JP2001182747A - Electromagnetic suction type active magnetic bearing and control method therefor, and design method for rotor thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an electromagnetic suction type active magnetic bearing which enables ning improvement in estimation accuracy for an unknown vibration frequency, while realizing vibration control for a plurality of vibration frequencies. SOLUTION: This electromagnetic suction type active magnetic bearing, in order to apply an adaptive control to cyclic disturbances such as a rotation synchronous vibration where R.P.M. varies, fluctuates in frequency and appears or disappears during the rotation of a rotor 5 which is due to an unbalanced exciting force of the rotor 5 as a noncontact floatation body, adaptively modifies Fourier coefficients as control inputs, formulates feed-forward control signals from the Fourier coefficients for control of the electromagnetic suction force of bearing, and when frequency estimate errors of the cyclic disturbances exist due to observed noises, adaptively modifies the Fourier coefficients by modifying the frequencies using a frequency estimate modification rule, then controls the rotation synchronous vibration and rotation asynchronous vibration arising during the rotation of the rotor by inputting the feed-forward control signals to bearing controllers 3, 4.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electromagnetic attraction type active magnetic bearing, a control method thereof, and a method of designing a rotating body thereof.

[0002]

2. Description of the Related Art Conventionally, in a magnetic bearing, when the vibration of a rotating body becomes large, it becomes impossible to pass through a dangerous speed and a destruction phenomenon occurs, or the rotating body may become unable to rotate. An important problem is said to be the vibration of the rotating body caused by the unbalanced excitation force.

[0003] Therefore, in this type of magnetic bearing, in addition to feedback control for stabilizing the rotation of the rotating body, control for suppressing the periodic vibration of the rotating body due to the unbalanced excitation force is required. In order to suppress the periodic vibration of the rotating body, various methods of suppressing the vibration of the rotating body have been proposed.

[0004]

However, the vibration suppression methods of various types of rotating bodies that have been conventionally proposed cannot avoid the existence of observation noise, and thus cannot improve the accuracy of estimating the unknown vibration frequency. On the contrary, the vibration of the rotating body may be amplified and diverged, which is not practical.

In the design of a rotating body, when it is assumed that the vibration of the rotating body becomes too large to pass a critical speed due to the unbalanced excitation force of the rotating body, or that the rotating body becomes unable to rotate. However, there is also a problem in that the design of the rotating body must be changed.

SUMMARY OF THE INVENTION The present invention provides an electromagnetically attractable active type magnetic bearing capable of improving the accuracy of estimating an unknown vibration frequency and realizing vibration suppression for a plurality of vibration frequencies, a control method thereof, and a method of designing a rotating body thereof. I do.

[0007]

According to a first aspect of the present invention, there is provided an electromagnetically attractable active type magnetic bearing, comprising:
Due to the unbalanced excitation force of the rotating body as a non-contact floating body, the rotating speed changes during the rotation of the rotating body, and the frequency fluctuates, and the rotating synchronous vibration and the non-synchronous vibration occur. In order to adaptively control the periodic disturbance as described above, the Fourier coefficient as a control input is adaptively modified to generate a feedforward control signal for the bearing electromagnetic attraction force control from the Fourier coefficient, and for observation noise. When there is a frequency estimation error of the periodic disturbance, the frequency is corrected by a frequency estimation correction rule to adaptively correct the Fourier coefficient, and the feedforward control signal is input to a bearing control unit, and the rotating body is The feature is that rotation-synchronous vibration and rotation-unsynchronous vibration that occur during rotation of the motor are suppressed.

According to another aspect of the present invention, there is provided a method for controlling an electromagnetic attracting type active magnetic bearing, wherein the rotating body as a non-contact floating body is caused by an unbalanced excitation force of the rotating body. Adaptively corrects Fourier coefficients as control inputs to adaptively control periodic disturbances as rotation synchronous vibration and rotation asynchronous vibration where the frequency changes and the frequency fluctuates and disappears during rotation of the Then, a feedforward control signal for bearing electromagnetic attraction force control is generated from the Fourier coefficient, and when there is a frequency estimation error of periodic disturbance due to observation noise, the frequency estimation correction rule To correct the Fourier coefficient adaptively, input the feedforward control signal to the bearing control unit, and generate a rotation-synchronous vibration generated during rotation of the rotating body. Characterized by rolling suppress asynchronous vibration.

In order to solve the above problem, a control method of an electromagnetic attraction type active magnetic bearing according to a third aspect is characterized in that the vibration of the rotating body is suppressed by using a feedback control signal together.

In order to solve the above-mentioned problems, a method for designing a rotating body according to a fourth aspect is directed to an electromagnetically attractable active magnetic bearing according to the first aspect or an electromagnetically attractable active type magnetic bearing according to the second aspect. The rotating body is designed using a bearing control method.

According to the active magnetic bearing of the present invention, the control method thereof, and the method of designing the rotating body thereof, the accuracy of estimating the unknown vibration frequency is improved, and the vibration is suppressed even for a plurality of vibration frequencies. Can be realized.

[0012]

FIG. 1 is a longitudinal sectional view of an electromagnetic attraction type active magnetic bearing device to which the present invention is applied. In FIG. 1, reference numeral 1 denotes a casing. An axial magnetic bearing 2, radial magnetic bearings 3 and 4, and a cylindrical rotating body (rotor) 5 are provided in the casing 1. The axial type magnetic bearing 2 is a high temperature superconductor 2a.
And the coil 2b. The radial type magnetic bearings 3 and 4 are composed of an X-direction radial type magnetic bearing and a Y-direction radial type magnetic bearing which are orthogonal to each other. Here, the X-direction radial type magnetic bearing is shown.

The radial type magnetic bearings 3 and 4 are generally constituted by a pair of electromagnets 6 and 7 opposed to each other with the columnar rotating body 5 interposed therebetween, and the pair of electromagnets 6 and 7 includes iron cores 6a and 7a and coils 6b and 7b. Approximately.

An induction motor 8 is provided between the radial magnetic bearing 3 and the radial magnetic bearing 4. The induction motor 8 includes a stator 8a and a coil 8b.

In the casing 1, a rotation speed detection sensor 9 for detecting the rotation speed of the columnar rotating body 5 and outputting a rotation speed detection signal, and detecting the displacement of the cylindrical rotating body 5 in the thrust direction. A displacement detection sensor 9 ′ that outputs a signal, and displacement detection sensors 10 and 11 that detect a radial displacement (X-direction displacement, Y-direction displacement) of the columnar rotating body 5 and output a displacement detection signal are provided. . The columnar rotating body 5 is provided with iron plate laminates 12 to 16.

The iron plate laminate 12 is disposed to face the displacement detection sensor 10, the iron plate laminate 13 is disposed to face the radial magnetic bearing 3, and the iron plate laminate 14 is disposed to face the induction motor 8. The iron plate laminate 15 is arranged to face the radial magnetic bearing 4, and the iron plate laminate 16 is arranged to face the displacement detection sensor 11.

This electromagnetic attraction type active type magnetic bearing device comprises:
A blade member 5 'is provided at an end of the columnar rotating body 5, and is used as a vacuum pump.

The cylindrical rotating body 5 is driven to rotate by an induction motor 8, and the rotational speed changes during the rotation of the cylindrical rotating body 5 and the frequency increases due to the unbalanced excitation force of the cylindrical rotating body 5. As a result, the rotation synchronous vibration and the rotation asynchronous vibration appear or disappear.

The columnar rotating body 5 is displaced in a radial direction from its neutral position O. The stable gap length G between the cylindrical rotator 5 and the electromagnets 6 and 7 is about 1 mm. In order to prevent the electromagnetic attraction type active magnetic bearing device from being destroyed due to the displacement of the cylindrical rotator 5, a touchdown is performed. Type ball bearings 17 and 18 are provided at both ends of the columnar rotating body 5. When both ends of the columnar rotating body 5 are to be displaced by 1 mm or more, the both ends come into contact with the touch-down type ball bearings 17 and 18, thereby preventing the electromagnetic attraction type active magnetic bearing device from being broken.

A bias current Bi is applied to each of the coils 6b and 7b.
Is flowing, and the displacement detection sensor 9 ′ is
In the thrust direction (axial direction), displacement detection sensor 1
When 0 and 11 detect the radial displacement of the cylindrical rotator 5, as shown in FIG. 2, those displacement detection signals are input to the analog linear controller 19, and the analog linear controller 19 outputs the displacement result. And outputs a feedback signal toward the amplifier 20 in a direction to cancel the displacement.

The displacement detection signal and the rotation number detection signal are input to the digital non-linear controller 21. The digital non-linear controller 21 is an analog / digital converter 22
And a digital sampling processor 23 and a digital / analog converter 24.

In order to suppress the periodic disturbance, its frequency must be estimated. The estimation method has been Tsao, Qi
Although there is an evaluation function method of an (Publication 1), since only one disturbance frequency can be estimated, a difference equation method capable of newly estimating a plurality of disturbance frequencies has been devised (Reference Material 1).

On the other hand, when the observation noise of the periodic disturbance is not taken into account, there is already an adaptive correction law of the Fourier coefficient of the control input for adaptively suppressing the disturbance (see Reference 2). The authors newly devised an adaptive suppression method and an adaptive frequency tracking method for a plurality of periodic disturbances in consideration of observation noise according to Reference Material 2.

According to this, even considering the observation noise,
When there is no frequency estimation error of the periodic disturbance, the same adaptive correction rule as when there is no observation noise can be used. Modify the frequency of sexual disturbance,
We devised that the disturbance can be adaptively suppressed by using the adaptive correction rule when there is no observation noise.

That is, the digital nonlinear controller 2
Reference numeral 1 denotes a rotation-synchronous vibration in which the frequency changes and the frequency fluctuates and appears or disappears during rotation of the rotating body 5 due to the unbalanced excitation force of the rotating body 5 as a non-contact floating body. In order to suppress the application of periodic disturbances as rotation asynchronous vibrations, adaptively modify the Fourier coefficient as a control input, generate a feedforward control signal for bearing electromagnetic attraction force control from the Fourier coefficient, and observe If there is a frequency estimation error of the periodic disturbance due to noise, the frequency is corrected by a frequency estimation correction rule to adaptively correct the Fourier coefficient, and a feedforward control signal is input to a bearing control unit to perform the rotation. It suppresses rotational synchronous vibration and rotational asynchronous vibration generated during rotation of the body.

Here, the rotation synchronous vibration refers to a vibration that appears and disappears in proportion to an integral multiple of the rotation speed, and the rotation asynchronous vibration refers to a vibration that appears and disappears regardless of the rotation speed. Say.

In the case of the conventional control method, the rotational speed is 4368r.
At pm, the Lissajous waveforms Q1 and Q2 indicating the vibration and displacement of the rotating body 5 change as shown in FIGS. 3A and 3B, but according to the embodiment of the present invention,
As shown in FIGS. 3C and 3D, the Lissajous waveforms Q1 and Q2 converge to almost one point, and the vibration of the rotating body 5 could be suppressed. For example, in the case of the conventional control method, when the rotational speed is 12052 rpm, the Lissajous waveforms Q1 and Q
2 changes as shown in FIGS. 4 (a) and 4 (b),
According to the embodiment of the present invention, FIG.
As shown in (d), the Lissajous waveforms Q1 and Q2 converged to almost one point, and the vibration and displacement of the rotating body 5 could be suppressed over a range of low to high rotational speeds.

3 (a), 3 (c), 4 (a),
(C) shows the radial displacement of the columnar rotating body 5 near the radial bearing 4, and FIGS. 3 (b), (d), and FIG.
(B) and (d) show the radial displacement of the columnar rotating body 5 near the radial bearing 3.

The contents to be published as papers are described below as Reference Material 1 and Reference Material 2.

Reference 1-Method of estimating the frequency of a plurality of periodic disturbances using difference equation-In order to suppress the periodic disturbance using the active adaptive suppression method, the frequency of the disturbance is often unknown. Therefore, it is necessary to estimate the frequency of the disturbance. In this case, the evaluation function method can estimate only one frequency of the disturbance. For example, in the case of an actual high-speed rotating machine, a subharmonic vibration or a harmonic vibration may sometimes be observed in addition to rotationally synchronized vibration due to unbalance. In this case, this method cannot be applied. On the other hand, the difference equation method has a feature that several disturbance frequencies can be estimated at the same time. Therefore, in the case of the above-mentioned example, it is an extremely effective method. Here, a method of estimating a plurality of disturbance frequencies using a difference equation will be described.

Consider the following stationary single harmonic signal:

Χ [n] = sin (ωn) (1) With respect to equation (1), the shortest difference equation can be derived as follows.

Χ [n] = aχ [n-1] -χ [n-2] (2) where initial values χ [n ₀ ] = sin (ωn ₀ ), χ [n ₀ -1] = sin ( ω [n ₀
-1]), a = 2 cos (ω) Next, consider a case where the signal χ [n] includes two stationary harmonic signals as follows.

Χ [n] = χ ₁ [n] + χ ₂ [n] = sin (ω ₁ n) + sin (ω ₂ n) (3) At this time, as in the case of a stationary single harmonic signal,
_The shortest difference equations for ₁ [n] and χ ₂ [n] can be expressed as follows, respectively.

Χ ₁ [n] = c ₁ χ ₁ [n−1] −χ ₁ [n−2] (4) χ ₂ [n] = c ₂ χ ₂ [n−1] −χ ₂ [n− 2] Using equation (4), the difference equation for x [n] is as follows.

Χ [n] = a ₁ χ [n-1] -a ₂ χ [n-2] + a ₃ χ [n-3] -a ₂ χ [n-4] (5) where a _{1 = c 1 + c 2, a} 2 = c l c 2 + 2, a 3 = C 1 +
C ₂ , a ₄ = 1.

Now, in the general case where the signal χ [n] is composed of M stationary harmonic signals, equations (4) and (5) are as follows.

Χ _m [n] = _cm χ _m (n−1) −χ _m [n−2] (6) χ [n] = Σχ _m [n], χ _m [n] = sin (ω _n (7) Σ integrates from m = 1 to M.

At this time, the following 2Μ-dimensional shortest difference equation (AR model) can be derived.

{[N] = {aκ} [n−κ] (8)} integrates from κ = 1 to 2M. However, Eikappa is a function of c _m of formula (6). In this study, we assume for simplicity that the signal χ [n] consists of up to four stationary harmonic signals. In this case, the samples χ [n], χ [n−1],
Using [n-2],..., the coefficient aκ (κ = 1... 2M) of the equation (7) can be estimated by the least square method.
Using these coefficients, _cm (m = 1... M) can be calculated, and an estimated value of the frequency ω _m (i = 1... M) can be obtained.

Reference Material 2-Adaptive suppression method and adaptive frequency tracking method for a plurality of periodic disturbances in consideration of observation noise- Adaptive Suppression Method of Single Periodic Disturbance Considering Observation Noise This section describes an adaptive algorithm that suppresses periodic disturbance. The biggest feature of this method is that it does not require a model to be controlled. The block diagram of the active control of the periodic disturbance by the adaptive control method is shown in FIG. It is shown in FIG.
Further, details of this adaptive suppression algorithm are described in FIG. 2
Shown in

[0042]

[Fig. 1)

[0043]

[Fig. 2]

FIG. In the first block of 2, calculate the energy of the sine and cosine components of the error signal. In the next block, the Fourier coefficients α and β of the control input to the plant are adaptively corrected. Then, in the last block, a control input to the plant is generated from the Fourier coefficients. As described above, FIG. 2 to generate a pseudo feedforward control input to the plant, FIG. The purpose of this adaptive algorithm is to overlap with a disturbance of one and consequently reduce or eliminate the deviation e.

References [1] and [2] have proposed adaptive algorithms that do not consider observation noise. In this paper, we consider that the method of Ref. [2] is an adaptive algorithm that can sufficiently withstand observation noise. First, a disturbance d having a single frequency is given by the following equation.

D = α _d sin (ω ₀ t) + β _d cos (ω ₀ t) (9) where ω ₀ is the frequency of the disturbance: α _d , and β _d is the amplitude of the disturbance. Now, actually, observation noise (white noise and color noise) always exists. Therefore, observation noise is defined as follows. N _d = {(α _i sin (ω _i t) + β _i cos (ω _i t) + {· rand (t) (10)} integrates from i = 1 to i = n.

In Equation (10), ω _i is the frequency of the i-th color noise, and α _i and β _i are the amplitudes of the color noise. Rand (t) and ζ indicate white noise and its level coefficient. Where α _i β _i << α _d , β _d (i = 1
.. N), ω ₀ ≪ω _i is assumed. Since the noise of the equation (10) is mixed in the equation (9), the disturbance of the system has the following form.

[0048] _{d = α d sin (ω 0} t) + β d cos (ω 0 t) + N d (11) plant transfer function of the ^{G (s) = Ae j θ} . Here, the control input r to the plant is defined as follows.

R = αsin (ωt) + βcos (ωt) (12) where ω is the frequency estimated by the frequency estimation algorithm proposed in Reference 1, and α and β are Fourier coefficients corrected by the adaptive control algorithm. At this time, the stationary force y of the plant is as follows.

Y = rG (jω) = A [α (t) sin (ωt + θ) + β (t) cos (ωt + θ)] (13) where A and θ are the gain and phase of the plant at the frequency ω. Further, the steady state error signal e of the system is as follows.

[0051] e = y + d = A [ α (t) sin (ωt + θ) + β (t) cos (ωt + θ)] + α d sin (ω 0 t) + β d cos (ω 0 t) + N d (14)

[0052]

[Fig. 3]

The deviation signal e is set to FIG. 3, the steady-state outputs of the two low-pass filters h (t) can be approximately written as follows.

N1 (t) = e (t) sin (ωt) n2 (t) = e (t) cos (ωt) (15) First, consider n1 (t).

[0055] n1 (t) = A [α (t) sin (ωt + θ) + β (t) cos (ωt + θ)] sin (ωt) + [α d sin (ω 0 t) + β d cosω 0 t] sin (ωt _{) + {Σ [α i sin} (ω i t) + β i cos (ω i t) + ∫rand (t)]} sin (ωt) = 0.5A {α (t) [cos (2ωt + θ) -cosθ] + β (t) [sin ( 2ωt + θ) -sinθ]} +0.5 {α d [cos (ω 0- ω) t-cos (ω 0+ ω) t)] + β d [sin (ω 0- ω) t −sin (ω ₀ + ω) t]｝ + {0.5 ｛Σα _i [cos (ω _{i +} ω) t−cos (ω _i −ω) t] + β _i [sin (ω _{i +} ω) t−sin ( ω _i− ω) t]｝ + ζ · rand (t) sin (ωt) (16) where the cutoff frequency ω _B of the low-pass filter is ω _B
≪2ω _0, and ω _B ≪ω _i assuming the color noise frequency ω _i in equation (10). As a result, the disturbance frequency true value ω
High frequency components having a relatively small gain with respect to ₀ can be ignored. The disturbance frequency estimation error is represented by the following equation as Δω.

Δω = ω ₀ −ω (17) In a steady state, the output of the low-pass filter can be approximately written as follows.

[0057] n1 (t) = 0.5A [α (t) cosθ-β (t) sinθ] + 0.5A d [sin (Δωt + θd)] (18) ^{_{However, A d = (α d 2}} + β d 2) ^1/2 ; θd = tan ^-1 (α
_d / β _d ) Similarly, n2 (t) can be derived as follows.

[0058] n2 (t) = 0.5A [β (t) cosθ + α (t) sinθ] + 0.5A d [cos (Δωt + θd)] (19) First, consider the case of △ ω = 0. At this time, reference [2]
It becomes the same as the adaptive law which does not depend on the phase θ proposed in the above, and defines the following equation.

Α (K + 1) = α (k) −μ ₁ (k + 1) n1 (k) β (K + 1) = β (k) −μ ₂ (k + 1) n2 (k) ( 20) where μ _i is the step size. Further, n1 (K + 1) = n1 (k) + 0.5A [μ 2 (k + 1) n2 (k) sinθ -μ 1 (k + 1) n1 (k) cosθ] (21) n2 (K + 1) = n2 (k) −0.5A [μ ₂ (k + 1) n2 (k) cos θ + μ ₁ (k + 1) n1 (k) sin θ] (22) where μ ₁ (k + 1) = μ ₁ (k) sgn (n1 (k-1) ² − n1 (k) ² ) (23) μ ₂ (k + 1) = μ ₂ (k) sgn (n2 (k-1) ² − n2 (k) ² ) The above equation is a nonlinear adaptive law.

From the results of Refs. [1] and [2], simulations show that as long as the initial value of μ _i satisfies a certain condition for different phases θ, this nonlinear system can guarantee asymptotic stability. Reveals. Next, consider the case of Δω ≠ 0. From Expression (18), a discrete expression of n1 (t) is obtained as follows. n1 (k + 1) = 0.5A [α (k + 1) cos θ−β (k + 1) sin θ] + 0.5A _d [sin (Δω (k + 1) + θ _d )] = 0.5A [α (k) −μ ₁ (k + 1) ) n1 (k)) cosθ - (β (k) -μ 2 (k + 1) n2 (k) sinθ)] + 0.5A d [sin (Δωk + θ d)] (24) is generally Derutaomega«omega. Here, cosΔω〜1; s
If in Δω to Δω, equation (24) is as follows. n1 (k + 1) = n1 (k) + 0.5A [μ 2 (k + 1) n2 (k) sinθ -μ 1 (k + 1) n1 (k) cosθ] + 0.5A d [sin (Δωk + θ d) + Δωcos (Δωk + θ d) (25) Similarly, n2 (k + 1) = n2 (k) −0.5A [μ ₂ (k + 1) n2 (k) cos θ−μ ₁ (k + 1) n1 (k) sin θ] −0.5A _d [cos the _{(Δω + θ d) + Δωsin} (Δωk + θ d)] (26) equation (25) equation (26), n1 (k + 1), n2
It can be seen that (k + 1) depends on not only n1 (k) and n2 (k) at the time k but also the frequency estimation error Δω.
In this case, when simulation is performed, μ _i (i = 1,
Regardless of the initial value of 2), the bias value e often diverges, indicating that this nonlinear system is not guaranteed asymptotic stability and becomes unstable. The cause of this instability is the existence of the frequency estimation error Δω. For this reason, it is necessary to correct the estimated frequency to approach the true value. Therefore, an algorithm for reducing the estimation error Δω to zero is proposed in the next section. Then, it is necessary to stabilize the adaptive active control system asymptotically. 2. Adaptive frequency tracking method The algorithm that makes the disturbance frequency estimation error Δω zero is referred to as adaptive frequency tracking method in this study. Then, an adaptive correction law of frequency is derived next. From Expressions (18) and (19), the following expression is obtained. N (t) = n1 (t) + n2 (t) = 0.5A [α (t) (cos θ + sin θ) + β (t) (cos θ−sin θ)] + 0.5A _d [sin (Δω + θ _d ) + cos (Δω + θ _d ) ] (27) The discrete expression of N (t) is as follows. N (k + 1) = N (k) + 0.5A [μ ₁ (k + 1) n1 (k) (cos θ + sin θ) + μ ₂ (k + 1) n2 (k) (cos θ−sin θ)] + 0.5A _d Δω [cos (Δω _{(k + 1) + θ d} ) from -sin (Δω (k + 1) + θ d)] = 0.5N (k) + 0.5A d Δω [cos (Δωk + θ) -sin (Δωk + θ)] (28) the above equation, k → ∞ In this case, it is necessary that Δω → 0.
To achieve this goal, from equation (28), a frequency correction law is defined as follows.

Ω (k + 1) = ω (k) −μ ₃ (k + 1) N (k) (29) where μ ₃ (k + 1) = μ ₃ (k) sgnN (k−1) ² −N (k) ² ) μ ₃ (0)> 0 (30) That is, the frequency is corrected using the output N (k + 1). At this time, μ ₃ (0) is a number in a certain range described later. That condition will be introduced later. The estimated frequency gradually approaches the true value, the disturbance output is suppressed, and asymptotic stability is guaranteed.

3. When modifying an adaptive frequency tracking method the M disturbance frequency estimates of a plurality of periodic disturbance in a single system, N _i and _{N j (j ≠ i; i} , j ≦ M) is interference between the Therefore, it is necessary to adjust the correction coefficient without fail. In this case, equations (20) and (29) are as follows. α _j (k + 1) = α _j (k) −μ _j1 (k + 1) n1 _j (k) β _j (k + 1) = β _j (k) −μ _j2 (k + 1) n2 _j (k) ω _j (k + 1) = ω _j (k) −μ _j3 (k + 1) N _j (k) (31) where μ _j1 (k + 1) = μ _j1 (k) sgn (n1 _j (k−1) ² −n1 _j (k) ² ) μ _j2 (k + 1) = μ _j2 (k) sgn (n2 _j (k−1) ² −n2 _j (k) ² ) μ _j3 (k + 1) = μ _3j (k) sgn (N _j (k−1) ² −N _j (k) ² ) (32) It has been confirmed that the simulation using this method can effectively suppress not only a single disturbance frequency but also a disturbance composed of a plurality of harmonic signals having noise of Expression (10). Was done.

4. Proof of stability of adaptive suppression algorithm of adaptive disturbance and adaptive frequency tracking method In this section, we use the global stability theorem based on Lyapunov's stability theory to modify the adaptive suppression algorithm of equations (20) to (23) and study this study. We prove the asymptotic stability of the proposed adaptive frequency tracking method, that is, the adaptive frequency correction law.

4.1 Demonstration of Asymptotic Stability of Disturbance Adaptive Suppression Algorithm As described above, equation (20) indicates that when Δω = 0, the phase θ
This is a correction rule for α and β that does not depend on. N (k + 1) = n
Assuming that 1 (k + 1) + n2 (k + 1), from equation (21) and equation (22), N (k + 1) = N (k) −0.5A ｛[μ ₂ (k + 1) n2 (k) + μ ₁ (k + 1) ) N1 (k)] (cos θ + sin θ)｝ (33) μ (k + 1) N (k) = μ ₂ (k + 1) n2
If defined as (k) + μ ₁ (k + 1) n1 (k), μ
(K + 1) can be expressed as follows. μ (k + 1) = (μ ₂ (k + 1) n2 (k) + μ ₁ (k + 1) n1 (k)) / N (k) (34) where | μ ₂ (k + 1) | ≦ | μ ₁ (k + 1) | = | Μ ₁
Assuming that (0) | = | μ (0) |, equation (34) can be written as follows. | Μ (k + 1) | = | μ 2 (k + 1) n2 (k) + μ 1 (k + 1) n1 (k) | / | N (k) | ≦ | μ 2 (k + 1) n2 (k) | + | μ 1 (K + 1) n1 (k) | / | N (k) | ≦ | μ (0) | (| n2 (k) | + | n1 (k) |) / | N (k) | ≦ | μ (0) | (35) Equation (33) can be written as follows. N (k + 1) = N (k) −0.5 A [(μ (k + 1) N (k) (cos θ + sin θ) (36) Let the candidate of the Lyapunov function be V (k) = N (k) ² .
From the Lyapunov asymptotic stability theorem, the asymptotic stability condition of the system is V (k + 1) -V (k) <0. When both sides of the equation (36) are squared, V (k + 1) −V (k) = N (k + 1) ² −N (k) ² = −2 × 0.5 A [μ (k + 1) N (k) ² (cos θ + sin θ) )] + [0.5Aμ (k + 1) N (k) (cos θ + sin θ)] ² ≦ [−√2Aμ (k + 1) + (0.5√2Aμ (k + 1)) ² ] N (k) ² (37) η = If 0.5√2Aη (k + 1), V (k + 1)
The necessary and sufficient condition for −V (k) <0 is 0 <η <2.
Therefore, | μ (k + 1) | <2√2 / A. Equation (3
7), the initial value μ of μ ₁ (k + 1) and μ ₂ (k + 1)
If (0) is set in the next region, the asymptotic stability of the adaptive algorithm is guaranteed. That is, | μ (0) | <2√2 / A (38). From the simulation results, | μ (0) | <
It has been found that the asymptotic stability of the adaptive suppression system is reliably guaranteed if the setting is made within 2.83 / A. This is given by equation (38)
Also matches.

Next, asymptotic stability will be considered for the case where Δω ≠ 0. In this case, the following equation is defined using equations (25) and (26). N ′ (k + 1) = n1 (k + 1) + n2 (k + 1) + Θ = N (k + 1) + Θ (39) where Θ = 0.5A _d [sin (Δωk + θ _d ) −cos (Δωk + θ _d )] + Δω [cos (Δω + θ _d) ) + Sin (Δωk + θ _d )] (40) Here, the candidate of the Lyapunov function is V (k) = N ′ (k)
^{Assuming 2} , equation (37) becomes as follows. V (k + 1) −V (k) = N ′ (k + 1) ² −N ′ (k) ² = N (k + 1) ² −N (k) ² + 2ΔN (k + 1) Θ (41) Δω in equation (40) is Since it is constant, Θ in the above equation is | Θ |
≦ √2 [0.5A _d + Δω]. That is, Θ is bounded. Further, N (k + 1) is μ ₁ (k + 1), μ ₂ (k + 1) according to the above proof result.
If the initial value μ (0) of satisfies Expression (38), the asymptotic stability of the adaptive suppression algorithm is guaranteed. That is, k →
In the case of ∞, since ΔN (k + 1) → 0, N ′ (k
It can be seen that the asymptotic stability of +1) is also guaranteed. 4.2
Proof of asymptotic stability of adaptive frequency tracking method (1
8), n1 (k + 1) = 0.5A [α (k + 1) cos θ−β (k + 1) sin θ] + 0.5A _d [sin (Δω (k + 1) + θ _d )] = 0.5n1 (k) + 0.5A by _{d Δωcos (Δωk + θ d)} (42) Similarly equation (19), n2 (k + 1) = 0.5n2 (k) -0.5A d Δωsin (Δωk + θ d) (43) in this case, N (k + 1) = n1 (K + 1) + n2 (k +
1) becomes the following equation from the equations (42) and (43). N (k + 1) = 0.5N (k) + 0.5A _d Δω [cos (Δωk + θ _d ) −sin (Δωk + θ _d )] (44) The above equation is nonlinear when N (k + 1) ≠ 0. Let V (k) = N (k) ^{2 as} a candidate of the Lyapunov function, and ΔN
If (k + 1) = N (k + 1) -N (k), then V (k + 1) -V (k) = N (k + 1) ^2- N (k) ² = 2ΔN (k + 1) N (k) + ΔN (k + 1) ² ) (45).

When the right side of the above equation is smaller than 0, the control system becomes stable. Expanding equation (45), ν (k + λ) −ν (k) = 2 [−0.5N (k) + 0.5A _d Δω (cos (Δωk + θ _d ) −sin (Δωk + θ _d )] N (k) + [− 0.5N (k) + 0.5A _d Δω (cos (Δωk + θ _d ) −sin (Δωk + θ _d ))] ² = −0.75N (k) ² + 0.5N (k) ΔωA _d [cos (Δωk + θ _d ) ] -sin from _{(Δωk + θ d)] +} 0.25A d 2 Δω 2 [cos (Δωk + θ d) -sin (Δωk + θd)] 2 (46) equation (29), △ ω = ω (k + 1) -ω (k) = μ
₃ (k + 1) N (k), which is substituted into the above equation, ν (k
+1) −ν (k) = − N (k) ² + N (k) ² [A _d μ ₃ (k + 1) [(cos (Δωk + θ _d ) −sin (Δωk + θ _d )) − 1] ² (47) , −√2 ≦ cos (Δωk + θ _d ) −sin (Δωk +
θ _d ) ≦ √2, ν (k + 1) −ν (k) ≦ −N (k) ² + 0.25N (k) ² [√2A _d | [μ ₃ (k + 1) |] +1] ² (48) Therefore, when 0 <[μ ₃ (k + 1)] <1 / (√2A _d ),
That is, the condition that the initial value of mu ₃ is _{0 <μ 3 (0) <} 1 / (√2A d) (49), the ν (k + 1) -ν ( k) <0. Simulations have shown that the control system becomes asymptotically stable when the appropriate initial value of μ ₃ is selected within this range and the frequency approaches the true value. −Appendix− Lemma Equations (18) and (19) regarding the proof of asymptotic stability when the observation noise is imagined represent the filter output signal when the observation noise is ignored. We consider the asymptotic stability of the adaptive suppression algorithm and the asymptotic stability of the frequency tracking method. In this case, when the filter output signal is defined as N (t) and the expression of the discrete time system is used, Expressions (10) and (3)
The following equation is obtained in consideration of 3) and (44).

N (k + 1) = N (k + 1) + N _d (50) In this case, Expressions (37) and (45) are given by ν (k) = (k) = N
(K) Rewritten as ² as follows. ν (k + 1) −ν (k) = N (k + 1) ² −N (k) ² = N (k + 1) ² −N (k) ² + 2ΔN (k + 1) N _d (51) According to the proof of 4.1, the initial value μ (0) of the adaptive correction coefficient of Expression (20) is [μ (0 )] <2√2 / A), the asymptotic stability of the adaptive suppression algorithm is guaranteed.
In this case, since it is proved that N (k + 1) ² −N (k) ² <0, it is clear that ΔN (k + 1) → 0 when k → ∞. Also, according to the proof of 4.2, the expression (2)
9) The initial value μ ₃ (0) of the frequency correction coefficient is 0 <μ ₃ (0)
If set in the range of <1 / (√2A _d ), the asymptotic stability of this algorithm is guaranteed. In this case, N (k +
Since 1) ² one N (k) ² that <0 evidenced, k
At the time of ∞, it is clear that ΔN (k + 1) → 0.

Note that, although the observation noise of the equation (10) is defined, assuming that the level of the observation noise does not fluctuate in a steady state, it is apparent that Nd has the maximum value of the following equation.

[N _d ] <Hmax (52) That is, since N _d is bounded, if the coefficient μ (0) of the Fourier coefficient modification rule satisfies Expression (38), the case where observation noise is considered This also guarantees the asymptotic stability of the adaptive suppression algorithm. Similarly, if μ3 (0) satisfies Expression (49), it can be seen that the asymptotic stability of the adaptive frequency tracking method is also guaranteed. Known Document 1 (Tsao. TC and Qian.
Y. X. ) An adaptive repetitive cont
lol scheme for tradingperiod
signals with unknown period, Proe.
Amer. contr. conf. (1993), 17
36-1740, San Francisco, CA Known Document 2 (Normal, Wild Wave) Active noise control for a plurality of periodic noises. Theory, C, 64-622, (1998), 977-
984

[0070]

According to the active magnetic bearing of the present invention, its control method and its design method, the accuracy of estimating unknown vibration frequencies can be improved and vibration can be suppressed even for a plurality of vibration frequencies. realizable.

[Brief description of the drawings]

FIG. 1 is a longitudinal sectional view of an electromagnetic attraction type active magnetic bearing according to the present invention.

FIG. 2 is a block diagram of a control method of an electromagnetic attraction type active magnetic bearing according to the present invention.

3A and 3B are explanatory diagrams of a vibration state of a rotating body when a rotation speed is 4368 rpm, where FIG. 3A shows a Lissajous waveform of the radial bearing 4 according to a conventional feedback control method, and FIG. 3C shows a Lissajous waveform of the radial bearing 3 according to the feedforward control method of the present invention, and FIG. 4D shows a Lissajous waveform of the radial bearing 3 according to the feedforward control method of the present invention. Is shown.

4A and 4B are explanatory diagrams of a vibration state of a rotating body when a rotation speed is 12052 rpm, where FIG. 4A shows a Lissajous waveform of the radial bearing 4 according to a conventional feedback control method, and FIG. 3C shows a Lissajous waveform of the radial bearing 3 according to the feedforward control method of the present invention, and FIG. 4D shows a Lissajous waveform of the radial bearing 3 according to the feedforward control method of the present invention. Is shown.

[Explanation of symbols]

 3, 4 Radial magnetic bearing (bearing control unit) 5 Cylindrical rotating body

 ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Takuchi Ueyama 3-5-8 Minamisenba, Chuo-ku, Osaka City, Osaka Prefecture Inside of Koyo Seiko Co., Ltd. Company Shikoku Research Institute F term (reference) 3J102 AA01 BA03 BA19 CA02 DA02 DA03 DA09 DB05 DB10 DB37 GA06 5H607 AA04 BB01 BB06 BB14 CC01 CC05 CC07 DD01 DD08 FF07 GG01 GG02 GG08 GG20 GG23 HH01 HH03

Claims (4)

[Claims] 1. A rotation synchronization in which the frequency of rotation changes and the frequency fluctuates and appears or disappears during rotation of the rotating body due to an unbalanced excitation force of the rotating body as a non-contact floating body. In order to adaptively suppress the periodic disturbance as vibration and rotation asynchronous vibration, adaptively correct the Fourier coefficient as a control input, generate a feedforward control signal for bearing electromagnetic attraction force control from the Fourier coefficient,
And, when there is a frequency estimation error of the periodic disturbance due to observation noise, the frequency is corrected by the frequency estimation correction rule to adaptively correct the Fourier coefficient, and the feedforward control signal is transmitted to the bearing control unit. An active magnetic bearing of an electromagnetic attraction type, wherein a rotationally synchronous vibration and a rotationally asynchronous vibration which occur during rotation of the rotating body upon input are suppressed. 2. A rotation synchronization in which the rotation speed changes and the frequency fluctuates during rotation of the rotating body due to an unbalanced excitation force of the rotating body as a non-contact floating body, and appears and disappears. In order to adaptively suppress the periodic disturbance as vibration and rotation asynchronous vibration, adaptively correct the Fourier coefficient as a control input, generate a feedforward control signal for bearing electromagnetic attraction force control from the Fourier coefficient,
And, when there is a frequency estimation error of the periodic disturbance due to observation noise, the frequency is corrected by the frequency estimation correction rule to adaptively correct the Fourier coefficient, and the feedforward control signal is transmitted to the bearing control unit. A method for controlling an active magnetic bearing of an electromagnetic attraction type, characterized by suppressing rotation synchronous vibration and rotational non-synchronous vibration generated during rotation of the rotating body upon input. 3. The method according to claim 2, wherein the vibration of the rotating body is suppressed by using a feedback control signal together. 4. The rotating body is designed by using the electromagnetic attraction type active magnetic bearing according to claim 1 or the electromagnetic attraction type active magnetic bearing control method according to claim 2. How to design the body.