Control device and control method for magnetic bearing

Abstract

To highly adjust a controller for a magnetic bearing even with respect to an asymmetric rotor.SOLUTION: A control device comprising a plant 40 including a rotor and an electric magnet, a controller 30 for controlling it, a block 33 of offset gain for a negative spring portion, an outer disturbance input terminal (1), and an evaluation output terminal (2), constructs a model for the rotor controlled by a magnetic bearing, that gives feedback to a command displacement side from an output displacement (3), measures signals of the evaluation output terminal (2) when an excitation signal is superimposed on the outer disturbance input terminal (1) in the state of zero rotation and low speed rotation of the rotor to acquire each sensitivity function, identifies and adjusts a parameter of a gyro matrix of a mode synthesis method model such that the signal of the evaluation output terminal (2) becomes a setting signal when the excitation signal is superimposed on an outer disturbance input of a state space model in which a known parameter of the model is substituted from the sensitivity function during the low speed rotation, and estimates a frequency response of the plant with the maximum rotation speed from the mode synthesis method model to adjust the parameter of the controller 30.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a magnetic bearing control technique, and more particularly to a technique for controlling and levitating an asymmetric rotating body using electromagnets in a magnetic bearing. [Background technology]

[0002] In a magnetic bearing device that supports a rotor by means of a magnetic bearing, when the rotor's position is controlled and levitated by controlling the current in an electromagnet, the frequency response of the rotor's shaft is measured and the frequency response of the controller is adjusted.

[0003] Conventionally, magnetic bearing control technologies have been disclosed, for example, in Patent Document 1, Non-Patent Document 1, and Non-Patent Document 2. Patent Document 1 describes designing a controller using a degenerated model obtained by superposing low-frequency eigenmodes based on the results of analysis using the finite element method.

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

[0005] Non-Patent Document 2 describes a mode separation control method for a magnetic bearing flexible rotor that makes use of the symmetry of the magnetic bearing flexible rotor.

[0006] An example of a conventional magnetic bearing device is shown in Fig. 1. Fig. 1 shows the configuration of a rotating electric machine equipped with a radial magnetic bearing device having an impeller used in an aeration blower.

[0007] In FIG. 1, reference numeral 11 denotes an impeller (such as an impeller wheel) provided at the tip of a rotating shaft 12.

[0008] A circular thrust disk 13 is fixed to the outer periphery of the rotating shaft 12 at a predetermined axial distance from the impeller 11. An electromagnet 14 is disposed on the impeller side of the thrust disk 13, and an electromagnet 15 is disposed on the opposite side of the thrust disk 13 to face the electromagnet 14 with the thrust disk 13 in between.

[0009] A radial magnetic bearing 1 is provided on the outer periphery of a rotating shaft 12 located between an impeller 11 and a thrust disk 13, for supporting the rotating shaft 12 in a radial direction in a non-contact manner.

[0010] The electromagnet of this radial magnetic bearing 1 is connected to a power converter (not shown) capable of controlling the current flowing through the electromagnet.

[0011] Reference numeral 16 denotes 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 configured as a touchdown bearing using, for example, a ball bearing.

[0012] A permanent magnet rotor 17 is fixed to the outer periphery of the rotating shaft 12 a predetermined distance away from the thrust disk 13 on the axially opposite side to the impeller, and a stator core 18 is disposed on the radial outer periphery of the rotating shaft 12 from the permanent magnet rotor 17 with a gap therebetween.

[0013] Reference numeral 19a denotes a stator winding provided at the impeller side end of the stator core 18, and reference numeral 19b denotes a stator winding provided at the opposite side end of the stator core 18 to the impeller side.

[0014] 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 at a predetermined distance from the stator winding 19b on the opposite axial side to the impeller.

[0015] The electromagnet of this radial magnetic bearing 2 is connected to a power converter (not shown) capable of controlling the current flowing through the electromagnet.

[0016] Reference numeral 20 denotes a protective bearing disposed on the outer periphery of the rotating shaft 12 on the side opposite the impeller of the radial magnetic bearing 2 (having the same configuration as the protective bearing 16). [Prior art documents] [Patent documents]

[0017] [Patent Document 1] JP 2008-45687 A [Non-patent literature]

[0018] [Non-Patent Document 1] Hirotoshi Ueyama, "Recent Development Trends of Magnetic Bearings for Turbomolecular Pumps", Turbo Machinery, Vol. 32, No. 7, pp. 48-53, July 2004 [Non-Patent Document 2] Hiroyuki Fujiwara et al., "Mode Separation Control Method for Flexible Rotors with Magnetic Bearings," Transactions of the Japan Society of Mechanical Engineers, Series C, Vol. 70, No. 698, pp. 2797-2804 (2004-10) Summary of the Invention [Problem to be solved by the invention]

[0019] In the technology of Patent Document 1, if the rotor is not a simple structure such as being asymmetric, there may be a discrepancy with the result of excitation on the actual machine, which reduces the accuracy of position control of the rotor.

[0020] In addition, the mode superposition model has problems in applying it to objects in which the natural modes of the object may change due to state feedback control, such as a rotating body levitated by a radial magnetic bearing, in which an electromagnet controls force in response to measured displacement.

[0021] In addition, in the technology of Non-Patent Document 1, a frequency stiffness characteristic called plant dynamic stiffness is obtained by measuring a displacement signal against an excitation force applied to a rotor by a radial magnetic bearing. In parameter adjustment of the controller, adjustment is performed manually while measuring the frequency characteristic of this plant dynamic stiffness. Therefore, adjustment is time-consuming. There is also a concern that the parameters may deviate from the appropriate ones due to the skill of the adjuster.

[0022] Furthermore, as in the technology of Non-Patent Document 2, when a rotating body is symmetrical, the motion of the rotating body is separated into translational motion and tilt motion, so that in a mode-separated coordinate system, it is possible to control the eigenmode for each motion independently.

[0023] However, in a rotor equipped with a radial magnetic bearing device having an impeller used in an aeration blower as shown in FIG. 1, since the rotor is an asymmetric overhang rotor, the characteristics of the controller for radial magnetic bearing 1 affect the control characteristics of radial magnetic bearing 2, making it difficult to adjust the controller parameters.

[0024] The present invention is intended to solve the above-mentioned problems, and an object of the present invention is to provide a magnetic bearing control device that can highly adjust the magnetic bearing controller even for a rotating body that is asymmetrical from left to right.

[0025] Specifically, we propose a radial magnetic bearing control device that measures the sensitivity function by vibration testing, compares it with a model using the mode synthesis method, adjusts the parameters to match the vibration results, and determines the parameters of the controller for that model after taking into consideration the sensitivity function, stability margin, disturbance response, and frequency response of current, etc. The sensitivity function is measured because a model that uses the plant dynamic stiffness as input and output is an unstable system as a model and cannot be identified. [Means for solving the problem]

[0026] The magnetic bearing control device according to claim 1 for solving the above problem comprises: In a magnetic bearing device that supports a rotating body by a magnetic bearing, a model of a rotor controlled by a magnetic bearing is constructed, the model comprising a plant including a rotor and electromagnets arranged on the left and right sides of the rotor in the axial direction, a controller for controlling the plant, a current control block, a negative spring compensation gain block, a control input, a disturbance input, an evaluation output, and a control output, and feedback is provided from the control output to the control input; a sensitivity function acquisition unit that measures the evaluation output when a vibration signal is superimposed on a disturbance input of the model while the rotor is levitated and in a state of zero rotation, thereby acquiring a sensitivity function of the frequency response at zero rotation, and that measures the evaluation output when a forward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, and a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the model while the rotor is levitated and in a state of low rotation speed in which unbalanced excitation force can be ignored) thereby acquiring a sensitivity function of the frequency response at low rotation speed; Identifying and adjusting parameters of the mass matrix, stiffness matrix, and damping matrix of the mode synthesis model so that an evaluation output becomes a set signal when an excitation signal is superimposed on a disturbance input of a state space model in which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted from the acquired sensitivity function at zero rotation; a parameter estimation unit that identifies and adjusts parameters of a gyro matrix of a mode synthesis model so that an evaluation output becomes a set signal when the excitation signal is superimposed on a disturbance input of a state space model in which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted based on the acquired sensitivity function during low speed rotation; and a controller parameter adjustment unit that estimates a frequency response of the plant at the maximum rotation speed from the mode synthesis model whose parameters have been identified and adjusted by the parameter estimation unit, and adjusts the parameters of the controller by loop shaping the parameters of the controller using an H∞ norm.

[0027] The magnetic bearing control device according to claim 2 includes the steps of: a tracking filter that extracts and removes a synchronous component of a rotation speed due to a forward vibration signal that is superimposed when the sensitivity function acquisition unit acquires the sensitivity function during the low-speed rotation, The parameter estimation unit is characterized in that, during low-speed rotation, when a backward vibration signal (considering a right-handed system in which the axial direction of the rotating body is z, a vibration signal with a magnitude of Asin(ωt) in the x direction and Acos(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the state space model in place of the vibration signal, the evaluation output becomes a set signal by identifying and adjusting parameters of a gyro matrix of a mode synthesis model.

[0028] The magnetic bearing control device according to claim 3 includes the steps of: a tracking filter that extracts and removes a synchronous component of a rotation speed due to a forward vibration signal and a synchronous component of a rotation speed due to a backward vibration signal, which are superimposed when the sensitivity function acquisition unit acquires the sensitivity function during low-speed rotation; The sensitivity function acquisition unit is characterized in that it measures the evaluation output when the forward vibration signal or the backward vibration signal is superimposed on the disturbance input of the model during the low-speed rotation, and acquires a sensitivity function of the frequency response during the low-speed rotation.

[0029] The magnetic bearing control device according to claim 4 includes the steps of: The tracking filter includes: a signal generating unit that generates a cos(Ωt) signal and a sin(Ωt) signal synchronized with the rotational angular velocity of the rotor; a first calculation unit that performs a product-sum operation on two-axis displacement signals in the x and y directions of the evaluation output measured by the sensitivity function acquisition unit during low-speed rotation and the cos(Ωt) signal and sin(Ωt) signal generated by the signal generation unit; a low-pass filter which receives the output of the first calculation unit and outputs the amplitude of a rotation speed synchronous component; and a second calculation unit that performs a product-and-sum operation on the amplitude of the rotation speed synchronous component output from the low-pass filter and a cos(Ωt) signal and a sin(Ωt) signal synchronized with the rotation angular velocity of the rotor to extract the synchronous components of the rotation speeds in the two axial directions.

[0030] The magnetic bearing control device according to claim 5 includes the steps of: The tracking filter includes: a signal generating unit that generates a cos(Ωt) signal and a sin(Ωt) signal synchronized with the rotational angular velocity of the rotor; a first calculation unit that integrates a uniaxial displacement signal of the evaluation output measured by the sensitivity function acquisition unit during low-speed rotation and a cos(Ωt) signal and a sin(Ωt) signal generated by the signal generation unit; a low-pass filter which receives the output of the first calculation unit and outputs the amplitude of a rotation speed synchronous component; and a second calculation unit that performs a product-and-sum operation on the amplitude of the rotation speed synchronous component output from the low-pass filter, and a cos(Ωt) signal and a sin(Ωt) signal that are synchronized with the rotation angular velocity of the rotor, to extract a synchronous component of the rotation speed in one axial direction.

[0031] The magnetic bearing control device according to claim 6 includes any one of claims 1 to 5, The sensitivity function at zero rotation acquired by the sensitivity function acquisition unit is expressed in state space by the following equations (29) and (30):

[0032]

number

[0033]

number

[0034] The sensitivity function during low-speed rotation acquired by the sensitivity function acquisition unit is expressed in state space by the following equations (32) to (44):

[0035]

number

[0036]

number

[0037]

number

[0038]

number

[0039]

number

[0040]

number

[0041]

number

[0042]

number

[0043]

number

[0044]

number

[0045]

number

[0046]

number

[0047]

number

[0048] (X 1 ,X 2 are the state vectors in the x direction of the plant rotor in the mode synthesis method, and Y 1 ,Y 2 are the state vectors in the y direction of the plant rotor in the mode synthesis method, and F il ,I nt are the state vectors of the PID controllers, and T ra is the state vector corresponding to the current control low-pass, y is the output vector, u is the input vector, E n is an n × n unit matrix, 0 n is an n × n zero matrix, 0 m,n is an m×n zero matrix, m is the number of internal system eigenmodes, M q is the mass matrix, D is the damping matrix, K n is the stiffness matrix, Ω is the rotation speed, P is the proportional term of the PID controller, k i =2K(I 1 +I 2 ) / δ 0 2 (K is the electromagnet attraction force coefficient, I 1 is the bias current of the electromagnet coil placed on either the left or right side of the rotor, I 2 is the bias current of the electromagnet coil located on either the left or right side of the rotor, δ 0 is the air gap between the electromagnet and the rotor), k s is the gain to compensate for the negative spring effect, ω c is the cutoff frequency (angular frequency) of the low-pass filter of the current control block. The mass matrix identified by the parameter estimation unit is expressed by equation (12),

[0049]

number

[0050] (T q is the transformation by mode synthesis, M,M q is the mass matrix, φ is the internal system eigenmode, and δ is the deformation mode. The stiffness matrix identified by the parameter estimation unit is expressed by equation (14),

[0051]

number

[0052] (K,K q is the stiffness matrix, K eq is the force required to lift the bearing point by 1 The damping matrix identified by the parameter estimation unit is expressed by equation (26),

[0053]

number

[0054] (diagonal is a diagonal matrix) The gyro matrix identified by the parameter estimation unit is expressed by equation (13).

[0055]

number

[0056] (G,G q is the gyro matrix, T q is a mode synthesis transformation) It is characterized by:

[0057] The magnetic bearing control device according to claim 7 includes any one of claims 1 to 5, The rotating body is characterized in that it is asymmetrical.

[0058] The magnetic bearing control device according to claim 8 further comprises the steps of: The rotating body is characterized in that it is asymmetrical.

[0059] A method for controlling a magnetic bearing according to claim 9, A method for controlling a magnetic bearing that supports a rotating body by the magnetic bearing, comprising: a model of a rotor controlled by a magnetic bearing is constructed, the model comprising a plant including a rotor and electromagnets arranged on the left and right sides of the rotor in the axial direction, a controller for controlling the plant, a current control block, a negative spring compensation gain block, a control input, a disturbance input, an evaluation output, and a control output, and feedback is provided from the control output to the control input; a sensitivity function acquisition unit measuring the evaluation output when a vibration signal is superimposed on a disturbance input of the model while the rotor is levitated and in a state of zero rotation, thereby acquiring a sensitivity function of the frequency response at zero rotation; and measuring the evaluation output when a forward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the model while the rotor is levitated and in a state of low rotation speed in which unbalanced excitation force can be ignored) thereby acquiring a sensitivity function of the frequency response at low rotation speed; a parameter estimation unit performing identification and adjustment of parameters of a mass matrix, a stiffness matrix, and a damping matrix of a mode synthesis model so that an evaluation output becomes a set signal when an excitation signal is superimposed on a disturbance input of a state space model into which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted from the acquired sensitivity function at zero rotation; a parameter estimation unit, based on the acquired sensitivity function during low-speed rotation, identifying and adjusting parameters of a gyro matrix of a mode synthesis model so that an evaluation output becomes a set signal when the excitation signal is superimposed on a disturbance input of a state space model into which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted, so that an evaluation output becomes a set signal; The method is characterized in that it comprises a step in which a controller parameter adjustment unit estimates a frequency response of the plant at the maximum rotation speed from the mode synthesis model whose parameters have been identified and adjusted by the parameter estimation unit, and adjusts the parameters of the controller by loop shaping the parameters of the controller with an H∞ norm.

[0060] The method for controlling a magnetic bearing according to claim 10 is the same as claim 9, further comprising the steps of: a tracking filter is provided to extract and remove a synchronous component of the rotation speed due to a forward vibration signal that is superimposed when the sensitivity function acquisition unit acquires the sensitivity function during the low rotation speed; The method is characterized in that the parameter estimation unit comprises a step of identifying and adjusting parameters of a gyro matrix of a mode synthesis model so that the evaluation output becomes a set signal when, during low-speed rotation, a backward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, a vibration signal with a magnitude of Asin(ωt) in the x direction and Acos(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the state space model instead of the vibration signal.

[0061] The method for controlling a magnetic bearing according to claim 11 further comprises the steps of: a tracking filter is provided to extract and remove a synchronous component of the rotation speed due to a forward vibration signal and a synchronous component of the rotation speed due to a backward vibration signal, which are superimposed when the sensitivity function acquisition unit acquires the sensitivity function during low-speed rotation; The sensitivity function acquisition unit is characterized by comprising a step of measuring the evaluation output when the forward vibration signal or the backward vibration signal is superimposed on a disturbance input of the model during the low-speed rotation, and acquiring a sensitivity function of the frequency response during the low-speed rotation. Effect of the Invention

[0062] (1) According to the inventions described in claims 1 to 11, it is possible to use a model to perform advanced adjustments even for asymmetric rotors, for which adjustment of the magnetic bearing controllers is difficult due to the mutual influence of the controllers of two radial magnetic bearings in the axial direction. This improves the accuracy of position control of the rotor.

[0063] In addition, because a model is used, the influence of the gyro effect, which changes the natural frequency of the rotor depending on the rotation speed, can be identified from the results of vibration tests at low rotation speeds without rotating at the rated rotation speed, and there is an advantage in that the frequency response at the rated rotation speed can be estimated. It is also possible to adjust the parameters of the controller to a high degree by taking into account the change in frequency response due to the change in natural frequency caused by the gyro effect.

[0064] In addition, there is no need to conduct high-speed vibration tests, which require more advanced safety measures, so the time and effort required for testing can be reduced. (2) According to the inventions described in claims 2, 4, and 10, it is possible to remove the influence of the forward rotation-synchronous component due to imbalance in the sensitivity function acquired during low-speed rotation. In addition, by removing the influence of the forward rotation-synchronous component when identifying the gyro matrix, it is possible to ignore the change in the response of the evaluation output, thereby increasing the estimation accuracy of the gyro matrix. (3) According to the inventions recited in claims 3, 5 and 11, it is possible to remove the influence of the forward rotation-synchronous component due to imbalance and the backward rotation-synchronous component due to anisotropy of the bearing support stiffness, etc., in the sensitivity function acquired during low-speed rotation. In addition, by removing the influence of the forward rotation-synchronous component and the backward rotation-synchronous component due to anisotropy of the bearing support stiffness, etc., when identifying the gyro matrix, it is possible to ignore changes in the response of the evaluation output, thereby increasing the estimation accuracy of the gyro matrix. [Brief description of the drawings]

[0065] [Figure 1] 1 is a configuration diagram showing an example of a magnetic bearing control device to which the present invention is applied; [Diagram 2]FIG. 2 is a block diagram showing a control configuration and an excitation signal for system identification in this embodiment. [Diagram 3] FIG. 4 is a block diagram of a model of a rotor controlled by a magnetic bearing for system identification in this embodiment. [Figure 4] FIG. 1 is an explanatory diagram of internal system eigenmodes and deformation modes in a model using the mode synthesis method. [Diagram 5] Block diagram of the current control transfer function. [Figure 6] An explanatory diagram of the magnetic force generated by the electromagnets of a magnetic bearing. [Figure 7] FIG. 4 is a signal waveform diagram of a sine sweep used in the embodiment. [Figure 8] FIG. 4 is a waveform diagram of a response when a sine sweep used in this embodiment is subjected to disturbance excitation. [Figure 9] FIG. 4 is a waveform diagram of a sine sweep signal of forward vibration used in this embodiment. [Figure 10] FIG. 4 is a waveform diagram of a response when a sine sweep used in this embodiment is subjected to disturbance excitation. [Figure 11] FIG. 4 is an explanatory diagram of forward vibration used in this embodiment. [Figure 12] 4 is a diagram showing natural frequencies of a rotor according to the embodiment of the present invention; [Figure 13] 5 is an explanatory diagram showing the adjustment of a sensitivity function in the embodiment; FIG. [Figure 14] 5 is an explanatory diagram showing adjustment of a stability margin in the embodiment; FIG. [Figure 15] 5 is an explanatory diagram showing how a disturbance response is adjusted in the embodiment; FIG. [Figure 16] 5 is an explanatory diagram showing the state of adjustment of the response from a displacement command to a current command in the embodiment; FIG. [Figure 17] FIG. 2 is a block diagram showing a control configuration and an excitation signal for system identification in this embodiment. [Figure 18] FIG. 6 is a block diagram of a tracking filter according to a second embodiment of the present invention. [Figure 19] FIG. 11 is a block diagram of a tracking filter according to a third embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0066] Hereinafter, an embodiment of the present invention will be described with reference to the drawings, but the present invention is not limited to the following embodiment. Below, an embodiment in which the present invention is applied to the magnetic bearing device shown in Fig. 1 will be described, but the present invention is not limited to this and may be applied to magnetic bearing devices of other configurations.

[0067] Fig. 2 shows the overall configuration of the control for levitating a rotor with a magnetic bearing and the excitation signal for system identification. In Fig. 2, 30 is a controller consisting of PID and the like, which controls a plant 40. The plant 40 is composed of a rotor (rotating shaft 12 in Fig. 1) and electromagnets of radial magnetic bearings 1 and 2.

[0068] A subtractor 31 subtracts the deviation of a command displacement input as a control input to the controller 30 from a feedback component from the control output of the plant 40. An adder 32 adds (superimposes) an excitation signal for system identification input from a disturbance input terminal (1) to the output of the controller 30.

[0069] Reference numeral 33 denotes a block of a gain (Ks, described later) that offsets the negative spring effect of the electromagnet of the magnetic bearing. A subtractor 34 subtracts the gain 33 from the output of the adder 32 .

[0070] (2) in the figure is an evaluation output terminal for measuring the result of vibration applied to the disturbance input terminal (1), and (3) in the figure is a control output terminal from which an output displacement is output.

[0071] In FIG. 2, the PID of the controller 30 measures the displacement in one direction of one of the radial magnetic bearings (either 1 or 2) and controls the electromagnet in response to the measured displacement to control the electromagnetic force.

[0072] When controlling the levitation of a rotating body with magnetic bearings, it is necessary to control the two orthogonal axial directions of x and y with radial magnetic bearing 1 and radial magnetic bearing 2 in Fig. 1, but here we will use side-by-side control with the same controller parameters for all four axes. As an example here, we will target the simplest controller, PID, as shown in Fig. 2, but other higher-order controllers can also be used. It is sufficient that the controller parameters are known when identifying the system.

[0073] FIG. 3 shows a block diagram of a model for estimating parameters of the plant 40 from measurement data of the vibration results for system identification.

[0074] In Fig. 3, the same parts as 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 a current command conversion block 35 that converts a control command into a current command, a current control block 36 (a block consisting of a low-pass filter constituting a transfer function block of current control in Fig. 5 described later) to which the current command of the current command conversion block 35 is input, an electromagnet attractive force linearization block 37 (related to the third term of equation (21) described later) that linearizes the attractive force of the electromagnet, a negative spring effect block 38 (related to the second term of equation (21) described later), and an adder 39 (related to equation (21) described later) that adds the output of the electromagnet attractive force linearization block 37 and the output of the negative spring effect block 38 are provided between the subtractor 34 and the plant rotor 41, and the other parts are configured in the same manner as in Fig. 2.

[0075] In FIG. 3, (4) is a control input terminal to which a command displacement is input, and (5) is a current command output terminal.

[0076] A mode synthesis model is used for the model of the plant rotor 41 in Fig. 3. The mode synthesis model will be described below.

[0077] The equations of motion for the rotor-bearing system in the finite element method are expressed as the following equations (1) and (2).

[0078]

number

[0079]

number

[0080] M: mass matrix, G: gyro matrix, K: stiffness matrix, Q: bearing reaction force, U: unbalance vector, Ω: rotation speed.

[0081] Converting to Z=X+jY, we get the following equation (3).

[0082]

number

[0083] The bearing point is the master node and the boundary point is the Z 2 , and other internal points are slave nodes, Z 1 This is expressed as equation (4).

[0084]

number

[0085] By substituting equation (4) into equation (3), the equation of motion of the rotor-bearing system is expressed as the following equation (5).

[0086]

number

[0087] The eigenmode of the internal system, ignoring the gyroscopic effect, is considered as given by equation (6).

[0088]

number

[0089] By solving equation (6) and setting the eigenmode of the internal system to φ, we obtain equations (7) and (8).

[0090]

number

[0091]

number

[0092] Here, "diagonal" means a diagonal matrix.

[0093] If the deformation mode in which the bearing is forcibly displaced by a unit amount is δ, the following equation (9) holds true.

[0094]

number

[0095] 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, it is K eq = 0. Using the internal system eigenmode φ and the deformation mode δ, the transformation T q and coordinate Z q is expressed as the following equation (10), where E is the unit matrix and η is the mode coordinate.

[0096]

number

[0097] Substituting equation (10) into equation (5), we get T t q Multiplying this gives the equation of motion for the mode synthesis method, equation (11).

[0098]

number

[0099] where

[0100]

number

[0101]

number

[0102]

number

[0103] The mode synthesis method M q :mass matrix, G q : The gyro matrix is ​​a symmetric matrix. K q : The stiffness matrix is ​​a diagonal matrix. Using the mode synthesis method, the number of degrees of freedom of the nodes in the finite element method is compressed to the number of internal system eigenmodes φ and the number of deformation modes δ, i.e., the number of bearings, as shown in Figure 4. In Figure 4, the solid dots correspond to the modes of the internal system eigenmodes φ, and the open dots correspond to the deformation modes δ.

[0104] Next, we will explain the current command conversion block 35 and the current control block 36 of the model in Figure 3. Regarding the electromagnet and its current control in the model in Figure 3, PI control is considered for the current control. Figure 5 shows a transfer function block diagram.

[0105] i ref is the current command output from the current command conversion block 35 in FIG. ref and the control output current i out The deviation (of the feedback portion) is taken by a subtractor 51, and the output of the subtractor 51 is input to the current controller.

[0106] v cmdis a voltage command for a power converter (not shown), and in Fig. 5, the PWM process in the power converter is omitted and the transfer function is expressed in a continuous system. Here, the control transfer function Gc(s) is PI control and is expressed by equation (15). The electromagnet transfer function Gem(s) is expressed by equation (16) by regarding the electromagnet as a series connection of winding resistance Rem and winding inductance Lem. Therefore, the feedback transfer function G FB (s) is expressed by equation (17). This form corresponds to the angular frequency ω c It is expressed as a first-order LPF (low-pass filter) with a cutoff frequency of

[0107]

number

[0108]

number

[0109]

number

[0110] Next, the electromagnet attractive force linearization block 37 and the negative spring effect block 38 of the model in FIG. 3 will be described.

[0111] The negative spring effect of the electromagnets in the magnetic bearing model of Figure 3 is considered as follows. In the magnetic bearing, as shown in Figure 6, electromagnets 1 and 2 are arranged facing each other on either side of the rotating shaft (12) for one-way control, and they pull on each other from both sides, generating a control force from the difference. The coil of the electromagnet is supplied with a DC component bias current I 1 ,I 2 and the dynamic alternating current i required to suppress the vibration component. 1 , i 2 The sum of these flows as a current. The force F acting on the rotor is calculated from the difference in the attractive forces of the two electromagnets 1 and 2 of the magnetic bearing. b [N] is expressed as in formula (18). In the following, F1 is the attractive force of electromagnet 1 [N], F 2 is the attractive force of electromagnet 2 [N], δ 0 is the distance (gap) between the electromagnet and the rotor [m], x is the displacement of the rotor shaft 12 [m], 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 in the coil of electromagnet 1 [A], i 2 is the alternating current in the coil of electromagnet 2 [A], and the electromagnet attraction force coefficient K [Nm 2 / A 2 ].

[0112]

number

[0113] In equation (18), the displacement x of the rotor is the distance δ between the electromagnet and the rotor. 0 (void), i.e., x≪δ 0 Therefore, it can be expressed as equation (19).

[0114]

number

[0115] The current for suppressing the vibration component is sufficiently smaller than the bias current, i.e., 1 , i 2 ≪I 1 ,I 2 Therefore, i 1 , i 2 If we ignore the infinitesimal second-order terms, it can be expressed as equation (20).

[0116]

number

[0117] Where:

[0118]

number

[0119] Suppose 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, we obtain equation (21).

[0120]

number

[0121] Here, k in equation (21) i is the attraction coefficient for the current [N / A], k n is the attractive force coefficient with respect to displacement [N / m]. The first term in equation (21) is the force term with respect 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 electromagnet with respect to attractive force, and this force balances the weight of the rotating body. In the case of the radial magnetic bearing of the rotating body in Figure 3, the two radial magnetic bearings are designed to balance the total weight of the rotating body.

[0122] The PID controller (30) of the model in FIG. 3 includes a pseudo differential and is expressed as the transfer function of a continuous system in the s-domain as shown in Equation (22).

[0123]

number

[0124] where P is the proportional term, I is the integral term, D is the differential term, and N is the pseudo-differential filter coefficient. In addition, it is expressed in state space as equations (23) and (24). Here, F il ,I ntare the state variables of the PID controller, y is the output, and u is the input.

[0125]

number

[0126]

number

[0127] From equation (11), the model of the mode synthesis method without the gyro matrix at zero rotation in the x direction is expressed as equation (25).

[0128]

number

[0129] D is the damping matrix. For simplicity, consider a diagonal matrix for damping as shown in equation (26).

[0130]

number

[0131] In state space representation, it is expressed as equation (27) and equation (28). Here, X 1 ,X 2 are the state vectors in the x direction of the plant rotor in the mode synthesis method, y is the output vector, and u is the input vector.

[0132]

number

[0133]

number

[0134] E is the identity matrix.

[0135] From the above, considering the two radial magnetic bearings 1 and 2 in FIG. 1 at zero rotation, a disturbance (for example, a vibration signal described later) is input in the x direction to the disturbance input terminal (1) in FIG. 3, and the signal at the evaluation output terminal (2) is measured. The sensitivity function based on the measured signal is expressed in state space terms as shown in Equations (29) and (30).

[0136]

number

[0137]

number

[0138] Where X 1 ,X 2 are the state vectors in the x direction of the plant rotor in the mode synthesis method, and Y 1 ,Y 2 are the state vectors in the y direction of the plant rotor in the mode synthesis method, and F il ,I nt are the state vectors of the PID controller (30), and T ra is the state vector corresponding to the current control low-pass, y is the output vector, u is the input vector, E n is an n × n unit matrix, 0 n is an n × n zero matrix, 0 m,n is an m × n zero matrix, where m is the number of internal system eigenmodes.

[0139] Since two radial magnetic bearings are considered, the dimension of the input and output vectors is 2. In equation (29), the stiffness matrix due to the negative spring effect of the electromagnets of the magnetic bearings is

[0140]

number

[0141] and k n =k n E 2 Also, k sis a gain to offset the negative spring effect.

[0142] Furthermore, when rotating, due to the influence of the gyro matrix, the degrees of freedom in the x and y directions are considered as follows, and a disturbance is input to the disturbance input terminal (1) in the x direction of the two radial magnetic bearings 1 and 2 in Figure 3, and the signal at the evaluation output terminal (2) is measured. The sensitivity function based on this measured signal is expressed in state space terms as shown in Equations (32) and (33).

[0143]

number

[0144]

number

[0145] Where:

[0146]

number

[0147]

number

[0148]

number

[0149]

number

[0150]

number

[0151]

number

[0152]

number

[0153]

number

[0154]

number

[0155]

number

[0156]

number

[0157] (However, M q is the mass matrix, D is the damping matrix, K n is the stiffness matrix, Ω is the rotation speed, P is the proportional term of the PID controller (30), k i =2K(I 1 +I 2 ) / δ 0 2 (K is the electromagnet attraction force coefficient, I 1 is the bias current of the electromagnet coil placed on either the left or right side of the rotor, I 2 is the bias current of the electromagnet coil located on either the left or right side of the rotor, δ 0 is the air gap between the electromagnet and the rotor), k s is the gain to compensate for the negative spring effect, ω c is the cutoff frequency (angular frequency) of the low-pass filter of the current control block. Since we consider the degrees of freedom in both the x and y directions with two radial magnetic bearings, the dimension of the input and output vectors is four. EXAMPLES

[0158] As shown in Figs. 2 and 3, the magnetic bearing control device of the first embodiment includes a plant 40 including a rotor and electromagnets arranged on the left and right sides of the rotor in the axial direction, a controller 30 for controlling the plant 40, a current control block 36, a block 33 of a gain for canceling a 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 rotor controlled by a magnetic bearing, in which feedback is provided from the control output to the control input, a sensitivity function acquisition unit that measures an evaluation output (2) when a vibration signal is superimposed on a disturbance input (1) of the model while the rotor is levitated and in a state of zero rotation, thereby acquiring a sensitivity function (equations (29) and (30)) of a frequency response at zero rotation, and that measures an evaluation output (2) when a forward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, and a vibration signal with a magnitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input (1) while the rotor is levitated and in a state of low rotation speed in which an unbalanced excitation force can be ignored) to acquire a sensitivity function (equations (32) and (33)) of a frequency response at low rotation speed. From the sensitivity function at zero rotation obtained, known parameters of the controller, the current control block, and the block of the offset gain of the negative spring component in the model of the rotor controlled by the magnetic bearing are substituted, and the disturbance input (1) of the state space model is superimposed with an excitation signal, which will be described later, to identify and adjust the parameters of the mass matrix (Equation (12)), stiffness matrix (Equation (14)), and damping matrix (Equation (26)) of the mode synthesis model so that the evaluation output becomes a set signal. a parameter estimation unit that identifies and adjusts parameters of a gyro matrix (equation (13)) of a mode synthesis model so that an evaluation output becomes a set signal when an excitation signal, which will be described later, is superimposed on a disturbance input (1) of a state space model obtained by substituting known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing from the acquired sensitivity function during low-speed rotation; and a controller parameter adjustment unit that estimates the frequency response of the plant at the maximum rotation speed from the mode synthesis model whose parameters have been identified and adjusted by the parameter estimation unit, as will be described later, and adjusts the parameters of the controller by loop shaping the parameters of the controller using the H∞ norm.

[0159] The processing procedures performed by the sensitivity function acquisition unit, the parameter estimation unit, and the controller parameter adjustment unit will be described below.

[0160] <Step 1> The rotating body (rotating shaft 12) is levitated using a simple controller such as a PID.

[0161] <Step 2> At zero rotation, vibration is applied by superimposing a sine sweep signal only in the x (or y) direction on the disturbance input terminal (1) in Figure 2, and the frequency response sensitivity function (Equation (29) and Equation (30)) is measured by measuring the signal at the evaluation output terminal (2) in the x (or y) direction.

[0162] In this case, as shown in Figures 7(a) and (b), sine sweep signals are superimposed separately on radial magnetic bearings 1 and 2. A sine sweep is a signal that has a constant amplitude of Asin(ωt) and a frequency of ω=bt, where b is a constant, increasing at a constant rotation speed.

[0163] <Step 3> From the results of the sine sweep excitation test, the parameters of the mass matrix (Eq. (12), damping matrix (Eq. (26), and stiffness matrix (Eq. (14)) of the mode synthesis model are identified so that when the signal in Fig. 7 corresponding to the external input terminal (1) of the state space model of the sensitivity function of Eq. (29) and Eq. (30) is input, the signal at the evaluation output terminal (2) becomes the corresponding signal in Fig. 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.

[0164] <Step 4> According to the above-mentioned equation (11) of the mode synthesis method, the rotor is rotated at a low speed so that the unbalanced excitation force can be neglected.

[0165] <Step 5> While rotating, vibration is applied by superimposing a signal (forward excitation signal) that sweeps a sine wave frequency forward in the x and y directions on the disturbance input terminal (1) in Figure 2, and the frequency response sensitivity function (Equation (32) and Equation (33)) is measured by measuring the signals at the evaluation output terminal (2) in the x and y directions. The signal that sweeps a sine wave frequency forward is a signal that, considering a right-handed system in which the axial direction of the rotor is the z direction, has a constant amplitude of Acos(ωt) in the x direction and Asin(ωt) in the y direction, and increases at a constant rotation speed with ω=bt, where b is a constant, when considering a right-handed system in which the axial direction of the rotor is the z direction, and when the rotation direction is counterclockwise as shown by the arrow in the figure.

[0166] When the rotation direction is clockwise, an excitation signal of Acos(-ωt) is applied in the x direction and an excitation signal of Asin(-ωt) is applied in the y direction.

[0167] <Step 6> From the results of the sine sweep vibration test, the parameters of the gyro matrix (equation (13)) of the mode synthesis model are identified so that when forward vibration signals shown in Figures 9(a) to (d) are input to the x- and y-direction disturbance input terminals (1) of the state space model of the sensitivity functions of equations (32) and (33), the signals at the x- and y-direction evaluation output terminals (2) become the signals shown in Figures 10(a) to (d).

[0168] The parameters are adjusted for each parameter of the mode related to each peak of the measurement result of the evaluation output terminal (2) as shown in Fig. 10. Note that the gyro matrix may be estimated by repeating <Step 1> to <Step 6> at a different rotation speed.

[0169] <Step 7> The frequency response of the plant 40 at the maximum rotation speed is estimated from the mode synthesis model with the adjusted parameters, and the PID parameters of the controller 30 are loop shaped with the H∞ norm. Specifically, the sensitivity function, i.e., (2) / (1) in Fig. 3, the stability margin, the disturbance response, i.e., (3) / (1) in Fig. 3, and the response (5) / (4) of the current command (5) to the command displacement (4) in Fig. 3 are multiplied by a target frequency weighting function to adjust the parameters of the controller by minimizing the H∞ norm, which is the evaluation index of the transfer function.

[0170] The results of tuning the above four items using the control system tuner tool of Matlab (MATrix LABoratory) are shown in Figures 13, 14, 15, and 16.

[0171] Fig. 13 is a characteristic diagram of frequency vs. error in the item of sensitivity function ((2) / (1) in Fig. 3). Fig. 14 is a characteristic diagram of frequency vs. gain margin in the upper part and frequency vs. phase margin in the lower part, for the item of stability margin in Fig. 3. Fig. 15 is a characteristic diagram of time vs. amplitude in the item of disturbance response ((3) / (1) in Fig. 3). Fig. 16 is a characteristic diagram of frequency vs. singular value plot in the item of current command response to command displacement ((5) / (4) in Fig. 3).

[0172] 13 to 16, L1 indicates the characteristic before adjustment, L2 indicates the characteristic after adjustment, LH in FIG. 13 indicates the target threshold, LH in FIG. 15 indicates the target response, and LG in FIG. 16 indicates the maximum gain.

[0173] 13, 14 and 16, if the frequency response is not in the Y region but is in the H region, then the target is met, and in FIG. 15 the target response is shown by the dashed line LH.

[0174] The Matlab control system tuner tool tunes the controller parameters by minimizing the H∞ norm multiplied by a target frequency weighting function.

[0175] This system identification procedure involves identifying the change in the natural frequency due to the gyroscopic effect of the rotor, as shown by the dashed line RS in Figure 12. L As shown in Fig. 1, by identifying the parameters of the gyro matrix at low rotation speeds, it is possible to efficiently estimate the frequency response at the rated rotation speed.

[0176] Figure 12 shows the characteristic of the natural frequency due to the gyroscopic effect versus the rotation speed. 0 So, As shown in <Step 2> above, vibration is applied by superimposing a sine sweep signal at zero rotation to measure the sensitivity function.

[0177] The dashed line RS in Figure 12 L Then, as shown in <Step 5> above, vibration is applied by superimposing a sine sweep signal while rotating at low speed, and the sensitivity function is measured.

[0178] The dashed line RS in Figure 12 H represents the frequency response of the plant including the influence of the gyro at full speed.

[0179] The present invention is L Using the parameters of the gyro matrix identified by vibrating at a low rotation speed of H Therefore, the frequency response of a plant with a high rotation speed can be estimated from the information of the gyro matrix identified at a low rotation speed, without increasing the rotation speed to the maximum rotation speed.

[0180] As described above, according to the first embodiment, it is possible to use a model to perform advanced adjustments even for an asymmetric rotor, which is difficult to adjust the magnetic bearing controllers for because the controllers of the two axial radial magnetic bearings influence each other. This makes it possible to improve the accuracy of the position control of the rotor.

[0181] When the shaft response of a rotating body rotates, the natural frequency is split into forward and backward components due to the gyro effect, but the control parameters can be adjusted from the results of vibration tests at low rotation speeds without having to perform vibration tests at the rated rotation speed to measure the frequency response. This means that there is no need to perform high-speed vibration tests, which require more advanced safety measures, and the effort and man-hours required for testing can be reduced. EXAMPLES

[0182] The displacement signal (signal at evaluation output terminal (2)) measured in <Step 5> of the first embodiment has an amplitude that is different from that of the state space models of the sensitivity functions of equations (32) and (33) due to the influence of rotation-synchronous components caused by unbalance.

[0183] Therefore, in the second embodiment, vibration is applied under a controlled state using UFRC (Unbalance Force Rejection Control) that removes the influence of the forward rotation synchronous component due to the unbalance with a tracking filter as shown in Figures 17 and 18. Note that the processing procedure is the same as in the first embodiment, with <Procedure 1> to <Procedure 7> being performed.

[0184] Figure 17 is a block diagram showing the control configuration and excitation signals for system identification in the second embodiment, with the same parts as in Figure 2 being denoted by the same reference numerals. Figure 17 differs from Figure 2 in that it includes a tracking filter 60 that extracts the synchronous component of the rotation speed due to the forward excitation signal that is superimposed when acquiring the sensitivity function (Equations (32) and (33)) during low-speed rotation, and a subtractor 61 that subtracts the extracted synchronous component of the rotation speed due to the excitation signal from the output of the subtractor 31 for command change, and the other parts are configured in the same way as in Figure 2.

[0185] FIG. 18 shows a block diagram of the tracking filter 60 for removing the influence of the forward rotation-synchronous component in the s-domain of a continuous system.

[0186] 18, cos(Ωt) and sin(Ωt) synchronized with the rotational angular velocity are generated by a rotational pulse meter (signal generating unit) not shown in the figure, etc. A first calculation unit performs a product-sum calculation on the displacement signals in the x and y directions of two orthogonal axes on the output side of the subtractor 31 in FIG. 17 and the generated cos(Ωt) and sin(Ωt).

[0187] The first calculation unit includes a multiplier 71 that multiplies the displacement signal x by cos(Ωt), a multiplier 72 that multiplies the displacement signal x by sin(Ωt), a multiplier 73 that multiplies the displacement signal y by sin(Ωt), a multiplier 74 that multiplies the displacement signal y by cos(Ωt), an adder 75 that adds the output of the multiplier 71 and the output of the multiplier 73, and a subtractor 76 that subtracts the output of the multiplier 72 from the output of the multiplier 74.

[0188] Reference numerals 77 and 78 denote low-pass filters which receive the output of the adder 75 and the output of the subtractor 76, respectively, and output the amplitude of the rotation speed synchronous component, respectively. τ is the time constant of the low-pass filter.

[0189] The amplitude of the rotation speed synchronous component output from the low pass filters 77, 78 and the cos(Ωt) signal and sin(Ωt) signal synchronized with the rotation angular velocity of the rotor are subjected to a product-sum operation by the next second calculation unit.

[0190] The second calculation unit includes a multiplier 79 that multiplies the output of low-pass filter 77 by cos(Ωt), a multiplier 80 that multiplies the output of low-pass filter 77 by sin(Ωt), a multiplier 81 that multiplies the output of low-pass filter 78 by sin(Ωt), a multiplier 82 that multiplies the output of low-pass filter 78 by cos(Ωt), a subtractor 83 that subtracts the output of multiplier 81 from the output of multiplier 79, and an adder 84 that adds the output of multiplier 80 and the output of multiplier 82.

[0191] With the configuration of Figure 18, the forward rotation speed synchronous component x is generated from the x and y displacement signals on the input side. out ,y out Only the forward rotation speed synchronous component x out ,y outis removed in subtractor 61 in FIG.

[0192] If a phase lag occurs due to the controller's calculation processing, AD conversion, DA conversion, the sensor, or the power amplifier, the phase is advanced to perform correction.

[0193] In the above-mentioned <Step 5>, a signal that sweeps a sine wave frequency backward in the x and y directions is superimposed on the disturbance input terminal (1) in Fig. 17 while rotating, and the sensitivity function of the frequency response is measured by measuring the signal at the evaluation output terminal (2) in the x and y directions. By performing backward vibration, it is possible to ignore the change in the response of the signal at the evaluation output terminal (2) caused by removing the forward synchronous component by the UFRC in Fig. 18, which has the effect of improving the estimation accuracy of the gyro matrix using the state space model of the sensitivity function of Equation (32) and Equation (33) in <Step 6>. The other steps are the same as those in the first embodiment. EXAMPLES

[0194] The displacement signal (signal at evaluation output terminal (2)) measured in <Step 5> of Example 1 may be affected not only by the forward rotation-synchronous component due to the imbalance, but also by the backward rotation-synchronous component due to the anisotropy of the bearing support stiffness, etc. Therefore, the magnitude of the amplitude is different from that of the state space model of the sensitivity functions of Equations (32) and (33).

[0195] Therefore, in the present embodiment 3, the influence of the forward and backward rotation-synchronous components is removed by a uniaxial tracking filter shown in Fig. 19 instead of the one shown in Fig. 18. Fig. 19 shows the configuration of the tracking filter 60 of Fig. 17 according to the embodiment 3. Note that in the embodiment 3, the processing procedures are carried out in the same manner as in the embodiment 1, that is, <Procedure 1> to <Procedure 7>.

[0196] In the one-axis tracking filter of FIG. 19, cos(Ωt) and sin(Ωt) synchronized with the rotational angular velocity are generated by a rotational pulse meter (signal generating unit) or the like (not shown).

[0197] The uniaxial displacement signal x at the output side of the subtractor 31 in FIG. 17 and the generated cos(Ωt) and sin(Ωt) are multiplied by a first calculation unit.

[0198] The first calculation section includes a multiplier 85 that multiplies the displacement signal x by cos(Ωt), and a multiplier 86 that multiplies the displacement signal x by sin(Ωt).

[0199] Reference numerals 87 and 88 denote low-pass filters which receive the outputs of the multipliers 85 and 86, respectively, and output the amplitude of the rotation speed synchronous component, respectively. τ is the time constant of the low-pass filter.

[0200] The amplitudes of the rotation speed synchronous components output from the low pass filters 87 and 88, and the cos(Ωt) signal and sin(Ωt) signal synchronized with the rotation angular velocity of the rotor are subjected to a product-sum operation by the next second calculation unit.

[0201] The second calculation unit includes a multiplier 89 that multiplies the output of low-pass filter 87 by cos(Ωt), a multiplier 90 that multiplies the output of low-pass filter 88 by sin(Ωt), and an adder 91 that adds the output of multiplier 89 and the output of multiplier 90.

[0202] The sum output of the adder 91 is multiplied by two by a 2x multiplier 92 to obtain the forward and backward rotation speed synchronous components x out is extracted.

[0203] With the configuration of Figure 19, forward and backward rotation speed synchronous components x are generated from the displacement signal x on the input side. out can be extracted, and the forward and backward rotation speed synchronous components are removed in subtractor 61 in FIG.

[0204] The plant 40 in FIG. 17 is affected by a forward component synchronous with the rotational speed due to imbalance, and by an excitation force that generates a backward component synchronous with the rotational speed due to anisotropy in the support stiffness of the bearings, etc., but these two effects can be removed by the tracking filter in FIG. 19.

[0205] If a phase lag occurs due to the controller's calculation processing, AD conversion, DA conversion, the sensor, or the power amplifier, the phase is advanced to perform correction.

[0206] FIG. 19 differs from FIG. 18 in that the rotation-synchronous component is extracted only in one axial direction.

[0207] In the above <Step 5>, vibration is applied by superimposing a signal that sweeps a sine wave frequency forward or backward in the x and y directions on the disturbance input terminal (1) in Figure 17 while rotating, and the frequency response sensitivity function is measured by measuring the signals at the evaluation output terminal (2) in the x and y directions.

[0208] In this case, the tracking filter in FIG. 19 and the subtractor 61 in FIG. 17 are used to remove the forward rotational speed synchronous component due to the imbalance and the backward rotational speed synchronous component due to the anisotropy of the bearing support stiffness, and thus the change in the response of the signal at the evaluation output terminal (2) can be ignored.

[0209] In other words, since the change in the response of the signal at the evaluation output terminal (2) caused by removing the rotation speed synchronous components other than the excitation signal can be ignored, there is an effect that the estimation accuracy of the gyro matrix using the state space model of the sensitivity functions of equations (32) and (33) in <Step 6> above is improved.

[0210] By performing vibration tests at multiple low rotation speeds when estimating the gyro matrix, it is possible to reduce the effect of removing rotation-synchronous components from the vibration signal that sweeps the frequency, which is caused by using the uniaxial tracking filter in Fig. 19. The other procedures are the same as those in the first embodiment.

[0211] In the third embodiment, when a backward sine sweep signal is superimposed on the disturbance input terminal (1) in the above-mentioned <Step 5> to apply vibration, although the change in the response of the signal at the evaluation output terminal (2) caused by removing both the forward component in synchronization with the rotation speed and the backward component in synchronization with the rotation speed can be ignored, the backward component in synchronization with the rotation of the vibration signal is also removed.

[0212] In contrast, in the second embodiment, a backward vibration signal is applied to the disturbance input terminal (1), so the backward component of the vibration signal that is synchronous with the rotation is not removed. In general, the influence of the backward component that is synchronous with the rotation due to the anisotropy of the support stiffness is smaller than the forward component that is synchronous with the rotation due to the imbalance. Therefore, a sufficient effect can be obtained in the second embodiment.

[0213] The present invention is not limited to application to an asymmetric rotating body, but may also be applied to a symmetric rotating body. [Explanation of symbols]

[0214] 11...Impeller 12...Rotation axis 13...Thrust disk 14, 15…Electromagnets 16,20…Protective bearing 17...Permanent magnet rotor 18…Stator core 19a, 19b...Stator windings 31, 34, 51, 61, 76, 83…Subtractor 32, 39, 75, 84, 91…Adder 33…Block for compensating for negative spring gain 35...Current command conversion block 36…Current control block 37...Electromagnetic attraction force linearization block 38…Negative spring effect block 40…Plant 41...Plant rotor 71~74,79~82,85,86,89,90...Multiplier 77,78,87,88…Low pass filters 92...2x multiplier

Claims

1. In a magnetic bearing device that supports a rotating body by a magnetic bearing, a model of a rotor controlled by a magnetic bearing is constructed, the model comprising a plant including a rotor and electromagnets arranged on the left and right sides of the rotor in the axial direction, a controller for controlling the plant, a current control block, a negative spring compensation gain block, a control input, a disturbance input, an evaluation output, and a control output, and feedback is provided from the control output to the control input; a sensitivity function acquisition unit that measures the evaluation output when a vibration signal is superimposed on a disturbance input of the model while the rotor is levitated and in a state of zero rotation, thereby acquiring a sensitivity function of the frequency response at zero rotation, and that measures the evaluation output when a forward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, and a vibration signal with a magnitude of A cos(ωt) in the x direction and A sin(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the model while the rotor is levitated and in a state of low rotation speed in which an unbalanced vibration force can be ignored) thereby acquiring a sensitivity function of the frequency response at low rotation speed; Identifying and adjusting parameters of the mass matrix, stiffness matrix, and damping matrix of the mode synthesis model so that an evaluation output becomes a set signal when an excitation signal is superimposed on a disturbance input of a state space model in which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted from the acquired sensitivity function at zero rotation; a parameter estimation unit that identifies and adjusts parameters of a gyro matrix of a mode synthesis model so that an evaluation output becomes a set signal when the excitation signal is superimposed on a disturbance input of a state space model in which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted based on the acquired sensitivity function during low speed rotation; a controller parameter adjustment unit that estimates the frequency response of the plant at the maximum rotation speed from the mode synthesis model whose parameters have been identified and adjusted by the parameter estimation unit, and adjusts the parameters of the controller by loop shaping the parameters of the controller with the H∞ norm.

2. a tracking filter that extracts and removes a synchronous component of a rotation speed due to a forward vibration signal that is superimposed when the sensitivity function acquisition unit acquires the sensitivity function during the low-speed rotation, 2. The magnetic bearing control device according to claim 1, wherein the parameter estimation unit identifies and adjusts parameters of a gyro matrix of a mode synthesis model so that the evaluation output becomes a set signal when, during low-speed rotation, a backward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, a vibration signal having a magnitude of A sin(ωt) in the x direction and A cos(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the state space model instead of the vibration signal.

3. a tracking filter that extracts and removes a synchronous component of a rotation speed due to a forward vibration signal and a synchronous component of a rotation speed due to a backward vibration signal, which are superimposed when the sensitivity function acquisition unit acquires the sensitivity function during low-speed rotation; 2. The magnetic bearing control device according to claim 1, wherein the sensitivity function acquisition unit acquires a sensitivity function of the frequency response at the low rotation speed by measuring the evaluation output when the forward vibration signal or the backward vibration signal is superimposed on the disturbance input of the model at the low rotation speed.

4. The tracking filter includes: a signal generating unit that generates a cos(Ωt) signal and a sin(Ωt) signal synchronized with a rotational angular velocity of the rotor; a first calculation unit that performs a product-sum operation on two-axis displacement signals in the x and y directions of the evaluation output measured by the sensitivity function acquisition unit during low-speed rotation and the cos(Ωt) signal and sin(Ωt) signal generated by the signal generation unit; a low-pass filter which receives the output of the first calculation unit and outputs the amplitude of a rotation speed synchronous component; a second calculation unit that performs a product-sum operation on the amplitude of the rotational speed synchronous component output from the low-pass filter and a cos(Ωt) signal and a sin(Ωt) signal synchronized with the rotational angular velocity of the rotor to extract the rotational speed synchronous components in two axial directions.

5. The tracking filter includes: a signal generating unit that generates a cos(Ωt) signal and a sin(Ωt) signal synchronized with a rotational angular velocity of the rotor; a first calculation unit that integrates a uniaxial displacement signal of the evaluation output measured by the sensitivity function acquisition unit during low-speed rotation and a cos(Ωt) signal and a sin(Ωt) signal generated by the signal generation unit; a low-pass filter which receives the output of the first calculation unit and outputs the amplitude of a rotation speed synchronous component; a second calculation unit that performs a product-sum operation on the amplitude of the rotational speed synchronous component output from the low-pass filter, and a cos(Ωt) signal and a sin(Ωt) signal synchronized with the rotational angular velocity of the rotor, to extract a synchronous component of the rotational speed in one axial direction.

6. The sensitivity function at zero rotation acquired by the sensitivity function acquisition unit is expressed in state space by the following equations (29) and (30): [0029] [0030] The sensitivity function during low-speed rotation acquired by the sensitivity function acquisition unit is expressed in state space by the following equations (32) to (44): [0032] [Equation 33] [0034] [Equation 35] [0036] [Equation 37] [Equation 38] [0039] [0040] [0041] [0042] [0043] [0044] (X １ , X ２ are the state vectors in the x direction of the plant rotor in the mode synthesis method, and Y １ , Y ２ are the state vectors in the y direction of the plant rotor in the mode synthesis method, and F ｉｌ , I ｎｔ are the state vectors of the PID controller, T ｒａ is the state vector corresponding to the current control low pass, y is the output vector, u is the input vector, E ｎ is an n x n unit matrix, 0 ｎ is an n × n zero matrix, 0 ｍ,ｎ is an m × n zero matrix, m is the number of internal system eigenmodes, M ｑ is the mass matrix, D is the damping matrix, K ｎ is the stiffness matrix, Ω is the rotation speed, P is the proportional term of the PID controller, k ｉ = 2K (I １ +I ２ ) / δ ０ ２ (K is the electromagnet attraction coefficient, I １ is the bias current of the electromagnet coil arranged on either the left or right side of the rotor, I ２ is the bias current of the electromagnet coil located on either the left or right side of the rotor, δ ０ is the air gap between the electromagnet and the rotor), k ｓ is the gain to compensate for the negative spring effect, ω ｃ is the cutoff frequency (angular frequency) of the low-pass filter of the current control block. The mass matrix identified by the parameter estimation unit is expressed by equation (12): ##EQU00012## (T ｑ is the transformation by mode synthesis, M,M ｑ is the mass matrix, φ is the internal system eigenmode, and δ is the deformation mode. The stiffness matrix identified by the parameter estimation unit is expressed by equation (14): ##EQU14## (K,K ｑ is the stiffness matrix, K ｅｑ is the force required to lift the bearing point by 1. The damping matrix identified by the parameter estimation unit is expressed by equation (26): [0026] (diagonal is a diagonal matrix) The gyro matrix identified by the parameter estimation unit is expressed by equation (13): ##EQU00013## (G, G ｑ is the gyro matrix, T ｑ is a conversion by mode synthesis) 6. A control device for a magnetic bearing according to claim 1.

7. 6. The magnetic bearing control device according to claim 1, wherein the rotor is asymmetric.

8. 7. The magnetic bearing control device according to claim 6, wherein the rotor is asymmetric.

9. A method for controlling a magnetic bearing that supports a rotating body by the magnetic bearing, comprising: a model of a rotor controlled by a magnetic bearing is constructed, the model comprising a plant including a rotor and electromagnets arranged on the left and right sides of the rotor in the axial direction, a controller for controlling the plant, a current control block, a negative spring compensation gain block, a control input, a disturbance input, an evaluation output, and a control output, and feedback is provided from the control output to the control input; a sensitivity function acquisition unit measuring the evaluation output when a vibration signal is superimposed on a disturbance input of the model while the rotor is levitated and in a state of zero rotation, thereby acquiring a sensitivity function of the frequency response at zero rotation; and measuring the evaluation output when a forward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, and a vibration signal with a magnitude of A cos(ωt) in the x direction and A sin(ωt) in the y direction when the rotation direction is counterclockwise) is superimposed on the disturbance input of the model while the rotor is levitated and in a state of low rotation speed in which unbalanced excitation force can be ignored) thereby acquiring a sensitivity function of the frequency response at low rotation speed; a parameter estimation unit performing identification and adjustment of parameters of a mass matrix, a stiffness matrix, and a damping matrix of a mode synthesis model so that an evaluation output becomes a set signal when an excitation signal is superimposed on a disturbance input of a state space model into which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted from the acquired sensitivity function at zero rotation; a parameter estimation unit, based on the acquired sensitivity function during low-speed rotation, identifying and adjusting parameters of a gyro matrix of a mode synthesis model so that an evaluation output becomes a set signal when the excitation signal is superimposed on a disturbance input of a state space model into which known parameters of a controller, a current control block, and a block of a negative spring compensation gain in a model of a rotor controlled by the magnetic bearing are substituted, so that an evaluation output becomes a set signal; a controller parameter adjustment unit estimating a frequency response of the plant at the maximum rotation speed from the mode synthesis model whose parameters have been identified and adjusted by the parameter estimation unit, and adjusting the controller parameters by loop shaping the controller parameters with the H∞ norm.

10. a tracking filter is provided to extract and remove a synchronous component of the rotation speed due to a forward vibration signal that is superimposed when the sensitivity function acquisition unit acquires the sensitivity function during the low rotation speed; 10. The magnetic bearing control method according to claim 9, further comprising a step of identifying and adjusting parameters of a gyro matrix of a mode synthesis model so that the evaluation output becomes a set signal when, during low-speed rotation, the parameter estimation unit superimposes a backward vibration signal (considering a right-handed system in which the axial direction of the rotor is z, a vibration signal having a magnitude of A sin(ωt) in the x direction and A cos(ωt) in the y direction when the rotation direction is counterclockwise) on the disturbance input of the state space model instead of the vibration signal.

11. a tracking filter is provided to extract and remove a synchronous component of the rotation speed due to a forward vibration signal and a synchronous component of the rotation speed due to a backward vibration signal, which are superimposed when the sensitivity function acquisition unit acquires the sensitivity function during low-speed rotation; 10. The method for controlling a magnetic bearing according to claim 9, further comprising a step of measuring the evaluation output when the forward vibration signal or the backward vibration signal is superimposed on a disturbance input of the model during the low-speed rotation, and acquiring a sensitivity function of a frequency response during the low-speed rotation.

Images