FR2634527A1 - ADJUSTING SYSTEM FOR MAGNETIC BEARING - Google Patents

Abstract

An adjustment device causes movement of a movable member magnetically supported in accordance with a control signal. A feedback circuit 1, 2, 3, 4, 6 detects the displacement of the member 15 for its servo control, in order to ensure the stability and robustness of the magnetic levitation system 7. A direct-acting compensator 8 to 12, with input terminal 14 for the control signal and with output terminal 11 connected to the feedback circuit, cooperates with the feedback circuit to produce the displacement of the member 15 according to the signal applied to the input 14. Applicable to positioning of a table in semiconductor fabrication and vibration micromachining.

Description

* 1 Adjustment system for a magnetic bearing The present invention

  relates to an adjustment system for a magnetic bearing using the magnetic attraction force of an electromagnet and serving to support a mobile member rotating at high speed with high precision by positioning the movable member

by magnetic means.

  From the point of view of the theory of tuning, a magnetic bearing using the magnetic attraction force of an electromagnet is classified as an unstable system. Indeed, it has a pole on the real axis of the right half of the complex coordinate system. This instability can be well understood by considering the following physical phenomenon occurring in a magnetic bearing. If a closed-loop control device were not provided for such a bearing, the electromagnet would fix the movable member when the

  Magnetic attraction force is excessive or

  would distance the moving organ when the

attraction force is too weak.

  A compensator is therefore necessary to stabilize the bearing. This compensator can act to stabilize the entire system forming the magnetic support structure and to ensure its robustness. However, complicated adjustment work is required to achieve both stability

  sufficient magnetic levitation and a robust

  sufficient capacity, that is, to obtain a func-

  in which the disturbances are suppressed with a sufficient margin. In such a situation, it would be quite difficult to add a setting control to move or position the moving member in response

  to a control signal applied to an input.

  This situation can be explained theoretically

  as follows. As is evident from the Report of the Japanese Mechanic Society, "Vol. 255, 1967," when a magnetically supported member is subjected to gravity m and a force of electromagnetic attraction F applied in the opposite direction to the organ, the kinetic equation for the organ supported in the Z direction is as follows: m dz -dtz = mg-F (Z, I). (1)

  Since mg = F (Z0, I1) is established at a point of equilibrium

  free, the relation (1) is developed in terms of small displacements z and i, as indicated below: m dZ (Zo + z) a F aF = - .. = (zd- + ij) g dtz DZ aI dz ! d2 z * -z - = --- - (2) P dtz o B = 2g / Z0, km = Z 0/2 (I + A

  F KF (I + IA) Z and IA: remanent compensation.

  If the state variable is represented by x = T [Z, Z], the state equation is as follows:

x = Ax + bi, y = cx -

  A2 (011), b = C = (1, 0 Therefore, the transfer function P (s) of the set object is represented as follows: P km P (s) = c (slz -A) - 'b =. ..-- (4)

s -

  It follows from the transfer function (4) that the magnetic bearing is an unstable system having a pole s = v B on the real axis of the right half of the

complex coordinate plan.

  Figure 2 shows a setting device

  Conventional closed loop for a magnetic bearing.

  The displacement of the supported member is detected by a displacement detector 1. A detection signal of this detector is applied to an integral compensator 2 to improve the stability characteristics. A phase compensator (3) then performs signal processing in order to maintain the s = VB pole of the unstable set object on the stable side. Finally, an electric power amplifier 4 is suitably driven to activate an electromagnet 7 so that the set object 15, representing the object or the supported member,

  be kept in place in a gap.

  To indicate the characteristics of

  In the closed-loop system, the sensitivity S (s) and a complementary sensitivity T (s) are introduced, as follows: S (s) = (1 + P (s) C (s)) 1 T (s) ) = 1 - S (s) --- (5) C (s): transfer function of the entire compensator.

  We know that relation (5) indicates the

  bility and robustness. Figure 3 shows an example of the operating characteristics. In order to establish a balance between stability and robustness, it is desirable to adjust a transfer frequency without changing the forms of S (jw) and T (jw). However, by looking more closely at the relation (5), it can be seen that there is no compensator parameter making it possible to adjust only the transfer frequency. The variation of any parameter of the compensator would cause the change of the forms of S (jw) and T (j) as well as that of the transfer frequency between them. In other words, to strike a balance between

  stability and robustness, it is necessary to adjust

  several compensator parameters. In such a situation, it is relatively difficult to establish a certain level of response sensitivity to control signals applied to an input to move

  the supported member according to these signals.

  In the systems of the prior art, it takes a considerable time to establish a balance between stability and robustness throughout the system, which is due to its complicated operation. Therefore, although the conventional system can establish a stable magnetic levitation state during actual operation, it has the disadvantage that it does not achieve at the same time a certain

  sensitivity level of response to a communication signal

  mande. In order to eliminate the drawback mentioned above, one of the aims of the present invention is to add to the conventional closed-loop control device, which has demonstrated that it makes it possible to obtain

  stable and safe practical operation, compensation

  direct acting or precompensator in order to create a response sensitivity to a control signal and thereby to enable the movement of the magnetically supported member to be controlled in accordance with this control signal.

  According to the invention, therefore, a compensation is

  direct action to give the system the

  desired response sensitivity to communication signals

  mande. It thus becomes possible, while maintaining the stability and robustness conditions of the magnetic bearing by means of the conventional feedback control, to produce the effective displacement of the supported member in accordance with a control signal applied to an input. The direct acting compensator, added according to the invention, acts indeed as a signal source which converts the frequency response characteristic of the conventional control device - having stalls at a relatively low frequency - into a

  desired frequency response characteristic.

  According to the invention, an adjusting device for producing the displacement of a magnetically supported movable member in accordance with a control signal is characterized in that it comprises: - a feedback circuit for detecting the displacement of the movable member for the servo control of this member to thereby ensure the stability and robustness of the magnetic levitation; and - a direct acting circuit having an input terminal receiving the control signal and an output terminal connected to the feedback circuit, and cooperating with the feedback circuit, without disturbing the stability and robustness of the magnetic levitation, for produce the displacement of the organ

  mobile in accordance with the control signal.

  According to another characteristic of the invention

  the direct feedback circuit, forming the compensa-

  direct-response receiver, has an output terminal connected to an input port of the

electric power.

  Other features and benefits of

  the invention will become clearer from the description of

  following examples of non-limited

  and annexed drawings in which:

  FIG. 1 is a block diagram of a device

  adjusting device according to the invention for a magnetic bearing; FIG. 2 is a block diagram of a conventional adjustment device for a magnetic bearing; FIG. 3 is a diagram representing the S-T characteristic; FIG. 4 is a diagram representing the frequency response for a command in which the value e contains an error; FIG. 5 is a diagram showing the response curve as a function of time for a command in which the value 8 contains an error; FIG. 6A is a diagram showing the measured result of the frequency response for a command according to the prior art; FIG. 6B is a diagram showing the measured result of the frequency response for a command according to the invention; Fig. 7A is a diagram showing the measured result of the response for a scaled control input signal of the prior art; FIG. 7B is a diagram showing the measured result of the response for a stepped control input signal according to the invention; FIG. 8 is a schematic perspective view of a positioning table device to which the invention is applied; - Figure 9 is a schematic section showing the spindle of a machine tool to which the invention is applied; FIG. 10 is a diagram showing the frequency response for commands in

  conventional adjustment devices and according to the invention.

  tion; Fig. 11A is a diagram showing the time behavior at f = fl for the conventional control device of Fig. 10; FIG. 11B is a diagram showing the

  response as a function of time at f = f2 for the device-

  Fig. 10C is a diagram showing the response as a function of time at f = fl for the adjustment device according to the invention of Fig. 10; FIG. 11D is a diagram showing the response as a function of time at f = f2 for the adjustment device according to the invention of FIG. 10; and - Figure 12 is a diagram showing an embodiment of the direct acting compensator according to the invention. The invention will now be described in more detail with reference to the drawings. Figure 1 is a diagram showing the structure of the adjusting device

  according to the invention for a magnetic bearing. accordance

  In this figure, the adjustment device comprises a closed loop composed of a displacement sensor 6, a displacement sensor 1, a compensator

  integral 2, a phase compensator 3 and an ampli-

  electric power indicator 4 to stabilize the magnetic support structure by a servo control. To this closed loop is added a direct-acting compensator 13, which is composed of different elements comprising a low-pass filter 8 (hereinafter referred to as "LPF"), a high-pass filter 9 (hereinafter referred to as " HPF "), a gain regulator 10,

  a differential amplifier 11 and a compensating filter

  12 (hereinafter referred to as "CF"). Transfer functions of the various elements are suitably adjusted to obtain the desired frequency response characteristic for the displacement of a supported member 15, movable, under the effect of a signal of

  control applied to an input terminal 14.

  It should be noted that the addition of compensation

  direct acting unit 13 does not disturb the steady state of support of the supported member 15

magnetic.

  In the following, we will indicate the transfer functions for the different transfer elements that constitute the compensator 13 direct action. LPF filter 8 is assigned the transfer function GLPF (s) having the optimal frequency response characteristic desired by the one designing the system, which function is represented by: m GLPF (s) ......... (6) (s / a) + (s / w I) + ow 1 determines the bandwidth and a1 determines a

damping factor.

  The transfer function GHPF (s) is assigned to the series connection of the HPF filter 9 and the gain regulator 10 and this function is represented by: is 52 n GH r F (S) = -----. (7) (s / l) Z + aX (s /) + I Indeed, GHPF (s) has a denominator formed by a

  polynomial of the second degree, having identical coefficients

  with those of the polynomial of the second degree in the

  denominator of GLPG (s) indicated by relation (6).

  According to relations (6) and (7), the transfer function GDIF (s) is determined for the

  direct acting compensator 13, between the terminal block

  14 for the control and the output terminal of the differential amplifier 11, and this function is represented by:! s 1

G D F (S) = --- (8)

  kg. kmn (s /,) Z -i a, (s /,) +1 o 1 / KInKmn represents the gain of the amplifier

differential 11.

  The filter CF12 serves to compensate for the distortion of the frequency response by the control value, which distortion is caused by the error due to the

  modeling of the set object. In this mode of

  The transfer function of the filter CF12 is set to 1. When the transfer functions are adjusted as described above for the different transfer elements of the direct-acting compensator 13 and the following relations: Bn KIn = KI 'Kmn = Km ---- (9) n = 'Kin = K'iKmn Km are satisfied, the transfer function Gzh (s) of the input terminal 14 (r) for the control signal to the displacement of the organ supported 15, is adjusted as follows: Gzr (s) = GLPF (S) .. ...)

(s / u) Z + a, (s /,) ±

  Indeed, the transfer function Gzr (S) can be

  made equal to the transfer function GLPF (S), the

  what is given as the optimum characteristic according to the desires of the designer. In general, it would be relatively difficult to provisionally establish such a situation of concordance with the model at the moment

of the circuit design.

  So, if *, K K and Kmn k, the transft function Gzr (S) is represented as follows transfer function Gz (S) is represented as follows! k! km Gzr (S) = x

(s / @,) z +; J, (s / e),) +! k ,. k ..

  k1. k.n ktoop (SZ / P.-I) (1 + T ze) (1 + Tzs) + '(1+ ri) (1 + Tis) k. km (s2 / f 1) (1hr zs) (I + Tzs) + ktoop (lt rts) (1 + Tis) LOOP KBOUCLE = KsKpKIKm. By fitting n to, KIT to K T and Kmn to Km, the transfer function Gzr (S) represented by the general relation (11) can be modified so that it becomes equal to the one represented

by the relation (10) specific. -

  The parameter l / KINKmn refers to the gain of the differential amplifier 11 and can therefore be tuned without difficulty. In addition, the l / n parameter can also be tuned without difficulty by regulating the gain regulator 10 mounted subsequent to the HPF9 filter. Such adjustment or tuning operations are illustrated schematically in FIGS. 4 and 5.

  case KIN K Kmn = Km and B n = B, the frequency response

  quential is shown in Figure 4 and the characteristic

  In the figures, e + 20 indicates a deviation of + 20% from the value 0. Therefore, while monitoring the characteristic curves represented by FIGS. 4 and 5, the gain of the regulator 10 is tuned to match the response characteristic

  in frequency to that fixed by the relation (6).

  The different elements making up the compensation

  direct acting 13 have the functions of trans-

  fert represented by relations (6), (7) and (8). The particular structure of the circuit can be designed in different ways to perform these transfer functions. FIG. 12 is a diagram of an embodiment of the direct acting compensator circuit

  according to the invention. In this scheme, a circuit 23 consis-

  LPF8, a circuit 24 constitutes the filter HPF9, a circuit 25 constitutes the gain regulator 10 and a circuit 26 constitutes the differential amplifier 11. As for the compensating filter CF12, the structure of

  its circuit can not be uniquely determined

  void, so that this filter is indicated simply by a block, because it aims to compensate finely for the distortion of the frequency response caused by the deviation from an ideal model of the set object, such as indicated by relation (4). Such a scheme makes it possible to produce a compensator 13 with direct action

according to the invention.

  The operation of the adjustment device according to the invention will be described below in relation to various characteristic diagrams. In the example described below, the adjustment device is applied to a magnetic bearing structure which supports a movable member with a weight of 7.8 kg-, having a set of 300 im on each side. FIG. 6A shows the frequency response in the case of a control device

  Convention and Figure 6B shows the frequency response

  quential in the case of the device according to the invention.

  As can be seen in FIG. 6B, the device according to the invention has a flat characteristic having an enlarged frequency band and represents an improvement in that it responds well to the control signal applied to the input. FIGS. 6A and 6B show a distortion of the frequency response (a decrease followed by a rise) around the frequency of Hz, which distortion is caused by a mechanical resonance. Although this distortion of frequency response due to mechanical resonance is not suppressed in this embodiment, it may be appropriate to introduce a compensating function for

  eliminate this distortion using the CF12 filter.

  Figures 7A and 7B show the results of

  states of a test response to a scaled control signal applied to the input. Figure 7A relates to the conventional control device and indicates the existence of a considerable overshoot and a relatively long time for stabilization. On the other hand,

  FIG. 7B, referring to the device according to the invention.

  tion, does not indicate overtaking and shows a time

  short to reach steady state.

  The advantages provided by the invention

  can be better understood by reading the description

  which will follow industrial applications of the pre-

  this invention. FIG. 8 is a first example of application to a positioning table 17 supported and positioned magnetically by means of two electromagnets 16a and 16b and on which is placed a

  slab 18 for integrated circuits. A table of posi-

  17 of this type is normally fitted with a

  important game in order to obtain the necessary displacement.

  Therefore, it is not easy to obtain conditions of high rigidity and normally the rigidity obtained is low. In this case, the response to the application of a control signal to the input, response constituted by the displacement of the table, is slow. However, by using the adjustment device according to the invention, the positioning table 17 can be moved at high speed, without exceeding, which

  improves its operating characteristics.

  Figure 9 shows a second application.

  tion of the device according to the invention relating to the spindle of a machine tool having a motor 23, displacement sensors 24 and an axial displacement sensor, which spindle is supported by electromagnets 19a and 19b and by an axial electromagnet 19c. A machine tool spindle of this type can be used for vibration machining. For such machining, a sinusoidal signal is applied to the input as a displacement control signal, in order to axially vibrate a rotational member 20, magnetically supported, in order to reduce the energy required for machining. The "Tarchan Company" in the United States of America has reported that by applying a vibration of an amplitude of 0.05 to 13 mm and a frequency of 2 kHz to the rotary member 20 in the thrust direction of this here, the cutting energy can be reduced up to 50%. As stated in this

  ratio, the amplitude of the sinusoidal signal and the frequency

  Vibration conditions are parameters that must be adjusted during work. With a conventional adjustment device, having only one answer

  frequency with closed loop, the parameters of

  They can not be adjusted freely due to the resonance characteristic of the closed-loop system and because of the stalls at relatively low frequencies. On the other hand, if, in accordance with the present invention, a direct acting compensator is added to the conventional control system in order to create the desired response sensitivity to the control signal, the disadvantage which has just been indicated can be avoided. prior art. The situations described above are illustrated schematically in FIGS. 10, 11A, 11B, 11C and 11D. In FIG. 10, showing the frequency response to the control signal, the dashed curve applies to the conventional adjustment device and the solid line curve applies to the device according to the invention. FIGS. 11A and 11C show the behavior as a function of time at the frequency f = f1 respectively for the conventional device and the device according to the invention, indicating good characteristics for monitoring the input signal in both cases. On the other hand, FIGS. 11B: 4 and 11D show the behavior as a function of time at the frequency f = f2 for the conventional device and the device according to the invention respectively, from which it appears that the response amplitude is reduced in the conventional device. On the other hand, with the adjustment device according to the invention, a good tracking characteristic of the input signal is obtained. During the vibration machining described above, using the adjusting device according to the invention, a tool 22, see FIG. 9, is driven at high speed and with a high precision for cutting into a workpiece 21.

  view of the execution of a micromachining.

  As is clear from the foregoing, the

  The invention provides considerable industrial benefits without compromising the reliability provided by the

  conventional setting during normal operation

tick.

Claims (5)

  1. Adjustment device to produce the displacement   cement of a magnetically supported mobile member in accordance with a control signal, characterized in that it comprises: - a feedback circuit for detecting the displacement of the movable member (15) with a view to the servocontrol of this organ to thereby ensure the stability and robustness of the magnetic levitation system; and - a direct-acting circuit (13) having an input terminal (14) receiving the control signal and an output terminal (on 11) connected to the feedback circuit, and cooperating with the feedback circuit, without disturbing the stability and robustness of the magnetic levitation system, for producing the displacement of the movable member (15) in accordance with with the control signal.   2. Adjusting device according to claim 1, wherein the feedback circuit comprises a closed loop composed of a displacement detector (1), an integral compensator (2), a compensator   phase (3) and an electric power amplifier   (4) to provide magnetic levitation.   An adjusting device according to claim 2, wherein the direct acting circuit (13) has an output terminal (on 11) connected to a gate   input of the electric power amplifier (4).   An adjusting device according to claim 1, wherein the direct-acting circuit (13) comprises a low-pass filter (8) connected to the input terminal (14), a high-pass filter (9) connected to the input terminal (14), a compensating filter (12) for compensating the output signal of the low-pass filter (8), a gain regulator (10) for regulating the gain of the output signal of the pass filter -haut (9), as well as a differential amplifier (11) for the differential processing of the output signals of the low-pass filter and the high-pass filter.   An adjusting device according to claim 4, wherein the low-pass filter (8) has a transfer function having a pre-adjusted poly-denominator according to the response characteristic desired at the control, and the high-pass filter (9). ) has another transfer function comprising another denominator having coefficients identical to those of the polynomial denominator of the function of transfer of the low-pass filter.