Control device and control method for magnetic bearing

Abstract

To provide a control device for a magnetic bearing that enables mode separation of a natural vibration mode with high precision and can design a stable controller with the degree of the controller made small.SOLUTION: With respect to a model for a rotary body controlled by radial magnetic bearings 1, 2, a status space model is structured by excluding a controller which controls a plant from a mode composition model having parameters of a mass matrix, a rigidity matrix, and an attenuation matrix identified and adjusted by a parameter estimation part, and a mode separation part 61 on the input side of controllers 1, 2 inputs a measurement signal of a displacement sensor from the radial magnetic bearings 1, 2 to perform mode separation with a mode separation coefficient. A mode composition part 62 on the output side of the controllers 1, 2 performs mode composition with a mode composition coefficient, and outputs a drive command signal (current, voltage) to electric magnets of the radial magnetic bearings 1, 2.SELECTED DRAWING: Figure 14

Description

Technical Field

[0001] The present invention relates to magnetic axis control technology, and particularly to a technology for controlling and levitating a left-right asymmetric rotating body with an electromagnet of a magnetic bearing.

Background Art

[0002] In a magnetic bearing device that supports a rotating body by a magnetic bearing, when controlling the current of an electromagnet to control the position of the rotating body and levitate it, the frequency response of the axis of the rotating body is measured to adjust the frequency response of the controller.

[0003] Conventionally, as magnetic axis control technology, for example, the technologies described in Patent Document 1, Non-Patent Document 1, Non-Patent Document 2, and Non-Patent Document 3 have been disclosed. Patent Document 1 describes designing a controller using a model degenerate by mode superposition of low-frequency eigenmodes from the results of analysis by the finite element method.

[0004] Non-Patent Document 1 introduces a method of diagnosing a rotating body by a method called "magnetic hammering" in which the rotating body is vibrated in a state of being magnetically levitated by a radial magnetic bearing.

[0005] Non-Patent Document 2 describes a mode separation control method for a magnetic bearing elastic rotor that takes advantage of the symmetry of the magnetic bearing elastic rotor.

[0006] Non-Patent Document 3 describes obtaining the inherent vibration modes with both ends as free end conditions for a left-right asymmetric rotating body by the finite element method and performing a process of separating specific inherent vibration modes.

[0007] An example of a conventional magnetic bearing device is shown in FIG. 1. FIG. 1 shows the configuration of a rotating electrical machine provided with a radial magnetic bearing device having an impeller (such as a blower) used in an aeration blower.

[0008] In FIG. 1, reference numeral 11 denotes an impeller (such as a blower) provided at the tip of a rotating shaft 12.

[0009] A disk-shaped thrust disk 13 is fixed to the outer periphery of a rotating shaft 12 that is axially spaced from the impeller 11 by a predetermined distance. 14 is an electromagnet disposed on the impeller side of the thrust disk 13, and 15 is an electromagnet disposed on the side opposite to the impeller of the thrust disk 13 and facing the electromagnet 14 with the thrust disk 13 interposed therebetween.

[0010] A radial magnetic bearing 1 that supports the rotating shaft 12 in a non-contact manner in the radial direction is provided on the outer periphery of the rotating shaft 12 located between the impeller 11 and the thrust disk 13.

[0011] A power converter (not shown) capable of controlling the current flowing through the electromagnet is connected to the electromagnet of this radial magnetic bearing 1.

[0012] 16 is a protective bearing disposed on the outer periphery of the rotating shaft 12 on the impeller 11 side of the radial magnetic bearing 1. This protective bearing 16 is composed of, for example, a touchdown bearing using a ball bearing.

[0013] A permanent magnet rotor 17 is fixed to the outer periphery of the rotating shaft 12 that is axially spaced from the thrust disk 13 by a predetermined distance on the side opposite to the impeller, and a stator core 18 is disposed with a gap from the outer periphery in the radial direction of the rotating shaft 12 from the permanent magnet rotor 17.

[0014] 19a is a stator winding provided at the impeller side end of the stator core 18, and 19b is a stator winding provided at the side opposite to the impeller of the stator core 18.

[0015] A radial magnetic bearing 2 that supports the rotating shaft 12 in a non-contact manner in the radial direction is provided on the outer periphery of the rotating shaft 12 that is axially spaced from the stator winding 19b by a predetermined distance on the side opposite to the impeller.

[0016] A power converter (not shown) capable of controlling the current flowing through the electromagnet is connected to the electromagnet of this radial magnetic bearing 2.

[0017] 20 is a protective bearing disposed on the outer periphery of the rotating shaft 12 on the anti-impeller side of the radial magnetic bearing 2 (same configuration as the protective bearing 16).

Prior Art Documents

Patent Documents

[0018]

Patent Document 1

Non-Patent Documents

[0019]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0020] In the technology of Patent Document 1, when the rotating body is not a simple structure with left-right asymmetry, there may be a deviation from the result of exciting the actual machine. In this case, the accuracy of position control of the rotating body decreases.

[0021] Also, the model of mode superposition has a problem in application to objects where the natural mode of the object may change due to state feedback control that controls the force with an electromagnet with respect to the measured displacement like a rotating body levitated by a radial magnetic bearing.

[0022] In the technique of Non-Patent Document 1, a displacement signal is measured with respect to the excitation force applied to the rotating body by the radial magnetic bearing, and the frequency rigidity characteristic called the plant dynamic rigidity is obtained. In the adjustment of the parameters of the controller, while measuring the frequency characteristics of this plant dynamic rigidity, manual adjustment is performed. Therefore, the adjustment is time-consuming. In addition, a deviation from appropriate parameters due to the skill of the adjuster is also a concern.

[0023] Also, as in the technique of Non-Patent Document 2, when the rotating body is bilaterally symmetric, since the motion of the rotating body is separated into translational motion and tilting motion, in the mode-separated coordinate system, it is possible to control each motion independently with respect to the natural mode for each motion.

[0024] However, in a rotating body equipped with a radial magnetic bearing device having an impeller used in an aeration blower as shown in FIG. 1, since it is an overhung rotor with left-right asymmetry, the characteristics of the controller of the radial magnetic bearing 1 affect the control characteristics of the radial magnetic bearing 2, and it is difficult to adjust the parameters of the controller.

[0025] Also, in the technique of Non-Patent Document 3, in a left-right asymmetric system, it is possible to estimate the mode shape at the bearing support part of a specific natural vibration mode and separate the system by removing the specific natural vibration mode, but a technique for estimating the mode shape is required. However, in the method of obtaining the natural vibration mode using the finite element method, there are effects such as errors during design, the influence of current control in the control system by controlling the electromagnet acting as a low-pass filter, the negative spring effect of the electromagnet, and the influence of delay elements such as sensors.

[0026] The present invention solves the above problems, and its object is to provide a control device for a magnetic bearing that can perform mode separation of natural vibration modes with high accuracy and design a stable controller while reducing the order of the controller. Specifically, it aims to estimate the parameters of a model including the natural mode of the rotating body and adjust the parameters of the controller of the magnetic bearing in consideration of the sensitivity function, stability margin, disturbance response, current, etc.

Means for Solving the Problems

[0027] The control device for a magnetic bearing according to claim 1 for solving the above problems is, In a magnetic bearing device that supports a rotating body by a magnetic bearing, A plant including a rotating body and electromagnets respectively arranged on the left and right sides in the axial direction of the rotating body, a controller for controlling the plant, a current control block, a cancellation gain block for negative spring, a control input, a disturbance input, an evaluation output, and a control output, and constructing a model of a rotating body controlled by a magnetic bearing, where feedback is applied from the control output to the control input. A sensitivity function acquisition unit that performs a vibration test to measure the evaluation output when a vibration signal is superimposed on the disturbance input of the model with the rotating body levitated in a zero-rotation state to obtain the sensitivity function at zero rotation of the frequency response, levitates the rotating body, and in a low-speed rotation state where the unbalanced vibration force can be ignored, measures the evaluation output when a forward vibration signal (considering a right-handed coordinate system with the axial direction of the rotating body as z, and when the rotation direction is counterclockwise, a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction) is superimposed on the disturbance input of the model to obtain the sensitivity function at low-speed rotation of the frequency response. From the obtained sensitivity function at zero rotation, identify and adjust the parameters of the mass matrix, stiffness matrix, and damping matrix of the mode synthesis method model so that the evaluation output becomes a set signal when a vibration signal is superimposed on the disturbance input of the state-space model with the known parameters of the controller, current control block, and cancellation gain block for negative spring in the model of the rotating body controlled by the magnetic bearing substituted. From the obtained sensitivity function at low-speed rotation, identify and adjust the parameters of the gyro matrix of the mode synthesis method model so that the evaluation output becomes a set signal when the vibration signal is superimposed on the disturbance input of the state-space model with the known parameters of the controller, current control block, and cancellation gain block for negative spring in the model of the rotating body controlled by the magnetic bearing substituted. From the mode synthesis method model in which the parameters of the mass matrix, stiffness matrix, and damping matrix are identified and adjusted by the parameter estimation unit, a state space model is constructed by excluding the controller that controls the plant, and the mode shape at the position of the magnetic bearing is estimated using the state space model. From the estimated mode shape, the mode separation coefficient on the input side of the controller that performs mode control and the mode synthesis coefficient on the output side of the controller that performs mode control are obtained, and using these mode separation coefficients, controller, and mode synthesis coefficients, a mode separation process for separating the natural vibration modes is performed on the state space model, and a mode control unit that performs mode control in the mode separation system is provided.

[0028] The control device for a magnetic bearing according to claim 2, in claim 1, Based on the result of the excitation test in the sensitivity function acquisition unit, the transfer function of the plant from the evaluation output of the model of the rotating body to the control output is measured, the transfer function is expanded in a Bode diagram and the phase frequency response is plotted, and the delay element of the plant is evaluated by at least one of the first-order Pade approximation or the second-order Pade approximation of the continuous system to obtain a delay element block for estimating the dead time, and the delay element block is added to the control output side of the state space model constructed by the mode control unit.

[0029] The control device for a magnetic bearing according to claim 3, in claim 2, The first-order Pade approximation transfer function of the delay element block is the following formula (57)

[0030]

Equation

[0031] and The second-order Pade approximation transfer function of the delay element block is the following formula (58)

[0032]

Equation

[0033] where Gφ is the transfer function of the lag element, and τ and τs are the dead times), characterized in that.

[0034] The method for controlling a magnetic bearing according to claim 4 is In a method for controlling a magnetic bearing that supports a rotating body by a magnetic bearing, A plant including a rotating body and electromagnets respectively arranged on the left and right sides in the axial direction of the rotating body, a controller for controlling the plant, a current control block, a cancellation gain block for the negative spring component, a control input, a disturbance input, an evaluation output, and a control output, and constructing a model of a rotating body controlled by a magnetic bearing that feeds back from the control output to the control input, A sensitivity function acquisition unit performs a vibration test to measure the evaluation output when a vibration signal is superimposed on the disturbance input of the model in a state where the rotating body is levitated and has zero rotation, and obtains the sensitivity function at zero rotation of the frequency response. The rotating body is levitated and in a low-speed rotation state where the unbalanced vibration force can be ignored. When a forward vibration signal (considering a right-handed coordinate system with the axial direction of the rotating body as z, and when the rotation direction is counterclockwise, a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction) is superimposed on the disturbance input of the model, the evaluation output is measured to obtain the sensitivity function at low-speed rotation of the frequency response; A parameter estimation unit substitutes the known parameters of the controller, the current control block, and the cancellation gain block of the negative spring component in the model of the rotating body controlled by the magnetic bearing from the obtained sensitivity function at zero rotation, and superimposes a vibration signal on the disturbance input of the state-space model. The step of identifying and adjusting the parameters of the mass matrix, stiffness matrix, and damping matrix of the mode synthesis method model so that the evaluation output becomes a set signal; The parameter estimation unit superimposes the excitation signal on the disturbance input of the state-space model obtained by substituting the known parameters of the controller, current control block, and cancellation gain block for the negative spring in the model of the rotating body controlled by the magnetic bearing from the sensitivity function at the time of the obtained low-speed rotation, and identifies and adjusts the parameters of the gyro matrix of the mode synthesis method model so that the evaluation output becomes the set signal; The mode control unit constructs a state-space model by excluding the controller for controlling the plant from the mode synthesis method model in which the parameters of the mass matrix, stiffness matrix, and damping matrix have been identified and adjusted by the parameter estimation unit, and uses this state-space model to estimate the mode shape at the position of the magnetic bearing, obtain the mode separation coefficient on the input side of the controller for performing mode control and the mode synthesis coefficient on the output side of the controller for performing mode control from the estimated mode shape, and perform a mode separation process for separating the natural vibration modes on the state-space model using these mode separation coefficients, controller, and mode synthesis coefficients, and a mode control step of performing mode control in the mode separation system.

Advantages of the Invention

[0035] (1) According to the invention described in claims 1 to 4, since the mode shape at the position of the magnetic bearing is estimated from the mode synthesis method model in which parameter identification and adjustment have been performed, and a specific natural vibration mode is subjected to mode separation processing, it is possible to perform magnetic levitation control that robustly stabilizes high-order vibration modes while reducing the order of the controller.

[0036] (2) According to the invention described in claim 2, since the delay element of the plant is evaluated by the first-order and second-order transfer functions of the continuous system Pade approximation, it is possible to estimate the dead time corresponding to a non-integer multiple of the control sampling time by the delay element block. And since the delay element block is added to the control output side of the state-space model, it is possible to estimate the mode shape at the bearing position and perform mode separation with higher accuracy.

Brief Description of the Drawings

[0037]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Mode for Carrying Out the Invention

[0038] Hereinafter, embodiments of the present invention will be described with reference to the drawings, but the present invention is not limited to the following embodiment examples. In the following, an embodiment example in which the present invention is applied to the magnetic bearing device of FIG. 1 will be described, but the present invention is not limited thereto and may be applied to magnetic bearing devices having other configurations.

[0039] FIG. 2 shows the overall configuration of the control for levitating a rotating body with a magnetic bearing and the excitation signal for system identification. In FIG. 2, 30 is a controller composed of, for example, a PID and controls the plant 40. The plant 40 is composed of a rotating body (rotating shaft 12 in FIG. 1) and electromagnets of the radial magnetic bearings 1 and 2.

[0040] The command displacement input as the control input of the controller 30 has its deviation from the feedback component from the control output of the plant 40 taken in the subtractor 31. An excitation signal for system identification input from the disturbance input terminal (1) is added (superimposed) in the adder 32 to the output of the controller 30.

[0041] 33 is a block of a gain (Ks described later) that cancels the negative spring effect of the electromagnet of the magnetic bearing, and the gain 33 is subtracted from the output of the adder 32 in the subtractor 34.

[0042] In the figure, (2) is an evaluation output terminal for measuring the vibration excitation result to the disturbance input terminal (1), and (3) in the figure is a control output terminal from which the output displacement is output.

[0043] In FIG. 2, the PID of the controller 30 measures the displacement with respect to one direction of one of the radial magnetic bearings (either one of 1 and 2), and controls the electromagnetic force by controlling the electromagnet with respect to the measured displacement.

[0044] When levitating and controlling a rotating body with magnetic bearings, it is necessary to control the two orthogonal x and y axes with the radial magnetic bearing 1 and the radial magnetic bearing 2 in FIG. 1 respectively. Here, a side-by-side control with the same controller parameters for all four axes is adopted. Here, as an example, as shown in FIG. 2, the controller deals with the simplest PID, but other higher-order ones may also be dealt with. It is only necessary that the parameters of the controller are known when identifying the system.

[0045] FIG. 3 shows a block diagram of a model for estimating the parameters of the plant 40 from the measurement data of the vibration excitation result for system identification.

[0046] In FIG. 3, the same parts as those in FIG. 2 are denoted by the same reference numerals. The difference between FIG. 3 and FIG. 2 is that the plant rotor of the plant 40 is designated as 41, and between the subtractor 34 and the plant rotor 41, a current command conversion block 35 for converting a control command into a current command, a current control block 36 (a block composed of a low-pass filter that constitutes the transfer function block of the current control in FIG. 5 described later) that takes the current command of the current command conversion block 35 as an input, an electromagnet attractive force linearization block 37 (related to the third term of the following formula (21)) for linearizing the attractive force of the electromagnet, a negative spring effect block 38 of the electromagnet (related to the second term of the following formula (21)), and an adder 39 for adding the output of the electromagnet attractive force linearization block 37 and the output of the negative spring effect block 38 (related to the following formula (21)) are provided, and other parts are configured in the same manner as in FIG. 2.

[0047] In Fig. 3, (4) is the control input terminal where the command displacement is input, and (5) is the current command output terminal.

[0048] The model of the plant rotor 41 in Fig. 3 uses the model of the mode synthesis method. The model of the mode synthesis method will be described below.

[0049] The motion equations of the rotor bearing system by the finite element method are expressed as the following equations (1) and (2).

[0050]

Number

[0051]

Number

[0052] M: mass matrix, G: gyro matrix, K: stiffness matrix, Q: bearing reaction force, U: unbalance vector, Ω: rotational speed.

[0053] When converting to Z = X + jY, the following equation (3) is obtained.

[0054]

Number

[0055] Taking the bearing point as the master node and the boundary point as Z 2 and other internal points as slave nodes as Z 1 and expressing it as equation (4).

[0056]

Number

[0057] Substituting equation (4) into equation (3), the motion equation of the rotor bearing system is expressed as the following equation (5).

[0058]

Number

[0059] Consider the natural mode of the internal system ignoring the gyroscopic effect as shown in Equation (6).

[0060]

Equation

[0061] When solving Equation (6) and taking the natural mode of the internal system as φ, we get Equations (7) and (8).

[0062]

Equation

[0063]

Equation

[0064] However, "diagonal" is a diagonal matrix.

[0065] Let δ be the deformation mode when the bearing is forced to displace by a unit amount. Then the following Equation (9) holds.

[0066]

Equation

[0067] K eq is the force required to lift the bearing point by 1, which corresponds to the equivalent spring constant. In a two-bearing system, K eq = 0. Using the natural mode φ of the internal system and the deformation mode δ, the conversion T q by the mode synthesis method and the coordinate Z q are expressed as shown in the following Equation (10). E is the identity matrix and η is the modal coordinate.

[0068]

Equation

[0069] Substitute Equation (10) into Equation (5), and multiply by T from the front to obtain the equation of motion of the mode synthesis method, Equation (11). t q This gives the equation of motion of the mode synthesis method, Equation (11).

[0070] [Number]

[0071] Here

[0072] [Number]

[0073] [Number]

[0074] [Number]

[0075] is the case. The M of the mode synthesis method q : mass matrix, G q : gyro matrix is a symmetric matrix. K q : stiffness matrix is a diagonal matrix. From the number of degrees of freedom of the nodes of the finite element method, by the mode synthesis method, as shown in Fig. 4, it is compressed into the number of internal system natural modes φ and the number of deformation modes δ, that is, the number of bearings. In Fig. 4, the filled points correspond to the modes of the internal system natural modes φ, and the open points correspond to the deformation modes δ.

[0076] Next, the current command conversion block 35 and the current control block 36 of the model in Fig. 3 will be described. Regarding the electromagnet and its current control in the model of Fig. 3, PI control is considered for the current control. Fig. 5 shows the transfer function block diagram.

[0077] i refis the current command output from the current command conversion block 35 in FIG. 3, i ref and the deviation from the control output current i out (feedback component) is taken by the subtractor 51, and the output of the subtractor 51 is input to the current controller.

[0078] v cmd is the voltage command for the power converter (not shown). In FIG. 5, the PWM process in the power converter is omitted, and the continuous system transfer function notation is used. Here, the control transfer function Gc(s) is PI control and is expressed by Equation (15). The transfer function Gem(s) of the electromagnet is expressed by Equation (16) considering the series connection of the winding resistance R em and the winding inductance L em . Therefore, the feedback transfer function G FB (s) becomes Equation (17). This form represents a first-order LPF (low-pass filter) with the angular frequency ω c as the cut-off frequency.

[0079]

Equation

[0080]

Equation

[0081]

Equation

[0082] Next, the electromagnet attractive force linearization block 37 and the negative spring effect block 38 in the model of FIG. 3 will be described.

[0083] Regarding the negative spring effect caused by the electromagnets of the magnetic bearing of the model in Fig. 3, it is considered as follows. In a magnetic bearing, as shown in Fig. 6, for one-way control, electromagnets 1 and 2 are arranged opposite each other across the rotating shaft (12), and they pull against each other, and the control force is generated by the difference between them. In the coils of the electromagnets, there is a bias current I 1 , I 2 for linearizing the magnetic attraction force and supporting the gravity of the rotating body, and a dynamic alternating current i 1 , i 2 required to suppress the vibration component flows as the current. The force F b [N] applied to the rotating body calculated from the difference in the attraction forces of the two electromagnets 1 and 2 of the magnetic bearing is expressed as in Equation (18). However, hereinafter, F 1 is the attraction force [N] of electromagnet 1, F 2 is the attraction force [N] of electromagnet 2, δ 0 is the distance (air gap) between the electromagnet and the rotating body [m], x is the displacement [m] of the rotating shaft 12, I 1 is the bias current of the coil of electromagnet 1, I 2 is the coil bias current of electromagnet 2, i 1 is the alternating current [A] of the coil of electromagnet 1, i 2 is the alternating current [A] of the coil of electromagnet 2, and the electromagnetic attraction coefficient K [Nm 2 / A 2 .

[0084]

Equation

[0085] In Equation (18), since the displacement x of the rotating body is much smaller than the distance δ 0 (air gap) between the electromagnet and the rotating body, that is, x ≪ δ 0 , it is expressed as in Equation (19).

[0086]

Equation

[0087] The current for suppressing the vibration component is much smaller than the bias current, that is, i1 , i 2 ≪I 1 ,I 2 Since it is, i 1 , i 2 Ignoring the second-order small term of, it is expressed as in Equation (20).

[0088]

Number

[0089] Here,[[]]END]]

[0090]

Number

[0091] Assuming that and i=(i 1 +i 2 ) / 2, and k i =2K(I 1 +I 2 ) / δ 0 2 , k n =2K(I 1 2 +I 2 2 ) / δ 0 3 Then, it becomes as in Equation (21).

[0092]

Number

[0093] Here, k i in Equation (21) is the attractive force coefficient related to the current [N / A], k nis the attractive force coefficient [N / m] related to displacement. The first term in Equation (21) is the force term related to the control current, the second term is the force term due to the negative spring effect, and the third term is the force term due to the bias current required to linearize the electromagnetic attraction force of the electromagnet. The weight of the rotating body balances this force. In the case of the radial magnetic bearing of the rotating body in Figure 3, the sum of the weights of the rotating body is balanced by two radial magnetic bearings. In the case of an overhang rotor, since the loads supported by the two radial magnetic bearings are different, the bias currents are different.

[0094] The PID controller (30) of the model in Figure 3 includes pseudo-differentiation and is expressed as in Equation (22) in the transfer function representation of the continuous system in the s domain.

[0095]

Number

[0096] Here, P is the proportional term, I is the integral term, D is the differential term, and N is the pseudo-differential filter coefficient. Also, it is expressed as in Equations (23) and (24) in the state space representation. Here, F il , I nt are the state variables of the PID controller, y is the output, and u is the input, respectively.

[0097]

Number

[0098]

Number

[0099] From Equation (11), the model of the mode synthesis method without the gyro matrix at zero rotation in the x direction is expressed as in Equation (25).

[0100]

Number

[0101] D is a damping matrix. For simplicity, consider a diagonal matrix for damping as in Equation (26).

[0102]

Number

[0103] It is expressed as in Equations (27) and (28) in the state - space representation. Here, X 1 , X 2 are the state vectors in the x - direction of the plant rotor of the mode synthesis method, y is the output vector, and u is the input vector, respectively.

[0104]

Number

[0105]

Number

[0106] E is the identity matrix.

[0107] From the above, considering the two radial magnetic bearings 1 and 2 in Figure 1 at zero rotation, when an external disturbance (for example, the excitation signal described later) is input in the x - direction to the external disturbance input terminal (1) in Figure 3, the signal at the evaluation output terminal (2) is measured, and the sensitivity function based on the measured signal is expressed as in Equations (29) and (30) in the state - space representation.

[0108]

Number

[0109]

Number

[0110] Here,

[0111]

Number

[0112]

Number

[0113] is.

[0114] Also here, X 1 , X 2 are respectively the state vectors in the x - direction of the plant rotor of the mode synthesis method, Y 1 , Y 2 are respectively the state vectors in the y - direction of the plant rotor of the mode synthesis method, F il , I nt are respectively the state vectors of the PID controller (30), T ra is the state vector corresponding to the current control low - pass filter, y is the output vector, u is the input vector, E n is the n×n identity matrix, 0 n is the n×n zero matrix, 0 m,n is the m×n zero matrix, and m is the number of internal system natural modes.

[0115] Since two radial magnetic bearings are considered, the dimensions of the input and output vectors are 2. In Equation (29), the stiffness matrix due to the negative spring effect of the electromagnets of the magnetic bearings is,

[0116]

Number

[0117] is,

[0118]

Number

[0119] is.

[0120] In an overhang rotor, since the loads supported by the two radial magnetic bearings are different, the bias currents are different. Therefore, the negative spring effect K n1 , K n2 and the attraction coefficient K i1 , K i2 with respect to the current are different between the radial magnetic bearing 1 and the radial magnetic bearing 2.

[0121] Also, K s is the gain of the control parameter for canceling the negative spring effect. Here, different values K s1 , K s2 will be taken for the radial magnetic bearing 1 and the radial magnetic bearing 2. K s1 , K s2 is the control parameter for canceling the negative spring effect. Therefore, K s1 = K s2 may be used.

[0122] K npid in the formula (29) is

[0123]

Number

[0124]

Number

[0125] as follows.

[0126] Also, when rotating, due to the influence of the gyro matrix, considering the degrees of freedom in the x and y directions as follows, a disturbance is input to the disturbance input terminal (1) in the x direction of the two radial magnetic bearings 1 and 2 in FIG. 3, the signal at the evaluation output terminal (2) is measured, and the sensitivity function based on the measured signal is expressed by equations (37) and (38) in state - space representation.

[0127]

Number

[0128]

Number

[0129] Here,

[0130]

Number

[0131]

Number

[0132]

Number

[0133]

Number

[0134]

Number

[0135]

Number

[0136]

Number

[0137]

Number

[0138]

Number

[0139]

Number

[0140]

Number

[0141] (However, M q is the mass matrix, D is the damping matrix, K n is the stiffness matrix, Ω is the rotational speed, P is the proportional term of the PID controller (30), k i =2K(I 1 +I 2 ) / δ 0 2 (K is the electromagnetic attraction coefficient, I 1 is the bias current of the coil of the electromagnet arranged on either the left or right side of the rotating body, I 2 is the bias current of the coil of the electromagnet arranged on the other side of the left or right of the rotating body, δ 0 is the air gap between the electromagnet and the rotating body), k s is the gain to cancel the negative spring effect, ω c is the cut-off frequency (angular frequency) of the low-pass filter of the current control block) Since both degrees of freedom in the x and y directions are considered with two radial magnetic bearings, the dimension of the input and output vectors is 4.

Example

[0142] As shown in FIGS. 2 and 3, the control device for the magnetic bearing of this Example 1 includes a plant 40 including a rotating body and electromagnets respectively arranged on the left and right sides in the axial direction of the rotating body, a controller 30 for controlling the plant 40, a current control block 36, a block 33 for canceling the gain of the negative spring component, a control input (4), a disturbance input (1), an evaluation output (2), and a control output (3), and constructs a model of a rotating body controlled by a magnetic bearing, with feedback from the control output to the control input. With the rotating body levitated and in a zero-rotation state, measure the evaluation output (2) when a vibration signal is superimposed on the disturbance input (1) of the model to obtain the sensitivity function at zero rotation of the frequency response (Equations (29) and (30)). With the rotating body levitated and in a low-speed rotation state where the unbalanced vibration force can be ignored, superimpose a forward vibration signal (considering a right-handed coordinate system with the axial direction of the rotating body as z, when the rotation direction is counterclockwise, a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction) on the disturbance input (1), and measure the evaluation output (2) to obtain the sensitivity function at low-speed rotation of the frequency response (Equations (32) and (33)), which is a sensitivity function acquisition unit. From the obtained sensitivity function at zero rotation, substitute the known parameters of the controller, current control block, and cancellation gain block for the negative spring in the model of the rotating body controlled by the magnetic bearing into the disturbance input (1) of the state-space model. Then, identify and adjust the parameters of the mass matrix (Equation (12)), stiffness matrix (Equation (14)), and damping matrix (Equation (26)) of the mode synthesis method model so that the evaluation output becomes the set signal when a vibration signal (described later) is superimposed. From the obtained sensitivity function at low-speed rotation, substitute the known parameters of the controller, current control block, and cancellation gain block for the negative spring in the model of the rotating body controlled by the magnetic bearing into the disturbance input (1) of the state-space model. Then, identify and adjust the parameters of the gyro matrix (Equation (13)) of the mode synthesis method model so that the evaluation output becomes the set signal when a vibration signal (described later) is superimposed, which is a parameter estimation unit. Exclude the controller for controlling the plant from the mode synthesis method model in which the parameters of the mass matrix, stiffness matrix, and damping matrix have been identified and adjusted by the parameter estimation unit to construct a state-space model. Use this state-space model to estimate the mode shape at the position of the magnetic bearing. From the estimated mode shape, obtain the mode separation coefficient on the input side of the controller for performing mode control and the mode synthesis coefficient on the output side of the controller for performing mode control. Perform mode separation processing for separating the natural vibration modes on the state-space model using these mode separation coefficients, controller, and mode synthesis coefficients, which is a mode control unit for performing mode control in the mode separation system.

[0143] The adjustment procedure of the controller of the magnetic bearing in the mode separation control (the processing procedures performed by the sensitivity function acquisition unit, the parameter estimation unit, and the mode control unit) will be described below.

[0144] <Step 1> Levitate the rotating body (rotating shaft 12) with a simple controller such as a PID.

[0145] <Step 2> At zero rotation, vibrate by superimposing a sine sweep signal only in the x (or y) direction on the disturbance input terminal (1) of FIG. 2, and measure the sensitivity function (Equations (29) and (30)) of the frequency response by measuring the signal at the evaluation output terminal (2) in the x (or y) direction.

[0146] At this time, as shown in FIGS. 7(a) and (b), superimpose the sine sweep signal separately with the radial magnetic bearings 1 and 2. The sine sweep is a signal with a constant amplitude of Asin(ωt), and the frequency is ω = bt, where b is a constant and the rotation speed increases at a constant rate.

[0147] <Step 3> From the results of the sine sweep vibration test, when the signal in FIG. 7 corresponding to the external input terminal (1) of the state space model of the sensitivity function in Equations (29) and (30) is input, the parameters of the mass matrix Equation (12), the damping matrix Equation (26), and the stiffness matrix Equation (14) of the mode synthesis method model are identified so that the signal at the evaluation output terminal (2) becomes the corresponding signal in FIGS. 8(a) and (b). The parameters are adjusted for each parameter of the mode related to each peak of the measurement result at the evaluation output terminal (2) as shown in FIG. 8.

[0148] <Step 4> Rotate the rotating body at a low speed such that the unbalanced excitation force can be ignored according to Equation (11) of the mode synthesis method.

[0149] <Step 5> In the rotated state, the system is vibrated by superimposing signals (forward excitation signals) that sweep the frequencies of sine waves in the forward x and y directions on the disturbance input ends (1) in FIG. 2, and the sensitivity functions (Equations (32) and (33)) of the frequency response are measured by measuring the signals at the evaluation output ends (2) in the x and y directions. The signal that sweeps the frequency of the sine wave forward means that considering a right-handed coordinate system with the axial direction of the rotating body as the z direction, when the rotation direction is counterclockwise as shown by the arrow in FIG. 11, the amplitude is constant with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction, and the frequency is ω = bt, where b is a constant and the frequency increases at a constant rotational speed. FIG. 11 is a conceptual diagram of the forward direction.

[0150] When the rotation direction is clockwise, excitation signals of Acos(-ωt) in the x direction and Asin(-ωt) in the y direction are applied.

[0151] <Step 6> From the results of the sine sweep vibration test, when the corresponding forward excitation signals shown in FIGS. 9(a) to (d) are input to the disturbance input ends (1) in the x and y directions of the state-space model of the sensitivity function in Equations (37) and (38) such that the signals at the evaluation output ends (2) in the x and y directions become the signals in FIGS. 10(a) to (d), the parameters of the gyro matrix (Equation (13)) of the mode synthesis method model are identified.

[0152] The parameters are adjusted for each parameter of the mode related to each peak of the measurement result at the evaluation output end (2) as shown in FIG. 10. Note that the gyro matrix may be estimated by repeating <Steps 1> to <Step 6> at different rotational speeds.

[0153] <Step 7> This system identification procedure corresponds to efficiently estimating the frequency response at the rated rotational speed by identifying the parameters of the gyro matrix at a low rotational speed as shown by the dashed line RS in FIG. 12 for the change in the natural frequency due to the gyro effect of the rotating body. L This system identification procedure corresponds to efficiently estimating the frequency response at the rated rotational speed by identifying the parameters of the gyro matrix at a low rotational speed as shown by the dashed line RS in FIG. 12 for the change in the natural frequency due to the gyro effect of the rotating body.

[0154] FIG. 12 shows the characteristics of the natural frequency due to the gyro effect versus the rotational speed, and in the dashed line RS 0 it shows Vibration excitation is performed by superimposing a sine sweep signal at zero rotation as shown in the above <Procedure 2>, and the sensitivity function is measured.

[0155] The dashed line RS in FIG. 12 L Then, vibration excitation is performed by superimposing a sine sweep signal in a low-speed rotation state as shown in the above <Procedure 5>, and the sensitivity function is measured.

[0156] The dashed line RS in FIG. 12 H It represents the frequency response of the plant including the influence of the gyro at the maximum rotational speed.

[0157] The present invention uses the parameters of the gyro matrix identified by vibration excitation at a low rotational speed of the dashed line RS L to estimate the frequency response of the plant including the influence of the gyro at the maximum rotational speed of the dashed line RS H Therefore, even if the rotational speed is not increased to the maximum rotational speed, the frequency response of the high-rotational-speed plant can be estimated from the information of the gyro matrix identified at a low rotational speed.

[0158] <Procedure 8> From the mode synthesis method model of the plant rotor at zero rotation estimated in the above <Procedure 3>, a state space model of the control output end (3) is constructed from the evaluation output end (2) after the disturbance input in FIG. 3, which is an input / output other than the PID controller, and the mode shape is estimated. The mode separation coefficient and the mode synthesis coefficient are obtained from the mode shape at the position of the bearing of each unique vibration mode.

[0159] Since there are two bearings, two eigenmodes are selected from the eigenmodes of the plant rotor. An example of the unique vibration mode is shown in FIG. 13. FIG. 13 shows the result of analyzing the unique vibration mode when the support of the bearing is a free end by the finite element method, which is a conventional method.

[0160] Generally, two bending modes with low natural frequencies are often selected. Here, for the unique vibration modes 3 and 4, which are bending modes, mode separation processing is performed on the state space model from the evaluation output end (2) to the control output end (3) in FIG. 3 by the block of the mode control unit in FIG. 14.

[0161] The mode control unit in FIG. 14 estimates the mode shape at the positions of the magnetic bearings (radial magnetic bearings 1 and 2), and from the estimated mode shape, obtains the mode separation coefficients (matrix C described later) on the input side of controllers 1 and 2 that perform mode control, and the mode synthesis coefficients (matrix D described later) on the output side of controllers 1 and 2 that perform mode control. Using these mode separation coefficients, controllers, and mode synthesis coefficients, a mode separation process for separating the inherent vibration modes is performed on the state space model, and mode control in the mode separation system is carried out.

[0162] In FIG. 14, the mode separation unit 61 on the input side of controllers 1 and 2 inputs the measurement signals of the displacement sensors from the radial magnetic bearings 1 and 2 and performs mode separation using the mode separation coefficients. The mode synthesis unit 62 on the output side of controllers 1 and 2 performs mode synthesis using the mode synthesis coefficients and outputs drive command signals (current, voltage) to the electromagnets of the radial magnetic bearings 1 and 2.

[0163] The Bode diagrams of the transfer functions of the plant from the input of the mode synthesis unit (62) to the output of the mode separation unit (61) of the blocks shown in FIG. 14 are shown in FIGS. 15 and 16.

[0164] FIG. 15 is the Bode diagram before mode separation, and FIG. 16 is the Bode diagram after mode separation. Here, the matrix C of the mode separation unit 61 is, for example, Equation (50) in this embodiment, and the matrix B of the mode synthesis unit 62 is, for example, Equation (51) in this embodiment.

[0165]

Equation

[0166]

Equation

[0167] As shown in Fig. 3, considering the influence of the current control block 36 acting as a low-pass filter, the negative spring effect of the electromagnet, and the cancellation gain of the negative spring, it can be seen that the results are different from the equations (55) and (56) obtained by analyzing the bearing support at the free end using the conventional finite element method described later.

[0168] The board diagram before mode separation shown in Fig. 15 represents the plant transfer function that outputs the displacement of the radial magnetic bearing 1 (or 2) with respect to the command input to the electromagnet of the radial magnetic bearing 1 (or 2).

[0169] In Fig. 15, the point where the amplitude becomes maximum corresponds to the resonance frequency of the natural vibration mode. In the board diagram after mode separation in Fig. 16, it can be seen that the response of the natural frequency corresponding to the natural vibration mode 3 is separated in the separation system 1 shown by the broken line, and the response of the natural frequency corresponding to the natural vibration mode 4 is separated in the separation system 2 shown by the solid line.

[0170] Next, regarding the analysis results of the natural vibration mode in Fig. 13, the derivation of the matrices C and B of the analysis results when the bearing support is at the free end using the conventional finite element method instead of the method of the present invention will be described together with the following equations (52) to (56).

[0171] The displacement (z 21 , z 22 ) of the left and right magnetic bearings is converted into the displacement (w 1 , w 2 ) of the separated system by the matrix C of the mode separation section as follows (conversion matrix of equation (52)).

[0172]

Equation

[0173] When using the values of the sensor and magnetic bearing parts of the natural vibration modes 3 and 4 in Fig. 13 to determine the conversion matrix C, the relationships of equations (53) (for vibration mode 3) and (54) (for vibration mode 4) hold. The black parts in Fig. 13 are the positions of the bearings.

[0174]

Mathematics

[0175]

Mathematics

[0176] Therefore, matrix C is determined as shown in the following equation (55).

[0177]

Mathematics

[0178] It is possible to perform control in the mode separation system using matrix B, which is the inverse matrix of this C, of the mode synthesis unit. B is given by the following equation (56).

[0179]

Mathematics

[0180] <Procedure 9> For the two separated systems shown in Fig. 16, prepare separate controllers (1, 2) as shown in Fig. 14 for each. Considering the change in the natural frequency due to rotation by the gyroscopic effect, design a controller for each separated system. Here, the case where the controller is designed using a PID controller (70) as shown in Fig. 17 and three secondary filters (81, 82, 83) is considered, and the board diagrams of the controllers for mode separation system 1 and mode separation system 2 are shown in Figs. 18 and 19, respectively. Also, the plant dynamic stiffness in the separated systems is shown.

[0181] The intersections of the plant dynamic stiffness characteristic lines (solid lines) and the controller characteristic lines (dashed lines) in the upper parts of Figs. 18 and 19 are the resonance points of the system, and at these points, the phase (dashed line) of the controller in each lower part is advanced.

[0182] In this way, by separating specific unique vibration modes through mode separation, the order of the controller is reduced, and stable control can be performed to advance the phase of the frequency response at the resonance frequency corresponding to the unique vibration mode as shown in the board diagrams of FIGS. 18 and 19.

[0183] According to the first embodiment as described above, the following effects can be obtained. In the method of obtaining unique vibration modes using the finite element method, there are errors during design, the influence of current control in the control system due to controlling the electromagnet acting as a low-pass filter, the negative spring effect of the electromagnet, and the influence of delay elements such as sensors. However, by performing a vibration test and estimating the mode shape from the model obtained through system identification, a matrix for mode separation can be determined with high accuracy.

[0184] Also, by estimating the mode shape at the bearing position from the model obtained through system identification using the mode synthesis method model of the rotating body, a system with separated specific unique vibration modes is obtained. Compared with the case of performing control to advance the phase with respect to the unique vibration mode in a system where the modes are not separated, since the modes are separated, magnetic levitation control can be performed to robustly stabilize the higher-order vibration modes while keeping the order of the controller small.

Embodiment

[0185] In a system levitated by a magnetic bearing, in addition to the delay element of the controller, a delay element of the sensor is included. Since the phase delay caused by the delay element affects stability, it is also necessary to identify the system for the delay element.

[0186] Therefore, in the second embodiment, the delay element is considered as follows. That is, from the result of the excitation test of the plant's sine sweep in the above <Step 2>, only from the input of the command of the electromagnet of the radial magnetic bearing 1 or the radial magnetic bearing 2, which is the evaluation output terminal (2) in FIG. 3, in only the x direction (or only the y direction), the transfer function of the plant at the control output terminal (3) of only the output in the x direction (or only the y direction) of the displacement sensor is measured, a Bode diagram is drawn, the phase frequency response is plotted, and the delay element is linearly approximated (Pade approximation (Padé approximation) first order) by the transfer function of a continuous system in the following form for evaluation, thereby considering the delay element. In the case of single input single output (SISO), it is the following formula (57). τ is the dead time.

[0187]

Number

[0188] τ is estimated from the result of the excitation test of the sine sweep. A state space model of the plant of the output with the first-order delay element of the Pade approximation added is constructed from the evaluation output terminal (2) to the control output terminal (3) of the mode synthesis method model of the plant rotor at zero rotation (the state space model from the evaluation output terminal (2) to the output terminal (6) in FIG. 20), and the mode shape is estimated.

[0189] FIG. 20 is a block diagram of a rotating body controlled by a magnetic bearing for system identification including a delay element according to the second embodiment. The difference between FIG. 20 and FIG. 3 is that a delay element block 90 with the dead time estimated by the above formula (57) is added to the control output terminal (3), and its output (output terminal (6)) is fed back to the subtractor 31, and the other parts are configured the same as in FIG. 3.

[0190] The mode separation coefficient and the mode synthesis coefficient are obtained from the mode shape at the position of the bearing of each inherent vibration mode. Since the delay element is also system-identified, there is an advantage that mode separation can be performed with higher accuracy.

[0191] In the above, the delay element was approximated by single-input single-output (SISO). However, it may also be approximated by a multi-input multi-output (MIMO) state-space model with two inputs and two outputs, where the input is the input only in the x-direction (or only in the y-direction) of the commands of the electromagnets of each of the radial magnetic bearings 1 and 2, and the output is the output only in the x-direction (or only in the y-direction) of the displacement sensors of each of the radial magnetic bearings 1 and 2.

[0192] As described above, according to the second embodiment, since the delay element of the plant is evaluated by the transfer function of the first-order Pade approximation of the continuous system, it is possible to estimate the dead time corresponding to a non-integer multiple of the control sampling time by the delay element block. And since the delay element block is added to the control output side of the state-space model, it is possible to estimate the mode shape at the bearing position and perform mode separation with higher accuracy.

Example

[0193] In the third embodiment, the delay element is considered as follows. That is, from the result of the sine sweep excitation test of the plant in the above <Procedure 2>, from the input only in the x-direction (or only in the y-direction) of the command of the electromagnet of the radial magnetic bearing 1 or the radial magnetic bearing 2 which is the evaluation output end (2) in FIG. 3, the transfer function of the plant which is the control output end (3) of the output only in the x-direction (or only in the y-direction) of the displacement sensor is measured, a Bode diagram is drawn, the frequency response of the phase is plotted, and the delay element is linearly approximated (second-order Pade approximation) by the transfer function of the continuous system of the following form for evaluation, thereby considering the delay element. In the case of single-input single-output (SISO), it is the following formula (58). τ s is the dead time.

[0194]

Equation

[0195] Compared with the second embodiment, it is possible to capture higher-order effects and approximate high frequencies precisely.

[0196] From the evaluation output terminal (2) to the control output terminal (3) of the mode synthesis method model of the plant rotor at zero rotation, a state space model of the output plant (the state space model from the evaluation output terminal (2) to the output terminal (6) in Fig. 20) with the Pade approximation second-order delay element added is constructed to estimate the mode shape.

[0197] The block diagram of the rotating body controlled by the magnetic bearing for system identification including the delay element according to Example 3 is also configured in the same manner as Fig. 20. The delay element block 90 added to the control output terminal (3) uses the delay element obtained by estimating the dead time according to the above formula (58).

[0198] The mode separation coefficient and the mode synthesis coefficient are obtained from the mode shape at the position of the bearing of each natural vibration mode. Since the delay element is also system-identified, there is an advantage that the mode separation of the high-frequency natural vibration mode can be performed with higher accuracy.

[0199] In the above, the delay element was approximated by single input single output (SISO), but it may also be approximated by a multi-input multi-output (MIMO) state space model with two inputs and two outputs, where the input is only in the x direction (or only in the y direction) of the commands of the electromagnets of each of the radial magnetic bearings 1 and 2, and the output is only in the x direction (or only in the y direction) of the outputs of the displacement sensors of each of the radial magnetic bearings 1 and 2.

[0200] For comparison, the delay element was set with a dead time τ = 1×10 -4 (sec), and the sample time of the discrete system was made the same as the dead time. The comparison of the transfer function of the discrete system delay element in the following formula (59) with the first-order Pade approximation formula (57) and the second-order Pade approximation formula (58) is shown in Figs. 21 and 22.

[0201]

Equation

[0202] Fig. 21 shows the step response, and Fig. 22 shows the Bode diagram showing the frequency response showing only the phase characteristics of the transfer function.

[0203] In FIGS. 21 and 22, the solid line indicates the characteristics of the delay element of the discrete system, the dashed line indicates the characteristics of the first-order Pade approximation delay element, and the one-dot chain line indicates the characteristics of the second-order Pade approximation delay element, respectively.

[0204] Comparing the first-order and second-order Pade approximations in FIG. 21, the value tends to decrease once in the second order. Comparing the first-order and second-order Pade approximations for the phase characteristics in FIG. 22, the difference is large for the first order compared to the ideal transfer function of the discrete system at high frequencies of 2 kHz and above. When it becomes the second order, the difference at high frequencies of 2 kHz and above becomes smaller compared to the ideal transfer function of the discrete system.

[0205] Note that, as in Equation (59), it becomes an integer multiple of the control sampling time for the transfer function of the delay element of the discrete system, but by performing Pade approximation for the continuous system, it is possible to handle delay elements with non-integer multiples of the control sampling time.

[0206] As described above, according to the third embodiment, since the delay element of the plant is evaluated by the transfer function of the second-order Pade approximation of the continuous system, it is possible to estimate the dead time corresponding to non-integer multiples of the control sampling time with the delay element block. And since the delay element block is added to the control output side of the state space model, it is possible to estimate the mode shape at the bearing position and perform mode separation with higher accuracy.

[0207] In addition, the present invention is not limited to separating two specific vibration modes as in the above embodiment, and depending on the number of magnetic bearings, for example, when the number of magnetic bearings is 3, mode separation is performed for three specific vibration modes.

[0208] Further, the present invention is not limited to being applied to a rotationally asymmetric body, and there is no problem even if it is applied to a rotationally symmetric body.

Explanation of Signs

[0209] 11... Impeller 12... Rotating shaft 13... Thrust disk 14, 15... Electromagnets 16, 20… Protection bearing 17… Permanent magnet rotor 18… Stator core 19a, 19b… Stator winding 31, 34, 51… Subtractor 32, 39… Adder 33… Block for canceling gain of negative spring 35… Current command conversion block 36… Current control block 37… Electromagnetic attraction linearization block 38… Negative spring effect block 40… Plant 41… Plant rotor 61… Mode separation unit 62… Mode synthesis unit 70… PID controller 81~83… Second-order filter 90… Delay element block

Claims

1. In a magnetic bearing device that supports a rotating body by a magnetic bearing, a plant including a rotating body and electromagnets respectively arranged on the left and right sides in the axial direction of the rotating body, a controller that controls the plant, a current control block, a cancellation gain block for negative spring, a control input, a disturbance input, an evaluation output, and a control output, and constructs a model of a rotating body controlled by a magnetic bearing, with feedback from the control output to the control input, a sensitivity function acquisition unit that performs a vibration test to measure the evaluation output when a vibration signal is superimposed on the disturbance input of the model with the rotating body levitated in a zero-rotation state to obtain the sensitivity function at zero rotation of the frequency response, levitates the rotating body, and in a low-speed rotation state where the unbalanced vibration force can be ignored, superimposes a forward vibration signal (considering a right-handed coordinate system with the axial direction of the rotating body as z, when the rotation direction is counterclockwise, a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction) on the disturbance input of the model and measures the evaluation output to obtain the sensitivity function at low-speed rotation of the frequency response, substitute the known parameters of the controller, current control block, and cancellation gain block for negative spring in the model of the rotating body controlled by the magnetic bearing into the disturbance input of the state-space model, and identify and adjust the parameters of the mass matrix, stiffness matrix, and damping matrix of the mode synthesis method model so that the evaluation output becomes a set signal when a vibration signal is superimposed, substitute the known parameters of the controller, current control block, and cancellation gain block for negative spring in the model of the rotating body controlled by the magnetic bearing into the disturbance input of the state-space model, and identify and adjust the parameters of the gyro matrix of the mode synthesis method model so that the evaluation output becomes a set signal when the vibration signal is superimposed, based on the obtained sensitivity function at low-speed rotation, From the mode synthesis method model in which the parameters of the mass matrix, stiffness matrix, and damping matrix are identified and adjusted by the parameter estimation unit, a state space model is constructed by excluding the controller that controls the plant. Using this state space model, the mode shape at the position of the magnetic bearing is estimated. From the estimated mode shape, the mode separation coefficient on the input side of the controller that performs mode control and the mode synthesis coefficient on the output side of the controller that performs mode control are obtained. Using these mode separation coefficients, the controller, and the mode synthesis coefficients, a mode separation process for separating the natural vibration modes is performed on the state space model, and a mode control unit that performs mode control in the mode separation system. A control device for a magnetic bearing, characterized by comprising:

2. Based on the results of the excitation test in the sensitivity function acquisition unit, the transfer function of the plant from the evaluation output of the model of the rotating body to the control output is measured. The transfer function is expanded into a Bode diagram and the phase frequency response is plotted. The delay element of the plant is evaluated by at least one of the first-order Padé approximation or the second-order Padé approximation of the continuous system, and a delay element block for estimating the dead time is obtained. The delay element block is added to the control output side of the state space model constructed by the mode control unit. The control device for a magnetic bearing according to claim 1, characterized in that:

3. The first-order Padé approximation transfer function of the delay element block is the following equation (57) 【Number 57】 and The second-order Padé approximation transfer function of the delay element block is the following equation (58) 【Number 58】 (where Gφ is the transfer function of the delay element, τ and τs are the dead times), The control device for a magnetic bearing according to claim 2, characterized in that:

4. In a control method for a magnetic bearing that supports a rotating body by a magnetic bearing, A plant including a rotating body and electromagnets arranged on the left and right sides in the axial direction of the rotating body, a controller that controls the plant, a current control block, a cancellation gain block for the negative spring component, a control input, a disturbance input, an evaluation output, and a control output. A model of a rotating body controlled by a magnetic bearing is constructed, with feedback from the control output to the control input. The sensitivity function acquisition unit performs a vibration test to measure the evaluation output when a vibration signal is superimposed on the disturbance input of the model with the rotating body levitated and in a zero-rotation state, and obtains the sensitivity function at zero rotation of the frequency response. Then, with the rotating body levitated and in a low-speed rotation state where the unbalanced vibration force can be ignored, a forward vibration signal (in a right-handed coordinate system with the axial direction of the rotating body taken as z, when the rotation direction is counterclockwise, a vibration signal with an amplitude of A cos(ωt) in the x direction and A sin(ωt) in the y direction) is superimposed on the disturbance input of the model, and the evaluation output is measured to obtain the sensitivity function at low-speed rotation of the frequency response. The parameter estimation unit substitutes the known parameters of the controller, current control block, and cancellation gain block for the negative spring in the model of the rotating body controlled by the magnetic bearing into the disturbance input of the state-space model, and identifies and adjusts the parameters of the mass matrix, stiffness matrix, and damping matrix of the mode synthesis method model so that the evaluation output becomes the set signal when a vibration signal is superimposed. The parameter estimation unit substitutes the known parameters of the controller, current control block, and cancellation gain block for the negative spring in the model of the rotating body controlled by the magnetic bearing into the disturbance input of the state-space model, and identifies and adjusts the parameters of the gyro matrix of the mode synthesis method model so that the evaluation output becomes the set signal when the vibration signal is superimposed. The mode control unit constructs a state-space model by excluding the controller for controlling the plant from the mode synthesis method model in which the parameters of the mass matrix, stiffness matrix, and damping matrix have been identified and adjusted by the parameter estimation unit, estimates the mode shape at the position of the magnetic bearing using the state-space model, obtains the mode separation coefficient on the input side of the controller for performing mode control and the mode synthesis coefficient on the output side of the controller for performing mode control from the estimated mode shape, and performs a mode separation process for separating the natural vibration modes on the state-space model using these mode separation coefficients, controller, and mode synthesis coefficients, and a mode control step for performing mode control in the mode separation system. A control method for a magnetic bearing, characterized by comprising the above steps.

Images