JP3696926B2 - Active vibration isolation device and sensor placement method for the device - Google Patents

Description

で示される連立方程式の係数行列Ａの条件数が最小となるように前記センサのそれぞれの計測方向を決定することを特徴としている。
【００１２】
本発明のアクティブ除振装置は、前記運動パラメータＰ_ｘ，Ｐ_ｙ，Ｐθ_ｚのそれぞれに重み付けする際、前記係数行列Ａに重み行列Ｗをかけた係数行列ＡＷの条件数が最小となるように前記センサのそれぞれの計測方向を決定したり、前記センサと前記除振台の重心位置を結ぶ直線と前記センサの運動検出方向に実質的に一致する直線とが前記ＸＹ平面上でなす角度が、前記センサのそれぞれにおいて実質的に同一となるように前記センサのそれぞれの計測方向を決定したりしても良い。
【００１３】
またこの場合、前記センサのそれぞれは実質的に正３角形の各頂点近傍に配置されたり、前記除振台は実質的に正３角形構造を有し、前記センサのそれぞれは前記除振台の各頂点近傍に配置されたり、更に前記アクチュエータのそれぞれは前記センサに対応するように前記除振台の各頂点近傍に配置されても良い。
【００１４】
また、本発明は、機器を３点支持する支持台の運動を３つのセンサのそれぞれで検出し、前記センサの検出出力に基づいてアクチュエータを制御することにより前記支持台の除振を行うアクティブ除振装置のセンサ配置方法において、前記除振台のＸＹ平面に関する運動の内、Ｘ方向の運動パラメータをＰ_ｘ、Ｙ方向の運動パラメータをＰ_ｙ、前記ＸＹ平面上の回転方向であるθ方向の運動パラメータをＰθ_ｚとし、前記センサのそれぞれの出力信号をＳ１，Ｓ２，Ｓ３とするとき、前記センサのそれぞれの幾何学的な配置からベクトル〔Ｐ_ｘ，Ｐ_ｙ，Ｐθ_ｚ〕とベクトル〔Ｓ１，Ｓ２，Ｓ３〕の間に成り立つ
【００１５】
【外４】

で示される連立方程式の係数行列Ａの条件数が最小となるように前記センサのそれぞれの計測方向を決定することを特徴としている。
【００１６】
本発明のアクティブ除振装置のセンサ配置方法では、前記運動パラメータＰ_ｘ，Ｐ_ｙ，Ｐθ_ｚのそれぞれに重み付けする際、前記係数行列Ａに重み行列Ｗをかけた係数行列ＡＷの条件数が最小となるように前記センサのそれぞれの計測方向を決定したり、前記センサと前記除振台の重心位置を結ぶ直線と前記センサの運動検出方向に実質的に一致する直線とが前記ＸＹ平面上でなす角度が、前記センサのそれぞれにおいて実質的に同一となるように前記センサのそれぞれの計測方向を決定しても良い。
【００１７】
【作用】
このように本発明は、センサの配置から定まるセンサ出力信号と除振台の運動としての並進及び回転運動との間に成り立つ連立方程式において、解である除振台の並進及び回転運動が方程式中の誤差によって受ける影響の大きさを示す尺度である係数行列の条件数に着目し、この条件数をセンサ配置のための定量的指標としている。そして、条件数を最小にするようなセンサ配置を行なうことによって、除振台の並進及び回転運動を観測ノイズの影響を最小限に抑えて精度よく算出することを可能にしている。
【００１８】
また、除振台の剛体運動としての並進及び回転方向運動に重みを付け、上記係数行列と重み行列の積である行列の条件数を最小とするようにセンサを配置することによって、並進運動と回転運動との間の物理的次元の違いを考慮に入れた、または特定の運動の算出精度を重視した、観測ノイズの影響を最小限に抑えた精度よい除振台の並進及び回転運動の算出を可能にする。
【００１９】
本発明によれば、係数行列の条件数が最小となるようにセンサを配置しているから、求めた除振台の並進および回転運動は、センサ出力信号に含まれる観測ノイズやセンサ位置の公称値と真値との差など誤差要因の影響を最小に抑えた、精度の最も高いものである。
【００２０】
【実施例】
図１は本発明によるアクティブ除振装置、及びそれに内蔵するセンサの配置の代表的な実施例を示す図面である。図１はアクティブ除振装置の上面図であり、その上部に半導体製造用露光装置のＸＹステージ等の精密機器が載置される正三角形構造の支持台（以降除振台と呼ぶ）４は、その各頂点部を支持機構である除振装置１ａ，１ｂ，１ｃによって支持されている。除振装置１ａ，１ｂ，１ｃにはそれぞれ加速度、速度、及び移動量といった除振台４の運動を計測するセンサ２ａ，２ｂ，２ｃと、除振台４へ力を作用させるアクチュエータ３ａ，３ｂ，３ｃが備えられている。
【００２１】
以下に、除振台４の水平方向振動を精度良く計測するためのセンサ２ａ，２ｂ，２ｃとの最適配置について説明する。除振台４は剛体であるとすると、その水平方向の運動は水平面内における重心点の並進運動２自由度と重心点を通る鉛直軸回りの回転運動１自由度との合計３自由度に分類される。
【００２２】
除振台４の重心点をＧとして、原点がＧであるＸＹＺ直交座標系を除振台に固定する。ＸＹ平面は水平面と一致させる。すると除振台４の水平方向運動はＸ，Ｙ方向の並進運動及びＧを通る鉛直軸（Ｚ）回りのθ_z方向の回転運動で代表できる。これら運動方向のことを除振台４の運動モード、そして運動モードごとの除振台の変位や加速度といった運動を表すパラメータを運動パラメータと定義する。除振台４の水平方向の運動モードはＸ、Ｙ、θ_Zであり、そして各モードごとの運動パラメータはＰ_x，Ｐ_y，Ｐθ_zと表記することにする。
【００２３】
ここでいうセンサ２ａ，２ｂ，２ｃとは加速度、速度、及び移動位置など機械的な１軸直線運動が計測可能なものである。各センサ２ａ，２ｂ，２ｃの計測点は除振台４の頂点位置にあり、且つ各センサ２ａ，２ｂ，２ｃの計測方向ベクトルと各アクチュエータ３ａ，３ｂ，３ｃの発生力の作用方向ベクトルは重心Ｇを通る水平面（ＸＹ平面）内にあるものとする。すると、各センサ２ａ，２ｂ，２ｃの配置の自由度は、除振台４の各頂点を通る鉛直軸回りの回転１自由度である。除振台４は正三角形構造であるから重心Ｇから除振台４の各頂点までの距離、即ち重心Ｇから各センサ２ａ，２ｂ，２ｃまでの距離は等しくｒである。
【００２４】
図１に示すように、重心Ｇに固定したＸＹ座標系からみたセンサ２ａの座標を（ｘ_a，ｙ_a）とし、またこのセンサ２ａの座標点から計測方向に沿って正の向きに向かうベクトルとＸ軸とがなす角度をθ_2axとする。除振台４が運動パラメータＰ_x，Ｐ_y，Ｐθ_zで表される運動をしているときのセンサ２ａの出力信号をｓ_aとすると、運動パラメータとセンサ出力信号ｓ_aは下記の(3)式のような関係にある。
【００２５】
【外５】

【００２６】
センサ２ｂ，２ｃについても同様に、重心Ｇに固定したＸＹ座標系からみたセンサ２ｂ，２ｃの座標をそれぞれ（ｘ_b，ｙ_b）、及び（ｘ_c，ｙ_c）とし、これら座標点から計測方向に沿って正の向きに向かうベクトルとＸ軸とがなす角度をθ_2bx、θ_2cxとすると、３つのセンサ出力信号ｓ_a，ｓ_b，ｓ_cと前記運動パラメータＰ_x、Ｐ_y、Ｐθ_zは下記の(4)式の線形方程式で結び付けられる。
【００２７】
ここで、(4)式、(5)式のＡはセンサ２ａ，２ｂ，２ｃの位置と計測向きによって決まる係数行列である。センサ２ａ，２ｂ，２ｃの座標は下記の(6)式に示すように除振台４の３つの頂点を通る円の半径ｒから定まる。よって係数行列Ａは半径ｒとセンサ計測向き（θ_2ax，θ_2bx，θ_2cx）の関数として表される。(4)式の線形方程式を利用すれば、除振台４の運動パラメータＰ_x，Ｐ_y，Ｐθ_zは３つのセンサ出力信号から求められることがわかる。
【００２８】
【外６】

【００２９】
アクティブ除振装置の制御方法としては、それぞれの除振装置１ａ，１ｂ，１ｃに内蔵されたセンサ２ａ，２ｂ，２ｃとアクチュエータ３ａ，３ｂ，３ｃとで制御ループを閉じて各除振装置独立に制御をするほかに、除振台４の運動モードごとに制御ループを構成することが行なわれている。この場合はセンサ情報から除振台４の運動パラメータを測定して、運動モード別に除振台４に加える操作力を決定し、その運動モード別の操作力を実現するようにアクチュエータ３ａ，３ｂ，３ｃを駆動する。
【００３０】
センサ情報から除振台４の運動パラメータを測定するためには上記（４）式を利用する。（４）式に示す線形一次の連立方程式を解けば運動パラメータＰｘ，Ｐｙ，Ｐθｚが求められる。ところで、（４）式の左辺は各センサ２ａ，２ｂ，２ｃの出力信号であるから測定ノイズが含まれる。また、センサ配置で定まる係数行列Ａにも誤差が混在する可能性がある。
【００３１】
このような観測データ中に含まれる誤差によって解である運動パラメータが受ける影響を定量的に評価するには、係数行列Ａの条件数（Condition Number）を調べればよい。条件数は最小値が１の正の数である。条件数が大きい（悪い）と、センサ出力信号のわずかな差によって解である運動パラメータが大きく変化する。あるいはセンサの位置と方向の実測値と真値とのわずかなずれが解である運動パラメータの信頼性を大きく損ねてしまう。条件数が無限大になると、係数行列Ａにランク落ちが発生する。即ち、運動パラメータを解くことができなくなる。
【００３２】
条件数が最も１に近く（最も良く）なるようなセンサ２ａ，２ｂ，２ｃの配置が、運動パラメータを測定するために最適なセンサ配置である。これはまた、除振台４の水平３自由度運動を最も計測しやすいセンサ配置であるということもできる。よって、運動モードごとに除振台４を制御する場合の運動パラメータ測定にとって最適なセンサ配置であることは、各除振装置独立に制御をする場合でもまた最適なセンサ配置となる。
【００３３】
以上より、(5)式に示した係数行列Ａの条件数が最小となるようにセンサ２ａ，２ｂ，２ｃの計測方向を決定すれば、それが最適なセンサ配置である。条件数をセンサ配置のための定量的指標とすることができる。
【００３４】
図１は条件数を最小とするセンサ配置を示している。各センサ２ａ，２ｂ，２ｃはそのセンサ計測方向の直線と、センサの位置する除振台４の各頂点と重心Ｇとを結ぶ線とがなす鋭角が全て同一の角度θとなり、且つその鋭角θは鋭角をなす除振台４の各頂点と重心Ｇとを結ぶ線の左側にくるように配置される。
【００３５】
また、図２に示すように、同じ鋭角θが鋭角をなす除振台４の各頂点と重心Ｇとを結ぶ線の右側にくるようなセンサ配置でも条件数は最小となる。(5)式に示した係数行列Ａの条件数が最小となるセンサ配置は、図１と図２に示した配置のみである。センサ角度θは除振台４の半径ｒの大きさによって０度から９０度の範囲に一意的に決まる。図１、図２の矢線はセンサ測定方向の正の向きをあらわす。センサ２ａ，２ｂ，２ｃごとに矢線は同一方向反対の向きである。つまり測定の正の向きは問題とならない。
【００３６】
センサ角度θは半径ｒが小さいほど大きくなる。これは理にかなったことである。θ_Z方向の回転運動を最も検出しやすいセンサ配置は、図３に示すような重心と頂点を結ぶ線に対して直角方向（円周方向）である。これに対してＸ，Ｙ方向の並進運動を最も検出しやすいセンサ配置は、図４に示すような重心Ｇを向く方向（半径方向）である。除振台４の半径ｒが小さいほどθ_Z方向の回転運動は検出しづらくなるから、センサ２ａ，２ｂ，２ｃはより円周方向に向けなくてはならない。すなわち、センサ角度θは大きくなる。このように、半径ｒによって係数行列Ａの条件数を最小にするセンサ配置は異なってくる。
【００３７】
例として、半径ｒ＝１の場合はセンサ角度θ＝４５度で(4)式の行列Ａの条件数は最小となる。これは、円周方向と半径方向の中間の方向である。最小値は１である。
【００３８】
図１、図２に示した実施例では、アクチュエータ３ａ，３ｂ，３ｃをセンサ２ａ，２ｂ，２ｃと同一方向に配置している。これによってアクティブ除振装置の制御方法としては、除振台４の運動モードごとに制御ループを構成する方法と、各除振台毎に閉じた制御ループを構成する方法の双方を実現することができる。
【００３９】
先の実施例において、センサ最適配置を導くための基礎式となった(4)式では、運動パラメータＰ_x，Ｐ_y，Ｐθ_zの物理的次元は同一ではない。並進パラメータＰ_x，Ｐ_yと回転パラメータＰθ_zでは次元が異なるので、先の実施例では物理的に次元が違う量を同列に扱ってセンサの最適配置を導出していることになる。長さの単位を〔ｍ〕、回転量の単位を〔ｒａｄ〕として運動パラメータをあらわした場合に、実際の除振台４の運動が並進パラメータＰ_x、Ｐ_yと回転パラメータＰθ_zとで、そのとる値が同等であるようなときは、(4)式を基礎式としてよい。
【００４０】
それ以外のときには、並進パラメータと回転パラメータとの間に重み付けをする必要がある。また、特定の運動パラメータを精度良く測定するために他の運動パラメータの測定精度をある程度犠牲にする場合にも、運動パラメータに重みをつける。運動パラメータ間の重みを考慮したセンサの最適配置のための基礎式は下記の(7)式、(8)式のようになる。
【００４１】
【外７】

【００４２】
この(7)式、(8)式で示された線形連立方程式の係数行列ＡＷの条件数を最小にするセンサの配置が、最適なセンサ配置である。重みの付け方は、精度よく測定したい運動モードの重みｗ_i（ｉ＝ｘ，ｙ，θ_z）を大きく設定すればよい。また除振台４の運動を運動モード別にあらわしたときに各運動パラメータＰ_x，Ｐ_y，Ｐθ_zのとる値が同等であり、且つどの運動パラメータも同等の精度で測定するのならば、重みは同一となる（ｗ_x＝ｗ_y＝ｗθ_z＝１）。
【００４３】
並進方向運動パラメータＰ_x，Ｐ_yの重み値ｗ_x，ｗ_yが同値である場合には、先の実施例と同様に３つのセンサ２ａ，２ｂ，２ｃは、センサ２ａ，２ｂ，２ｃの位置する除振台４の各頂点と重心Ｇとを結ぶ線に対して同一の角度θの方向を向く。
【００４４】
センサ角度θの値は重みｗ_x（＝ｗ_y）とｗθ_zの比、そして除振台４の半径ｒによって変化する。重みｗ_x，ｗ_yが異なる場合には、センサ角度は３つのセンサ２ａ，２ｂ，２ｃについて同一とはならない。例として、Ｙ方向並進運動パラメータＰ_yの精度を重視したセンサの最適配置を示す。重みはｗ_y＝２、ｗ_x＝ｗθ_z＝１、そして除振台４の半径ｒ＝１として計算したものである。係数行列ＡＷの条件数を最小とするセンサ配置は図５の（ａ），（ｂ）に示す２通りである。Ｙ方向の測定精度を重視したため、センサ測定方向はＹ方向に近づいている。
【００４５】
なお、以上の実施例は３点支持機構の除振台の水平３自由度の除振を対象として説明しているが、運動パラメータとセンサ信号出力とを結びつける連立方程式の係数行列の条件数を最小とする本発明は、３点支持機構の除振台だけを対象とするものではなく、また水平３自由度のみを対象としているものでもない。本発明は算出を行なう運動パラメータと同数のセンサの配置に関して、あらゆる場合に適用することができる。
【００４６】
【発明の効果】
以上に説明したとおり、本発明によれば、除振台の例えば水平方向３自由度の振動を支持機構である除振台に内蔵する振動センサで、観測ノイズの影響を最小限に抑えて精度よく算出することができる。また、センサ配置の定量的指標を提供することができる。
【図面の簡単な説明】
【図１】本発明のアクティブ除振装置の最も代表的な一実施例を示す図。
【図２】図１に示した実施例の変形例を示す図。
【図３】回転運動を最も測定しやすい状態にしたセンサ配置を示す図。
【図４】並進運動を最も測定しやすい状態にしたセンサ配置を示す図。
【図５】ｙ方向並進運動の測定精度を重視した本発明の他の実施例を示す図。
【符号の説明】
１ａ，１ｂ，１ｃ 除振装置
２ａ，２ｂ，２ｃ 振動センサ
３ａ，３ｂ，３ｃ アクチュエータ
４ 除振台[0001]
[Industrial application fields]
The present invention relates to an active vibration isolation device and a sensor arrangement method for the device, and more particularly to an active vibration isolation device that serves as a support mechanism in any mechanical system such as a precision instrument represented by a semiconductor exposure apparatus and a sensor arrangement method for the device.
[0002]
[Prior art]
As precision instruments such as electron microscopes, step-and-repeat (scan) types, and other semiconductor exposure apparatuses become more precise, there is a need for higher performance of precision vibration isolation devices that mount them.
[0003]
In particular, in a semiconductor exposure apparatus, in order to perform appropriate and quick exposure, a vibration isolation table that removes vibrations transmitted from the outside such as vibrations of an installation floor as much as possible is required. This is because, when exposing each shot area on the semiconductor wafer, the XY stage that moves the semiconductor wafer along the XY plane must be completely stopped. Further, the XY stage is characterized by an intermittent operation called step-and-repeat, and repeated step vibrations thereby excite the vibration of the support base (vibration isolation base) supporting the device itself.
[0004]
Therefore, the vibration isolation table is required to achieve a good balance between the vibration isolation performance against external vibration and the vibration suppression performance against vibration generated by the operation of the device itself. In response to this demand, an active vibration isolator that actively controls vibration by detecting vibration of the vibration isolation table using a vibration sensor, compensating the output signal, and feeding back to the actuator has been put into practical use. Yes. The active vibration isolation device enables a balanced realization of vibration isolation performance and vibration suppression performance, which is difficult with a conventional passive vibration isolation device composed only of a support mechanism having a spring and a damper characteristic.
[0005]
An example of the active vibration isolator is disclosed in, for example, Japanese Patent Laid-Open No. 6-167414. In this conventional example, a total of seven sensors are arranged to calculate translational and rotational motions with respect to six degrees of freedom of the vibration isolation table. The breakdown of the sensor arrangement is 1 in the X-axis direction, 2 in the Y-axis direction, and 2 in the Z-axis direction as seen from the Cartesian coordinate system in which the long side direction of the rectangular vibration isolation table is aligned with the X axis, and the vertical direction is aligned with the Z axis. There are 4 in the direction.
[0006]
[Problems to be solved by the invention]
By the way, as described above, in the control of the vibration isolation table by the active vibration isolation device, the translation and rotation motion of the vibration isolation table as a rigid body motion is calculated from the output signal of the sensor, and a feedback loop is configured for each motion direction. Things have been done. Therefore, the sensor must be arranged so that the translational and rotational movements as the rigid body motion of the vibration isolation table can be detected, and the observation noise and the nominal and true values of the sensor position included in the sensor output signal. It is desirable to arrange so as to minimize the error in the calculation result caused by the difference between the two.
[0007]
With the sensor arrangement described in Japanese Patent Laid-Open No. 6-167414, it is possible to calculate translational and rotational motions with respect to six degrees of freedom of the vibration isolation table. However, the observation noise included in the sensor output signal and the nominal value of the sensor position No consideration is given to the influence of the difference between the value and the true value on the calculation result. In addition, a clear quantitative index is not shown for the sensor arrangement in order to accurately calculate the translational and rotational motion with respect to the six degrees of freedom of the vibration isolation table.
[0008]
The present invention has been made in view of such circumstances, and its purpose is to accurately calculate the translational and rotational motions as the rigid body motion of the vibration isolation table while minimizing the influence of error factors such as observation noise. It is an object of the present invention to provide an active vibration isolating apparatus that enables proper vibration isolation.
[0009]
Another object of the present invention is to provide a sensor arrangement for an active vibration isolator capable of accurately calculating the translational and rotational motion of the vibration isolation table as a rigid body motion while minimizing the influence of error factors such as observation noise. It is to provide a method.
[0010]
[Means for Solving the Problems]
In order to achieve the above object, the present invention detects vibration of a support base that supports three points of equipment by each of three sensors, and controls the actuator based on the detection output of the sensor to thereby isolate the vibration of the support base. In the active vibration isolator that performs the above, the motion parameter in the X direction is P _x , the motion parameter in the Y direction is P _y , and the θ direction is the rotational direction on the XY plane. motion parameters and Pshita _z, when the respective output signals S1, S2, S3 of the sensor, each of the geometric arrangement of the vector of the sensor _{[P x, P y, Pθ z]} and vector [S1 , S2, S3 ].
[Outside 3]

Each measuring direction of the sensor is determined so that the condition number of the coefficient matrix A of the simultaneous equations expressed by
[0012]
In the active vibration isolator of the present invention, when weighting each of the motion parameters P _x , P _y , Pθ _z , the condition number of the coefficient matrix AW obtained by multiplying the coefficient matrix A by the weight matrix W is minimized. The measurement direction of each of the sensors is determined, or an angle formed on the XY plane by a straight line that connects the center of gravity position of the sensor and the vibration isolation table and a straight line that substantially matches the motion detection direction of the sensor, The measurement direction of each of the sensors may be determined so as to be substantially the same in each of the sensors.
[0013]
Also in this case, each or is substantially disposed at each apex near the regular triangle of the previous SL sensor, the anti-vibration table has a substantially regular triangular structure, each of said sensor said anti-vibration table The actuators may be arranged near the vertices of the vibration isolation table so as to correspond to the sensors.
[0014]
In addition, the present invention detects the movement of the support base that supports the device at three points by each of the three sensors, and controls the actuator based on the detection output of the sensor to perform vibration isolation of the support base. In the vibration sensor arrangement method, among the movements of the vibration isolation table with respect to the XY plane, the movement parameter in the X direction is P _x , the movement parameter in the Y direction is P _y , and the rotation direction on the XY plane is the θ direction. motion parameters and Pshita _z, when the respective output signals S1, S2, S3 of the sensor, each of the geometric arrangement of the vector of the sensor _{[P x, P y, Pθ z]} and vector [S1 , S2, S3 ].
[Outside 4]

Each measuring direction of the sensor is determined so that the condition number of the coefficient matrix A of the simultaneous equations expressed by
[0016]
In the sensor placement method of the active vibration isolator of the present invention, when weighting each of the motion parameters P _x , P _y , Pθ _z , the condition number of the coefficient matrix AW obtained by multiplying the coefficient matrix A by the weight matrix W is the smallest. The measurement direction of each of the sensors is determined such that the straight line connecting the sensor and the position of the center of gravity of the vibration isolation table and the straight line substantially matching the motion detection direction of the sensor are on the XY plane. The measurement direction of each of the sensors may be determined so that the angle formed is substantially the same in each of the sensors.
[0017]
[Action]
Thus, in the present invention, in the simultaneous equations established between the sensor output signal determined from the sensor arrangement and the translation and rotation motions as the motion of the vibration isolation table, the translation and rotation motions of the vibration isolation table as a solution are in the equation. Focusing on the condition number of the coefficient matrix, which is a measure indicating the magnitude of the effect of the error, the condition number is used as a quantitative index for sensor placement. By arranging the sensors so as to minimize the number of conditions, it is possible to accurately calculate the translation and rotation of the vibration isolation table while minimizing the influence of observation noise.
[0018]
In addition, the translational motion and the rotational motion as the rigid body motion of the vibration isolation table are weighted, and the sensor is arranged so as to minimize the condition number of the matrix which is the product of the coefficient matrix and the weight matrix, so that the translational motion and Accurate translational and rotational motion calculation of the vibration isolation table with minimal influence of observation noise, taking into account the physical dimension difference from the rotational motion, or focusing on the calculation accuracy of specific motion Enable.
[0019]
According to the present invention, since the sensors are arranged so that the condition number of the coefficient matrix is minimized, the obtained translational and rotational motions of the vibration isolation table are the nominal values of the observation noise and the sensor position included in the sensor output signal. It is the one with the highest accuracy that minimizes the influence of error factors such as the difference between the value and the true value.
[0020]
【Example】
FIG. 1 is a drawing showing a typical embodiment of the arrangement of an active vibration isolator according to the present invention and sensors incorporated therein. FIG. 1 is a top view of an active vibration isolation device, and a support base (hereinafter referred to as a vibration isolation table) 4 having an equilateral triangular structure on which precision equipment such as an XY stage of an exposure apparatus for semiconductor manufacturing is placed is shown in FIG. Each vertex is supported by vibration isolation devices 1a, 1b and 1c which are support mechanisms. The vibration isolation devices 1a, 1b, and 1c include sensors 2a, 2b, and 2c that measure the motion of the vibration isolation table 4 such as acceleration, speed, and amount of movement, and actuators 3a, 3b, and 3b that apply force to the vibration isolation table 4, respectively. 3c is provided.
[0021]
Below, the optimal arrangement | positioning with the sensors 2a, 2b, 2c for measuring the horizontal direction vibration of the vibration isolator 4 with sufficient accuracy is demonstrated. Assuming that the vibration isolation table 4 is a rigid body, its horizontal movement is classified into a total of three degrees of freedom, ie, two degrees of freedom of translational movement of the center of gravity in the horizontal plane and one degree of freedom of rotational movement about the vertical axis passing through the center of gravity. Is done.
[0022]
The center of gravity of the vibration isolation table 4 is G, and an XYZ orthogonal coordinate system whose origin is G is fixed to the vibration isolation table. The XY plane coincides with the horizontal plane. Then, the horizontal motion of the vibration isolation table 4 can be represented by the translational motion in the X and Y directions and the rotational motion in the _θz direction around the vertical axis (Z) passing through G. These motion directions are defined as motion parameters, which are motion modes of the vibration isolation table 4 and parameters representing motion such as displacement and acceleration of the vibration isolation table for each motion mode. The horizontal motion modes of the vibration isolation table 4 are X, Y, and θ _Z , and the motion parameters for each mode are expressed as P _x , P _y , and Pθ _z .
[0023]
The sensors 2a, 2b, and 2c here can measure mechanical uniaxial linear motion such as acceleration, speed, and moving position. The measurement point of each sensor 2a, 2b, 2c is at the apex position of the vibration isolation table 4, and the measurement direction vector of each sensor 2a, 2b, 2c and the action direction vector of the generated force of each actuator 3a, 3b, 3c are the center of gravity. It is assumed that it is in a horizontal plane (XY plane) passing through G. Then, the freedom degree of arrangement | positioning of each sensor 2a, 2b, 2c is 1 degree of freedom of rotation around the vertical axis which passes each vertex of the vibration isolator 4. Since the vibration isolation table 4 has an equilateral triangle structure, the distance from the center of gravity G to each vertex of the vibration isolation table 4, that is, the distance from the center of gravity G to each sensor 2a, 2b, 2c is equal r.
[0024]
As shown in FIG. 1, the coordinates of the sensor 2a viewed from the XY coordinate system fixed to the center of gravity G are set to (x _a , y _a ), and the vector heads in the positive direction along the measurement direction from the coordinate point of the sensor 2a. And the angle formed by the X axis is θ _2ax . Anti-vibration table 4 are motion parameters P _x, P _y, and the output signal of the sensor 2a and s _a time that the motion represented by Pθ _z, motion parameters and the sensor output signal s _a is the following (3 There is a relationship like
[0025]
[Outside 5]

[0026]
Similarly, for the sensors 2b and 2c, the coordinates of the sensors 2b and 2c as viewed from the XY coordinate system fixed to the center of gravity G are (x _b , y _b ) and (x _c , y _c ), respectively. the angle formed between the vector and the X-axis toward the positive direction along the direction theta _2bx, When theta _2cx, 3 one sensor output signal s _a, s _b, s _c and the motion parameters P _x, P _y, Pθ _z is linked by the following linear equation (4).
[0027]
Here, A in the equations (4) and (5) is a coefficient matrix determined by the positions and measurement directions of the sensors 2a, 2b, and 2c. The coordinates of the sensors 2a, 2b, 2c are determined from the radius r of a circle passing through the three vertices of the vibration isolation table 4 as shown in the following equation (6). Thus the coefficient matrix A radius r and the sensor measurement direction _{(θ 2ax, θ 2bx, θ} 2cx) expressed as a function of. If the linear equation (4) is used, it can be seen that the motion parameters P _x , P _y , Pθ _z of the vibration isolation table 4 can be obtained from the three sensor output signals.
[0028]
[Outside 6]

[0029]
As a method for controlling the active vibration isolator, the control loop is closed by the sensors 2a, 2b, 2c and the actuators 3a, 3b, 3c built in the respective vibration isolators 1a, 1b, 1c, and each vibration isolator is independent of each other. Besides the control, a control loop is formed for each motion mode of the vibration isolation table 4. In this case, the motion parameters of the vibration isolation table 4 are measured from the sensor information, the operation force applied to the vibration isolation table 4 is determined for each motion mode, and the actuators 3a, 3b, 3c is driven.
[0030]
In order to measure the motion parameter of the vibration isolation table 4 from the sensor information, the above equation (4) is used. The motion parameters Px, Py, Pθz can be obtained by solving the linear linear simultaneous equations shown in the equation (4). Incidentally, since the left side of the equation (4) is an output signal of each sensor 2a, 2b, 2c, measurement noise is included. Further, there is a possibility that an error is mixed in the coefficient matrix A determined by the sensor arrangement.
[0031]
In order to quantitatively evaluate the influence of the motion parameter as a solution due to the error included in such observation data, the condition number of the coefficient matrix A may be examined. The condition number is a positive number having a minimum value of 1. If the condition number is large (bad), the motion parameter as a solution changes greatly due to a slight difference in sensor output signals. Alternatively, a slight deviation between the measured value and true value of the sensor position and direction greatly impairs the reliability of the motion parameter as a solution. When the condition number becomes infinite, rank drop occurs in the coefficient matrix A. That is, the motion parameters cannot be solved.
[0032]
The arrangement of the sensors 2a, 2b, 2c so that the condition number is closest to 1 (best) is the optimum sensor arrangement for measuring the motion parameter. It can also be said that this is a sensor arrangement that can most easily measure the horizontal three-degree-of-freedom movement of the vibration isolation table 4. Therefore, the optimal sensor arrangement for measuring the movement parameters when the vibration isolation table 4 is controlled for each movement mode is also the optimum sensor arrangement even when the vibration isolation devices are controlled independently.
[0033]
As described above, if the measurement directions of the sensors 2a, 2b, and 2c are determined so that the condition number of the coefficient matrix A shown in the equation (5) is minimized, this is the optimum sensor arrangement. The condition number can be a quantitative indicator for sensor placement.
[0034]
FIG. 1 shows a sensor arrangement that minimizes the number of conditions. In each sensor 2a, 2b, 2c, the acute angle formed by the straight line in the sensor measurement direction and the line connecting each vertex of the vibration isolation table 4 where the sensor is located and the center of gravity G is the same angle θ, and the acute angle θ Are arranged so as to be on the left side of a line connecting each vertex of the vibration isolation table 4 having an acute angle and the center of gravity G.
[0035]
In addition, as shown in FIG. 2, the number of conditions is minimized even when the sensor arrangement is on the right side of the line connecting each vertex of the vibration isolation table 4 and the center of gravity G where the same acute angle θ forms an acute angle. The sensor arrangement that minimizes the condition number of the coefficient matrix A shown in the equation (5) is only the arrangement shown in FIGS. The sensor angle θ is uniquely determined in the range of 0 to 90 degrees depending on the size of the radius r of the vibration isolation table 4. 1 and 2 indicate the positive direction of the sensor measurement direction. For each of the sensors 2a, 2b and 2c, the arrow lines are in the opposite direction. In other words, the positive direction of measurement does not matter.
[0036]
The sensor angle θ increases as the radius r decreases. This makes sense. The most easily detected sensor arrangement the rotary motion of the theta _Z direction is perpendicular (circumferential direction) with respect to a line connecting the center of gravity and the vertex, as shown in FIG. On the other hand, the sensor arrangement that most easily detects the translational motion in the X and Y directions is the direction (radial direction) that faces the center of gravity G as shown in FIG. Since the anti-vibration table rotational movement of the more theta _Z-direction radius r is small for 4 becomes difficult to detect, the sensor 2a, 2b, 2c must be directed more circumferentially. That is, the sensor angle θ increases. As described above, the sensor arrangement for minimizing the condition number of the coefficient matrix A varies depending on the radius r.
[0037]
As an example, when the radius r = 1, the sensor angle θ = 45 degrees, and the condition number of the matrix A in the equation (4) is minimum. This is an intermediate direction between the circumferential direction and the radial direction. The minimum value is 1.
[0038]
In the embodiment shown in FIGS. 1 and 2, the actuators 3a, 3b and 3c are arranged in the same direction as the sensors 2a, 2b and 2c. Thus, as a control method of the active vibration isolation device, it is possible to realize both a method of configuring a control loop for each motion mode of the vibration isolation table 4 and a method of configuring a closed control loop for each vibration isolation table. it can.
[0039]
In the previous embodiment, the physical dimensions of the motion parameters P _x , P _y , Pθ _z are not the same in equation (4), which is the basic equation for deriving the optimum sensor arrangement. Since the translation parameters P _x , P _y and the rotation parameter Pθ _z have different dimensions, the previous embodiment derives the optimal arrangement of the sensors by treating the physically different quantities in the same row. When the unit of length is [m] and the unit of rotation is [rad] and the motion parameters are expressed, the actual motion of the vibration isolation table 4 is represented by the translation parameters P _x and P _y and the rotation parameter Pθ _z . If the values are equivalent, equation (4) may be used as the basic equation.
[0040]
In other cases, it is necessary to weight between the translation parameter and the rotation parameter. Also, in order to accurately measure a specific motion parameter, the motion parameter is also weighted when the accuracy of measurement of other motion parameters is sacrificed to some extent. The basic equations for optimal sensor placement considering the weights between motion parameters are as shown in the following equations (7) and (8).
[0041]
[Outside 7]

[0042]
The sensor arrangement that minimizes the condition number of the coefficient matrix AW of the linear simultaneous equations expressed by the equations (7) and (8) is the optimum sensor arrangement. As a weighting method, the weight w _i (i = x, y, θ _z ) of the motion mode to be measured with high accuracy may be set large. If the motion of the vibration isolation table 4 is represented by motion mode, the values of the motion parameters P _x , P _y , Pθ _z are equivalent, and any motion parameter is measured with the same accuracy, the weight Are the same (w _x = w _y = wθ _z = 1).
[0043]
When the weight values w _x and w _{y of the} translational direction motion parameters P _x and P _y are the same, the three sensors 2a, 2b, and 2c are positioned at the positions of the sensors 2a, 2b, and 2c as in the previous embodiment. The direction of the same angle θ with respect to the line connecting each vertex of the vibration isolation table 4 and the center of gravity G.
[0044]
The value of the sensor angle θ varies depending on the ratio of the weights w _x (= w _y ) and wθ _z and the radius r of the vibration isolation table 4. When the weights w _x and w _y are different, the sensor angles are not the same for the three sensors 2a, 2b, and 2c. As an example, the optimal placement of the sensor with an emphasis on accuracy of Y-direction translation motion parameters P _y. The weights are calculated with w _y = 2, w _x = wθ _z = 1, and the radius r = 1 of the vibration isolation table 4. There are two sensor arrangements shown in FIGS. 5A and 5B that minimize the condition number of the coefficient matrix AW. Since the measurement accuracy in the Y direction is emphasized, the sensor measurement direction is close to the Y direction.
[0045]
Although the above embodiment has been described for vibration isolation with three horizontal degrees of freedom of the vibration isolation table of the three-point support mechanism, the condition number of the coefficient matrix of the simultaneous equations connecting the motion parameter and the sensor signal output is The present invention to be minimized is not intended only for the vibration isolation table of the three-point support mechanism, and is not intended only for the three horizontal degrees of freedom. The present invention can be applied in all cases with respect to the arrangement of the same number of sensors as the motion parameters to be calculated.
[0046]
【The invention's effect】
As described above, according to the present invention, the vibration sensor with built-in vibration of the vibration isolation table, for example, three degrees of freedom in the horizontal direction in the vibration isolation table that is the support mechanism can minimize the influence of the observation noise and improve the accuracy. It can be calculated well. In addition, a quantitative indicator of sensor placement can be provided.
[Brief description of the drawings]
FIG. 1 is a diagram showing a most typical embodiment of an active vibration isolator according to the present invention.
FIG. 2 is a diagram showing a modification of the embodiment shown in FIG.
FIG. 3 is a diagram showing a sensor arrangement in which rotational movement is most easily measured.
FIG. 4 is a diagram showing a sensor arrangement in which translational movement is most easily measured.
FIG. 5 is a diagram showing another embodiment of the present invention in which importance is attached to the measurement accuracy of the y-direction translational movement.
[Explanation of symbols]
1a, 1b, 1c Vibration isolator 2a, 2b, 2c Vibration sensor 3a, 3b, 3c Actuator 4 Vibration isolation table

Claims (9)

In the active vibration isolator for detecting vibration of the support base by detecting the motion of the support base that supports the device at three points by each of the three sensors and controlling the actuator based on the detection output of the sensor. Among the motions of the shaking table in relation to the XY plane, the motion parameter in the X direction is Px, the motion parameter in the Y direction is Py, and the motion parameter in the θ direction, which is the rotational direction on the XY plane, is Pθz. When the signals are S1, S2, and S3 , the relationship between the vector [Px, Py, Pθz] and the vector [ S1, S2, S3 ] is established from the respective geometrical arrangements of the sensors.

An active vibration isolation device that determines the measurement direction of each of the sensors so that the condition number of the coefficient matrix A of the simultaneous equations represented by When each of the motion parameters Px, Py, Pθz is weighted, each measurement direction of the sensor is determined so that the condition number of the coefficient matrix AW obtained by multiplying the coefficient matrix A by the weight matrix W is minimized. The active vibration isolator according to claim 1. The angle formed on the XY plane by a straight line connecting the center of gravity of the sensor and the vibration isolation table and a straight line substantially matching the motion detection direction of the sensor is substantially the same in each of the sensors. The active vibration isolation device according to claim 1, wherein a measurement direction of each of the sensors is determined. The active vibration isolator according to claim 3, wherein each of the sensors is arranged in the vicinity of each vertex of a regular triangle. 4. The active vibration isolation device according to claim 3, wherein the vibration isolation table has a substantially triangular structure, and each of the sensors is disposed near each vertex of the vibration isolation table. The active vibration isolation device according to claim 5, wherein each of the actuators is disposed near each vertex of the vibration isolation table so as to correspond to the sensor. A sensor placement method for an active vibration isolator that detects the motion of a support base that supports three devices by each of three sensors and controls the actuator based on the detection output of the sensor to perform vibration isolation of the support base. The motion parameter in the X direction is Px, the motion parameter in the Y direction is Py, and the motion parameter in the θ direction, which is the rotational direction on the XY plane, is Pθz. When the respective output signals of S1, S2, and S3 are S1, S2, and S3 , the relationship between the vector [Px, Py, Pθz] and the vector [ S1, S2, S3 ] is established based on the geometrical arrangement of the sensors. ]

A sensor placement method for an active vibration isolator, wherein the measurement direction of each of the sensors is determined so that the condition number of the coefficient matrix A of the simultaneous equations expressed by When each of the motion parameters Px, Py, Pθz is weighted, each measurement direction of the sensor is determined so that the condition number of the coefficient matrix AW obtained by multiplying the coefficient matrix A by the weight matrix W is minimized. The sensor placement method of the active vibration isolator according to claim 7. The angle formed on the XY plane by a straight line connecting the center of gravity of the sensor and the vibration isolation table and a straight line substantially matching the motion detection direction of the sensor is substantially the same in each of the sensors. 8. The sensor placement method for an active vibration isolator according to claim 7, wherein a measurement direction of each of the sensors is determined.

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