JPS63308215A - Control method for magnetic bearing - Google Patents

Abstract

PURPOSE:To make it possible to control a magnetic bearing stably and still precisely by providing a means which controls inclination of a rotary shaft around the center of gravity to 0 and a means which controls position of the center of gravity of the rotary shaft to be supported to a fixed position. CONSTITUTION:A rotary shaft 1 is supported in non-contact by magnetic attracting forces of electromagnets 2A, 2B, 3A, 3B attached to both end portions of the rotary shaft 1. Together with setting a time constant of the first order lag of magnetic flux of one side of these electromagnets equal to a time constant of the first order lag of magnetic flux of the other side, magnetic attracting force of the electromagnet of this one side is made to be constant times as strong as magnetic attracting force of the electromagnet of the other side. Under this condition, magnetic attracting forces of electromagnets are corrected by compensators 6, 7 based on a set position of a displacement detecter 4 which detects displacement of the rotary shaft 1 and distances of set positions of respective electromagnets from the position of the center of gravity of the rotary shaft. On this occasion, a transfer function of a means controlling inclination of the rotary shaft 1 around the center of gravity to 0 exists as a function multiplied by fixed multiplier a transfer function of a means controlling the position of the center of gravity of the rotary shaft 1 to be supported to fixed position.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a control system for magnetic bearings, and is particularly applicable when a rotating shaft supported in a non-contact manner by magnetic attraction is physically asymmetric in the axial direction. [Prior Art] As a bearing for a rotating body that rotates at high speed or a bearing for a rotating body that requires extremely low friction, there is a support system using a magnetic bearing. Among these systems, the so-called active magnetic bearing uses the attractive force of an electromagnet to support the rotating shaft in a non-contact manner. Control of this active magnetic bearing consists of a feedback control system that detects the gap between the rotating shaft and the electromagnet and provides negative feedback to the electromagnet coil current to maintain a predetermined gap without the rotating shaft touching the electromagnet. are doing.

For example, in Japanese Patent Application Laid-Open No. 58-81217, in order to control the displacement (translational movement) of the center of gravity of a rotating body and the tilting movement (tilting movement) of the rotation axis around the center of gravity, independent control systems are used. has been established.

[Problem that the invention seeks to solve]

However, with these conventional methods, control is possible only when the rigid body motion of the shaft can be separated into translational motion and tilting motion of the center of gravity, that is, when the rotating shaft supported without contact is physically symmetrical in the axial direction. There was a problem.

On the other hand, Japanese Patent Laid-Open No. 61-211523 proposes control in an asymmetrical case in which the center of gravity of a rotating body is not located at the center of two radial electromagnets and sensors. However, this method
It is assumed that the position of the electromagnet and the position of the sensor are the same, so it cannot be applied as is when designing an actual magnetic bearing structure where the distance between the electromagnet and sensor is different from the center of gravity of the rotating body. There was a problem.

Therefore, an object of the present invention is to provide a method that can stably and accurately control a magnetic bearing even in such a case.

[Means for solving problems]

In order to achieve this object, the magnetic bearing control method of the present invention is an active magnetic bearing in which electromagnets are provided at both ends of a rotating shaft, and the rotating shaft is supported in a non-contact manner by the magnetic attraction force of the electromagnets. Displacement detectors for detecting displacement of the rotating shaft are installed on both sides of the rotating shaft, means for controlling the center of gravity of the rotating shaft is supported at a predetermined position, and means for controlling the center of gravity of the rotating shaft so that the angle of inclination around the center of gravity of the rotating shaft is 0. a first-order lag time constant of one magnetic flux of the electromagnet and a first-order lag time constant of the other magnetic flux of the electromagnet are set equal, and the magnetic attraction force of the one electromagnet is controlled to be equal to the first-order lag time constant of the magnetic flux of the other electromagnet. The magnetic attraction force of the electromagnet is corrected based on the distance from the center of gravity of the rotation axis of the displacement detector installation position and each of the electromagnet installation positions.

The transfer function of the means for controlling the tilt angle to be 0 is a function obtained by multiplying the transfer function of the means for controlling so that the center of gravity of the rotating shaft is supported at a predetermined position by a predetermined coefficient. Accordingly, a control device can be realized using control circuits having the same configuration.

〔Example〕

Hereinafter, features of the present invention will be specifically explained based on embodiments shown in the drawings.

FIG. 2 schematically shows a radial magnetic bearing device to which the present invention is applied. In the figure, 1 is a rotation axis.

The rotation axis l has two electromagnets 2A, 28.3A, 3B.
The bearings are supported by suction in the gravity direction and horizontal direction, respectively. The displacement of the rotating shaft 1 is detected by displacement detectors 4 and 5.
The outputs thereof are output to compensators 6 and 7, respectively. Pair of electromagnets 2^ and 2B and 3A and 3B
A bias current flows through the coils due to the bias attraction force, and a control signal based on the shaft displacement is added to each bias current with the same magnitude and opposite sign. At this time, it is assumed that the static characteristics of the pair of electromagnets are equal. The bias current is amplified by power amplifiers 8^, 8B, 9A, 9B, and electromagnets 2A, 2B, 3^, respectively.
It is passed through the 3B coil.

FIG. 3 shows a coordinate system of rigid body motion in the direction of gravity of the rotation axis l. Regarding horizontal motion, the gravitational acceleration g may be set to 0 in the following results.

In FIG. 3, X: displacement of the center of gravity of the shaft θ: inclination angle of the shaft xl, x2 = shaft displacement at the center of the bearing section yl-3'2: shaft displacement at the displacement detection point L1. Alx: Distance between bearing center and center of gravity L21+1
z2: Distance between the displacement detection point and the center of gravity L31: Distance between the point of external force application and the center of gravity M: Mass of the shaft J: Moment of inertia around the radial axis of the shaft at the center of gravity Fl, b: Positive direction displacement side (lower side ) electromagnet attraction force F1
□, F22: Electromagnetic attraction force d on the negative direction displacement side (lower side)
:The translational motion of the center of gravity due to external force and the tilting motion ignoring the gyroscopic effect due to the rotation of the axis are given by the following equation when the tilt angle is sufficiently small.

Af, 'r-ΔF1+ΔF+ + Afg + d
(l l)θ”'-/IIΔF+ + 112
ΔL)-8+d (2] Here, ΔFj= FlFar, Δh= A Wl (
3) For the jaw in steady state when no external force is acting, from the above equation, the equation of motion above is the variation of the suction force 11 - ΔF1 - ΔF. , h-Δh-ΔF,. (
5) can be written as follows.

A box/1+/+ + d
(6) Jθ = luA + /11/l-m, d (7) On the other hand, when the axial displacement and the change in the electromagnet's magnetic flux are sufficiently small, the variation in the attractive force can be expressed by linear approximation as follows: . However, it is assumed that the shaft is supported at the center of the bearing in a steady state. For 1=1.2, f・−−haq・
(8) 11t(l+ q, -
a, sxt = b, cl (91 where, ・,・−mugi c,, (l + (Iwa) 1 go (12) b,
= 4, (1,000 Iwa) (13) In the above equation, k, mu: twice the attractive force coefficient of the lower electromagnet q1: variable T1, which is equivalent to magnetic flux and has the unit of current. First-order lag time constant of magnetic flux aI3: Constant that indicates the degree of change in magnetic flux (attractive force) due to changes in the gap between the electromagnet core and the shaft b1: Constant that indicates the magnitude of increase in magnetic flux (attractive force) due to the control input terminal CI: Control input Terminal F+o: Bias attraction force of the lower electromagnet Bo: Bias coil current of the lower electromagnet KPI: Attraction force constant xIo: Gap between the electromagnet core and rotating shaft, long radial gap of the bearing) CMI: Coefficient determined by the shape of the electromagnet (0<C,l<1
) 1120: Upper electromagnet coil bias current 1'@
l: Gradient of power amplifier input terminal-output coil current characteristics Also, the attractive force constant KF is given by the following equation.

Here, CF: Coefficient μ determined by the shape of the electromagnet. - The magnetic permeability of air (-4πx 1O-7H/m) A, the cross-sectional area N of the electromagnet core, and the number of turns of the coil. Therefore, the overall dynamic characteristics are expressed as follows.

Ar1” ktlq juice kB (h+d (
14) Jθ=-1, and 7. qket11□ktrQz lh
+d (+51T1ql 10q, -aI, xl=
b1e1(16)Tr(h+(h-(lnXr = b
rer (+7+This equation of motion can also be expressed using the displacement of the bearing part. That is, by using the relationship obtained from FIG. 3, the following equation can be obtained from equations (14) and (15).

Here, the above equation is an interference system between xl and z2 when a12≠0, but is it generally quite difficult to make these two variables non-interfering? J (This is complicated. In addition, it is not necessarily desirable in practice to make the two bearings non-interfering.

From the positional relationship shown in FIG. 3, the following relationship exists between the displacement of the bearing center and the displacement of the displacement detection point with respect to rigid body motion.

The dynamic characteristics of the shaft displacement are expressed by equations (16), (17), (19)
When expressed using (21), the block diagram becomes as shown in FIG.

In equations (12>, (13)), the ratio of bias current is expressed by equation (11) of attraction force and relational equation (3) of bias attraction force.
, (4) is expressed as follows.

(231) Next, we will explain the separation of translational motion and tilting motion.Now, regarding the two bearings, the magnetic flux Assume that the delay time constants of are equal and the ratio of the attraction force coefficients is given appropriately.In other words, Condition 1 T meeting T, = T2 (241 Condition 2 p, meeting!!-L= =亙p Yu 7,111, 2. (25) At this time, the equations of motion (14) to (17) are separated into translational motion and tilting motion as follows.

Here, XR meeting-1, θ= (r+ r+)/2
(281Condition 2 of formula (25) is formula (10), (
12), (22), and (23), it can be expressed as follows.

h=βfriend+-L-(β-1)blood! ! ! ! L(31)Fl
,ll,4muF,.

Here, β knee - Cl12 1+* In other words, condition 2 is the bias attraction force of the electromagnet, taking into account the shape of the electromagnet, the bearing clearance, and the position of the center of gravity, and formula (31)
It is to give so as to satisfy. Considering the case where the shape of the electromagnet and the bearing clearance are equal (β d1), this condition indicates that the moments around the axle load 6 created by the two sets of lower bias attraction forces are balanced.

Since each controlled object is separated into a third-order system, control laws can be determined independently. Regarding the translational system equation (26), the feedback control law U, (s) = −C(
s) .

X(s) = −'−”−D(sl
(33n2#(s) 11(s)=4(Ts+l)s”+kt+ [bac
(s)4(7,] (Similar to 341, (/2(sl = -CxCslXa(s)
(Considering 351, X5(s)=Blood-""D(s) (3
61271Ha'5) Jin(s) =2<F (Ts +1 +5' +
&/heart+C5(S) ',','(1,sJ (
371 The characteristics of this output and displacement detection section are expressed as follows using the relationship shown in FIG.

Y・(・)=÷(±10~Yel) X(Ts+11D(sl (39a)Y・
(•)=Kei (±-Chitou) x(Ts+IID(sJ) (39b) Next, the configuration of the control system will be explained.

From equation (29), the actual control human power is expressed as follows.

Therefore, using equations (32) and (35), and from FIG. 3, the following relationship can be obtained.

From the above, the configuration of the control system is as shown in FIG.

The mode separation described above can be considered to be achieved by equalizing the two control forces, as inferred from the form of the control force e2 in equation (40) or the Bronk diagram in FIG. Equations (19), (16).

(17) can be written as follows using conditional expressions (24) and (25).

Here, Qr = f)hQz,' e: = 1! -! −”'
th (44)b.

From the equation of motion above, it can be seen that the influences exerted by the two bearings are fairly well aligned.

In other words, separation of the two modes is considered to be achieved by making the bearing system nearly symmetrical in terms of software.

By the way, the compensation elements C(S) and CR(S) of the control system mentioned above
) could be determined independently. On the other hand, the two modes are both cubic systems, and one with the same characteristic equation can be selected as the optimal characteristic. Formula (34)
(37), the characteristic equation H(S)-〇.

The following relationship is obtained as a condition for HR(S)=O to be equal.

Cm(s)= &C(s)+-! -PL-'1 (rose on 1-)711 (ll, J = kC(s)-1--a+* (45)/+
b-111In Here, k: French (46) In the above formula, C* (S) is the degree of interference between bearings a12 (
(see equations (19), (20)), C(S
) is a form in which the gain of the proportional operation is adjusted or subtracted.

On the other hand, in terms of simplifying the control system, it is conceivable to match the shapes of the two compensation elements. That is, Cp(s)=
kC(s) (47) This means that two modes are compensated with the same compensation element, so
To determine C(S), it is necessary to consider both modes. For this purpose, the following characteristic equation, which is a neutral compromise between the two, is considered appropriate.

#o(s) =2 (Ts+1)S'+kl
+X[b, C(s)-Fσ, (-#+-F%')]
(, +sl At this time, the characteristic expressions for both modes are written as follows.

tt(s) = tlo(s)-h, ao
(+19+Ib(s) = &[/Io(s)+
kt + ao) (50) Here, ... = 〒 seat (1 - ÷) = L loss... (51)
The compensation element C(S) may be determined so as to have a sufficient stability margin with respect to characteristic equation (48). For this purpose, a term a related to the degree of interference between bearings is required. What is necessary is to set the proportional operation gain to a sufficiently large value.

When the compensation element is given by equation (47), the control human power equation (41) is expressed as follows using equation (42).

E+(s) = -CCs)(pn y+(5) 10pl
ff )'+(s) ) (52a) Here, at this time, the configuration of the control system is expressed as shown in FIG. Compared to FIG. 5, the configuration of FIG. 1 is significantly simplified. This is a feature of the present invention.

Next, calculation of frequency characteristics will be explained.

As a disturbance acting on the system, consider an actual case and consider an external force that acts directly on the axis. However, when experimenting with frequency responses, it is generally difficult to apply a sinusoidal external force directly to the shaft. Therefore, instead, consider adding a sine wave human power to the control input signal to the power amplifier to vary the coil current and thereby vary the attraction force.

The input signals are γ1(t) and γ2(t), and the human power signal of the power amplifier is given as follows.

When the above equation is used in place of eI+''2 in equation (29), 1, -1.- te, U I (S), I/ 2 (S
) Lt, equation (29) and Sunawachi equation (32).

It is given by (35).

Expression (55) is converted into “In u2” of expressions (26) and (27)
As can be seen by comparing the following equations (33) and (36) with the above equation, the human power in the power amplifier population is delayed by the magnetic flux delay compared to the direct external force.

In order to treat the two modes independently in experiments, R,, R2 must be given so that the other becomes 0 in equation (56). The responses are shown below.

Translation mode: /? 1(s)=Blood” /?+(s) 'Ht)-be (58)/Y(5
) = ” ”” /?+(sl (59)
/121f(s) Tilt mode: )Us) = “” /? +(s) (
61) IIR<s) On the other hand, the relationship b+ between equations (56), (57) and Fig. 3
−by 3+1 = x +πx*, y* −x−5xa
(From 62+, the relationship between the human power #, (s), R2 (s) and the output y, (s), )'2 (S) is given as follows.

Y+(S)= person kl+lB (fun+separate stripping)””+
', kBbx (mei-wkato) R"5) (63a3"'
= 2"" (//L) 'l: 硼平(sl)""The above equation is the block diagram of FIG. 5 or equation (43).

It can also be obtained from (41), (54), and (62), but
The calculation is quite complicated. In particular, it requires a considerable amount of calculation to show that the characteristic polynomial can be factorized into two modes: translation and tilt. This means that for a symmetrical bearing system,
This illustrates the complexity of handling asymmetric bearing systems, compared to the fact that for any symmetrical control law the characteristic polynomial immediately factorizes into two modes.

〔Effect of the invention〕

As explained above, in the present invention, a controller having a common transfer function is used as a configuration of the control means for controlling translational motion and tilting motion. Therefore, even in actual equipment in which the magnetic bearing installation position and the displacement detector installation position are shifted from the center of gravity of the rotating shaft, highly accurate control can be easily realized.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing the configuration of a control system according to the present invention,
Figure 2 shows the configuration of the active magnetic bearing control device, Figure 3 shows the configuration of the active magnetic bearing control device.
The figure is an explanatory diagram of the rigid body motion coordinate system of the rotating shaft, FIG. 4 is a block diagram of the object to be controlled by the magnetic bearing system, and FIG. 5 is a block diagram showing the configuration of the control system using mode separation. Rotating shaft 2A, 2B, 3A, 38: Electromagnet 4.5: Displacement detector 6, 7: Compensator 8A, 8B, 9A, 9B: Power amplifier Patent applicant Anyo Electric Manufacturing Co., Ltd. Agent
Masu Kobori (2 idiots) Figure 1 Figure 2

Claims (1)

[Claims] 1. In an active magnetic bearing in which electromagnets are provided at both ends of the rotating shaft and the rotating shaft is supported in a non-contact manner by the magnetic attraction of the electromagnets, displacement of the rotating shaft is provided on both sides of the rotating shaft. means for controlling the position of the center of gravity of the rotating shaft to be supported at a predetermined position; and means for controlling the angle of inclination of the rotating shaft around the center of gravity to be 0. and setting the first-order lag time constant of one magnetic flux of the electromagnet to be equal to the first-order lag time constant of the other magnetic flux, and setting the magnetic attraction force of the one electromagnet to be a constant times the magnetic attraction force of the other electromagnet, A control method for a magnetic bearing, characterized in that the magnetic attraction force of the electromagnet is corrected based on the distance of the displacement detector installation position and each of the electromagnet installation positions from the center of gravity of the rotation axis. 2. The transfer function of the means for controlling the tilt angle to be 0 is a function obtained by multiplying the transfer function of the means for controlling so that the center of gravity of the rotating shaft is supported at a predetermined position by a predetermined coefficient. A control method for a magnetic bearing according to claim 1, characterized in that: