Multistage radial magnetic suspension bearing with fault-tolerant function and minimum power consumption control method thereof

Abstract

The multistage radial magnetic suspension bearing with the fault tolerance function comprises a stator and a rotor, and at least five mutually independent magnetic poles are arranged in the stator in the circumferential direction at intervals; the stator is divided into two halves by any plane passing through the center line of the stator, and each half stator is provided with at least one magnetic pole under the condition of neglecting the magnetic pole overlapped with the plane. The invention further discloses a minimum power consumption control method for the multistage radial magnetic suspension bearing with the fault-tolerant function. The invention discloses a multistage radial magnetic suspension bearing with a fault-tolerant function and a minimum power consumption control method thereof, and aims to realize that a control system is switched to a corresponding fault-tolerant state under the condition that at least one path of magnetic pole breaks down, so that stable suspension of the magnetic suspension bearing is kept. Aiming at the problem of power consumption increase possibly caused by multi-stage magnetic poles, the minimum power consumption control method aims to reduce power consumption.

Description

Technical Field

[0001] The invention belongs to the technical field of radial magnetic suspension bearings, and specifically relates to a multi-stage radial magnetic suspension bearing with a fault-tolerant function and a method for controlling the minimum power consumption thereof. Background Art

[0002] Since the magnetic bearing system needs to operate for a long time under high-speed load conditions, if a failure occurs during operation, it will not only damage the components but may also cause more serious safety problems. Therefore, its reliability and fault tolerance have become one of the research hotspots in the field in recent years.

[0003] When it comes to the research on the reliability and fault tolerance of magnetic bearings, more experts focus on the research of power amplifier circuits, sensors, controllers, etc. There is relatively little research on the fault tolerance of magnetic bearing coils when failures occur, but this aspect is also crucial.

[0004] The magnetic poles of traditional magnetic bearings are arranged symmetrically along the X and Y axes, and the coils are directly connected in series on a single pole regardless of the number of coils. This can minimize the number of power circuits, but if any coil fails, the corresponding pole will have no electromagnetic force, and the magnetic levitation rotor will directly lose control.

[0005] Although some scholars have conducted research on fault-tolerant magnetic pole radial magnetic bearings with fault-tolerant control functions, the existing research on magnetic pole fault-tolerant structures, whether it is eight-pole, twelve-pole or sixteen-pole, the magnetic poles are basically distributed symmetrically along the X and Y axes. Although fault-tolerant control can be performed when the coil fails, each magnetic pole needs to have an independent control circuit, which results in a larger controller size, a more complex control system, increased power consumption, and device failures.

[0006] Therefore, based on the above problems, the present invention proposes a five-pole radial magnetic bearing with fault tolerance function and a control method with minimum power consumption. The goal of the present invention is to minimize the power circuit required for the magnetic bearing while having fault tolerance capability. The present invention also proposes a corresponding control method with minimum power consumption to address the problem that an additional circuit may cause increased power consumption. Summary of the invention

[0007] In view of this, the object of the present invention is to provide a multi-stage radial magnetic bearing with fault-tolerant function and a minimum power consumption control method thereof, aiming to realize that when at least one magnetic pole fails, the control system switches to a corresponding fault-tolerant state to maintain the stable suspension of the magnetic bearing; in view of the problem of increased power consumption that may be caused by multi-stage magnetic poles, the proposed minimum power consumption control method aims to reduce power consumption.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] The present invention first proposes a multi-stage radial magnetic bearing with fault-tolerant function, including a stator and a rotor, wherein at least five mutually independent magnetic poles are arranged at intervals along the circumferential direction in the stator; the stator is divided into two halves by an arbitrary plane passing through the center line of the stator, and under the condition of ignoring the magnetic poles coinciding with the plane, there is at least one magnetic pole on each half of the stator.

[0010] Furthermore, the magnetic poles are arranged in an annularly uniform or non-uniform distribution along the circumferential direction of the stator.

[0011] Furthermore, when at least one of the magnetic poles fails, if the following conditions are met at the same time:

[0012] The stator is divided into two halves by any first radial plane passing through the center line of the stator. When the magnetic poles whose axes are located in the first radial plane are ignored, at least one magnetic pole in a non-fault state is present on each half of the stator; and the stator is divided into two halves by a second radial plane passing through the center line of the stator and perpendicular to the first radial plane. When the magnetic poles whose axes are located in the second radial plane are ignored, at least one magnetic pole in a non-fault state is present on each half of the stator;

[0013] If the fault-tolerant control condition is met, the magnetic bearing is subjected to fault-tolerant control; otherwise, the fault-tolerant control condition is not met.

[0014] The present invention also proposes a method for controlling the minimum power consumption of a multi-stage radial magnetic bearing with a fault-tolerant function, comprising the following steps:

[0015] Step 1: Establish a coordinate system with the center of the stator inner control circle as the origin, use the displacement sensor to collect the rotor displacement signals of the rotor in the x and y directions respectively, and transmit the collected rotor displacement signals to the magnetic bearing controller; the magnetic bearing controller calculates the rotor center of mass position and the air gap width between each magnetic pole and the rotor based on the rotor displacement signal;

[0016] Step 2: Based on the offset between the rotor center of mass and the origin of the coordinate system, calculate the electromagnetic force F in the x and y directions required to restore the rotor center to the origin of the coordinate system. x and Fy;

[0017] Step 3: Establish the electromagnetic force F x and F y The equation relationship with the pole coil current is:

[0018]

[0019] Where: I and I0 are current vectors; K is the electromagnetic force coefficient; D x and D yare the force weighting matrices of the rotor in the x and y directions respectively; S is the air gap matrix between the pole coil and the rotor; E is the pole state matrix; and:

[0020] E = diag[e1,e2,…,e n ]

[0021] Where: e j is the state parameter of the j-th magnetic pole, and: if the j-th magnetic pole is normal, then e j =1; if the jth magnetic pole fails, then e j =0; j=1, 2, ..., n, where n is the number of magnetic poles;

[0022] Step 4: Construct the objective function:

[0023] minJ(I)=I T I

[0024] Where: J(I) is the objective function, which represents the power consumption of the magnetic bearing;

[0025] Constraints:

[0026] I j ≥i min (i min >0, j=1, 2, ..., n)

[0027] Step 5: Solve the objective function to obtain the control current required for each magnetic pole under the condition of minimum power consumption.

[0028] Furthermore, in step 2, the dynamic equation of the magnetic bearing is:

[0029]

[0030] Where: M is the mass matrix; q is the coordinate of the center of mass of the magnetic bearing; G is the gyro effect matrix; L f is the arm coefficient matrix; W is the gravity vector;

[0031] After power is applied, the magnetic poles will exert electromagnetic force on the rotor. The electromagnetic force of each magnetic pole is:

[0032]

[0033] K=μN 2 A / 8

[0034] Among them: F j The j-th magnetic pole exerts electromagnetic force on the rotor; I j is the control current of the j-th magnetic pole; s j is the air gap width between the j-th magnetic pole and the rotor; K is the electromagnetic force coefficient; μ is the air magnetic permeability; N is the number of coil turns; A is the magnetic pole area;

[0035] Then the electromagnetic force in the x and y axis directions is:

[0036]

[0037] Where: θ j is the angle between the electromagnetic force of the jth magnetic pole and the x-axis.

[0038] Furthermore, in step 5, the Lagrangian equation of the objective function and the constraint condition is established in combination with the penalty function:

[0039]

[0040] Among them: λ1 and λ2 are Lagrangian operators; is a penalty function used to constrain the minimum value of the coil current; α is a penalty factor;

[0041] Solve the unknown quantities i1, i2, ..., i in the Lagrange equation respectively n , partial derivatives of λ1,λ2:

[0042]

[0043] Setting all partial derivatives equal to 0, we can obtain the control current required for each magnetic pole under the condition of minimum power consumption.

[0044] The beneficial effects of the present invention are:

[0045] The multi-stage radial magnetic bearing with fault tolerance function of the present invention is provided by setting the bearing winding structure to be composed of at least 5 magnetic poles arranged at intervals along the circumferential direction of the stator, and the magnetic poles are independent of each other; and the distribution of the magnetic poles can be evenly distributed according to the circumference, or unevenly distributed, but it is necessary to ensure that the stator is divided into two halves by any plane passing through the center line of the stator, and under the condition that the magnetic poles coincide with the plane are ignored, there is at least one magnetic pole on each half of the stator; in this way, since the magnetic poles are arranged at intervals of at least 5 along the circumferential direction of the stator, when at least one magnetic pole fails, the fault tolerance control condition can be met under certain conditions, that is: the magnetic poles passing through the center line of the stator are divided into two halves by any plane passing through the center line of the stator. The stator is divided into two halves by any first radial plane of the stator center line, and when the magnetic poles whose axes are located in the first radial plane are ignored, at least one magnetic pole in a non-fault state is on each half of the stator; and the stator is divided into two halves by a second radial plane passing through the stator center line and perpendicular to the first radial plane, and when the magnetic poles whose axes are located in the second radial plane are ignored, at least one magnetic pole in a non-fault state is on each half of the stator; in this way, the corresponding control current can be output to the remaining magnetic poles that are working normally through the power amplifier, so that the magnetic floating rotor is stabilized at the center of the bearing circle; in this way:

[0046] Under normal conditions, all magnetic poles work normally, and the power amplifier outputs corresponding control current to each magnetic pole, so that the magnetic levitation rotor is stabilized at the center of the bearing. When a magnetic pole fails, if the fault-tolerant control conditions are met: corresponding fault-tolerant control is performed on the remaining magnetic poles that can work normally, so that the magnetic levitation bearing can continue to maintain stable suspension of the magnetic levitation rotor when at least one magnetic pole fails.

[0047] In summary, the multi-stage radial magnetic bearing with fault tolerance function of the present invention can realize that when at least one magnetic pole fails, the control system switches to a corresponding fault-tolerant state to maintain stable suspension of the magnetic bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0049] Figure 1 It is a structural schematic diagram of an embodiment of a multi-stage radial magnetic suspension bearing with a fault-tolerant function of the present invention; specifically, it is a structural schematic diagram when 5 magnetic poles are evenly distributed in an annular shape;

[0050] Figure 2 It is a schematic diagram of the structure when the magnetic poles in the multi-stage radial magnetic bearing are unevenly distributed;

[0051] Figure 3 It is a principle diagram of the method for controlling the minimum power consumption of a multi-stage radial magnetic bearing with fault tolerance function according to the present invention;

[0052] Figure 4 This is a schematic diagram of a single magnetic pole failure;

[0053] Figure 5 It is a schematic diagram of two non-adjacent magnetic poles failing;

[0054] Figure 6 It is a schematic diagram of the first situation when two adjacent magnetic poles fail;

[0055] Figure 7 This is a schematic diagram of the second situation when two adjacent magnetic poles fail.

[0056] Description of reference numerals:

[0057] 10- stator; 20- rotor; 30- magnetic pole. DETAILED DESCRIPTION

[0058] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0059] The structure and control of conventional radial magnetic bearings can be simply described as follows: The radial magnetic bearing contains 4n magnetic poles. The center of the inner hole of the bearing is usually used as the reference point. A fixed plane coordinate system is established in a plane parallel to the end face of the bearing. The horizontal direction is usually marked as the x-axis, the vertical direction is marked as the y-axis, the right side is the positive direction of the x-axis, and the top is the positive direction of the y-axis. The 4k magnetic poles inside the magnetic bearing are divided into four groups: two groups of the x-axis (x A and X B ) and two groups of Y axis (Y A and Y B ). Each set of magnetic poles is usually connected in series to form two opposite magnetic pole regions: X zone and Y zone. The number of magnetic poles in each set is related to the value of k. When k is 1, 2, 3 or 4, the number of magnetic poles in each set is 1, 2, 3 or 4. When the magnetic levitation rotor is offset in the x and y directions, the position sensor collects the real-time position signal and inputs it into the digital controller. The controller calculates the control current Icx and Icy required for the magnetic levitation rotor to return to the equilibrium position based on the set algorithm, and uses differential control to perform current differential control on the x and y degrees of freedom. The power amplifier outputs the corresponding current to the magnetic levitation bearing coil, thereby achieving stable suspension of the rotor at the origin of the coordinate system.

[0060] It should be noted that in the conventional radial magnetic bearing magnetic pole arrangement and control, the magnetic pole arrangement of the x and y zones is arranged corresponding to the x and y axes, and the x A , X B , Y A , Y B The magnetic bearing coils in the four sets of magnetic poles are connected in series. Therefore, when a coil fails and cannot control the corresponding current, the magnetic bearing will immediately lose its support force in one direction, causing the magnetic rotor to lose control and the high-speed rotor to collide with the stator, resulting in serious consequences.

[0061] Although some scholars have conducted research on the above issues, the research is mainly based on magnetic levitation bearings with 4k magnetic poles. If the magnetic levitation bearings with 4k magnetic poles need to have the function of fault-tolerant control, the value of k must be greater than or equal to 2, so the total number of magnetic poles in the 4 groups of magnetic poles is at least 8. However, this brings another problem: too many magnetic poles will make the power amplifier too large, the control system more complicated, and the probability of device damage will also increase.

[0062] In response to the above problems, this embodiment proposes a multi-stage radial magnetic bearing with fault tolerance. Specifically, the multi-stage radial magnetic bearing with fault tolerance in this embodiment includes a stator 10 and a rotor 20, and at least 5 independent magnetic poles 30 are arranged in the stator 10 along the circumferential direction. And the arrangement of the magnetic poles 30 needs to meet the following conditions: the stator 10 is divided into two halves by any plane passing through the center line of the stator 10, and under the condition of ignoring the magnetic poles that coincide with the plane, there is at least one magnetic pole 30 on each half of the stator 10. Specifically, in the preferred implementation of this embodiment, the magnetic poles 30 are evenly distributed in an annular manner along the circumferential direction of the stator 10, which can meet the requirements of the arrangement of the magnetic poles 30.

[0063] Specifically, when at least one magnetic pole 30 fails, if fault-tolerant control is to be performed, the following conditions must be met at the same time: the stator 10 is divided into two halves by any first radial plane passing through the center line of the stator 10, and when the magnetic pole 30 whose axis is located in the first radial plane is ignored, there is at least one magnetic pole 30 in a non-fault state on each half of the stator 10; and the stator 10 is divided into two halves by a second radial plane passing through the center line of the stator 10 and perpendicular to the first radial plane, and when the magnetic pole whose axis is located in the second radial plane is ignored, there is at least one magnetic pole 30 in a non-fault state on each half of the stator 10. Specifically, if the fault-tolerant control condition is met when at least one magnetic pole 30 fails, the magnetic bearing is fault-tolerantly controlled; otherwise, the fault-tolerant control condition is not met, and the magnetic bearing cannot meet the use requirements.

[0064] In this embodiment, five independent magnetic poles 30 are arranged in the stator 10 along the circumferential direction at intervals. The five magnetic poles 30 are composed of five groups of coils, and the magnetic poles 30 are marked as ①②③④⑤ in clockwise order around the circumference. The center of the inner hole of the stator 10 is taken as the coordinate origin O, the vertical direction of the origin O is taken as the Y-axis, the direction from the coordinate origin to the stator circumference is taken as the positive direction of the Y-axis, and the direction rotated 90° clockwise from the positive direction of the Y-axis is taken as the positive direction of the X-axis, and a coordinate system XOY is established.

[0065] The arrangement of the magnetic poles 30 provided by the present invention can be as follows: Figure 1 The magnetic poles 30 are evenly distributed around the circumference (circular uniform distribution), and each magnetic pole 30 is spaced 72° apart, where θ j (j=1,2,3,4,5) is the angle between the coil axis and the X-axis.

[0066] For some special cases where the magnetic poles 30 cannot be evenly distributed, Figure 2The non-uniform distribution shown in the figure, but no matter which arrangement method is used, it is necessary to ensure that when the stator 10 is divided into two parts by a first radial plane passing through the Y axis and the center line of the stator 10, each part must have a magnetic pole 30 (if the axis of a certain magnetic pole 30 coincides with the first radial plane, then ignore the magnetic pole 30), and the stator 10 is divided into two parts by a second radial plane passing through the X axis and the center line of the stator 10, and each part must have a magnetic pole 30 (if the axis of a certain magnetic pole 30 coincides with the second radial plane, then ignore the magnetic pole 30). Specifically, the X axis and the Y axis are both radial directions passing through the center of the inner hole of the stator 10, and the radial directions where the X axis and the Y axis are located can be arbitrarily set and adjusted, but it is necessary to satisfy that the X axis and the Y axis are perpendicular to each other.

[0067] like Figure 2 In the case of the non-uniform distribution shown, when the stator 10 is divided into two parts by a first radial plane passing through the Y axis and the center line of the stator 10, there are magnetic poles ④⑤ in the left half and magnetic poles ②③ in the right half (because the axis of magnetic pole ① coincides with the first radial plane, magnetic pole ① is ignored); and the stator 10 is then divided into two parts by a second radial plane passing through the X axis and the center line of the stator 10, with magnetic poles ①②⑤ in the upper half and magnetic poles ③④ in the lower half, so the requirements for non-uniform distribution are met.

[0068] In this embodiment, two groups of displacement sensors are provided between the stator 10 and the rotor 20. The lines connecting the two groups of displacement sensors to the internal control center of the stator are perpendicular to each other. They are used to measure the displacement of the rotor 20 in two perpendicular directions and transmit the measured values ​​to the digital controller.

[0069] Specifically, Figure 3 As shown, this embodiment also proposes a method for controlling the minimum power consumption of a multi-stage radial magnetic bearing with a fault-tolerant function, which includes the following steps.

[0070] Step 1: Establish a coordinate system XOY with the inner control center of the stator 10 as the origin, use the displacement sensor to collect the rotor displacement signals of the rotor in the x and y directions respectively, and transmit the collected rotor displacement signals to the magnetic bearing controller; the magnetic bearing controller calculates the center of mass position of the rotor 20 and the air gap width between each magnetic pole 30 and the rotor 20 based on the rotor displacement signal.

[0071] Step 2: Based on the offset between the rotor mass center position and the origin of the coordinate system, calculate the electromagnetic force F in the x and y directions required to restore the center of the rotor 20 to the origin of the coordinate system x and F y .

[0072] like Figure 1 As shown, the radial magnetic bearing has two orthogonal directions (x direction and y direction) of electromagnetic force F x and the electromagnetic force F yNeed to be controlled. The electromagnetic force F in the x direction x , the electromagnetic force F in the y direction is determined by the electromagnetic force generated by the magnetic poles ②③④⑤ (i.e. the coils ②③④⑤ in the figure). y It is determined by the electromagnetic force generated by magnetic poles ①②③④⑤.

[0073] The radial control of the magnetic bearing is normally performed by two radial bearings, bearing a and bearing b. Specifically, for each magnetic bearing, there is the following dynamic equation:

[0074]

[0075] Where: M is the mass matrix; q is the coordinate of the center of mass of the magnetic bearing; G is the gyro effect matrix; L f is the arm coefficient matrix; W is the gravity vector. The above matrices are all known and measurable values.

[0076] In addition, F is the electromagnetic force vector:

[0077] F=[F ax ,F bx ,F ay ,F by ] T

[0078] Among them: F ax 、F bx 、F ay and F by are the electromagnetic forces of magnetic bearings a and b in the x and y directions respectively. The required electromagnetic force can be calculated by the above formula for each control cycle, and then the current value required for each coil can be calculated by the electromagnetic force. Since the control methods of the two electromagnetic bearings are the same, only the control of a single coil is discussed below.

[0079] After power is turned on, the five magnetic poles will simultaneously generate electromagnetic forces in different directions on the rotor. Ideally, magnetic leakage and magnetic coupling are not considered. Specifically, after power is turned on, the magnetic poles will exert electromagnetic forces on the rotor. The electromagnetic force of each magnetic pole is:

[0080]

[0081] K=μN 2 A / 8

[0082] Among them: F j The j-th magnetic pole exerts electromagnetic force on the rotor; I j is the control current of the j-th magnetic pole; s j is the air gap width between the j-th magnetic pole and the rotor; K is the electromagnetic force coefficient; μ is the air magnetic permeability; N is the number of coil turns; A is the magnetic pole area.

[0083] Then the electromagnetic force in the x and y axis directions is:

[0084]

[0085] Where: θ j is the angle between the electromagnetic force of the jth magnetic pole and the x-axis; I is the column vector of the current of each magnetic pole, I=[i1,i2,…,i n ] T ; S is the diagonal matrix of the air gaps between each magnetic pole and the rotor, S = diag[s1,s2,…,s n ]; n is the number of magnetic poles. In this embodiment, n=5.

[0086] Step 3: Establish the electromagnetic force F x and F y The equation relationship with the pole 30 coil current is:

[0087]

[0088] Where: I and I0 are current vectors; K is the electromagnetic force coefficient; D x and D y are the force weighting matrices of the rotor in the x and y directions respectively; S is the air gap matrix between the pole coil and the rotor; E is the pole state matrix; and:

[0089] E=diag[e1,e2,…,e n ]

[0090] Where: e j is the state parameter of the j-th magnetic pole, and: if the j-th magnetic pole is normal, then e j =1; if the jth magnetic pole fails, then e j =0; j=1,2,…,n, where n is the number of magnetic poles.

[0091] Specifically, in this embodiment, the number of magnetic poles 30 is set to 5, then:

[0092] E=diag[e1,e2,e3,e4,e5]

[0093] Among them: e1~e5 correspond to 5 magnetic poles 30 respectively. When the magnetic poles 30 work normally, e j =1, corresponding to the e of pole 30 when a fault occurs j = 0. Figure 4 As shown, magnetic pole ① is faulty, and the corresponding magnetic pole state matrix E=diag(0,1,1,1,1).

[0094] In this embodiment, the number of magnetic poles 30 evenly distributed in a ring is set to 5, and the fault of any magnetic pole 30 can meet the fault-tolerant control condition. It should be noted that when two magnetic poles 30 fail, only three magnetic poles 30 remain. If the fault-tolerant control condition is to be met, there are requirements for the arrangement of the remaining magnetic poles 30. Therefore, when two magnetic poles 30 fail, the applicability of the method of this embodiment needs to be discussed separately according to the position of the faulty magnetic pole 30.

[0095] When the two magnetic poles 30 are non-adjacent magnetic poles, the method of this embodiment is applicable. Figure 5 As shown, when magnetic poles ①③ fail, when the stator 10 is divided into two parts by a first radial plane passing through the Y axis and the center line of the stator 10, there are magnetic poles ④⑤ in the left half and magnetic pole ② in the right half; and when the stator 10 is divided into two parts by a second radial plane passing through the X axis and the center line of the stator 10, there are magnetic poles ②⑤ in the upper half and magnetic pole ④ in the lower half, which meets the requirements of the fault-tolerant control conditions. Therefore, the electromagnetic force generated by the remaining magnetic poles can meet the control requirements.

[0096] When the two faulty magnetic poles 30 are adjacent magnetic poles 30 , the applicability of the method of this embodiment needs to be determined according to the specific arrangement and the fault location.

[0097] like Figure 6 As shown, magnetic poles ②③ fail. When the stator 10 is divided into two parts by a first radial plane passing through the Y-axis and the center line of the stator 10, there are magnetic poles ④⑤ in the left half and no magnetic pole in the right half (magnetic pole ① is ignored because the y-axis coincides with the axis of magnetic pole ①); and the stator 10 is then divided into two parts by a second radial plane passing through the X-axis and the center line of the stator 10, with magnetic poles ①⑤ in the upper half and magnetic pole ④ in the lower half, which does not meet the arrangement requirements. At this time, the electromagnetic force generated by the remaining magnetic poles is insufficient to meet the control requirements.

[0098] like Figure 7 As shown, magnetic poles ②③ fail, and when the stator 10 is divided into two parts by a first radial plane passing through the Y axis and the center line of the stator 10, there are magnetic poles ①⑤ in the left half and magnetic poles ④ in the right half; the stator 10 is then divided into two parts by a second radial plane passing through the X axis and the center line of the stator 10, there is magnetic pole ① in the upper half and magnetic poles ④⑤ in the lower half, which meets the arrangement requirements. At this time, the electromagnetic force generated by the remaining magnetic poles is sufficient to meet the control requirements.

[0099] Combination Figure 6 and Figure 7 It can be seen that when adjacent magnetic poles ②③ fail, different X-axis and Y-axis directions will affect whether the fault-tolerant control condition is met. Therefore, when at least two magnetic poles 30 fail, if the current X-axis and Y-axis directions do not meet the fault-tolerant control condition, the X-axis and Y-axis directions can be changed to determine whether the fault-tolerant control condition is finally met.

[0100] Step 4: Construct the objective function

[0101] (1) Objective function

[0102] The power consumption of the electromagnetic bearing is minimal, that is, the sum of the squares of the currents of the five magnetic poles 30 is minimal while the current required by each magnetic pole 30 is met, so there is an objective function:

[0103] minJ(I)=I T I

[0104] Where: J(I) is the objective function, which represents the power consumption of the magnetic bearing.

[0105] (2) Constraints

[0106] The goal at this time is to minimize the objective function J(I) and satisfy the following constraints:

[0107] Constraint 1: Satisfy the electromagnetic force required in the x direction, that is, F1 = KI T (S -1 ) T D X (S -1 )IF x ;

[0108] Constraint 2: Satisfy the electromagnetic force required in the y direction, that is, F2 = KI T (S -1 ) T D y (S -1 )IF y ;

[0109] Since the objective function, i.e., power, needs to be minimized, the solved current needs to be as small as possible. However, since the electromagnetic bearing has no contact during operation, the bearing support stiffness is related to the coil current, so it is necessary to consider the minimum power consumption under the premise of satisfying the support stiffness according to the actual situation. In this way, the minimum current of each coil can be defined according to the current rotor operating state parameters, such as speed, vibration, etc., to meet the support stiffness requirements of the magnetic bearing under different operating conditions.

[0110] Therefore, there is constraint 3: each coil needs to define the minimum current, that is:

[0111] I j ≥i min (i min >0, j=1, 2, ..., n)

[0112] Where: i min Indicates the minimum current allowed, the value is defined according to the actual operating conditions.

[0113] Step 5: Solve the objective function to obtain the control current required for each magnetic pole under the condition of minimum power consumption.

[0114] The problem is converted into solving the minimum value of the objective function under the constraints. In numerical analysis, the Lagrange multiplier method is more appropriate for this problem.

[0115] Introducing the Lagrange coefficient λ x and λ y , construct the Lagrange equation:

[0116] L=I T I+λ1F1+λ2F2

[0117] Since inequality constraints need to be considered, we choose to use the Lagrange multiplier method and the penalty function method to solve it, so the equation is further constructed as follows:

[0118]

[0119] That is, the Lagrange equation for establishing the objective function and constraint conditions by combining the penalty function is:

[0120]

[0121] Among them: λ1 and λ2 are Lagrangian operators; is a penalty function used to constrain the minimum value of the coil current; α is the penalty factor.

[0122] Solve the unknown quantities i1, i2, ..., i in the Lagrange equation respectively n , partial derivatives of λ1,λ2:

[0123]

[0124] Let all partial derivatives equal to 0, and combine the above equations to obtain:

[0125]

[0126] By solving the above equations, the control current required for each magnetic pole under the condition of minimum power consumption is obtained. Thus, the control current required for each magnetic pole 30 under the condition of minimum power consumption of the five magnetic poles 30 can be obtained.

[0127] In this embodiment, the radial magnetic bearing is controlled by dual-loop control, where the outer loop is the position loop and the inner loop is the current loop. The position loop calculates the current loop signal, i.e., the current command value on the five magnetic poles 30, through the relative position signal of the rotor 20 fed back by the position sensor, and converts the current command into the command value of the controllable switch duty cycle through carrier comparison to control the controllable switch of the power amplifier, and finally quickly tracks the five magnetic poles 30 through the current loop to achieve effective control.

[0128] Specifically, the radial magnetic bearing with at least five magnetic poles 30 in this embodiment has two working modes, namely a normal working mode and a fault-tolerant working mode. The specific method implementation steps are as follows:

[0129] (1) In the normal working mode, the five magnetic poles 30 work well. Through dual-loop control, the digital controller generates a control current I according to the offset of the rotor axis from the coordinate origin, and outputs the corresponding control current to the five magnetic poles 30 through the power amplifier, so that the magnetic floating rotor is stable at the center of the bearing circle;

[0130] (2) The working status of the five magnetic poles 30 is monitored in real time. When a magnetic pole 30 is broken or short-circuited, the bearing winding is judged to be faulty and the fault-tolerant working mode is entered. According to the faulty magnetic poles 30, the current of the remaining working magnetic poles 30 is controlled accordingly to ensure that the magnetic bearing can maintain stable suspension of the magnetic rotor when one or two magnetic poles 30 fail.

[0131] After entering the fault-tolerant mode, an alarm is sounded, and the control system reduces the speed of the rotor 20 to 0 while ensuring the stable suspension of the magnetic levitation rotor 20, thereby effectively avoiding damage to the rotor 20 and other components due to failure of some magnetic poles 30 under high speed conditions.

[0132] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A multi-stage radial magnetic bearing with fault tolerance function, comprising a stator and a rotor, characterized in that: At least five mutually independent magnetic poles are arranged at intervals along the circumferential direction in the stator; the stator is divided into two halves by an arbitrary plane passing through the center line of the stator, and under the condition of ignoring the magnetic poles coinciding with the plane, there is at least one magnetic pole on each half of the stator.

2. The multi-stage radial magnetic bearing with fault tolerance function according to claim 1, characterized in that: The magnetic poles are arranged in an annular uniform distribution or non-uniform distribution along the circumferential direction of the stator.

3. The multi-stage radial magnetic bearing with fault tolerance function according to claim 1, characterized in that: When at least one of the magnetic poles fails, if the following conditions are met at the same time: The stator is divided into two halves by any first radial plane passing through the center line of the stator. When the magnetic poles whose axes are located in the first radial plane are ignored, at least one magnetic pole in a non-fault state is present on each half of the stator; and the stator is divided into two halves by a second radial plane passing through the center line of the stator and perpendicular to the first radial plane. When the magnetic poles whose axes are located in the second radial plane are ignored, at least one magnetic pole in a non-fault state is present on each half of the stator; Then the fault-tolerant control condition is met and the magnetic bearing is subjected to fault-tolerant control; Otherwise, the fault-tolerant control condition is not met.

4. A method for controlling the minimum power consumption of a multi-stage radial magnetic bearing with fault tolerance, characterized in that: The steps include: Step 1: Establish a coordinate system with the center of the stator inner control circle as the origin, use the displacement sensor to collect the rotor displacement signals of the rotor in the x and y directions respectively, and transmit the collected rotor displacement signals to the magnetic bearing controller; the magnetic bearing controller calculates the rotor center of mass position and the air gap width between each magnetic pole and the rotor based on the rotor displacement signal; Step 2: Based on the offset between the rotor center of mass and the origin of the coordinate system, calculate the electromagnetic force F in the x and y directions required to restore the rotor center to the origin of the coordinate system. x and F y ; Step 3: Establish the electromagnetic force F x and F y The equation relationship with the pole coil current is: Where: I and I0 are current vectors; K is the electromagnetic force coefficient; D x and D y are the force weighting matrices of the rotor in the x and y directions respectively; S is the air gap matrix between the pole coil and the rotor; E is the pole state matrix; and: E=diag[e1,e2,…,e n ] Where: e j is the state parameter of the j-th magnetic pole, and: if the j-th magnetic pole is normal, then e j =1; if the jth magnetic pole fails, then e j =0; j = 1, 2, ..., n, where n is the number of magnetic poles; Step 4: Construct the objective function: minJ(I)=I T The Where: J(I) is the objective function, which represents the power consumption of the magnetic bearing; Constraints: I j ≥i min (i min >0,j=1,2,…,n) Step 5: Solve the objective function to obtain the control current required for each magnetic pole under the condition of minimum power consumption.

5. The method for controlling the minimum power consumption of a multi-stage radial magnetic bearing with fault tolerance function according to claim 4 is characterized in that: In step 2, the dynamic equation of the magnetic bearing is: Where: M is the mass matrix; q is the coordinate of the center of mass of the magnetic bearing; G is the gyro effect matrix; L f is the arm coefficient matrix; W is the gravity vector; After power is applied, the magnetic poles will exert electromagnetic force on the rotor. The electromagnetic force of each magnetic pole is: K=μN 2 A / 8 Among them: F j The j-th magnetic pole exerts electromagnetic force on the rotor; I j is the control current of the j-th magnetic pole; s j is the air gap width between the j-th magnetic pole and the rotor; K is the electromagnetic force coefficient; μ is the air magnetic permeability; N is the number of coil turns; A is the magnetic pole area; Then the electromagnetic force in the x and y axis directions is: Where: θ j is the angle between the electromagnetic force of the jth magnetic pole and the x-axis.

6. The method for controlling the minimum power consumption of a multi-stage radial magnetic bearing with fault tolerance function according to claim 4 is characterized in that: In step 5, the Lagrangian equation of the objective function and the constraint condition is established in combination with the penalty function: Among them: λ1 and λ2 are Lagrangian operators; is a penalty function used to constrain the minimum value of the coil current; α is a penalty factor; Solve the unknown quantities i1, i2, ..., i in the Lagrange equation respectively n , partial derivatives of λ1,λ2: Setting all partial derivatives equal to 0, we can obtain the control current required for each magnetic pole under the condition of minimum power consumption.

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