obtained by the observer_xestAnd v_yestGenerating a reference current signal i by comparing the current signals processed by the second P controller_xrefAnd i_yref；

The current generated by the voltage source inverter is adjusted to drive the magnetic bearing to realize closed-loop stable suspension, i.e.

While simultaneously converting the reference current signal i_xrefAnd i_yrefAfter comparing with the current obtained by the 2/3 converter, the comparison result is processed by a PID controller to obtain a control voltage u_xAnd u_yThen the control voltage u is applied_xAnd u_yGenerating a current I by a voltage source inverter_A，I_B，I_CThe magnetic bearing is driven to realize closed-loop stable suspension.

7. A radial magnetic bearing displacement detection system, comprising:

a feedback loop is constructed through a cubature Kalman filter to adjust the current generated by a voltage source inverter to drive the magnetic bearing to realize closed-loop stable suspension.

8. The radial magnetic bearing displacement detection system of claim 7, wherein the feedback loop comprises: the system comprises a volume Kalman filter, an observer, a first P controller and a second P controller;

generating a current I from a voltage source inverter by a volumetric Kalman filter_A，I_B，I_CExtracted current signal x_cubAnd y_cubAnd obtaining the displacement output signal x of the radial magnetic bearing in the x and y directions through an observer_estAnd y_estWith a given reference position signal x_refAnd y_refComparing, processing the obtained result by a first P controller, and respectively comparing with the rotating speed signal v obtained by the observer_xestAnd v_yestGenerating a reference current signal i by comparing the current signals processed by the second P controller_xrefAnd i_yref。

9. The radial magnetic bearing displacement detection system of claim 8,

the radial magnetic bearing displacement detection system further comprises: 2/3 converter, PID controller and voltage source inverter;

reference current signal i_xrefAnd i_yrefAfter comparing with the current obtained by the 2/3 converter, the comparison result is processed by a PID controller to obtain a control voltage u_xAnd u_yThen the control voltage u is applied_xAnd u_yI generation by a voltage source inverter_A，I_B，I_CThe magnetic bearing is driven to realize closed-loop stable suspension.