JPH0669096A - Micromotion positioning device - Google Patents

Abstract

PURPOSE:To achieve a more complete non-interference control and to improve positioning performance with a simple configuration by laying out the drive points by an actuator at the centers of impact of a rigid object each other. CONSTITUTION:In the (x, y) coordinates where the mass of a substrate 1 of a micromotion positioning mechanism is set to m and an inertial main axis center is set to an origin, inertia moments around the x and y axes are set to Jx and Jy, respectively. Actuators 2M, 2R, and 2L are laid out concentrically with a radius of ld in reference to the origin. Also, when 2 M out of three actuators is laid out at (0, ld) of the (x, y) coordinates, the remaining two actuators 2R and 2L are laid out at the fourth and third quadrants of the (x, y) coordinates, respectively. The layout angle is set to thetad for the x axis. In this case, a micromotion positioning mechanism satisfying the expression is taken, thus increasing the loop gain of a control system and improving the performance easily.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a submicron-order positioning device using a piezoelectric element (piezo) or an electrostrictive element as an actuator, and completely eliminates interference of multiple degrees of freedom both statically and dynamically. A fine movement positioning device is provided.

[0002]

2. Description of the Related Art In recent years, submicron-order positioning accuracy is required for fine positioning in precision machining, assembly, adjustment and the like. In particular, in an ultra-precision positioning stage for the purpose of exposing a fine pattern, a piezoelectric element (piezo) or an electrostrictive element is often used as an actuator in order to realize a high driving resolution and a wide frequency response band. As an example, FIG. 1 shows a fine movement positioning device that controls positioning with one degree of freedom in the vertical direction and two degrees of freedom of inclination in a horizontal plane. It should be noted that this figure is a diagram for explaining a fine movement positioning device realized within the range of the conventional technique and also shows an embodiment of the fine movement positioning control device according to the present invention.

In FIG. 1, reference numeral 1 is a flat plate substrate for positioning, and 2M, 2R, 2L are actuators that generate a displacement in the vertical direction. For example, a displacement magnifying mechanism having a piezoelectric element as a drive element is also included. . Further, along with a piezoelectric element that generates a displacement due to an applied voltage, a position sensor 3 that measures the displacement of the substrate 1 in the z direction near the driving position of the piezoelectric element.
There are M, 3R and 3L, and these are called fine movement positioning mechanism. Here, it is assumed that the position sensor corresponding to each actuator is installed at substantially the same position as this.

Now, the displacement of the substrate 1 measured by the position sensors 3M, 3R, 3L is calculated by the displacement amplifiers 4M, 4R,
It is converted into an electric signal by 4L. The electrical signal is
The deviation signals e _M , e _R , and e _L are compared with the voltage applied to the command voltage input terminals 5M, 5R, and 5L. This deviation signal is used as a preamplifier 6M, 6R, 6L to obtain a predetermined sensitivity.
The compensators 7M, 7R, 7 for stabilizing the control loop and satisfying the specification to the deviation signal zero with respect to the command voltage are introduced.
Guided by L. The power amplifier 8 with the output of this compensator
Exciting M, 8R, 8L, actuators 2M, 2R,
The vertical movement of 2 L causes the substrate 1 to translate in the vertical direction,
Alternatively, it is driven so as to be tilted with respect to the z axis. These closed loops will be called feedback devices.

In the above description, the power amplifier 8
When M, 8R and 8L are of a type that outputs a voltage with respect to a voltage input, the compensators 7M, 7R and 7L generally include an integrator, for example, a PI compensator. Here, P means proportional and I means integral operation. Also, the power amplifier 8M,
When 8R and 8L are of a type that outputs a current with respect to a voltage input, the functions of the compensators 7M, 7R and 7L may simply be P operations. Because the actuators 2M, 2R,
The piezoelectric element, which is a 2L constituent element, is an electrical capacitor, and since the transfer function including the power amplifiers 8M, 8R, and 8L and the piezoelectric elements driven by them includes integral operation, the so-called control loop is This is because the type 1 becomes and the steady state error is automatically guaranteed according to the control theory.

[0006]

The performance of the fine movement positioning apparatus is defined by the positioning time and the position accuracy, but these specifications are becoming severer year by year. However, substrate 1
When the actuators 2M, 2R, 2L and the position sensors 3M, 3R, 3L are properly arranged and the independent feedback devices are incorporated in the mechanism, the characteristic improvement between the drive shafts is There was a limit due to the interference of interaction. Therefore, in order to shorten the positioning time and further improve the accuracy of positioning, it is necessary to devise a method for removing interference. For example, in FIG.
In the precision positioning for the fine movement positioning mechanism as shown in (1), a control device has been developed which eliminates interference caused by the spatial arrangement of the actuator and the position sensor and causes only the designated axis of interest to respond. This technical content is described in the document “Tomita et al .: 6-degree-of-freedom positioning control of parallel link type fine movement stage (Journal of Japan Society for Precision Engineering 58/4/1992, pp. 68).
4-690) ”. Briefly, the transformation matrix from the displacement caused by the actuator drive to the positioning point posture and the transformation matrix from the posture to the output of the position sensor are estimated, and the inverse matrix calculation of each is performed in front of the power amplifier and the position sensor. It is inserted in the subsequent stage to form a closed loop control system. Here, this will be called decoupling control, and the conventional control that does not insert such an inverse matrix operation will be called independent control.

The decoupling control has the effect that static interference of the mechanism is released and decoupling is achieved. As a proof of the effect of decoupling control, the same document shows positioning characteristics. For example, there is an experimental result that the excitation of other motion modes is extremely suppressed when a rotational motion is commanded.

However, as a result of applying the method of the same document to the fine movement positioning mechanism shown in FIG. 1, it has been found that improvement in performance cannot always be expected. FIG. 2 shows the deviation signal e when the voltage is applied only to the command voltage input terminal 5L.
_This is the behavior of _M , e _R , and e _L. In the case of the conventional independent control, a deviation signal also appears on the axes M and R other than the L to which the command voltage is applied. However, when the decoupling control is performed, the deviation signals e _M and e _R other than the command voltage application axis L do not appear. Therefore, the decoupling control seemed to behave as intended. In other words, responses other than the designated axis do not leak into it, so it can be expected to shorten the positioning time and improve the positioning accuracy. However, there has been a suspicion that the superiority of the decoupling control over the independent control can be maintained with respect to all the movement postures instructing the board 1.

Therefore, the performance of the independent control and the decoupling control was compared by changing the pattern of the command voltage application. Fig. 3 shows that the command voltage input terminals 5M, 5R, and 5L each have a +5 [μ
This is the behavior of the deviation signals e _M , e _R , and e _L when command voltages equivalent to m], +5 [μm], and −5 [μm] are applied in steps. In this case, the response of the decoupling control is rather deteriorated, and the deviation signal e _R is particularly oscillatory. That is, the positioning performance of the non-interacting control is not always superior to that of the conventional independent control.
This phenomenon is caused by the fact that the decoupling method of the same document is purely static and does not even perform dynamic decoupling. Furthermore, according to the teaching of control theory, the eigenvalue of the whole system related to stability is invariant due to coordinate transformation called decoupling. On the other hand, it is well known that the difficulty of controllability is related to the zero point arrangement, and it is sufficiently considered in the same document that the zero point arrangement changes due to coordinate transformation called non-interference, which affects the response to the stepped command voltage. One of the causes is that it has not been done. Therefore, even if a simple static decoupling is performed without considering this zero point arrangement, a significant improvement in positioning performance cannot be expected,
Rather, it was concluded that it may cause deterioration of responsiveness. Here is a summary of the issues.

A fine movement positioning device incorporating a feedback device consisting of an independent position control loop for a positioning mechanism having three position sensors for three actuators is known, and conventionally, those actuators and position sensors have been used. The sensor and the sensor were appropriately arranged in space without considering the characteristics of the positioning mechanism. Therefore, there has been a limit in achieving a shorter positioning time and higher accuracy. To alleviate this limitation, a means has been proposed in which an inverse matrix calculation of a conversion matrix based on the spatial arrangement of actuators and position sensors is inserted into a feedback device to perform static decoupling. However, the insertion of the inverse matrix operation complicates the configuration of the control device, resulting in high cost.
There was a drawback. Also, the parameters of the inverse matrix operation to be inserted must be estimated by using some identification means,
Therefore, there is also a drawback that the adjustment work for satisfying the performance of the control device becomes complicated. The biggest drawback is that the method does not always improve the positioning performance, but rather often deteriorates the response.

In view of the above problems of the prior art, an object of the present invention is to achieve more complete decoupling control and improve positioning performance in a fine movement positioning device with a simple structure. .

[0012]

The present invention has been made in order to solve the above-mentioned drawbacks and achieve the above-mentioned object, and performs an inverse matrix calculation of a conversion matrix based on the spatial arrangement of actuators and the position sensor. The complicated decoupling control method of inserting in a closed loop is not adopted. Instead, it is intended to provide a fine movement positioning control device in which the fine movement positioning mechanism itself is statically or dynamically decoupled.
That is, the fine movement positioning mechanism itself is made to be non-interfering including static and dynamic interference, and a fine movement positioning device in which a feedback device for driving the actuator based on the output information of each position sensor is incorporated in the mechanism is provided. .

More specifically with reference to FIG. 1,
It is assumed that the mass of the substrate 1 of the fine movement positioning mechanism is m, and the moments of inertia about the x-axis and the y-axis at the (x, y) coordinates set with the center of the principal axis of inertia as the origin are J _x and J _y , respectively. The actuators 2M, 2R, 2L have a radius l centered on the origin.
It is placed on the concentric circle of _d . Further, of the three actuators, when 2M is arranged at (0, l _d ) of (x, y) coordinates, the remaining two actuators 2R and 2L are (x,
y) It is optimal in terms of balance to arrange them in the 4th and 3rd quadrants of the coordinates. This arrangement angle is θ with respect to the x-axis
_{Put d} . At this time, the fine movement positioning mechanism is formed so as to satisfy the following expressions (3) and (4).

[0014]

[Equation 3]

[0015]

[Equation 4] Next, with respect to the fine movement positioning mechanism based on the above formula, the deviation signals e _M , e _R , and e _L are obtained by comparing the outputs of the three position sensors 3M, 3R, and 3L with the command voltage, and the preamplifier 6M is used. , 6
The power amplifiers 8M, 8R, 8L are excited via the R, 6L and the compensators 7M, 7R, 7L to drive the actuators 2M, 2
A fine movement positioning device is constructed by incorporating a feedback device for driving R and 2L.

[0016]

Mathematical meaning of equations (3) and (4) is that the drive points by the actuators are the "center of impact" of the substrate 1 with each other, whereby the fine movement positioning mechanism itself is static. -It is configured to decoupling all dynamic interference. A closed loop that drives each actuator based on the position information of each sensor is configured for the mechanism. Therefore, the control loop is composed of three simple single loops. Further, since the fine movement positioning mechanism itself can be made non-interfering, it is easy to increase the loop gain of the control system to improve the performance. When three single loops are configured for the conventional fine-motion positioning mechanism that does not satisfy the relationship between equations (3) and (4), there is a limit to increasing the loop gain due to interference components from other axes. Therefore, the positioning performance is also controlled. Further, in the conventional decoupling control, since the inverse matrix operation is inserted in the control loop, the adjustment work is complicated together with the parameter determination. In addition, there is no guarantee that the positioning performance will be significantly improved as compared with the case where the inverse matrix calculation is not performed.

As described above, in the fine movement positioning apparatus of the present invention, complete decoupling control is realized and parameter identification and adjustment work are unnecessary, so that productivity is improved and the apparatus cost is kept low. To be

[0018]

1 is a block diagram showing an embodiment of a fine movement positioning device according to the present invention. As described in the "Prior Art" section with reference to this drawing, the actuators and position sensors that form the fine movement positioning mechanism are not properly spatially arranged within the range of the prior art. However, here, these arrangements are optimized as shown in the equations 3 and 4.

The derivation process of these equations will be described. First, FIG. 4 shows the coordinates of the substrate 1 shown from above. In the figure, black circles 2M, 2R, 2L are actuators,
It is placed at the coordinates entered in the figure. Further, it is assumed that the center of coordinates and the center of inertia coincide with each other, and (x,
y, z) Define the coordinates. At this time, the equation of motion is as shown in the following Equation 5.

[0020]

[Equation 5] However, the meanings of the symbols used are as follows. X = [z, θ _x , θ _y ] ^T : displacement vector of inertial principal axis z [m]: z-axis displacement of inertial principal axis of substrate 1 θ _x [rad]: rotation angle of substrate 1 around x-axis θ _y [ rad]: rotation angle of the substrate 1 around the y axis M = diag (m, J _x , J _y ): inertia matrix m [kg]: mass of the substrate 1 J _x [Kgm ² ]: around the x axis of the substrate 1 Moment of inertia J _y [Kgm ² ]: Moment of inertia about the y-axis of the substrate 1 [Z _dM , Z _dR , Z _dL ] ^T [m]: Actuator displacement in the z-axis direction K [N / m]: 2M, 2R , 2L spring constant d [Nsec / m]: 2M, 2R, 2L viscous friction coefficient A = diag (a _M , a _R , a _L ) [m / V]: voltage displacement conversion coefficient U = [u _M , ^{_{u R, u L] T [}} V]: voltage vector applied to the piezoelectric element θ _d [rad]: placement of the actuator angle l _d [m]: Diameter superscript subscript T: transposed matrix ^(·): time derivative s: Laplace operator J _xd: actuator drive displacement _{[Z dM, Z dR, Z} dL] T
To the displacement X expressed by the equation 6

[0021]

[Equation 6] D: Damping coefficient matrix expressed by Equation 7

[0022]

[Equation 7] K: Rigidity coefficient matrix expressed by Eq. 8

[0023]

[Equation 8] Now, based on the above preparation, the relationship from the applied voltage vector U to the displacement vector X is given by the equation (9).

[0024]

[Equation 9] In the above equation, the portion representing the relationship from U to X becomes the transfer function matrix G (s) of the fine movement positioning mechanism. Where each element is number 1
Put it like a 0 symbol.

[0025]

[Equation 10] At this time, the polynomials that give the respective zero points of G ₃₁ (s), G ₁₂ (s), and G ₃₂ (s) are as shown in Formulas 11 to 13.

[0026]

[Equation 11]

[0027]

[Equation 12]

[0028]

[Equation 13] Therefore, the conditions that all the coefficients of s can be zero in the polynomials of the above equations 11 to 13 are easily obtained, and the equations 14 and 15 are obtained.

[0029]

[Equation 14]

[0030]

[Equation 15] That is, when the equations 14 and 15 are satisfied, the transfer functions of the off-diagonal terms shown in the equation 10 are all zero,
Only the diagonal components G ₁₁ (s), G ₂₂ (s) and G ₃₃ (s) remain as non-zero. This means that the fine movement positioning mechanism is statically and dynamically decoupled. Here, the control system of the fine movement positioning apparatus in which the feedback device is incorporated in the fine movement positioning mechanism which has been completely decoupled will be referred to as complete decoupling control.

The equations (14) and (15) are G ₃₁ (s), G
_{In the} polynomial that gives the zeros of ₁₂ (s) and G ₃₂ (s), the condition was that the coefficient of s was set to zero at the same time, but this condition was G ₁₃ (s), G ₂₁ (s), and G ₂₃ ( It is also a condition for setting the coefficient of s of the polynomial that gives each zero point of s) to zero. Therefore, the formula 10 is obtained by the formulas 14 and 15.
The off-diagonal terms of the equation are all zero.

Further, the mass m of the substrate 1, x axis of the inertial moment J _x, can not be changed the moment of inertia J _y in y-axis, i.e. the number followed by a number 14 formula as given ones solving for l _d Equation 3 is obtained by solving Equation 15 with respect to θ _d . That is, m, J _x ,
Requesting an excessive design change to J _y is not realistic, so a solution was obtained for l _d and θ _d . Of course,
Fixing l _d and θ _d , m and J satisfying the equations 14 and 15
A combination of _x and J _y may be searched. In short, if the fine movement positioning mechanism is designed so as to satisfy the equations (14) and (15), there will be no interference components from other than the designated drive axis.

Next, the step response of the fine movement positioning device realizing the complete decoupling control is compared with that of the fine movement positioning device in which only the independent control is applied to the fine movement positioning mechanism in which the complete decoupling is not considered. The effectiveness of the present invention is shown. FIG. 5 shows that only the command voltage input terminal 5L has +5 [μ
m] the deviation signals e _M , e when a command voltage equivalent to
_R, it is a response waveform of e _L. According to the complete decoupling control of the present invention, the responses of the deviations e _R and e _L are completely zero, which clearly shows the effect of the present invention. Of course, no matter what pattern command is given to the command voltage input terminals 5M, 5R, 5L, the complete decoupling control operates perfectly. That is, in the conventional pure static decoupling control,
As shown in FIG. 3, depending on the voltage application pattern to the command voltage input terminals 5M, 5R, 5L, it may be deteriorated compared to the independent control, but such a situation does not occur in the complete decoupling control.

In this embodiment, the three actuators 2M, 2R and 2L are provided in the same plane, and their vertical z-axis displacement controls a total of 3 degrees of freedom including translational 1 degree of freedom and rotational 2 degrees of freedom. A fine movement positioning device that realizes complete decoupling control is shown for the fine movement positioning mechanism. However, the present invention is not limited to such a three-degree-of-freedom fine movement positioning mechanism, and can be applied to a mechanism having more degrees of freedom. Because the numbers 11-1
Equation 3 is a condition of a mechanical parameter such that each coefficient of a polynomial that gives a zero point simultaneously becomes zero.
The mechanical meaning of equations (15) and (15) is that each driving point is “center of impact”. Therefore, there is provided a feedback device that includes an actuator having at least a degree of freedom of movement for controlling a rigid object and a position sensor having at least a degree of freedom of movement, and feeds back the output of each position sensor to drive the corresponding actuator. In the assembled fine movement positioning device, the fine movement positioning device in which the driving points by the actuators are arranged at the centers of the impacts is also included in the scope of the present invention.

[0035]

According to the present invention, the fine movement positioning mechanism itself is constructed so as to be decoupling including all static and dynamic interferences, and each mechanism is provided based on the position information of each sensor. Since the closed loop for driving the actuator is formed, the control loop has three simple single loops, which is extremely simple. Further, since the fine movement positioning mechanism itself can be made non-interfering, there is an effect that it is easy to increase the loop gain of the control system to improve the performance. Further, complete decoupling control can be realized, and parameter identification and adjustment work are not required, so that there is an effect that productivity can be improved and the cost of the device can be kept low.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of a fine movement positioning device according to the present invention.

FIG. 2 is a step response waveform diagram showing a comparison between conventional independent control and decoupling control.

FIG. 3 is a step response waveform chart showing an example of positioning in which a step response becomes oscillating by conventional decoupling control.

4 is an explanatory diagram of a coordinate system showing an arrangement of actuators in the apparatus of FIG.

FIG. 5 is a step response waveform diagram showing a comparison between conventional independent control and complete decoupling of the present invention.

[Explanation of symbols]

1: substrate, 2M, 2R, 2L: actuator such as piezoelectric element, 3M, 3R, 3L: position sensor, 4M, 4
R, 4L: displacement amplifier, 5M, 5R, 5L: command voltage input terminal, e _M , e _R , e _L : deviation signal, 6M, 6R, 6
L: preamplifier, 7M, 7R, 7L: compensator, 8M, 8
R, 8L: power amplifier.

Continuation of the front page (51) Int.Cl. ⁵ Identification number Office reference number FI technical display location H01L 21/68 G 8418-4M 41/09

Claims (2)

[Claims] 1. A flat plate-like substrate for positioning translational 1-DOF and rotation 2-DOF, and three plate-shaped substrates arranged on substantially the same circle about the principal axis of inertia of the substrate for driving the substrate. An actuator, three position sensors arranged in the vicinity of the actuator to measure the displacement of the substrate, and outputs of the position sensor and a command voltage are compared to obtain a deviation signal, and a preamplifier and a compensator are provided. the positioning device provided with a feedback device for driving the actuator by energizing the power amplifier through the mass of the substrate m, the radius l _d of the same circle, the plane of the substrate the center as the origin The moments of inertia of the substrate about the x-axis and the y-axis of the (x, y) coordinates defined in paragraph 1 are defined as J _x and J _y , respectively, and one actuator is arranged at the coordinate (0, l _d ), If the remaining two actuators are arranged in the 3rd and 4th quadrants of the (x, y) coordinates at positions at an angle θ _{d with} respect to the x-axis, the fine movements characterized by the simultaneous establishment of the equations 1 and 2 Positioning device. [Equation 1] [Equation 2] 2. A rigid object to be positioned, and an actuator having a degree of freedom of movement for controlling positioning of at least the rigid object,
In a positioning device including at least a position sensor for the degree of freedom of movement, and incorporating a closed-loop feedback device that feeds back the outputs of the position sensors to drive the actuators, the driving points of the actuators are the rigid objects. The fine movement positioning device is arranged at the center of the impact of the.