JP3452305B2 - Magnetic levitation body positioning device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a magnetic levitation body positioning apparatus capable of accurately positioning a magnetic levitation body at a target position, and more particularly to a magnetic levitation body positioning apparatus that can be positioned while moving the magnetic levitation body.

[0002]

2. Description of the Related Art A magnetic levitation body positioning device is a device for positioning a magnetic levitation body levitated in the air at a specific target position by supporting it in a non-contact manner by the electromagnetic force of an electromagnet generated by supplying a predetermined electric power. is there.

An outline of positioning the magnetic levitation body at a target position by this magnetic levitation body positioning device is as follows.

When the current position of the magnetic levitation body is detected by a displacement sensor or the like provided in the positioning device, the control device for controlling the electromagnet positions the magnetic levitation body from the current position to the target position by the arithmetic means inside the electromagnet. The electromagnetic force to be applied above and the electric power to be supplied to the electromagnet corresponding to the electromagnetic force are obtained. Then, the magnetic levitation body is positioned at the target position by the action of the determined predetermined electromagnetic force.

The magnetic levitation apparatus positioning device has the following advantages because it is a mechanism that can perform positioning without contact. That is, in the case of a mechanical positioning mechanism, positioning is performed through a mechanical sliding member, so there is a limit to the positioning accuracy due to mechanical distortion, friction, etc. of the sliding member. Therefore, for example, in the case of fine processing, it is necessary to position the processing tool with high accuracy in accordance with the required high processing accuracy, but there is a limit to the positioning accuracy of the processing tool. There was a limit to the improvement in accuracy.

According to the positioning device for the magnetic levitation body, since the positioning can be performed by a non-contact mechanism without using a mechanical sliding member, it is possible to position the above-mentioned processing tool and the like with high accuracy. Further, in the case of the example of the fine processing, depending on the object to be processed, there is a thing which dislikes the fine dust generated by the mechanical sliding mechanism, but a magnetic levitation body positioning device can perform non-contact positioning. Therefore, the problem of such fine dust can be solved.

[0007]

In a conventional magnetic levitation body positioning device, for example, as is seen in the positioning of a magnetic bearing, control is performed so that the magnetic levitation body is positioned at a specific target position and made stationary. Was intended to do.
Therefore, it has been impossible to position the magnetic levitation body sequentially to the target position that changes with time, that is, to position the magnetic levitation body while moving it along the target trajectory composed of a plurality of target positions to be positioned.

Therefore, in the case of performing fine processing, there is a case where it is desired to move the processing tool along the target trajectory to perform positioning with high accuracy for processing, but according to the conventional magnetic levitation body positioning device, It was not possible to position it with high precision while moving it.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide a magnetic levitation body positioning apparatus capable of highly accurately positioning a magnetic levitation body while moving it along a target trajectory.

[0010]

In order to solve the above problems, a magnetic levitation body positioning apparatus according to the present invention comprises a magnetic levitation body in which a pair of coils arranged facing each other on the outside of the magnetic levitation body constitutes one set. An electromagnet that exerts a predetermined electromagnetic force on a magnetic levitation body, the non-linear dynamic characteristics of which can be approximated by a combination of a plurality of basic functions, and an electric magnet for generating a predetermined electromagnetic force on the electromagnet. Control means for outputting a control signal for controlling the magnetic levitation body, position detection means for detecting the position of the magnetic levitation body, and target trajectory input means for inputting a target trajectory which is a positioning target position of the magnetic levitation body and which changes with time. And a command position calculation means for calculating a command position for the magnetic levitation body based on the target trajectory, and a control from the command position and the position of the magnetic levitation body. Control signal calculation means for calculating a signal, the control signal calculation means for performing a calculation including a nonlinear parameter based on the mechanical characteristics of the electromagnet including a gain parameter consisting of a proportional gain and a differential gain and an external force elimination term, A parameter modifying means for modifying the non-linear parameter, the parameter modifying means comprising:
The gain parameter is corrected based on the first correction factor based on the error between the position of the magnetic levitation body and the target position, the basic function and the correction signal factor, and the external force is corrected based on the first correction factor and the basic function. The erase term is modified to move the magnetic levitation body along the target trajectory (claim 1).

Originally, when attempting to position a magnetic levitation body at a specific target position by an electromagnet, the electromagnetic force to be applied to the magnetic levitation body should be determined based on the mechanical characteristics between the levitation body and the electromagnet. Is. The dynamic characteristics between the levitation body and the electromagnet show non-linearity in which the gap, which is the distance between the electromagnet and the levitation body, is not proportional to the electromagnetic force.

Incidentally, in the conventional magnetic levitation body positioning device, it is not always necessary to control the electromagnet in consideration of the non-linear characteristics of the electromagnet. That is,
In the conventional positioning of the magnetic levitation body, for example, as seen in the positioning of the magnetic bearing, the purpose is to position and stand still at a target position. Therefore, the control of the electromagnet could be easily performed by the linear approximation of the mechanical characteristics of the electromagnet in the region where the gap is small.

However, when it is desired to position the magnetic levitation body in order to the target position which changes with time, that is, to move the magnetic levitation body along the target trajectory,
It is necessary to be able to control the electromagnet in the region where the gap is large, and in such a case, the electromagnetic force to be applied to the electromagnet needs to be obtained based on the non-linear mechanical characteristics between the levitation body and the electromagnet. That is, it is necessary to control the relationship between the levitation body and the electromagnet while reflecting the nonlinear mechanical characteristics.

According to the positioning apparatus of the present invention, the control that reflects the nonlinear mechanical characteristics of the electromagnet is possible as described below, and therefore the magnetic levitation body can be positioned while moving along the target trajectory. .

In the positioning device of the present invention, the control signal calculation means performs calculation including the command position calculated by the command position calculation means and the nonlinear parameter associated with the nonlinear mechanical characteristic of the electromagnet. The control signal for the electromagnet is calculated.

Here, the calculation of the command position based on the target trajectory by the command position calculating means is performed by the target position forming the target trajectory, the first-order differential coefficient with respect to the target position and the second floor with respect to the target position. It contains the derivative of.

The non-linear parameter associated with the mechanical characteristic of the electromagnet is adjusted by the parameter correction means until the position of the levitation table detected by the position detection means can be matched with the target position of the target trajectory. , Will be fixed repeatedly. Thereby, according to the positioning device of the present invention, the non-linear parameter is corrected until it reflects the non-linear dynamic characteristic between the levitating body and the electromagnet. As a result, the control signal output from the control means to the electromagnet reflects the non-linear dynamic characteristics of the electromagnet, and therefore the positioning of the levitation table can be performed based on the dynamic characteristics of the electromagnet. it can.

Therefore, according to the positioning device of the present invention,
The electromagnet can be controlled in the region where the gap is large, and the floating table can be positioned while moving along the target trajectory.

When the basic function is a basis function (claim 2), the nonlinear parameter between the levitation body and the electromagnet is made more efficient in correcting the nonlinear parameter by the parameter correcting means. Since it can be reflected as desired, it is easy to modify the nonlinear parameter.

The electromagnet includes two sets of coils arranged along one axis of two orthogonal axes and one set of coils arranged along another axis, and the command position calculation is performed. The means performs a calculation including an inertial parameter of the magnetic levitation body which is a non-linear parameter, and the parameter correction means applies a second correction factor based on an error between the position of the magnetic levitation body and a target position and the target trajectory. When the inertial parameter is modified based on the acceleration factor (claim 3), rotation of the magnetic levitation body can be suppressed, so that the positioning of the magnetic levitation body can be performed with higher accuracy. be able to. That is, also with respect to the inertial parameter related to the control of the rotation of the magnetic levitation body, the parameter correction means until the position of the levitation table detected by the position detection means can be matched with the target position forming the target trajectory. It is repeatedly corrected by. As a result, the control signal output from the control means to the electromagnet can suppress the rotation based on the mechanical characteristics of the electromagnet.

Here, the inertial parameters include the moment of inertia of the magnetic levitation body and the position of the center of gravity.

The acceleration factors applied to the target trajectory include the acceleration applied to the linear movement of the magnetic levitation body and the angular acceleration applied to the rotational movement.

Further, the control means is constructed so that the position of the magnetic levitation body is detected and the calculation of the control signal based on the position of the magnetic levitation body is distributed.
A case where the control signal is configured to be calculated a plurality of times while the parameter is modified by the parameter modifying means once, and the control signal calculated a plurality of times is filtered. In (Claim 4), noise components can be removed from the control signal,
By increasing the precision of the control signal output to the electromagnet, the electromagnet can be controlled with higher precision and the positioning precision can be further enhanced. In addition, by distributing the arithmetic processing by the control means,
It is possible to reduce the arithmetic load of each arithmetic processing unit. As a result, the manufacturing cost of the device can be reduced.

[0024]

DETAILED DESCRIPTION OF THE INVENTION An embodiment of the present invention will be described with reference to FIGS.

FIG. 1 is a perspective view showing the overall construction of an example of a magnetic levitation body positioning apparatus according to the present invention.
FIG. 2 is a plan view of the periphery of the floating table 1 positioned by the present device as viewed from above.

The levitation table 1, which is a magnetic levitation body, is an object to be positioned while moving along a target orbit by this device, and is formed by including a material having magnetic properties such as iron, which will be described later. It is affected by the electromagnetic force generated by the electromagnet.

As shown in FIGS. 1 and 2, the levitation table 1 is formed in the shape of a square plate, and is set in a space represented by a two-dimensional XY Cartesian coordinate system, as described later. Positioning along the orbit is performed. Before the positioning is started, the levitation table 1 has the center (X ₀ , Y ₀ ) of its square coincident with the origin of the XY orthogonal coordinate system, as shown in FIGS. 1 and 2. Moreover, each side of the square is arranged along the X-axis direction and the Y-axis direction. Further, in this embodiment, the center (X ₀ , Y ₀ ) of the levitation table 1 does not necessarily coincide with the center of gravity position (X _G , Y _G ) of the levitation table 1, as will be described later. The configuration is such that the center of gravity position (X _G , Y _G ) of the floating table 1 can be obtained.

The floating table 1 is provided with a first position detecting piece 2, a second position detecting piece 3 and a third position detecting piece 4 which are made of the same material as the main body of the table 1. These position detecting pieces are for detecting the position of the floating table 1, and the position of the position detecting piece detected by a displacement sensor described later is the position of the floating table 1.

The first position detecting piece 2 is attached so as to detect the movement of the table 1 in the X-axis direction due to the electromagnetic force by the first electromagnet 11 which will be described later, and the second position detecting piece 3 is the second. X of the table 1 due to the electromagnetic force of the electromagnet 12
The third position detecting piece 4 is attached so as to detect the movement in the axial direction, and the third position detecting piece 4 is attached so as to detect the movement of the table 1 in the Y-axis direction due to the electromagnetic force of the third electromagnet 13.

A first position detecting sensor 6, a second position detecting sensor 7, and a third position detecting sensor 8 are provided as displacement sensors. These displacement sensors have a distance l from the coordinate axis of each displacement sensor as shown in FIG.
It is arranged at a position s. First position detection sensor 6
Detects the position y ₁ of the first position detection piece 2, the second position detection sensor 7 detects the position y ₂ of the second position detection piece 3, and the third position detection sensor 8 detects the position y ₁ of the third position detection piece 4. Detect position y ₃ . As such a displacement sensor, an eddy current type non-contact displacement sensor can be used.

Then, the respective signals representing the positions y ₁ , y ₂ , y ₃ of the floating table 1 output from each of the displacement sensors are input to the controller 16 described later.

The positioning device includes a table 1
1 is provided with three coils 10 shown by a chain double-dashed line in FIG. 1, and three displacement sensors facing the coil 10 (not shown) provided below the table 1 are provided. It has a table floating mechanism. That is, the table levitation mechanism allows the table 1 to be levitated in the air by the magnetic force generated by the coil 10 to support the table 1 horizontally. The table levitating mechanism levitates the table 1 by executing a levitating program described later.

An electromagnet such as the first electromagnet 11 causes a predetermined electromagnetic force to act on the floating table 1. Each electromagnet is
For example, the first electromagnet 11 will be described. A pair of a coil P1 and a coil N1 is provided, and the coils P1 and N1 are located outside the levitation table 1 so that the center lines of the two coils coincide with the center line C1. Are disposed so as to face each other.
Then, the coil P1 and the coil N1 act on the floating table 1 together with an electromagnetic force acting as an attractive force. The electromagnetic force applied to the floating table 1 by the coils P1, N1 and the like is determined according to the electric power supplied to the coil as described later. Further, in which direction the table 1 can be moved with respect to one set of coils is determined by the relative difference between the attraction force by P1 and the attraction force by N1.

Further, in this embodiment, the first electromagnet 11, the second electromagnet 12 composed of the coils P2 and N2, and the third electromagnet 13 composed of the coils P3 and N3.
The three sets of electromagnets are arranged. As shown in FIGS. 1 and 2, the first electromagnet 11 and the second electromagnet 12 are arranged such that the center lines C1 and C2 of the pair of coils are along the X-axis direction, and An electromagnetic force is applied to the table 1 along the X-axis direction. Also, the first electromagnet 11
And the second electromagnet 12, the center lines C1 and C2 are symmetrical with respect to the X axis, and the distance from the X axis to the center line C1 is l.
As the _M, The distance from the X axis to the center line C2 is disposed so as to l _M.

The third electromagnet 13 is arranged so that the center line C3 of the pair of coils extends along the Y-axis direction, and applies an electromagnetic force to the floating table 1 along the Y-axis direction. Further, the third electromagnet 13 is arranged such that the distance of the center line C3 from the Y axis is 1 _M.

According to the positioning device of the present invention, since the three sets of electromagnets are provided in this way, in addition to being able to position the levitation table 1 along the X-axis direction and the Y-axis direction, rotation of the levitation table 1 is suppressed. You can also That is, X
Since two sets of electromagnets are arranged along the axial direction, regardless of the position of each electromagnet with respect to the position of the center of gravity of the table 1, it is possible to suppress the rotation of the levitation table 1 and perform highly accurate positioning. .

Then, each electromagnet is supplied with necessary power for applying an electromagnetic force from the amplifier 15. The amplifier 15 can be configured by a linear amplifier that can linearly amplify the input signal. And the amplifier 15 is
When a control signal v _i (i = 1, 2, 3) for each electromagnet is output from the controller 16 described later, the terminals represented by the formulas (1) and (2) for the two coils provided in each electromagnet. The voltages V _Pi and V _Ni are supplied.

[0038]

[Equation 1]

[0039]

[Equation 2]

In the expressions (1) and (2), i corresponds to three electromagnets, i = 1 corresponds to the first electromagnet 11, and i = 2 corresponds to the second electromagnet 12. It means that i = 3 corresponds to the third electromagnet 13. Then, for example, V _P1 represents the voltage applied to one coil P1 of the first electromagnet 11, and V _N1 is the first electromagnet 1
1 represents the voltage applied to the other coil N1. Also,
In the equations (1) and (2), g _i represents the amplification factor of the amplifier 15, and V _B represents the signal output from the controller 15 corresponding to the constant bias voltage.

When the voltages V _Pi and V _Ni are applied to the electromagnets, the currents I _Pi and I represented by the equations (3) and (4) are obtained.
_Ni conducts as a drive current for each electromagnet.

[0042]

[Equation 3]

[0043]

[Equation 4]

In equations (3) and (4), i corresponds to three electromagnets, and Pi represents one coil of each electromagnet and Ni represents the other coil of each electromagnet. The same as the above equations (1) and (2).
In the expressions (3) and (4), R _Pi represents the resistance of one coil of each electromagnet, and R _Ni represents the resistance of the other coil of each electromagnet.

Next, the mechanical characteristics of the electromagnetic force applied by the electromagnets to the levitation table 1 by the drive currents I _Pi and I _Ni will be described.

The electromagnetic force applied by each electromagnet to the levitation table 1 by the drive currents I _Pi and I _Ni is expressed by the equation (5).

[0047]

[Equation 5]

In this equation (5), k _Pi (y _i ), k
_Ni (y _i ) is a function that represents a non-linear mechanical characteristic between the levitation body and the electromagnet, which depends on the gap that is the gap between the levitation table 1 and the electromagnet. Then, equations (6) to (8) are obtained from the equations (1) to (5).

[0049]

[Equation 6]

[0050]

[Equation 7]

[0051]

[Equation 8]

K _i (y _i ) in the above equation (6) is (7)
This is represented by the equation, and f _Di (y _i ) in the above equation (6) is represented by the equation (8). Also, f _{Di in} equation (6)
(Y _i ) represents a term that acts as an external force when performing the positioning control of the floating table 1.

Here, when forces f ₁ , f ₂ , f ₃ acting in the same direction as the electromagnetic force of the electromagnet are applied to the levitation table 1, that is, f ₁ , f ₂ along the X-axis direction. A general equation of motion represented by the XY coordinate system when f ₃ is applied along the Y axis direction is represented by the equation (9).

[0054]

[Equation 9]

In the equation (9), m represents the mass of the levitation table 1, and X ″ represents the acceleration X generated in the levitation table 1.
Represents a component in the axial direction, Y ″ represents a component in the Y-axis direction of acceleration generated in the levitation table 1. Further, in the equation (9), Iz represents a moment of inertia of the levitation table 1,
θ ″ represents the angular acceleration associated with the rotation represented by the rotation angle θ of the levitation table 1. The above “″” represents the two-time differential coefficient of the attached variable. Also,"'"
Represents one-time differential coefficient. Hereinafter, the same applies to the present embodiment.

Then, the equation (9) is converted into the coordinate conversion equation (10).
By using the equations, the equations of motion (11) to (17) for the position y _i (i = 1, 2, 3) of the levitation table 1 detected by the displacement sensor are converted.

[0057]

[Equation 10]

[0058]

[Equation 11]

[0059]

[Equation 12]

[0060]

[Equation 13]

[0061]

[Equation 14]

[0062]

[Equation 15]

[0063]

[Equation 16]

[0064]

[Equation 17]

In the equation (10), θ is the floating table 1
Represents the rotation angle of.

The expression (11) is a matrix expression. The matrix M is expressed by the expression (12), the matrix y ″ is expressed by the expression (13), the matrix L is expressed by the expression (14), and the matrix K is expressed.
Is expressed by equation (15), and each element of the matrix f _D is (1
It is expressed by the equation 6).

Further, the above equations (13), (16), (1
“T” in the expression (7) represents a transposed matrix,
“Diag” in Expression (15) represents that it is a diagonal matrix.

Here, each element k _i (y _i ) (i = 1, 2, 3) of the matrix K included in the equation of motion (11) and each element f _Di (y _i ) (of the matrix f _D i = 1,2,3) is
It is determined based on the nonlinear mechanical characteristics of the electromagnet. Then, as shown in the equation (11), the control signal v to be output for controlling the position of the floating table 1
_i is determined by the relationship with the above k _i (y _i ) and f _Di (y _i ). Then, k _i (y _i ) and f _Di (y _i ) can be expressed by a linear combination of basic functions.

FIG. 3 shows an example of the basic function. FIG. 3 is an example of the basic functions, and shows a set of basis functions φ _j (y _i ) that can be used to express the nonlinear characteristics of the electromagnet. In FIG. 3, the horizontal axis corresponds to the table position y _i (i = 1, 2, 3) corresponding to the electromagnet gap, and the vertical axis corresponds to the function φ _j (y _i ) (j = 1, 2, 3). , 4,
It corresponds to the function values of 5, 6).

Φ _j (y _i ) shown in FIG. 3 is expressed by equation (18).

[0071]

[Equation 18]

As shown in FIG. 3, according to the equation (18), φ _j (y _i ) is a function having a distribution centered on each θ _j , and the spread of φ _j (y _i ) is It is determined by σ in the equation (18).

In the positioning device of the present invention, the above k _i (y _i ) and f _Di (y _i ) are expressed by the equation (19),
Based on the estimation that it can be expressed by equation (20), as will be described in detail later, k _i (y _i ) of k _i (y _i ) can be obtained by repeating correction of the estimated value w _ij ^{K *} of coefficient w _ij ^K of equation (19). F _Di by revising the estimated value k _i ^* (y _i ) and by revising the estimated value w _ij ^{D *} of the coefficient w _ij ^{D in} equation (20).
The estimated value f _Di ^* (y _i) modification of _{(y i), k i (} y i) accurately reflect the mechanical properties of the electromagnet, f _Di (y _i)
The estimated values of k _i ^* (y _i ) and f _Di ^* (y _i ) can be finally obtained.

[0074]

[Formula 19]

[0075]

[Equation 20]

[ ^* ] Attached to the above w _ij ^{K *} etc.
Means that the parameter to which it is attached is an estimate.

Further, the positioning device of the present invention has the above-mentioned (1
1) the moment of inertia Iz and the barycentric position is included as an element of (X _G, the even Y _G), as described in detail later, the estimate of Iz and the gravity center position (X _G, Y _G) Iz
By repeating the corrections of ^* , (X _G ^* , Y _G ^* ), Iz and the estimated value I of the center of gravity position (X _G , Y _G ) are determined based on the accurate mechanical characteristics of the electromagnet with respect to the levitation table 1.
z ^* , (X _G ^* , Y _G ^* ) is finally obtained.

Next, the controller 16 for controlling the electromagnet will be described with reference to FIG. 4 showing an overall block diagram. A personal computer can be used as the controller 16.

The controller 16 has a first I / O section 17, and the position of the floating table 1 detected by the displacement sensor is input to the controller 16 via the first I / O section 17, which will be described later. The position data y _i (i = 1, 2, 3) is stored in the second storage unit 21. In addition, the controller 16 uses the second I / O unit 18
And the control signal v _i (i = 1, 2, 3) calculated by the positioning control routine described later is the second I
The signal is output to the amplifier 15 via the / O section 18.

Then, the controller 16 has the arithmetic unit 19
And a first storage unit 20 and a second storage unit 21.

The calculation unit 19 performs various calculations associated with the execution of the positioning control routine. The first storage unit 20 stores a positioning control routine whose processing procedure is shown in FIGS. 5 and 6, which will be described later, and a floating program for floating the floating table 1 in the air. The second storage unit 21 has an area for storing various parameters associated with the execution of the positioning control routine. That is, as shown in FIG. 4, a position data area 21a, a non-linear parameter area 21b, and a target trajectory data area 21c are formed.

In the position data area 21a, the position y _i of the levitation table 1 detected by the displacement sensor (i = 1, i = 1,
2, 3) are stored. In the non-linear parameter area 21b, there are k _i ^* (y
_i ) and w _ij ^{K *} are stored.

Further, in the nonlinear parameter area 21b,
F which is a parameter corresponding to the mechanical characteristics
_Di ^* (y _i ) and w _ij ^{D *} are stored. In the nonlinear parameter region 21b, the differential gain k _di (y _i ) and the proportional gain k _pi (y _i ) and the external force elimination term u _Bi (y _i ) obtained based on the f _Di ^* (y _i ) are also included. Is stored. In the nonlinear parameter area 21b, the basis function φ _j (y _i )
Σ and θ _j (j = 1, 2, 3, 3, which are constant data representing
4, 5, 6) are also stored.

Further, in the non-linear parameter area 21b,
I estimate I ^* _Z and the estimated value of the center-of-gravity position of the table 1 the moment of inertia is the inertia parameter _{^{(X * G, Y * G}} ), The coefficient for determining these parameters _{^{w O I *, w O X}} * , W
_O ^{Y * is} also stored. In addition, the nonlinear parameter region 21b
Are coefficients a, b, c, α _K , α _D , and α that are constant data.
_I , α _X , α _Y , and initial data WK0, WD0, W
I0, WX0, WY0, JI0, JX0, and JY0 are stored. Also, the initial position data YD of the floating table
_i (i = 1, 2, 3) and initial data VD _i (i = 1, 2, 3) obtained based on the YD _i are also stored in the non-linear parameter area 21b.

Further, in the non-linear parameter area 21b,
Error e _i, and extended error epsilon _i obtained based on said error e _i between the position y _i and the target position y _Mi of floating table 1 is stored (i = 1,2,3).

The target trajectory data area 21c stores data of the target trajectory based on the target position for positioning the levitation table 1. The data of this target trajectory is stored as follows. That is, the position y _M1 corresponding to the three positions of the floating table 1 detected by the displacement sensor,
y _M2 and y _M3 are stored as one set of target positions for positioning by moving once. Also, as the data on the target trajectory, one set of the first-order differential coefficients y _M1 ', y _M2 ', y _M3 'and the second-time differential coefficients y _M1 ", y _M2 ", y _M3 "is set. Further, the acceleration data X _M ″ along the X-axis direction of the levitation table 1, the acceleration data Y _M ″ along the Y-axis direction, and the angular acceleration θ _M ″ of the levitation table 1 are stored. Is also stored as one set.

That is, as the data of the target trajectory, [y _M1 ,
y _M2 , y _M3 , y _M1 ', y _M2 ', y _M3 ', y _M1 ",
y _M2 ″, y _M3 ″, X _M ″, Y _M ″, θ _M ″] is set as one set, and the above one set for all target positions on the target trajectory sequentially positions the levitation table 1. It is stored according to the order of target positions to be tried.
Then, in the execution of the positioning control routine described later, according to the numerical value set in the positioning variable im,
The sets are sequentially read one by one according to the order of the target position to be positioned. Also,
The target trajectory data area 21c also stores the number C _M of the positioning target positions.

For one set of the target trajectories,
By using the input device 22 described later, target positions y _M1 , y _M2 ,
It is also possible to input only y _M3 and obtain other data expressed as a differential coefficient by a numerical operation based on the input target position. When obtaining the differential coefficient by such a numerical operation, an approximate calculation by the time width Δt corresponding to one cycle of the sampling rate at which the controller 16 executes the positioning control routine can be used.

The controller 16 is also provided with an input device 22 for inputting the target trajectory data.
That is, the target trajectory data is stored in the second storage unit 21 through the operation of the input device 22. The input device 22 may be configured to input the target trajectory data via a keyboard operation. Alternatively, a floppy disk drive may be provided as an input device to input the target trajectory data stored in the floppy disk. Alternatively, the target trajectory data may be input to the controller 16 from an external storage medium such as a hard disk.

The operation of the positioning device for the magnetic levitation in the above structure will be described. The controller 16 executes the levitation program to levitate the levitation table 1 in the air. Then, the position y _i at which the table 1 floats and stands still is detected, and the initial position data Y of the floating table 1 is detected.
It is stored as D _i (i = 1, 2, 3).

After this, the positioning control routine shown in FIGS. 5 and 6 is executed.

First, the positioning variable im is set to 1 (S1), and one set of data of the target trajectory for the first positioning of the levitation table 1 is read (S2). Next, the elements of the matrix J ^* are set (S3).

This matrix J ^* is obtained by the equations (21) and (22).

[0094]

[Equation 21]

[0095]

[Equation 22]

Here, when the positioning variable im is 1, among the elements included in J ^* , the initial data JI0 is set for the I _Z ^{* and} the initial data JX0 is set for the X _G ^*. JY for the above Y _G ^*
0 is set.

Next, the commanded position u _i is obtained (S
4). The command position u _i is obtained based on the equation (23).

[0098]

[Equation 23]

U in the equation (23) is the command position u _i (i
= 1, 2, 3) as an element, a matrix with three rows and one column is represented, that is, u _i is obtained as an element of the matrix u. Further, y _M ″, y _M ′, and y _M in the equation (23) are three-row, one-column matrices each having y _Mi ″, y _Mi ′, y _Mi (i = 1, 2, 3) as elements It represents. Moreover, a, b, and c in the equation (23) are constant data.

When the electromagnet is a set, the commanded position u ₁ is calculated by the equation (24).

[0101]

[Equation 24]

Next, parameters k _i ^* (y _i ) and f _Di ^* (y _i ) corresponding to the mechanical characteristics of the electromagnet are obtained (S5). k _i ^* (y _i ) is represented by the equation (25), and f
_Di ^* (y _i ) is represented by the equation (26).

[0103]

[Equation 25]

[0104]

[Equation 26]

Here, when the positioning variable im is 1, initial data WK0 is set in each element of w _ij ^{K *} , and initial data WD0 is set in each element of w _ij ^D. .

Then, the differential gain k _di (y _i ) and the proportional gain k _pi (y _i ) which are gain parameters are obtained, and the external force elimination term u _Bi is obtained (S6). The differential gain k _di (y _i ) is expressed by the equation (27), the proportional gain k _pi (y _i ) is expressed by the equation (28), and the external force elimination term u
_Bi is expressed by equation (29).

[0107]

[Equation 27]

[0108]

[Equation 28]

[0109]

[Equation 29]

Next, the control signal v _i is obtained (S
7). The control signal v _i is represented by the equation (30).

[0111]

[Equation 30]

In the equation (30), the control signal v _i is obtained according to the feedback control law. When the control signal v _i is output to the amplifier 15, a voltage corresponding to the signal v _i is output to the electromagnet, and the levitation table 1 moves by the electromagnetic force of the electromagnet.

Next, the position y _i of the floating table 1 is detected (S8), and the difference from the target position in the data of the target trajectory read in S2 is obtained as an error e _i (S8).
9). The error e _i is expressed by equation (31).

[0114]

[Equation 31]

Next, the expansion error ε _i is obtained (S1
0). The expansion error ε _i is obtained by the equation (32).

[0116]

[Equation 32]

Next, there are a gain correction factor for correcting the differential gain k _di (y _i ) and a proportional gain k _pi (y _i ) which are gain parameters, and an external force elimination term correction factor for correcting the external force elimination term. Required (S11).

The gain correction factor is expressed by equation (33).

[0119]

[Expression 33]

[0120] (33) As shown in equation gain correction factor, coefficient w _ij ^{K *} first floor with time of the derivative w _ij ^{K *} 'are the the extended error epsilon _i is the first modification factor It is given by the basis function φ _j (y _i ) and the modified signal factor v _FBi . In S11, the signal v _i in the previously obtained positioning variable (im-1) is set as the correction signal factor v _{FBi in the} equation (33) when the positioning variable is im> 1. In S11, the positioning variable i
When m is 1, the modified signal factor v _FBi is obtained by the equation (34) using the initial data WK0 and WD0.

[0121]

[Equation 34]

Y _i (i = 1, 2,
Initial position data YD _i (i = 1, 2, 3) is set in 3). In addition, y _i '(i = 1, 1 in the equation (34)
0 is set in 2, 3). And it takes (34)
The expression v _FBi is the initial data VD _i (i = 1, 2, 3).

The external force elimination term correction factor is expressed by equation (35).

[0124]

[Equation 35]

As shown in the equation (35), the external force elimination term correction factor is the first-order derivative w of the coefficient w _ij ^{D *} with _respect to time.
_ij ^{D *} 'is given by the expansion error ε _i which is the first correction factor and the basis function φ _j (y _i ).

Next, the coefficients w _ij ^{K *} and w _ij ^{D *} in S5 are modified (S12). The correction in S12 is (36)
Expression 37 is expressed by Expression (37).

[0127]

[Equation 36]

[0128]

[Equation 37]

In the equations (36) and (37), Δ
For t, a time width corresponding to one cycle of the sampling rate of the controller 16 can be used.

Next, an inertia moment correction factor for correcting the inertia moment I _Z ^* which is an inertia parameter and a center of gravity position correction factor for correcting the center of gravity position (X _G ^* , Y _G ^* ) which is an inertia parameter. Are required (S13).
The inertia moment correction factor is expressed by the equation (38), and the center-of-gravity position correction factor is expressed by the equations (39) and (40).

[0131]

[Equation 38]

[0132]

[Formula 39]

[0133]

[Formula 40]

As shown in the equation (38), the moment of inertia correction factor is the second correction factor (ε) where the first-order differential coefficient w _O ^{I *} 'of the coefficient w _O ^{I *} with time is obtained from the expansion error. ₁ −ε ₂ ) and the angular acceleration θ _M ″ applied to the target trajectory. Further, as shown in the equations (39) and (40), the center-of-gravity position correction factor is the time of the coefficient w _OX ^* . The second correction factor (ε ₁ −ε ₂ ) obtained from the expansion error and the first-order differential coefficient w _OX ^* 'according to
_M ″ and the second-order correction factor (ε ₁ −ε ₂ ) obtained by the first-order differential coefficient w _O ^{Y *} 'of the coefficient w _O ^{Y *} with time and the acceleration X _M applied to the target trajectory. Given by.

Next, the coefficients w _O ^{I *} , w _O ^{X *} , and w _O ^{Y *} are
Equation (41), Equation (42), Equation (43)
It is corrected (S14).

[0136]

[Formula 41]

[0137]

[Equation 42]

[0138]

[Equation 43]

In S14, when the positioning variable im is 1, the initial data WI0 is set to the uncorrected w _O ^{I *} and the initial data WX0 is set to the uncorrected w _O ^{X *.} Initial data WY0 is set in the previous w _O ^{Y *} .

Next, the moment of inertia I _Z ^* and the position of the center of gravity (X
_G ^*, Y _G ^*) is, equation (44), (45) formula, obtained by the expression (46), is modified (S15).

[0141]

[Equation 44]

[0142]

[Equation 45]

[0143]

[Equation 46]

I _Z ^* obtained in S15,
(X _G ^* , Y _G ^* ) is set as an element of the matrix J ^* in S3 when S2 and subsequent steps are re-executed as described later.

Next, when the positioning variable im is not equal to C _M (S16, N), 1 is added to im (S1).
7) The process is re-executed from S2.

Further, in S17, the positioning variable
im is the equal to C _M is determined that (S16, Y), and ends the transfer of all of the target position according to the target trajectory, position control routine ends (S18).

As described above, according to the positioning device for a magnetic levitation body of the present invention, the levitation table 1 can be positioned in a two-dimensional plane while sequentially moving along a target trajectory. Further, by including two sets of electromagnets arranged along the X-axis direction and one set of electromagnets arranged along the Y-axis direction, the center of gravity and the moment of inertia of the levitation table 1 are obtained. Since the three sets of electromagnets are controlled, rotation of the levitation table 1 can be suppressed, and the levitation table 1 can be positioned with high accuracy.

Of the above positioning control routine,
The arithmetic processing (S7) for obtaining the control signal v _i and the processing (S8) for detecting the position of the table may be distributed. That is, in the controller 16, the arithmetic unit 19 is used as a first arithmetic unit, and a second arithmetic unit for distributed processing (not shown) that can perform higher-speed processing than the first arithmetic unit is provided. Then, with respect to the positioning control routine, the steps S7 and S8 and the part of the processing procedure related to the modification of each parameter other than the procedure can be processed in parallel. Then, a processing procedure for directly feeding back the position of the table detected in S8 to S7 is configured, and the portion of this processing procedure is processed by the second computing unit. Then, while the calculation processing for correcting each parameter is performed once by the first calculation unit,
The processing procedure fed back from S8 to S7 is executed a plurality of times by the second arithmetic unit. Then, the filtering processing is performed on the signal y _{i at} the position of the table detected a plurality of times. As a result, the noise component can be removed from the signal y _i, so that the accuracy of the signal v _i output to the electromagnet can be increased, the control on the electromagnet can be performed with higher accuracy, and the positioning can be performed. The accuracy can be further increased. As an example of this filtering process, there is an average value process for obtaining an average value of signals obtained a plurality of times.

Further, if the distributed processing is configured as described above, the controller 1 can be realized by distributing the arithmetic processing.
As compared with the case where 6 has one arithmetic unit, the arithmetic load of each arithmetic processing unit can be reduced. This allows
Manufacturing cost can also be reduced when configuring the positioning device.

[0150]

EXAMPLES Examples of the present invention will be described below. As an example, a magnetic levitation device positioning device was constructed in the same manner as described in the embodiment. That is, as described in the embodiment, the configuration is such that three sets of electromagnets are provided and the controller 16 can control the levitation table 1 in three degrees of freedom.

Table 1 shows the constant data used in the examples.

[0152]

[Table 1]

For constants other than those shown in Table 1, WI0 is set to 0.45 and WX0 is set for initial data.
And WY0 were set to 0, all elements of WD0 were set to 0, and all elements of WK0 were set to 400. Also, J
For I0, JX0, and JY0, WI0, WX0, and W
Numerical values obtained from Y0 and conditions such as the mass m and dimensions of the table 1 described later were set.

Six basis functions were used as the basis functions (n = 6), and a constant σ that determines the spread of all basis functions was set to 6.0. Then, the center θ _j of the basis function is set to a position based on dividing a distance of 2 mm, which is larger than the maximum movement distance of the table 1, into six equal parts.

As the floating table 1, the size of one side is 80
An iron plate having a mass of 0.15 kg and having a square shape of 2 mm and a thickness of 2 mm was used. As the controller 16, a personal computer (i486, c
lock 20 MHz) and sampling was performed at 100 Hz. In addition, in this embodiment, the distributed processing is performed. A digital signal processor (DSP; TMS) is used as an arithmetic unit for distributed processing.
320C30, clock33MHz)
The P board was used by mounting it on a personal computer.
This DSP has a sampling frequency of 5 kHz, and the CPU of the personal computer can perform sampling 50 times by the DSP while sampling once. Then, in obtaining the control signal v _i (i = 1, 2, 3), a filtering process was performed. As a filtering process, 5 for y _i (i = 1, 2, 3) was used.
The average value treatment was performed 0 times.

Then, the trajectory 30 shown by the dotted line in FIG. 7 was given as the target trajectory. That is, as shown in FIG.
In the XY plane, a trajectory along a circle of a square having one side of 1 mm was given as a target trajectory. Further, on the target trajectory shown in FIG. 7, a positioning target position consisting of 400 points was set. It should be noted that each position of the target trajectory represented by the XY coordinate system shown in FIG. 7 can be converted into the position of the target trajectory corresponding to the position detected by the displacement sensor by the equation (10).

The result of positioning the floating table 1 is shown in FIG. The track 31 shown in FIG. 8 is a track according to the embodiment. That is, it shows the trajectory of the levitation table 1 after the parameters of the electromagnet have been corrected by the positioning apparatus of the present invention. On the other hand, FIG.
Is a comparative example, and is an example of the trajectory of the levitation table 1 when positioning is performed without modifying the above parameters.

As can be seen from FIG. 8, according to the positioning device of the present invention, by correcting the parameters,
It is confirmed that the levitation table 1 can be made to substantially coincide with the target trajectory.

[0159]

As described above, according to the first aspect of the invention, the magnetic levitation body can be positioned over a wide range based on the non-linear dynamic characteristics of the electromagnet, and the magnetic levitation body can be positioned along the target trajectory. The present invention has an effect of being able to sequentially position while moving.

According to the second aspect of the present invention, since the basic function is used as the basis function, the nonlinear mechanical characteristics of the electromagnet can be reflected more efficiently, and the nonlinear parameter can be easily corrected.

The invention according to claim 3 has an effect that the rotation of the magnetic levitation body can be suppressed, and the positioning of the magnetic levitation body can be performed with higher accuracy.

The invention according to claim 4 has an effect that the control of the electromagnet can be performed with higher accuracy and the positioning accuracy can be further improved. In addition, it is possible to reduce the calculation load of each arithmetic processing device alone, and to reduce the manufacturing cost of the device.

[Brief description of drawings]

FIG. 1 is a perspective view of a positioning device for a magnetic levitation body.

FIG. 2 is a plan view of the periphery of a floating table as viewed from above.

FIG. 3 is a diagram showing characteristics of basis functions.

FIG. 4 is a block diagram of a positioning device.

FIG. 5 is a diagram showing a positioning control routine.

FIG. 6 is a diagram showing a positioning control routine.

FIG. 7 is a diagram showing a target trajectory for a floating table.

FIG. 8 is a diagram showing a trajectory along which a floating table moves.

[Explanation of symbols]

1 floating table 2 First position detection piece 3 Second position detection piece 4 Third position detection piece 6 First position detection sensor 7 Second position detection sensor 8 Third position detection sensor 10 (for table levitation) coil 11 First Electromagnet 12 Second electromagnet 13 Third Electromagnet 15 Amplifier 16 controller 17 First I / O Section 18 Second I / O section 19 Operation part 20 First memory 21 second memory 21a Position data area 21b Non-linear parameter area 21c Target trajectory data area 30 Target trajectory 31 Trajectory of levitating table according to example 32 Orbit of Comparative Example

Front page continuation (58) Fields surveyed (Int.Cl. ⁷ , DB name) G05D 3/00-3/20 G05B 13/02

Claims (4)

(57) [Claims] 1. An electromagnet for applying a predetermined electromagnetic force to a magnetic levitation body, which comprises a pair of coils arranged on the outside of the magnetic levitation body so as to face each other.
Combination of multiple basic functions that can express linearity
The non-linear dynamic characteristics of the magnetic levitation body are
An electromagnet that can be resembled, a control unit that outputs a control signal corresponding to electric power for generating a predetermined electromagnetic force in the electromagnet, a position detection unit that detects the position of the magnetic levitation body, and a positioning target of the magnetic levitation body A target trajectory input means for inputting a target trajectory that is a position and that changes with time, and the control means calculates a command position for the magnetic levitation body based on the target trajectory; A control signal calculating means for calculating a control signal from the commanded position and the position of the magnetic levitation body, which is associated with a mechanical characteristic of the electromagnet including a gain parameter including a proportional gain and a differential gain and an external force elimination term. A control signal calculation means for performing a calculation including a nonlinear parameter, and a parameter correction means for correcting the nonlinear parameter, Parameter correcting means, obtained on the basis of the error between the position and the target position of the magnetic levitation member
The first correction factor, which is the expansion error, and the control signal already output.
Modified signal factor obtained based on the
The gain correction factor defined by
Corrected proportional gain and derivative gain among parameters
And it is defined by said primary function and the first modification factor
Due to the external force elimination term correction factor, the nonlinear parameter
It is designed to correct the external force elimination term of the above, and the nonlinear parameter between the magnetic levitation body and the electromagnet is
Magnetic levitation by reflecting the nonlinear mechanical characteristics of
Control of the electromagnet even when the body travels a long distance
A magnetic levitation body positioning apparatus configured to perform and move the magnetic levitation body along the target trajectory. 2. The positioning device for a magnetic levitation body according to claim 1, wherein the basic function is a basis function. 3. The command position calculation, wherein the electromagnet includes two sets of coils arranged along one axis of two orthogonal axes and one set of coils arranged along another axis. The means performs a calculation including an inertial parameter of the magnetic levitation body which is a non-linear parameter, and the parameter correcting means applies a second correction factor based on an error between the position of the magnetic levitation body and the target position and the target trajectory. The magnetic levitation body positioning device according to claim 1 or 2, wherein the inertial parameter is modified based on an acceleration factor. 4. The control means is configured such that the position of the magnetic levitation body is detected and the calculation of the control signal based on the position of the magnetic levitation body is distributed-processed. The control signal calculation is performed a plurality of times while the parameter is corrected once by the means, and the control signal calculated a plurality of times is filtered. The magnetic levitation body positioning device according to claim 3.