Multi-stage radial magnetic suspension bearing with fault-tolerant function and its minimum power consumption control method

Abstract

The application discloses a multi-stage radial magnetic suspension bearing with a fault-tolerant function, comprising a stator and a rotor, and at least five groups of magnetic poles are arranged in the stator in a circumferential direction and are independent of each other; the stator is divided into two halves by any plane of the center line of the stator, and at least one group of magnetic poles is arranged on each half of the stator under the condition that the magnetic poles coinciding with the plane are ignored. The application further discloses a lowest power consumption control method of the multi-stage radial magnetic suspension bearing with the fault-tolerant function. The multi-stage radial magnetic suspension bearing with the fault-tolerant function and the lowest power consumption control method thereof are aimed at switching the control system to a corresponding fault-tolerant state and keeping the stable suspension of the magnetic suspension bearing in the case that at least one group of magnetic poles fails. The lowest power consumption control method is aimed at reducing the power consumption in view of the problem of the power consumption increase caused by the multi-stage magnetic poles.

Description

Technical Field

[0001] This invention belongs to the field of radial magnetic levitation bearing technology, specifically a multi-stage radial magnetic levitation bearing with fault tolerance and its minimum power consumption control method. Background Technology

[0002] Since magnetic levitation bearing systems need to operate under high-speed loads for extended periods, failures during operation can not only damage components but also potentially cause more serious safety issues. Therefore, their reliability and fault tolerance have become a research hotspot in the field in recent years.

[0003] Research on the reliability and fault tolerance of magnetic levitation bearings has focused more on the power amplifier circuit, sensors, controllers, and other components, while relatively little research has been done on the fault tolerance of magnetic bearing coils when they fail, although this aspect is also crucial.

[0004] Traditional magnetic levitation bearings have their magnetic poles arranged symmetrically along the X and Y axes, and each magnetic pole, regardless of the number of coils, directly connects the coils in series. While this minimizes the number of power circuits, if any coil fails, the corresponding magnetic pole will have no electromagnetic force, causing the magnetic levitation rotor to lose control.

[0005] Although some scholars have studied fault-tolerant radial magnetic levitation bearings with fault-tolerant control functions, existing research on magnetic pole fault-tolerant structures, whether eight-pole, twelve-pole, or sixteen-pole, basically shows that the magnetic poles are symmetrically distributed 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, a more complex control system, increased power consumption, and more device failures.

[0006] Therefore, based on the above problems, this invention proposes a five-pole radial magnetic levitation bearing with fault tolerance and a control method for minimum power consumption. The goal of this invention is to make the magnetic levitation bearing have fault tolerance capabilities while requiring the least amount of power circuitry. Furthermore, this invention also proposes a corresponding control method for minimum power consumption to address the problem that adding an extra circuit may increase power consumption. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a multi-stage radial magnetic levitation bearing with fault tolerance and a method for controlling the lowest power consumption thereof, which aims to enable the control system to switch to the corresponding fault-tolerant state and maintain the stable levitation of the magnetic levitation bearing in the event of a failure of at least one magnetic pole; and to address the problem of increased power consumption that may be caused by multiple magnetic poles, the proposed method for controlling the lowest power consumption aims to reduce power consumption.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] This invention first proposes a multi-stage radial magnetic levitation bearing with fault tolerance, including a stator and a rotor. The stator has at least 5 independent magnetic poles arranged at intervals along the circumferential direction. The stator is divided into two halves by any plane passing through the center line of the stator. Under the condition of ignoring the magnetic poles coinciding with the plane, each half of the stator has at least one magnetic pole.

[0010] Furthermore, the magnetic poles are either evenly or non-uniformly distributed in a ring along the circumferential direction of the stator.

[0011] Furthermore, when at least one of the magnetic poles is faulty, if the following conditions are met simultaneously:

[0012] The stator is divided into two halves by any first radial plane passing through the stator centerline, and each half of the stator has at least one non-faulty magnetic pole, ignoring magnetic poles whose axes lie within the first radial plane; and the stator is divided into two halves by a second radial plane passing through the stator centerline and perpendicular to the first radial plane, and each half of the stator has at least one non-faulty magnetic pole, ignoring magnetic poles whose axes lie within the second radial plane.

[0013] If the fault-tolerant control conditions are met, fault-tolerant control can be implemented on the magnetic bearing; otherwise, the fault-tolerant control conditions are not met.

[0014] This invention also proposes a method for controlling the lowest power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance, comprising the following steps:

[0015] Step 1: Establish a coordinate system with the center of the stator inner control circle as the origin. Use displacement sensors to collect rotor displacement signals 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 centroid position and the air gap width between each magnetic pole and the rotor based on the rotor displacement signals.

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

[0017] Step 3: Establish electromagnetic force F x and F y The equation relating to the current in the magnetic pole coil:

[0018]

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

[0020] E = diag[e1, e2, ..., e] n ]

[0021] Where: e j Let be the state parameter of the j-th magnetic pole, and: if the j-th magnetic pole is normal, then e j =1; if the j-th magnetic pole is faulty, 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, representing 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 two, the dynamic equation of the magnetic bearing is:

[0029]

[0030] Where: M is the mass matrix; q is the coordinate of the magnetic bearing's center of mass; G is the gyro effect matrix; L f The lever arm coefficient matrix is ​​shown; W is the gravity vector.

[0031] When energized, the magnetic poles exert an electromagnetic force on the rotor. The electromagnetic force of each magnetic pole is:

[0032]

[0033] K = μN 2 A / 8

[0034] Wherein: F j The j-th magnetic pole applies an electromagnetic force to the rotor; I j s is the control current for the j-th magnetic pole; j denoted as , where is the air gap width between the j-th magnetic pole and the rotor; K is the electromagnetic force coefficient; μ is the air permeability; N is the number of coil turns; and A is the magnetic pole area.

[0035] The resultant electromagnetic force in the x and y directions is:

[0036]

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

[0038] Furthermore, in step five, the Lagrange equations for the objective function and constraints are established by combining the penalty function:

[0039]

[0040] Where: λ1 and λ2 are Lagrange operators; α is the penalty function used to constrain the minimum value of the coil current; α is the penalty factor.

[0041] Find the unknowns i1, i2, ..., i in the Lagrange equations. n Partial derivatives of λ1 and λ2:

[0042]

[0043] By setting all partial derivatives to zero, we obtain the control current required for each magnetic pole under minimum power consumption conditions.

[0044] The beneficial effects of this invention are as follows:

[0045] This invention relates to a fault-tolerant multi-stage radial magnetic levitation bearing. The bearing winding structure consists of at least five magnetic poles spaced at intervals along the circumferential direction of the stator, with each pole being independent of the others. The distribution of the magnetic poles can be either evenly or non-evenly distributed circumferentially, but it must ensure that, given an arbitrary plane passing through the stator centerline dividing the stator into two halves, and ignoring magnetic poles coinciding with that plane, each half of the stator has at least one of the aforementioned magnetic poles. Thus, since the magnetic poles are spaced at least five times along the circumferential direction of the stator, when at least one magnetic pole fails, the fault-tolerant control condition can be met under certain conditions, namely: [the condition is met when at least one magnetic pole fails]. An arbitrary first radial plane divides the stator into two halves. Ignoring the magnetic poles whose axes lie within this first radial plane, each half of the stator has at least one non-faulty magnetic pole. Furthermore, a second radial plane passing through the stator centerline and perpendicular to the first radial plane divides the stator into two halves. Ignoring the magnetic poles whose axes lie within this second radial plane, each half of the stator has at least one non-faulty magnetic pole. Thus, a power amplifier can output corresponding control currents to the remaining normally functioning magnetic poles, stabilizing the magnetic levitation rotor at the bearing center.

[0046] Under normal conditions, all magnetic poles work normally. The power amplifier outputs the corresponding control current to each magnetic pole, so that the magnetic levitation rotor is stable at the center of the bearing. When a magnetic pole fails, if the fault-tolerant control conditions are met, the remaining working magnetic poles are subjected to corresponding fault-tolerant control, so that the magnetic levitation bearing continues to maintain the stable levitation of the magnetic levitation rotor when at least one magnetic pole fails.

[0047] In summary, the multi-stage radial magnetic levitation bearing with fault tolerance of the present invention can switch the control system to the corresponding fault-tolerant state and maintain the stable levitation of the magnetic levitation bearing in the event of a failure of at least one magnetic pole. Attached Figure Description

[0048] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0049] Figure 1 This is a schematic diagram of a multi-stage radial magnetic levitation bearing embodiment with fault-tolerant function according to the present invention; specifically, it is a schematic diagram of the structure when 5 magnetic poles are evenly distributed in a ring.

[0050] Figure 2 This is a schematic diagram of a multi-stage radial magnetic levitation bearing with non-uniformly distributed magnetic poles.

[0051] Figure 3 This is a schematic diagram of the minimum power consumption control method for a multi-stage radial magnetic levitation bearing with fault tolerance function according to the present invention.

[0052] Figure 4 A schematic diagram of a single magnetic pole fault;

[0053] Figure 5 This is a schematic diagram of a fault in two non-adjacent magnetic poles.

[0054] Figure 6 This is a schematic diagram of the first scenario when two adjacent magnetic poles are faulty.

[0055] Figure 7 This is a schematic diagram of the second scenario when two adjacent magnetic poles are faulty.

[0056] Explanation of reference numerals in the attached figures:

[0057] 10-Stator; 20-Rotor; 30-Magnetic pole. Detailed Implementation

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

[0059] The structure and control of a conventional radial magnetic levitation bearing can be simply described as follows: A radial magnetic levitation bearing contains 4n magnetic poles. Typically, a fixed planar coordinate system is established in a plane parallel to the bearing end face, with the center of the bearing's inner bore as the reference point. The horizontal direction is usually marked as the x-axis, and the vertical direction 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 levitation bearing are divided into four groups: two groups along the x-axis (X... A and X B ) and the two sets of Y-axis (Y A and Y B Each set of magnetic poles is typically connected in series, forming two opposing magnetic pole regions: the X region and the Y region. The number of magnetic poles in each set depends on 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, respectively. When the magnetic levitation rotor deviates in the x and y directions, the position sensor collects real-time position signals and inputs them to the digital controller. The controller calculates the control currents Icx and Icy required for the magnetic levitation rotor to return to the equilibrium position based on a 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 levitation of the rotor at the origin of the coordinate system.

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

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

[0062] To address the aforementioned problems, this embodiment proposes a multi-stage radial magnetic levitation bearing with fault tolerance. Specifically, the multi-stage radial magnetic levitation bearing with fault tolerance in this embodiment includes a stator 10 and a rotor 20. At least five independent magnetic poles 30 are arranged at intervals along the circumferential direction within the stator 10. The arrangement of the magnetic poles 30 must satisfy the following condition: if the stator 10 is divided into two halves by any plane passing through its centerline, and ignoring magnetic poles coinciding with that plane, each half of the stator 10 must have at least one magnetic pole 30. Specifically, in a preferred embodiment, the magnetic poles 30 are evenly distributed in a ring along the circumferential direction of the stator 10, which satisfies the requirement for the arrangement of the magnetic poles 30.

[0063] Specifically, for fault-tolerant control to be implemented when at least one magnetic pole 30 fails, the following conditions must be met simultaneously: The stator 10 must be divided into two halves by any first radial plane passing through the center line of the stator 10, and ignoring magnetic poles 30 whose axes lie within this first radial plane, each half of the stator 10 must have at least one non-faulty magnetic pole 30; and the stator 10 must be 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 ignoring magnetic poles whose axes lie within this second radial plane, each half of the stator 10 must have at least one non-faulty magnetic pole 30. Specifically, if the fault-tolerant control conditions are met when at least one magnetic pole 30 fails, fault-tolerant control is implemented for the magnetic bearing; otherwise, the fault-tolerant control conditions are not met, and the magnetic bearing cannot meet the usage requirements.

[0064] In this embodiment, five independent magnetic poles 30 are arranged circumferentially within the stator 10. The five magnetic poles 30 are composed of five sets of coils, and are labeled as ①②③④⑤ in clockwise order. The coordinate system XOY is established with the center of the inner hole of the stator 10 as the origin O, the direction perpendicular to the origin O as the Y-axis, the direction pointing from the origin to the circumference of the stator as the positive direction of the Y-axis, and the direction of rotating 90° clockwise from the positive direction of the Y-axis as the positive direction of the X-axis.

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

[0066] For special cases where it is impossible to achieve an even distribution of magnetic poles 30, it can also be as follows: Figure 2The distribution shown is not uniform, but regardless of the arrangement, it must be ensured 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 magnetic pole 30 coincides with the first radial plane, then that magnetic pole 30 is ignored). Furthermore, 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 magnetic pole 30 coincides with the second radial plane, then that magnetic pole 30 is ignored). Specifically, both the X-axis and Y-axis are radial directions passing through the center of the inner hole of the stator 10, and the radial directions of the X-axis and Y-axis can be arbitrarily set and adjusted, but they must be perpendicular to each other.

[0067] like Figure 2 When the non-uniform distribution is shown, the stator 10 is divided into two parts by the first radial plane passing through the Y-axis and the center line of the stator 10. The left half has magnetic poles ④ and ⑤, and the right half has magnetic poles ② and ③ (since the axis of magnetic pole ① coincides with the first radial plane, magnetic pole ① is ignored). Then, the stator 10 is divided into two parts by the second radial plane passing through the X-axis and the center line of the stator 10. The upper half has magnetic poles ①, ② and ⑤, and the lower half has magnetic poles ③ and ④. Therefore, it meets the requirements for non-uniform distribution.

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

[0069] Specifically, such as Figure 3 As shown in the figure, this embodiment also proposes a method for controlling the lowest power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance, which includes the following steps.

[0070] Step 1: Establish a coordinate system XOY with the center of the inner control circle of stator 10 as the origin. Use displacement sensors to collect rotor displacement signals 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 position of the centroid of rotor 20 and the air gap width between each magnetic pole 30 and rotor 20 based on the rotor displacement signals.

[0071] Step 2: Based on the offset between the rotor's center of mass and the origin of the coordinate system, calculate the electromagnetic forces F in the x and y directions required for the rotor's center to return to the origin of the coordinate system. x and F y .

[0072] like Figure 1 As shown, the radial magnetic bearing has electromagnetic forces F in two orthogonal directions (x and Y directions). x and electromagnetic force F yIt needs 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 forces generated by magnetic poles ②③④⑤ (i.e., coils ②③④⑤ in the diagram). y The electromagnetic forces generated by magnetic poles ①②③④⑤ are used to determine the location.

[0073] Under normal circumstances, the radial control of the magnetic bearing is 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 magnetic bearing's center of mass; G is the gyro effect matrix; L f is the lever arm coefficient matrix; W is the gravity vector. All of the above matrices are known and measurable values.

[0076] Additionally, F is the electromagnetic force vector:

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

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

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

[0080]

[0081] K = μN 2 A / 8

[0082] Wherein: F j The j-th magnetic pole applies an electromagnetic force to the rotor; I j s is the control current for the j-th magnetic pole; j denoted as , where is the air gap width between the j-th magnetic pole and the rotor; K is the electromagnetic force coefficient; μ is the air permeability; N is the number of coil turns; and A is the magnetic pole area.

[0083] The resultant electromagnetic force in the x and y directions is:

[0084]

[0085] Where: θ j Let be the angle between the electromagnetic force of the j-th magnetic pole and the x-axis; I is the column vector of the magnetic pole currents, I = [i1, i2, ..., ij]. n ] T S is the diagonal matrix of the air gap 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 electromagnetic force F x and F y The equation relating to the current in the coil of magnetic pole 30:

[0087]

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

[0089] E = diag[e1,e2,…,e] n ]

[0090] Where: e j Let be the state parameter of the j-th magnetic pole, and: if the j-th magnetic pole is normal, then e j =1; if the j-th magnetic pole is faulty, 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] Where: e1~e5 correspond to the 5 magnetic poles 30 respectively. When the magnetic poles 30 are working normally, e j =1, when a fault occurs, the e of magnetic pole 30 j =0. For example... Figure 4 As shown, the magnetic pole ① is faulty, and the corresponding magnetic pole state matrix is ​​E=diag(0,1,1,1,1).

[0094] In this embodiment, the magnetic poles 30 are evenly distributed in a ring of five, ensuring that the fault-tolerant control conditions are met even if any one of the magnetic poles 30 fails. It should be noted that when two magnetic poles 30 fail, only three magnetic poles 30 remain. To meet the fault-tolerant control conditions, the arrangement of the remaining magnetic poles 30 is required. Therefore, the applicability of this embodiment's method when two magnetic poles 30 fail needs to be discussed separately based on the location of the faulty magnetic pole 30.

[0095] The method in this embodiment is applicable when the two magnetic poles 30 are not adjacent magnetic poles. For example... Figure 5 As shown, when magnetic poles ① and ③ fail, and the stator 10 is divided into two parts by the first radial plane passing through the Y-axis and the center line of the stator 10, the left half has magnetic poles ④ and ⑤, and the right half has magnetic pole ②; then, when the stator 10 is divided into two parts by the second radial plane passing through the X-axis and the center line of the stator 10, the upper half has magnetic poles ② and ⑤, and the lower half has magnetic pole ④, which meets the fault-tolerant control requirements. Therefore, the electromagnetic force generated by the remaining magnetic poles can meet the control requirements at this time.

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

[0097] like Figure 6 As shown, when magnetic poles ② and ③ malfunction, and the stator 10 is divided into two parts by the first radial plane passing through the Y-axis and the center line of the stator 10, the left half has magnetic poles ④ and ⑤, while the right half has no magnetic poles (since the Y-axis coincides with the axis of magnetic pole ①, magnetic pole ① is ignored); then, when the stator 10 is divided into two parts by the second radial plane passing through the X-axis and the center line of the stator 10, the upper half has magnetic poles ① and ⑤, and the lower half has magnetic pole ④, 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, when magnetic poles ② and ③ malfunction, and the stator 10 is divided into two parts by the first radial plane passing through the Y-axis and the center line of the stator 10, the left half has magnetic poles ① and ⑤, and the right half has magnetic pole ④; then, when the stator 10 is divided into two parts by the second radial plane passing through the X-axis and the center line of the stator 10, the upper half has magnetic pole ①, and the lower half has magnetic poles ④ and ⑤, 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 is known that even when adjacent magnetic poles ② and ③ fail, different X-axis and Y-axis directions will affect whether the fault-tolerant control conditions are met. Therefore, when at least two magnetic poles 30 fail, if the fault-tolerant control conditions are not met in the current X-axis and Y-axis directions, the X-axis and Y-axis directions can be changed to determine whether the fault-tolerant control conditions are ultimately met.

[0100] Step 4: Construct the objective function

[0101] (1) Objective function

[0102] The electromagnetic bearing consumes the least power, which means minimizing the sum of the squares of the currents of the five magnetic poles 30 while satisfying the current requirements of each magnetic pole 30. Therefore, the objective function is:

[0103] minJ(I)=I T I

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

[0105] (2) Constraints

[0106] The objective at this point is to minimize the objective function J(I) while satisfying the following constraints:

[0107] Constraint 1: The electromagnetic force required in the x-direction, i.e., F1 = KI T (S -1 ) T D X (S -1 )IF x ;

[0108] Constraint 2: The electromagnetic force required in the y-direction, i.e., F2 = KI. T (S -1 ) T D y (S -1 )IF y ;

[0109] Since the objective function is to minimize power, the calculated current must be as small as possible. However, because electromagnetic bearings operate without contact, the bearing's support stiffness is related to the coil current. Therefore, it is necessary to consider minimizing power consumption while meeting the support stiffness requirements, based on actual conditions. Thus, the minimum current for each coil can be defined according to the current rotor operating parameters, such as speed and vibration, to meet the support stiffness requirements of the magnetic bearing under different operating conditions.

[0110] Therefore, constraint 3 applies: a minimum current needs to be defined for each coil, i.e.:

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

[0112] Where: i min This indicates the minimum allowable current; the value is defined based on 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 transformed into finding the minimum value of the objective function under constraints. In numerical analysis, the Lagrange multiplier method is more suitable 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 also need to be considered, a combination of the Lagrange multiplier method and the penalty function method is chosen to solve the problem. Therefore, the equations are further constructed as follows:

[0118]

[0119] That is, the Lagrange equation for the objective function and constraints, combined with the penalty function, is as follows:

[0120]

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

[0122] Find the unknowns i1, i2, ..., i in the Lagrange equations. n Partial derivatives of λ1 and λ2:

[0123]

[0124] Setting all partial derivatives to zero and solving the above equations simultaneously, we get:

[0125]

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

[0127] In this embodiment, the radial magnetic bearing is controlled using a dual-loop control system: an outer control loop (position loop) and an inner control loop (current loop). The position loop calculates the current loop signal (current command value on the five magnetic poles 30) based on the relative position signal of the rotor 20 fed back from the position sensor. This current command is then converted into a controllable switch duty cycle command value via carrier comparison to control the controllable switch of the power amplifier. Finally, the current loop rapidly tracks and effectively controls the five magnetic poles 30.

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

[0129] (1) In normal working mode, the 5 magnetic poles 30 are in good working condition. Through dual-loop control, the digital controller generates control current I according to the offset of the rotor shaft center from the coordinate origin. The corresponding control current is output to the 5 magnetic poles 30 through the power amplifier, so that the magnetic levitation rotor is stable at the bearing center.

[0130] (2) Monitor the working status of the 5 magnetic poles 30 in real time. When a magnetic pole 30 has a fault such as open circuit or short circuit, it is determined that the bearing winding has a fault and enters the fault-tolerant working mode. According to the different faulty magnetic poles 30, the current of the remaining working magnetic poles 30 is controlled accordingly to ensure that the magnetic levitation bearing can maintain the stable suspension of the magnetic levitation rotor when one or two magnetic poles 30 fail.

[0131] After entering fault-tolerant mode, an alarm is issued. While ensuring the stable levitation of the magnetic levitation rotor 20, the control system reduces the rotor speed to 0, thereby effectively avoiding damage to the rotor 20 and other components caused by the failure of some magnetic poles 30 at high speeds.

[0132] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for controlling the lowest power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance, characterized in that: The fault-tolerant multi-stage radial magnetic levitation bearing includes a stator and a rotor, wherein at least five independent magnetic poles are arranged at intervals along the circumferential direction in the stator. Divide the stator into two halves by any plane passing through the center line of the stator, and ignoring the magnetic poles coinciding with the plane, each half of the stator shall have at least one magnetic pole. The method includes the following steps: Step 1: Establish a coordinate system with the center of the stator's inner control circle as the origin, and use displacement sensors to collect data on the rotor's position. and The rotor displacement signal in the direction is collected and transmitted to the magnetic bearing controller; the magnetic bearing controller calculates the rotor centroid 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's center of mass and the origin of the coordinate system, calculate the amount of time required for the rotor center to return to the origin of the coordinate system. and Electromagnetic force in direction and ; Step 3: Establish electromagnetic force and The equation relating to the current in the magnetic pole coil: in: and It is a current vector; It is the electromagnetic force coefficient; The rotor is respectively in Force weighting matrix in direction; This represents the air gap matrix between the magnetic pole coil and the rotor; Here is the magnetic pole state matrix; and: in: For the first The state parameters of the magnetic poles of the road, and: if the first If the magnetic poles of the road are normal, then If the first If the magnetic poles of the road are faulty, then ; , The number of magnetic poles; Step 4: Construct the objective function: in: Let be the objective function, representing the power consumption of the magnetic bearing; Constraints: Step 5: Solve the objective function to obtain the control current required for each magnetic pole under the condition of minimum power consumption.

2. The method for controlling the minimum power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance as described in claim 1, characterized in that: The magnetic poles are either evenly or non-evenly distributed in a ring along the circumferential direction of the stator.

3. The method for controlling the minimum power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance as described in claim 1, characterized in that: When at least one of the magnetic poles is faulty, if the following conditions are met simultaneously: The stator is divided into two halves by any first radial plane passing through the stator centerline, and each half of the stator has at least one non-faulty magnetic pole, ignoring magnetic poles whose axes lie within the first radial plane; and the stator is divided into two halves by a second radial plane passing through the stator centerline and perpendicular to the first radial plane, and each half of the stator has at least one non-faulty magnetic pole, ignoring magnetic poles whose axes lie within the second radial plane. This satisfies the fault-tolerant control conditions, allowing for fault-tolerant control of the magnetic bearing. Otherwise, the fault tolerance control conditions are not met.

4. The method for controlling the minimum power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance as described in claim 1, characterized in that: In step two, the dynamic equation of the magnetic bearing is: in: This is the quality matrix; The coordinates of the centroid of the magnetic bearing; The gyroscope effect matrix; This is the lever arm coefficient matrix; It is the gravity vector; When energized, the magnetic poles exert an electromagnetic force on the rotor. The electromagnetic force of each magnetic pole is: in: For the first The magnetic poles exert an electromagnetic force on the rotor; For the first The control current of the magnetic poles; For the first The width of the air gap between the magnetic poles and the rotor; It is the electromagnetic force coefficient; air permeability; This refers to the number of coil turns. The area of ​​the magnetic poles; but The resultant electromagnetic force in the axial direction is: in: For the first The electromagnetic force of each magnetic pole and The included angle of the axis.

5. The method for controlling the minimum power consumption of a multi-stage radial magnetic levitation bearing with fault tolerance as described in claim 1, characterized in that: In step five, the Lagrange equations for the objective function and constraints are established by combining the penalty function: in: and For Lagrange operators; This is a penalty function used to constrain the minimum value of the coil current; As a penalty factor; Find the unknowns in the Lagrange equations respectively. Partial derivatives: By setting all partial derivatives to zero, we obtain the control current required for each magnetic pole under minimum power consumption conditions.

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