Supports – With condition responsive control means
Reexamination Certificate
2001-10-09
2003-03-25
King, Anita (Department: 3632)
Supports
With condition responsive control means
C188S267000, C248S638000
Reexamination Certificate
active
06536735
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to a vibration isolating apparatus, and more particularly, to a highly accurate vibration isolating apparatus for blocking vibrations from a floor on which a semiconductor manufacturing apparatus, an electronic microscope or the like is installed, and for controlling a vibrating force from such an apparatus which adversely affects the yield of products and measurement/observation accuracies.
Conventionally, a vibration isolating apparatus of the type mentioned above has relied on a discrete point control method using a set of active actuators for controlling motions of a table. This method, however, has a problem in that control forces of the active actuators interfere with one another to generate unintended vibrations.
While the above problem could be solved by a method that controls each of degrees of motion freedom which are prevented from interfering with one another, this method would require a high performance controller because of complicated calculations needed for the control, resulting in an increased cost.
Considering now an equation of motion about the center of gravity (an inertial system) only taking into account a rigid motion (having a total of six degrees of freedom consisting of two degrees of freedom for translations in the horizontal direction, one degree of freedom for translation in the vertical direction, and three degrees of freedom for rotation about the axes of the translations, which are hereinafter denoted by X, Y, Z, &agr;, &bgr; and &ggr;) for a vibration isolating apparatus which has installed on its table a device sensitive to vibrations and is resiliently supported at respective active actuator points, the equation of motion is expressed by the following equation (1):
MX
+
CX
+
KX
=
F
M
=
diag
[
m
m
m
I
α
I
β
I
γ
]
C
=
[
∑
i
=
1
n
c
xi
0
0
0
∑
i
=
1
n
(
d
zi
·
c
xi
)
-
∑
i
=
1
n
(
d
yi
·
c
xi
)
0
∑
i
=
1
n
c
yi
0
-
∑
i
=
1
n
(
d
zi
·
c
yi
)
0
∑
i
=
1
n
(
d
xi
·
c
yi
)
0
0
∑
i
=
1
n
c
zi
∑
i
=
1
n
(
d
yi
·
c
zi
)
-
∑
i
=
1
n
(
d
xi
·
c
zi
)
0
0
-
∑
i
=
1
n
(
d
zi
·
c
yi
)
∑
i
=
1
n
(
d
yi
·
c
zi
)
∑
i
=
1
n
(
d
zi
2
·
c
yi
+
d
yi
2
·
c
zi
)
-
∑
i
=
1
n
(
d
xi
·
d
yi
·
c
zi
)
-
∑
i
=
1
n
(
d
xi
·
d
zi
·
c
yi
)
∑
i
=
1
n
(
d
zi
·
c
xi
)
0
-
∑
i
=
1
n
(
d
xi
·
c
zi
)
-
∑
i
=
1
n
(
d
xi
·
d
yi
·
c
zi
)
∑
i
=
1
n
(
d
zi
2
·
c
xi
+
d
xi
2
·
c
zi
)
-
∑
i
=
1
n
(
d
yi
·
d
zi
·
c
xi
)
-
∑
i
=
1
n
(
d
yi
·
c
xi
)
∑
i
=
1
n
(
d
xi
·
c
yi
)
0
-
∑
i
=
1
n
(
d
xi
·
d
zi
·
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yi
)
-
∑
i
=
1
n
(
d
yi
·
d
zi
·
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xi
)
∑
i
=
1
n
(
d
yi
2
·
c
xi
+
d
xi
2
·
c
yi
)
]
K
=
[
∑
i
=
1
n
k
xi
0
0
0
∑
i
=
1
n
(
d
zi
·
k
xi
)
-
∑
i
=
1
n
(
d
yi
·
k
xi
)
0
∑
i
=
1
n
k
yi
0
-
∑
i
=
1
n
(
d
zi
·
k
yi
)
0
∑
i
=
1
n
(
d
xi
·
k
yi
)
0
0
∑
i
=
1
n
k
zi
∑
i
=
1
n
(
d
yi
·
k
zi
)
-
∑
i
=
1
n
(
d
xi
·
k
zi
)
0
0
-
∑
i
=
1
n
(
d
zi
·
k
yi
)
∑
i
=
1
n
(
d
yi
·
k
zi
)
∑
i
=
1
n
(
d
zi
2
·
k
yi
+
d
yi
2
·
k
zi
)
-
∑
i
=
1
n
(
d
xi
·
d
yi
·
k
zi
)
-
∑
i
=
1
n
(
d
xi
·
d
zi
·
k
yi
)
∑
i
=
1
n
(
d
zi
·
k
xi
)
0
-
∑
i
=
1
n
(
d
xi
·
k
zi
)
-
∑
i
=
1
n
(
d
xi
·
d
yi
·
k
zi
)
∑
i
=
1
n
(
d
zi
2
·
k
xi
+
d
xi
2
·
k
zi
)
-
∑
i
=
1
n
(
d
yi
·
d
zi
·
k
xi
)
-
∑
i
=
1
n
(
d
yi
·
k
xi
)
∑
i
=
1
n
(
d
xi
·
k
yi
)
0
-
∑
i
=
1
n
(
d
xi
·
d
zi
·
k
yi
)
-
∑
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=
1
n
(
d
yi
·
d
zi
·
k
xi
)
∑
i
=
1
n
(
d
yi
2
·
k
xi
+
d
xi
2
·
k
yi
)
]
X
=
[
x
y
z
α
β
γ
]
F
=
[
f
z
f
y
f
z
f
α
f
β
f
γ
]
}
(
1
)
where m represents the overall mass of the table and device; I, moment of inertia about the center of gravity; c, an attenuation coefficient; k, a spring constant; x, y and z, relative displacements of the position of the center of gravity; &agr;, &bgr;, &ggr;, angular displacements of the center of gravity; d, the coordinate of a position with the center of gravity defined as the origin; and f, a force acting on the center of gravity. Also, suffixes x, y, z, &agr;, &bgr; &agr;&ngr;&dgr; &ggr; represent respective degrees of freedom; and i, each resilient supporting point, i.e., an identification number of an active actuator.
The existence of terms other than diagonal components in an attenuation matrix C and a rigid matrix K in the set of equation (1) causes complicated calculations in eliminating the interference.
SUMMARY OF THE INVENTION
The present invention has been made in view of the problem mentioned above, and it is an object of the invention to provide a vibration isolating apparatus and a control method therefor which are imposed less restrictions on the positioning of components forming part of the vibration isolating apparatus, such as active actuators, can be implemented by a relatively simple controller (for example, implemented by an analog circuit), and limit the interference of control forces to a practically ignorable degree.
For a vibration isolating apparatus having a common table, points at which the active actuators act their forces exist on substantially the same plane on which the active actuators can be relatively freely positioned. Here, when the active actuators are positioned such that the resilient supporting center thereof matches the Z-axis of the inertial system, the attenuation matrix C and rigid matrix K in the set of equation (1) are expressed as the following equation (2), wherein a vertical translational motion Z is independent of a rotational motion &ggr; about the axis:
C
=
&AutoLeftMatch;
&AutoRightMatch;
[
∑
i
=
1
n
c
xi
0
0
0
∑
i
=
1
n
(
d
zi
·
c
xi
)
0
0
∑
i
=
1
n
c
yi
0
-
∑
i
=
1
n
(
d
zi
·
c
yi
)
0
0
0
0
∑
i
=
1
n
c
zi
0
0
0
0
-
∑
i
=
1
n
(
d
zi
·
c
yi
)
0
∑
i
=
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n
(
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zi
2
·
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yi
+
d
yi
2
·
c
zi
)
0
0
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i
=
1
n
(
d
zi
·
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xi
)
0
0
0
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=
1
n
(
d
zi
2
·
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xi
+
d
xi
2
·
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zi
)
0
0
0
0
0
0
∑
i
=
1
n
(
d
yi
2
·
c
xi
+
d
xi
2
·
c
yi
)
]
K
=
&AutoLeftMatch;
[
∑
i
=
1
n
k
xi
0
0
0
∑
i
=
1
n
(
d
zi
·
k
xi
)
0
0
∑
i
=
1
n
k
yi
0
-
∑
i
=
1
n
(
d
zi
·
k
yi
)
0
0
0
0
∑
i
=
1
n
k
zi
0
0
0
0
-
∑
i
=
1
n
(
d
zi
·
Haga Takahide
Jouno Yoshinori
Watanabe Katsuhide
Ebara Corporation
King Anita
Le Tan
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