Patent Publication Number: US-2012045723-A1

Title: Vibration isolation device, exposure apparatus, and device manufacturing method using same

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a vibration isolation device, an exposure apparatus, and a device manufacturing method using the same. 
     2. Description of the Related Art 
     An exposure apparatus is an apparatus that transfers a pattern of an original (reticle or mask) onto a photosensitive substrate (e.g., wafer, glass plate, or the like, where the surface thereof is coated with a resist layer) via a projection optical system in a lithography process of a manufacturing process for a semiconductor device, a liquid crystal display device, or the like. In the exposure apparatus which is involved in the ultra-fining of a pattern, the vibration transmitted from the floor upon which the exposure apparatus stands to the apparatus body may cause degradation of overlapping exposure (overlay) accuracy, exposure image accuracy, and the like. Accordingly, the exposure apparatus is generally arranged via a vibration isolation device for reducing the influence of floor vibration. Likewise, for a highly accurate measuring apparatus, an electron beam plotting apparatus, a processing apparatus employing imprint technology, or the like, a method for supporting the main body thereof by a vibration isolation device is employed. 
     The conventional vibration isolation device uses a gas spring inserted between the vibration isolation table and the floor. In addition, to increase the damping characteristic of the vibration isolation device, the velocity feedback control is performed using an acceleration sensor arranged on the vibration isolation table and an actuator interposed between the vibration isolation table and the floor. However, the velocity feedback control may increase the damping characteristic of the vibration isolation device, but may not lower the natural frequency of the vibration isolation device. Hence, Japanese Patent Laid-Open No. 2007-240396 discloses a vibration isolation device in which a pendulum (reference body) supported by a spring member extended from a frame is arranged on a vibration isolation table and measures relative displacement between the frame and the pendulum to thereby feedback-control the position of the relative displacement to an actuator for driving the vibration isolation table. 
     In general, when a vibration isolation device feedback-controls the position of a vibration isolation table with respect to a reference body supported by an elastic system having a low natural frequency, the vibration isolation device may isolate the vibration at a frequency lower than the natural frequency defined by the mass of the vibration isolation table and the rigidity of the gas spring. As a means for realizing an elastic system having a low natural frequency, the reference body is typically supported by a spring member or a pendulum. In this case, in order to achieve a considerably low natural frequency of the reference body, the weight of the reference body, the rigidity of the spring, the length of the pendulum, and the like need to be mechanically adjusted. However, when the reference body is arranged on the vibration isolation table, it is difficult to realize the reference body having a considerably low natural frequency, for example, 1 Hz or lower due to installation space. 
     In general, as a compensator for a position feedback control system, a PID compensator is used. In this case, firstly, the relative position between the reference body of which the position is feedback-controlled by the PID compensator and the vibration isolation table is measured. When the relative position is position feed back to an actuator for driving the vibration isolation table, the integrator provided in the PID compensator of the reference body couples with the rigidity of the gas spring in the vibration isolation device, and thus, a sharp peak occurs in the transfer function from the base to the vibration isolation table. Therefore, when the sharp peak is excited due to floor vibration or the like, the vibration isolation table may oscillate significantly. 
     SUMMARY OF THE INVENTION 
     The present invention has been made in view of the aforementioned circumstances, and provides a vibration isolation device that exhibits excellent vibration isolation performance even at a low frequency. 
     In view of the foregoing, according to an aspect of the present invention, a vibration isolation device that isolates the vibration of an object to be isolated from vibration supported on a base is provided that includes a first position feedback control system including a reference body system that is fixed to the object to be isolated from vibration and includes a reference body; a first driving unit that drives the object to be isolated from vibration with respect to the base; and a first compensator that calculates a command value for the first driving unit based on position information obtained from the reference body system, wherein the reference body system includes a second position feedback control system including a second driving unit that drives the reference body with respect to the object to he isolated from vibration; a first measuring unit that measures the position of the reference body relative to the object to be isolated from vibration; and a second compensator that calculates a command value to the second driving unit based on position information obtained from the first measuring unit, and wherein the second compensator is a PD compensator. 
     According to the present invention, a vibration isolation device that exhibits excellent vibration isolation performance even at a low frequency may be provided. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a schematic diagram illustrating a reference body system that is arranged in the horizontal direction according to an embodiment of the present invention. 
         FIG. 1B  is a schematic diagram illustrating a first reference body system that is arranged in the vertical direction according to an embodiment of the present invention. 
         FIG. 1C  is a schematic diagram illustrating a second reference body system that is arranged in the vertical direction according to an embodiment of the present invention. 
         FIG. 2  is a schematic view illustrating the configuration of a vibration isolation device according to a first embodiment. 
         FIG. 3  is a Bode plot diagram of the transfer function H from a base to a vibration isolation table. 
         FIG. 4A  is a block diagram of the transfer function H from the base to the vibration isolation table. 
         FIG. 4B  is a block diagram of the transfer function H from the base to the vibration isolation table. 
         FIG. 4C  is a block diagram of the transfer function H from the base to the vibration isolation table. 
         FIG. 5  is a Bode plot diagram of the transfer function H and the transfer function G 1 ×H 1 . 
         FIG. 6A  is a pole arrangement diagram of the transfer function H Apid . 
         FIG. 6B  is a pole arrangement diagram of the transfer function H Apd . 
         FIG. 7A  is a schematic view illustrating the configuration of a vibration isolation device according to a second embodiment. 
         FIG. 7B  is a schematic view illustrating the configuration of a vibration isolation device according to a third embodiment. 
         FIG. 7C  is a schematic view illustrating the configuration of a vibration isolation device according to a fourth embodiment. 
         FIG. 7D  is a schematic view illustrating the configuration of a vibration isolation device according to a fifth embodiment. 
         FIG. 8A  is a Bode plot diagram of the transfer function H 2  from the base to the vibration isolation table. 
         FIG. 8B  is a Bode plot diagram of the transfer function H 3  from the base to the vibration isolation table. 
         FIG. 9A  is a block diagram of the transfer function H 2  from the base to the vibration isolation table. 
         FIG. 9B  is a block diagram of the transfer function H A2  from the base to the vibration isolation table. 
         FIG. 9C  is a block diagram of the transfer function H 3  from the base to the vibration isolation table. 
         FIG. 9D  is a block diagram of the transfer function H A3  from the base to the vibration isolation table. 
         FIG. 10A  is a Bode plot diagram of the transfer function H 4  from the base to the vibration isolation table. 
         FIG. 10B  is a Bode plot diagram of the transfer function H 5  from the base to the vibration isolation table. 
         FIG. 11  is a schematic view illustrating the configuration of a vibration isolation device according to an eighth embodiment. 
         FIG. 12  is a block diagram illustrating a method for controlling a vibration isolation device according to the eighth embodiment. 
         FIG. 13  is a schematic view illustrating the configuration of a vibration isolation device according to a ninth embodiment. 
         FIG. 14A  is a schematic view illustrating the configuration of a reference body system according to the ninth embodiment. 
         FIG. 14B  is a bottom plan view illustrating a reference body facing a base in a reference body system according to the ninth embodiment. 
         FIG. 14C  is a top plan view illustrating a base facing a reference body in a reference body system according to the ninth embodiment. 
         FIG. 15  is a block diagram illustrating a method for controlling a vibration isolation device according to the ninth embodiment. 
         FIG. 16  is a schematic view illustrating the configuration of an exposure apparatus according to an embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Hereinafter, preferred embodiments of the present invention will now be described with reference to the accompanying drawings. 
     First Embodiment 
     Firstly, a description will be given of a reference body system to be employed for a vibration isolation device according to an embodiment of the present invention.  FIGS. 1A to 1C  are schematic views illustrating the configuration of a reference body system for a single axis measurement to he employed for the vibration isolation device of the present invention. In particular,  FIG. 1A  is a schematic diagram illustrating a reference body system  10  that is arranged in the horizontal direction,  FIG. 1B  is a schematic diagram illustrating a first reference body system  20  that is arranged in the vertical direction, and  FIG. 1C  is a schematic diagram illustrating a second reference body system  30  that is arranged in the vertical direction. In the following drawings, a description will be given by taking the Z-axis in the vertical direction of the reference body system, and the X-axis and the Y-axis in the horizontal direction normal to the Z-axis. 
     Firstly, as shown in  FIG. 1A , the reference body system  10  for the horizontal direction includes a reference body base  11 , a linear guide  12 , an actuator  13  provided consecutively to the linear guide  12 , a reference body  14  supported by the linear guide  12 , and a position sensor  15 . The linear guide  12  is a guide unit that is rigidly fixed to the reference body base  11  so as to guide a linear slider  12   a.  For example, as the linear guide  12 , an air guide, an electromagnetic guide, or the like may be employed. For the linear slider  12   a  that is movable relative to the fixing section of the linear guide  12 , the actuator  13  is arranged at one end thereof and the reference body  14  is arranged at the other end thereof. The actuator  13  is a driving unit (second driving unit) that employs, for example, a voice coil motor or the like. The reference body  14  is an object that is supported by the reference body base  11  with a natural frequency lower than that of the object to be isolated from vibration so as to allow the position of the object to be isolated from vibration to be tracked to thereby enhance vibration isolation performance. Although, in the present embodiment, the reference body  14  is formed separately from the linear slider  12   a,  the reference body  14  may be integrally formed with the linear slider  12   a.  The position sensor  15  is a measuring unit (first measuring unit) that measures the relative position between the reference body base  11  and the reference body  14 . In order to reduce the measurement error of the position sensor  15 , the linear guide  12  is arranged as far as possible parallel to the reference body base  11 . 
     Furthermore, the reference body system  10  includes a compensator  16 , which is electrically connected to the actuator  13  and the position sensor  15 , as part of a control system. Here, the control system is a control unit (second position feedback control system) that feedback-controls the position of the reference body  14  relative to the reference body base  11  based on position information  17  obtained by the position sensor  15 . The compensator  16  is a unit (second compensator) that calculates a control signal  19 , which is a command value applied to the actuator  13 , based on the position information  17  and a preset target value  18 . In particular, in the present embodiment, a PD compensator is employed as the compensator  16 . Formula 1 is a formula indicative of the transfer function for the PD compensator, where reference symbol M r  denotes the mass of the reference body  14 , reference symbol W cr  denotes the crossover frequency of the feedback-control of the position of the reference body  14 , reference symbol W cr  denotes the break frequency of a differentiator, and reference symbol s is a complex number (Laplace operator). 
     
       
         
           
             
               
                 
                   
                     M 
                     r 
                   
                   · 
                   
                     W 
                     cr 
                   
                   · 
                   
                     
                       W 
                       dr 
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         
                           s 
                           
                             W 
                             dr 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Next, as shown in  FIG. 1B  and  FIG. 1C , each of first and second reference body systems  20  and  30  for the vertical direction includes a reference body base  21 , a linear guide  22 , an actuator  23 , a reference body  24 , a position sensor  25 , and a compensator  26 . Each of the reference body systems  20  and  30  is in a state in which the reference body system  10  is rotated by 90 degrees. Since the components of each of the first and second reference body systems  20  and  30  correspond to the components of the reference body system  10  and provide the same effects as those of the reference body system  10 , the explanation thereof will be omitted. Here, a description will be given of an own-weight compensation unit  27  for compensating the own-weight of the reference body  24 , which is the feature of the reference body systems  20  and  30  for the vertical direction. The own-weight compensation unit  27  is a compensation unit configured to compensate the own weight of a mobile unit including the reference body  24 . Examples of the own-weight compensation unit  27  include a permanent magnet or an own-weight compensation spring. Firstly, as shown in  FIG. 1B , the first reference body system  20  employs a permanent magnet  27   m  as the own-weight compensation unit  27 . In this case, the permanent magnet  27   m  compensates the own-weight of the reference body  24  by generating a repulsive force substantially balancing with a gravity force of the reference body  24 . On the other hand, as shown in  FIG. 1C , the second reference body system  30  employs an own-weight compensation spring  27   s  as the own-weight compensation unit  27 . The own-weight compensation spring  27   s  also compensates the own-weight of the reference body  24  by generating a repulsive force substantially balancing with a gravity force of the reference body  24 . When the own-weight compensation spring  27   s  is employed as shown in  FIG. 1C , the weight of the mobile units including the reference body  24  and the natural frequency defined by the spring rigidity of the own-weight compensation spring  27   s  are set so as to be lower than the crossover frequency of the feedback-control of the position of the reference body  24 . 
     Next, a description will be given of a vibration isolation device according to the present embodiment employing the reference body system.  FIG. 2  is a schematic view illustrating the configuration of a vibration isolation device according to the present embodiment. In the present embodiment, a description will be given on the assumption that a vibration isolation device is intended to isolate vibration in the vertical direction and the first reference body system  20  for the vertical direction is employed as shown in  FIG. 2 . Firstly, a vibration isolation device  1  includes a base  2  and a vibration isolation table  3  that is an object to be isolated from vibration, which is supported by the base  2 . A plurality of gas springs (air springs)  4  serving as vibration isolation units and a plurality of actuators  5  serving as first driving units are arranged between the base  2  and the vibration isolation table  3 . The vibration isolation device  1  further includes the reference body system  20  provided on the vibration isolation table  3 . The reference body system  20  is rigidly fixed to the vibration isolation table  3 , and thus, the position information  17  for the reference body system  20  is the relative position information between the reference body  24  and the vibration isolation table  3 . The control system (first position feedback control system) feedbacks the position information  17  to the actuator  5  to thereby feedback-control the position of the vibration isolation table  3  relative to the reference body  24 . Furthermore, the vibration isolation device  1  includes a compensator (first compensator)  8  that calculates a control signal  7  to be sent to the actuator  5  based on the position information  17  and a target value  6  transmitted from the control device in advance. In particular, in the present embodiment, a PID compensator is employed as the compensator  8 . Formula 2 is a formula indicative of the transfer function for the PID compensator, where reference symbol M j  denotes the mass of the vibration isolation table  3 , reference symbol W cj  denotes the crossover frequency of the feedback-control of the position of the vibration isolation table  3 , reference symbol W dj  denotes the break frequency of a differentiator, and reference symbol W ij  denotes the break frequency of an integrator. 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       j 
                     
                     · 
                     
                       W 
                       cj 
                     
                     · 
                     
                       
                         W 
                         dj 
                       
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                           + 
                           
                             s 
                             
                               W 
                               dj 
                             
                           
                         
                         ) 
                       
                     
                   
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                       1 
                       + 
                       
                         
                           W 
                           ij 
                         
                         s 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     Next, a case where a PD compensator is employed as the compensator  26  of the reference body system  20 , as in the present embodiment, is compared to an exemplary case where a PID compensator is employed as the same.  FIG. 3  is a Bode plot diagram of the transfer function H from the base  2  to the vibration isolation table  3  for a case where a PD compensator is employed as the compensator  26  and a case where a PID compensator is employed as the same. In  FIG. 3 , the horizontal axis represents frequency (Hz), and the vertical axis represents the gain (dB) of the transfer function H in the upper figure and represents the phase angle (deg) of the transfer function H in the lower figure. The vertical axis and the horizontal axis are similarly applied to the following Bode plot diagrams. As shown in  FIG. 3 , when a PID compensator is employed, a sharp peak occurs around 0.01 Hz. In contrast, when a PD compensator is employed as in the present embodiment, such a vibration isolation device exhibits excellent vibration isolation performance even at a low frequency without producing a sharp peak. In particular, the vibration isolation table  3  is isolated from vibration at a frequency lower than the natural frequency defined by the mass M j  of the vibration isolation table  3  and the rigidity k of the gas spring. Hereinafter, a lower-limit frequency that can be isolated from vibration by feedback-controlling the position of the vibration isolation table  3  relative to the reference body  24  is referred to as a “vibration isolation frequency”. 
     Next, a description will be given of a method for calculating the vibration isolation frequency.  FIGS. 4A to 4   c  are block diagrams illustrating the transfer function H from the base  2  to the vibration isolation table  3 . In  FIG. 4 , reference symbol G cr  denotes the compensator  26 , reference symbol G o  denotes the compensator  8  for the vibration isolation table  3 , reference symbol k j  denotes the rigidity of the gas spring, and reference symbol C j  denotes the viscosity of the gas spring. Here, when 1/(M r ×s 2 +G cr ) is replaced by Gr and 1/(M×s 2 +C×s+K j ) is replaced by G oj , the block diagram shown in  FIG. 4A  can be modified into the block diagram shown in  FIG. 4B . Furthermore, given that the product of G cj ×G oj  is represented by G 1  and the product of 1−G cr ×G r  is represented by H 1 , the transfer function H is represented as shown in Formula 3 when the product of G 1 ×H 1 &gt;1, whereas the transfer function H is represented as shown in Formula 4 when the product of G 1 ×H 1 &lt;1. 
     
       
         
           
             
               
                 
                   H 
                   = 
                   
                     
                       
                         
                           
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                     3 
                   
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                             2 
                           
                         
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                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     Here, the right side of Formula 4 is the transfer function, which is transferred from the base  2  to the vibration isolation table  3 , related to the vibration isolation table  3  when the position-feedback-control is not performed. In other words, Formula 3 and Formula 4 indicate that the vibration isolation frequency of the vibration isolation table  3  that provides position-feedback-control is the crossover frequency of the transfer function (G 1 ×H 1 ). Hence, when the crossover frequency of the transfer function (G 1 ×H 1 ) is calculated, the vibration isolation frequency of the vibration isolation table  3  that provides position-feedback-control may be determined. Since the vibration isolation frequency is low frequency, the transfer function (G 1 ×H 1 ) is represented by Formula 5 when only the factors that affect low frequency are taken into account. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     For comparison,  FIG. 5  shows a Bode plot diagram of the transfer function H and the transfer function (G 1 ×H 1 ) represented by Formula 5. As shown in  FIG. 5 , it is understood that the vibration isolation frequency of the vibration isolation table  3  subject to position-feedback-control is the crossover frequency of the transfer function (G 1 ×H 1 ). In other words, the crossover frequency of the transfer function (G 1 ×H 1 ) represented by Formula 5 is a solution obtained when the right side of Formula 5 is set to 1, and the value of the solution is represented by Formula 6. Also, Formula 6 may be approximated as in Formula 7 based on the relationship of M j ×W cj ×W dj &gt;&gt;K j . 
     
       
         
           
             
               
                 
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     It should be noted that the vibration isolation frequency of the vibration isolation table  3  subject to position-feedback-control must be lower than the natural frequency that is defined by the mass M j  of the vibration isolation table  3  and the rigidity K j  of the gas spring  4 . Thus, the relational formula represented by Formula 8 needs to be satisfied. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                      
                     8 
                   
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     Next, the reasons that a sharp peak occurs when a PID compensator is employed as the compensator  26  of the reference body system  20  whereas a sharp peak does not occur when a PD compensator is employed as in the present embodiment, as shown in  FIG. 3 , will be described below. Firstly, when the block diagram shown in  FIG. 4A  is transformed, the resulting block diagram is as shown in  FIG. 4C . Here, when the block diagram enclosed within the frame shown in  FIG. 4C  is defined as the transfer function H A , and is further transformed, the transfer function H A  is represented by Formula 9. 
     
       
         
           
             
               
                 
                   
                     H 
                     A 
                   
                   = 
                   
                     
                       
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                       · 
                       
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                         · 
                         
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                         · 
                         
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                           or 
                         
                       
                     
                   
                 
               
               
                 
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                      
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     Firstly, assume the case where a PID compensator is employed as the compensator  26 . In this case, the transfer function H A  is represented by the transfer function H Apid . When a PID compensator is employed as the compensator  26 , the transfer function of the compensator  26  is represented by Formula 10, provided that reference symbol W ir  denotes the break frequency of the integrator of the reference body  14 . 
     
       
         
           
             
               
                 
                   
                     G 
                     cr 
                   
                   = 
                   
                     
                       
                         M 
                         r 
                       
                       · 
                       
                         W 
                         cr 
                       
                       · 
                       
                         
                           W 
                           dr 
                         
                          
                         
                           ( 
                           
                             1 
                             + 
                             
                               s 
                               
                                 W 
                                 dr 
                               
                             
                           
                           ) 
                         
                       
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             W 
                             iv 
                           
                           s 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     Here, since a peak occurs in the transfer function H at a low frequency, reference symbols G cj , G oj , G cr , and G or  are represented by Formula 11, Formula 12, Formula 13, and Formula 14, respectively, when only the factors that affect low frequency are taken into account. 
     
       
         
           
             
               
                 
                   
                     G 
                     cj 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           M 
                           j 
                         
                         · 
                         
                           W 
                           cj 
                         
                         · 
                         
                           W 
                           dj 
                         
                       
                       ) 
                     
                      
                     
                       
                         s 
                         + 
                         
                           W 
                           ij 
                         
                       
                       s 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     G 
                     oj 
                   
                   = 
                   
                     1 
                     
                       K 
                       j 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     G 
                     cr 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           M 
                           r 
                         
                         · 
                         
                           W 
                           cr 
                         
                         · 
                         
                           W 
                           dr 
                         
                       
                       ) 
                     
                      
                     
                       
                         s 
                         + 
                         
                           W 
                           ir 
                         
                       
                       s 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     13 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     G 
                     or 
                   
                   = 
                   
                     1 
                     
                       
                         M 
                         r 
                       
                       · 
                       
                         s 
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     Here, when Formulae 11 to Formula 14 are substituted for Formula 9, the transfer function H Apid  is represented by Formula 15, provided that the relationships MW j =M j ×W cj ×W oj  and MW r =M r ×W cr ×W or  are satisfied. 
     
       
         
           
             
               
                 
                   
                     H 
                     Apid 
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 MW 
                                 j 
                               
                               · 
                               
                                 MW 
                                 r 
                               
                               · 
                               
                                 s 
                                 2 
                               
                             
                             + 
                             
                               
                                 
                                   MW 
                                   j 
                                 
                                 · 
                                 M 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   W 
                                   r 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       W 
                                       ij 
                                     
                                     + 
                                     
                                       W 
                                       ir 
                                     
                                   
                                   ) 
                                 
                               
                                
                               s 
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               MW 
                               j 
                             
                             · 
                             
                               MW 
                               r 
                             
                             · 
                             
                               W 
                               ij 
                             
                             · 
                             
                               W 
                               ir 
                             
                           
                         
                       
                     
                     
                       s 
                        
                       
                         { 
                         
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           K 
                                           j 
                                         
                                         · 
                                         
                                           M 
                                           r 
                                         
                                       
                                       + 
                                       
                                         
                                           MW 
                                           j 
                                         
                                         · 
                                         
                                           M 
                                           r 
                                         
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     s 
                                     3 
                                   
                                 
                                 + 
                                 
                                   
                                     MW 
                                     j 
                                   
                                   · 
                                   
                                     M 
                                     r 
                                   
                                   · 
                                   
                                     W 
                                     ij 
                                   
                                   · 
                                   
                                     s 
                                     2 
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     MW 
                                     r 
                                   
                                   · 
                                   
                                     K 
                                     j 
                                   
                                   · 
                                   s 
                                 
                                 + 
                                 
                                   
                                     MW 
                                     r 
                                   
                                   · 
                                   
                                     K 
                                     j 
                                   
                                   · 
                                   
                                     W 
                                     ir 
                                   
                                 
                               
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
       FIG. 6A  is a pole arrangement diagram of the transfer function H Apid  obtained when the values shown in Table 1 are substituted for M j , K j , W cj , W dj , W ij , M r , W cr , W dr , and W ir  in Formula 15 described above. In  FIG. 6A , the vertical axis represents the imaginary axis and the horizontal axis represents the real axis. The characteristic equation of the transfer function H Apid  has conjugate complex number solutions as shown by the “X” mark in  FIG. 6A , and more specifically, has two real number solutions (one of them is zero) and two conjugate complex number solutions as represented by Formula 16. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Symbol 
                 Value 
                 Unit 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 M j   
                 500.00 
                 Kg 
               
               
                 K j   
                 177650.00 
                 N/m 
               
               
                 W cj   
                 251.33 
                 rad/s 
               
               
                 W dj   
                 83.78 
                 rad/s 
               
               
                 W ij   
                 41.89 
                 rad/s 
               
               
                 M r   
                 0.67 
                 Kg 
               
               
                 W cr   
                 6.28 
                 rad/s 
               
               
                 W dr   
                 2.09 
                 rad/s 
               
               
                 W ir   
                 1.05 
                 rad/s 
               
               
                   
               
            
           
         
       
     
     
       
         
           
             
               
                 
                   
                     s 
                      
                     
                       { 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   K 
                                   j 
                                 
                                 · 
                                 
                                   M 
                                   r 
                                 
                               
                               + 
                               
                                 
                                   MW 
                                   j 
                                 
                                 · 
                                 
                                   M 
                                   r 
                                 
                               
                             
                             ) 
                           
                            
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             MW 
                             j 
                           
                           · 
                           
                             M 
                             r 
                           
                           · 
                           
                             W 
                             ij 
                           
                           · 
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             MW 
                             r 
                           
                           · 
                           
                             K 
                             j 
                           
                           · 
                           s 
                         
                         + 
                         
                           
                             MW 
                             r 
                           
                           · 
                           
                             K 
                             j 
                           
                           · 
                           
                             W 
                             ir 
                           
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       
                         s 
                          
                         
                           ( 
                           
                             s 
                             + 
                             a 
                           
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           s 
                           - 
                           
                             ( 
                             
                               
                                 - 
                                 b 
                               
                               - 
                               ic 
                             
                             ) 
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           s 
                           - 
                           
                             ( 
                             
                               
                                 - 
                                 b 
                               
                               + 
                               ic 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     = 
                     0 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
     In this way, when a PID compensator is employed as the compensator  26  of the reference body system  20 , the break frequency W ir  of the integrator of the PID compensator, the rigidity K j  of the gas spring  4 , M r , W cr , and W dr  are coupled to each other, and thus, the characteristic equation of the transfer function H Apid  have the conjugate complex number solutions. In other words, the damping ratio is in the range of 0&lt;ζ&lt;1 due to having conjugate complex number solutions, and thus the vibration isolation table  3  is in a deficient damping state. Thus, a sharp peak occurs in the transfer function H from the base  2  to the vibration isolation table  3 . 
     Next, assume the case where a PD compensator is employed as the compensator  26  according to the present embodiment. In this case, the transfer function H A  is represented by the transfer function H Apd . Since a sharp peak occurs at a low frequency in a case in which the PID compensator is employed, G cr  (the compensator  26 ) is represented by Formula 17 when only the factors that affect low frequency are taken into account. Furthermore, as in Formula 15, when Formula 11, Formula 12, Formula 14, and Formula 17 are substituted for Formula 9, the transfer function H Apd  in this case is represented by Formula 18. 
     
       
         
           
             
               
                 
                   
                     G 
                     cr 
                   
                   = 
                   
                     
                       M 
                       r 
                     
                     · 
                     
                       W 
                       cr 
                     
                     · 
                     
                       W 
                       dr 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     17 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     H 
                     Apd 
                   
                   = 
                   
                     
                       
                         MW 
                         j 
                       
                       · 
                       
                         
                           MW 
                           r 
                         
                          
                         
                           ( 
                           
                             s 
                             + 
                             
                               W 
                               ij 
                             
                           
                           ) 
                         
                       
                     
                     
                       s 
                        
                       
                         { 
                         
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           K 
                                           j 
                                         
                                         · 
                                         
                                           M 
                                           r 
                                         
                                       
                                       + 
                                       
                                         
                                           MW 
                                           j 
                                         
                                         · 
                                         
                                           M 
                                           r 
                                         
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     s 
                                     2 
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     MW 
                                     j 
                                   
                                   · 
                                   
                                     M 
                                     r 
                                   
                                   · 
                                   
                                     W 
                                     ij 
                                   
                                   · 
                                   s 
                                 
                                 + 
                                 
                                   
                                     MW 
                                     r 
                                   
                                   · 
                                   
                                     K 
                                     j 
                                   
                                 
                               
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
       FIG. 6B  is a pole arrangement diagram of the transfer function H Apd  obtained when the values shown in Table 2 are substituted for M j , K j , W cj , W dj , W ij , M r , W cr , and W dr  in Formula 18 described above.  FIG. 6B  corresponds to the pole arrangement diagram shown in  FIG. 6A . As shown in  FIG. 6B , the characteristic equation of the transfer function H Apd  does not have a conjugate complex number solution, but has three real number solutions (one of them is zero) as represented by Formula 19. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Symbol 
                 Value 
                 Unit 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 M j   
                 500.00 
                 Kg 
               
               
                 K j   
                 177650.00  
                 N/m 
               
               
                 W cj   
                 251.33 
                 rad/s 
               
               
                 W dj   
                 83.78 
                 rad/s 
               
               
                 W ij   
                 41.89 
                 rad/s 
               
               
                 M r   
                 0.67 
                 Kg 
               
               
                 W cr   
                 6.28 
                 rad/s 
               
               
                 W dr   
                 2.09 
                 rad/s 
               
               
                   
               
            
           
         
       
     
     
       
         
           
             
               
                 
                   
                     s 
                      
                     
                       { 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   K 
                                   j 
                                 
                                 · 
                                 
                                   M 
                                   r 
                                 
                               
                               + 
                               
                                 
                                   MW 
                                   j 
                                 
                                 · 
                                 
                                   M 
                                   r 
                                 
                               
                             
                             ) 
                           
                            
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             MW 
                             j 
                           
                           · 
                           
                             M 
                             r 
                           
                           · 
                           
                             W 
                             ij 
                           
                           · 
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             MW 
                             r 
                           
                           · 
                           
                             K 
                             j 
                           
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       
                         s 
                          
                         
                           ( 
                           
                             s 
                             + 
                             
                               a 
                               ′ 
                             
                           
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           s 
                           + 
                           
                             b 
                             ′ 
                           
                         
                         ) 
                       
                     
                     = 
                     0 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     19 
                   
                   ] 
                 
               
             
           
         
       
     
     In this way, when a PD compensator is employed as the compensator  26  of the reference body system  20 , the characteristic equation of the transfer function H Apd  does not have any conjugate complex number solution. In other words, the vibration isolation table  3  is in a critical damping state or in an excessive damping state, the occurrence of a sharp peak in the transfer function H from the base  2  to the vibration isolation table  3  can be suppressed. 
     As described above, according to the present invention, since a PD compensator is employed as the compensator of the reference body system and is controlled by the position feedback control system, a reference body having a considerably low natural frequency may be realized simply by adjusting the gain of the position-feedback. Thus, the vibration isolation device  1  employing the reference body system may exhibit excellent vibration isolation performance even at a low frequency. While a description has been given by taking an example where the vibration isolation device  1  is arranged in the vertical direction, the present invention is applicable to the case where the vibration isolation device  1  is arranged in the horizontal direction as well. 
     Second Embodiment 
     Next, a description will be given of a vibration isolation device according to a second embodiment of the present invention.  FIG. 7A  is a schematic view illustrating the configuration of a vibration isolation device according to the present embodiment. A vibration isolation device  40  of the present embodiment includes a reference body system  42  employing a PID compensator (second compensator)  41  instead of the compensator  26  that serves as the PD compensator of the reference body system  20  according to the first embodiment. Furthermore, the reference body system  42  includes a velocity sensor (second measuring unit)  43  that measures the velocity of the reference body  24  with respect to an absolute space. As shown in  FIG. 7A , the velocity sensor  43  is arranged, for example, on the side surface of the reference body  24 . In this case, a control system (velocity feedback control system) further feedback-controls the velocity of the reference body  24  relative to an absolute space via a compensator (third compensator)  45  based on the velocity information  44  obtained from the velocity sensor  43 . The compensator  45  calculates a drive signal  47  to be sent to the actuator  23  based on the velocity information  44  and a preset target value  46 . At this time, the control device applies the proportional gain C r2  to the compensator  45 . 
     Next, a case where a PID compensator  41  is employed for the reference body system  42  and the velocity of the reference body  24  relative to an absolute space is feedback-controlled is compared to another case where a PID compensator  41  is employed for the same and the velocity of the reference body  24  relative to an absolute space is not feedback-controlled.  FIG. 8A  is a Bode plot diagram of the transfer function H 2  from the base  2  to the vibration isolation table  3  for each of the two cases. As shown in  FIG. 8A , when a PID compensator is employed as in the present embodiment and a velocity feedback control is performed, a sharp peak around 0.01 Hz is damped, and thus, excellent vibration isolation performance is achieved even at a low frequency. 
     Next, the reasons why the aforementioned sharp peak is damped will be described below.  FIG. 9A  is a block diagram of the transfer function H 2  from the base  2  to the vibration isolation table  3  in this case. Firstly, the block diagram shown in  FIG. 9A  is transformed, the resulting block diagram is as shown in  FIG. 9B . Here, when the block diagram enclosed within the frame shown in  FIG. 9B  is defined as the transfer function and is further transformed, the transfer function H is represented by Formula 20. Also, G or2  is represented by Formula 21. 
     
       
         
           
             
               
                 
                   
                     H 
                     
                       A 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       
                         G 
                         cj 
                       
                       · 
                       
                         G 
                         oj 
                       
                       · 
                       
                         G 
                         cr 
                       
                       · 
                       
                         G 
                         
                           or 
                           2 
                         
                       
                     
                     
                       1 
                       + 
                       
                         
                           G 
                           cj 
                         
                         · 
                         
                           G 
                           oj 
                         
                       
                       + 
                       
                         
                           G 
                           cr 
                         
                         · 
                         
                           G 
                           
                             or 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     20 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     G 
                     
                       or 
                       2 
                     
                   
                   = 
                   
                     1 
                     
                       
                         
                           M 
                           r 
                         
                         · 
                         
                           s 
                           2 
                         
                       
                       + 
                       
                         
                           C 
                           
                             r 
                             2 
                           
                         
                         · 
                         s 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     21 
                   
                   ] 
                 
               
             
           
         
       
     
     Here, when Formulae 11 to 13 and Formula 21 are substituted for Formula 20, the transfer function H A2  is represented by Formula 22. Note that the small terms of M wj ×C r2  and K j ×C r2  are ignored. 
     
       
         
           
             
               
                 
                   
                     H 
                     
                       A 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 MW 
                                 j 
                               
                               · 
                               
                                 MW 
                                 r 
                               
                               · 
                               
                                 s 
                                 2 
                               
                             
                             + 
                             
                               
                                 
                                   MW 
                                   j 
                                 
                                 · 
                                 
                                   
                                     MW 
                                     r 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         W 
                                         ij 
                                       
                                       - 
                                       
                                         W 
                                         ir 
                                       
                                     
                                     ) 
                                   
                                 
                               
                                
                               s 
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               MW 
                               j 
                             
                             · 
                             
                               MW 
                               r 
                             
                             · 
                             
                               W 
                               ij 
                             
                             · 
                             
                               W 
                               ir 
                             
                           
                         
                       
                     
                     
                       s 
                        
                       
                           
                       
                        
                       
                         { 
                         
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           K 
                                           j 
                                         
                                         · 
                                         
                                           M 
                                           r 
                                         
                                       
                                       + 
                                       
                                         
                                           MW 
                                           j 
                                         
                                         · 
                                         
                                           M 
                                           r 
                                         
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     s 
                                     2 
                                   
                                 
                                 + 
                                 
                                   
                                     MW 
                                     j 
                                   
                                   · 
                                   
                                     M 
                                     r 
                                   
                                   · 
                                   
                                     W 
                                     ij 
                                   
                                   · 
                                   
                                     s 
                                     2 
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           MW 
                                           r 
                                         
                                         · 
                                         
                                           K 
                                           j 
                                         
                                       
                                       + 
                                       
                                         
                                           MW 
                                           j 
                                         
                                         · 
                                         
                                           W 
                                           ij 
                                         
                                         · 
                                         
                                           C 
                                           
                                             r 
                                              
                                             
                                                 
                                             
                                              
                                             2 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                    
                                   s 
                                 
                                 + 
                                 
                                   
                                     MW 
                                     r 
                                   
                                   · 
                                   
                                     K 
                                     j 
                                   
                                   · 
                                   
                                     W 
                                     ir 
                                   
                                 
                               
                             
                           
                         
                          
                         
                             
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     22 
                   
                   ] 
                 
               
             
           
         
       
     
     In this way, when the characteristic equation (Formula 22) of the transfer function of the present embodiment is compared with the characteristic equation (Formula 15) of the transfer function H Apid  of the first embodiment, only the first-order term of s within the double parentheses is changed. When iω is substituted into s, the first order term of s is a term including a complex number, and a term for determining the damping characteristic of the transfer function H A2 . Thus, if the velocity of the reference body  24  relative to an absolute space is feedback-controlled, a peak generated by the transfer function may be damped even when a PID compensator is employed for the compensator  41  of the reference body system  42 . 
     Third Embodiment 
     Next, a description will be given of a vibration isolation device according to a third embodiment of the present invention.  FIG. 7B  is a schematic view illustrating the configuration of a vibration isolation device according to the present embodiment. A vibration isolation device  50  of the present embodiment is modified from the reference body system  42  of the second embodiment, and includes a reference body system  52  employing the PID compensator  41 . In addition, the reference body system  52  includes an acceleration sensor (second measuring unit)  53  and an integrator  54  instead of the velocity sensor  43  for measuring the velocity of the reference body  24  relative to an absolute space. In this case, the integrator  54  integrates acceleration information  55  obtained from the acceleration sensor  53  one time to thereby calculate velocity information  56 . A control system feedback-controls the velocity of the reference body  24  relative to an absolute space via the compensator  45  based on the velocity information  56 . The compensator  45  calculates a drive signal  47  to be sent to the actuator  23  based on the velocity information  56  and a preset target value  46 . In this way, according to the present embodiment, the same effects as those of the second embodiment are obtained. 
     Fourth Embodiment 
     Next, a description will be given of a vibration isolation device according to a fourth embodiment of the present invention.  FIG. 7C  is a schematic view illustrating the configuration of a vibration isolation device according to the present embodiment. A vibration isolation device  60  of the present embodiment is also modified from the reference body system  42  of the second embodiment, and includes a reference body system  62  employing the PID compensator  41 . In addition, the reference body system  62  includes a position sensor  63  for measuring the displacement of the reference body  24  relative to the base  2 , and a differentiator  64 . In this case, the differentiator  64  differentiates position information  65  obtained from the position sensor  63  one time to thereby calculate velocity information  66 . A control system feedback-controls the velocity of the reference body  24  relative to the base  2  via the compensator  45  based on the velocity information  66 . As in the second embodiment, the compensator  45  calculates a drive signal  47  to be sent to the actuator  23  based on the velocity information  66  and a preset target value  46 . At this time, the control device applies the proportional gain to the compensator  45 . 
     Next, a case where a PID compensator  41  is employed for the reference body system  62  and the velocity of the reference body  24  relative to the base  2  is feedback-controlled is compared to another case where a PID compensator  41  is employed for the same and the velocity of the reference body  24  relative to the base  2  is not feedback-controlled.  FIG. 8B  is a Bode plot diagram of the transfer function H 3  from the base  2  to the vibration isolation table  3  for each of two cases. As shown in  FIG. 8B , when a PID compensator is employed as in the present embodiment and a velocity feedback control is performed, a sharp peak around 0.01 Hz is damped, and thus excellent vibration isolation performance is achieved even at a low frequency. 
     Next, the reasons why the aforementioned sharp peak is damped will be described below.  FIG. 9C  is a block diagram of the transfer function H from the base  2  to the vibration isolation table  3  in this case. Firstly, when the block diagram shown in  FIG. 9C  is transformed, the resulting block diagram is as shown in  FIG. 9D . Here, when the block diagram enclosed within the frame shown in  FIG. 9D  is defined as the transfer function H A3 , and is further transformed, the transfer function H A3  is represented by Formula 23. Also, G or3  is represented by Formula 24. 
     
       
         
           
             
               
                 
                   
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                     23 
                   
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     Here, when Formulae 11 to 13 and Formula 24 are substituted for Formula 23, the transfer function H A3  is represented by Formula 25. Note that the small terms of M wj ×C r3  and K j ×C r3  are ignored. 
     
       
         
           
             
               
                 
                   
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                     25 
                   
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     In this way, when the characteristic equation (Formula 25) of the transfer function of the present embodiment is compared with the characteristic equation (Formula 15) of the transfer function H Apid  of the first embodiment, only the first-order term of s within the double parentheses is changed. When iω is substituted into s, the first-order term of s is a term including a complex number, and a term for determining the damping characteristic of the transfer function H A3 . Thus, if the velocity of the reference body  24  relative to the base  2  is feedback-controlled, a peak generated by the transfer function may be damped even when a PID compensator is employed for the compensator  41  of the reference body system  62 . 
     Fifth Embodiment 
     Next, a description will be given of a vibration isolation device according to a fifth embodiment of the present invention.  FIG. 7D  is a schematic view illustrating the configuration of a vibration isolation device according to the present embodiment. A vibration isolation device  70  of the present embodiment is modified from the reference body system  42  of the fourth embodiment, and includes a reference body system  72  employing the PID compensator  41 . In addition, the reference body system  72  includes a position sensor (third measuring device)  73  for measuring the relative position between the vibration isolation table  3  on which the reference body  24  is disposed and the base  2 , and a differentiator  74 . The position sensor  73  is disposed either on the base  2  or on the vibration isolation table  3 . In this case, a control system calculates a sum of the position information  17  about the position sensor  25  provided in the reference body system  72  and the position information  75  about the position sensor  73  for measuring the relative position between the base  2  and the vibration isolation table  3  to thereby determine the relative position information  76  about the reference body  24  relative to the base  2 . The differentiator  74  differentiates the relative position information  76  one time to thereby calculate relative velocity information  77 . A control system feedback-controls the velocity of the reference body  24  relative to the base  2  via the compensator  45  based on the relative velocity information  77 . As in the second embodiment, the compensator  45  calculates a drive signal  47  to be sent to the actuator  23  based on the relative velocity information  77  and a preset target value  46 . At this time, the control system applies the proportional gain C r3  to the compensator  45 . In this way, according to the present embodiment, the same effects as those of the fourth embodiment are obtained. 
     Here, with reference to the Bode plot diagrams shown in  FIGS. 8A and 8B , the transfer function of the vibration isolation device according to the second and third embodiments shown in  FIG. 8A  is compared with that of the vibration isolation device according to the fourth and fifth embodiments shown in  FIG. 8B . In comparison to the transfer function shown in  FIG. 8A , the vibration isolation performance of the transfer function shown in  FIG. 8B  deteriorates in the range of 0.01 to 1 Hz. Thus, in theory, a vibration isolation device exhibiting an excellent vibration isolation performance may be provided when the second and the third embodiments are employed. However, when the second and the third embodiments are employed, a vibration isolation performance depends on the performance of the velocity sensor  43  and the acceleration sensor  53 . In general, it is highly probable that the velocity sensor and the acceleration sensor have a measurement error in the low frequency range. On the other hand, in the fourth and fifth embodiments, since velocity information is calculated by differentiating position information one time, velocity information exhibiting excellent measurement accuracy in the low frequency range may be obtained. 
     Sixth Embodiment 
     Next, a description will he given of a vibration isolation device according to a sixth embodiment of the present invention. In the vibration isolation device of the present embodiment, a PID compensator in which a high pass filter serving as a filter circuit is added is employed as the compensator of the reference body system. As described with reference to the Bode plot diagram shown in  FIG. 3  according to the first embodiment, a sharp peak occurs in the low frequency range when a PID compensator is employed as the compensator of the reference body system. Thus, in the present embodiment, a high pass filter is added between the break frequency W ir  of the integrator provided in the PID compensator and the frequency at which a sharp peak occurs such that the integrator provided in the PID compensator does not work at the frequency band at which a sharp peak occurs. 
     Next, a case where a bypass filter is added to the PID compensator of the reference body system is compared to another case where a bypass filter is not added thereto.  FIG. 10A  is a Bode plot diagram of the transfer function H 4  from the base  2  to the vibration isolation table  3  for each of two cases. As shown in  FIG. 10A , when a high pass filter is added to a PID compensator as in the present embodiment, a sharp peak around 0.01 Hz is damped, and thus, excellent vibration isolation performance is achieved even at a low frequency. In this case, the transfer function H 4  of a PID compensator to which a high pass filter is added is represented by Formula 26. For example, as compared with the third embodiment, the break frequency W er  of the high pass filter to he added needs to be smaller than the break frequency W ir  of the integrator used in the vibration isolation device  50  and greater than the frequency of a sharp peak generated when a PID compensator is employed as the compensator  41 . 
     
       
         
           
             
               
                 
                   
                     
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     Seventh Embodiment 
     Next, a description will be given of a vibration isolation device according to a seventh embodiment of the present invention. While, in the vibration isolation device of the sixth embodiment, a high pass filter is added to the PID compensator of the reference body system, in the present embodiment, a notch filter serving as a band-stop filter having a narrow blocking band instead of a high pass filter is added thereto. Likewise, a case where a notch filter is added to the PID compensator of the reference body system is compared to another case where a notch filter is not added thereto.  FIG. 10B  is a Bode plot diagram of the transfer function H 5  from the base  2  to the vibration isolation table  3  for each of two cases. As shown in  FIG. 10B , when a notch filter is added to a PID compensator, a sharp peak around 0.01 Hz is also damped, and thus, excellent vibration isolation performance is achieved even at a low frequency. 
     Eighth Embodiment 
     Next, a description will be given of a vibration isolation device according to an eighth embodiment of the present invention.  FIG. 11  is a schematic view illustrating the configuration of the vibration isolation device of the present embodiment. In  FIG. 11 , the same elements as those in the aforementioned embodiments shown in the preceding figures are designated by the same reference numerals, and thus, the explanation thereof will be omitted. The vibration isolation device of the present embodiment isolates the vibration of the vibration isolation table  3  in the multi-axis directions by using at least six or more reference body systems employed in any one of the vibration isolation devices according to the first to seventh embodiments, more specifically, by using three or more reference bodies in the horizontal direction and three or more reference bodies in the vertical direction. For example, a vibration isolation device  80  shown in  FIG. 11  includes three reference body systems  10  ( 10   a  to  10   c ) for the horizontal direction and three reference body systems  20  ( 20   a  to  20   c ) for the vertical direction on the vibration isolation table  3 . Further, the vibration isolation device  80  includes three Z-axis drive actuators  81   a  to  81   c  for driving the vibration isolation table  3  in the six-axis direction, one X-axis drive actuator  82 , and two Y-axis drive actuators  83   a  and  83   b  that are disposed between the base  2  and the vibration isolation table  3 . In  FIG. 11 , the portion of the actuators is not shown. 
       FIG. 12  is a block diagram illustrating a method for controlling a vibration isolation device  80 . Firstly, a control device acquires position information  17  ( 17   a  to  17   f ) from six position sensors  25  ( 25   a  to  25   f ) disposed on six reference body systems  10   a  to  10   c  and  20   a  to  20   c.  Next, the control device converts the six-position information  17  into six axis position information  201  ( 201   x,    201   y,    201   z,    201 θ x,    201 θ y,  and  201 θ z ) about the center of gravity of the vibration isolation table  3  by a non-interference matrix  200 . Next, the control device calculates deviations  203  ( 203   x,    203   y,    203   z,    203 θ x,    203 θ y,  and  203 θ z ) from the differences between six-position information  201  and preset target values  202  ( 202   x,    202   y,    202   z,    202   θx,    202 θ y,  and  202 θ z ). Next, the control device subjects these six deviations  203  to the compensator  204  to thereby determine six drive signals  205  ( 205   x,    205   y,    205   z,    205 θ x,    205 θ y,  and  205   z ) about the center of gravity of the vibration isolation table  3 . Next, the drive signals  205  are converted into the drive signals  207  ( 207 _ 81   a,    207 _ 81   b,    207 _ 81   c,    207 _ 82 ,  207 _ 83   a,  and  207 _ 83   b ) of the six actuators  81   a  to  81   c,    82 ,  83   a,  and  83   b  using a thrust distribution matrix  206 . Then, the actuators  81   a  to  81   c,    82 ,  83   a,  and  83   b  drive the vibration isolation table  3  in the six-axis direction based on these six drive signals  207 . In this way, according to the present embodiment, the vibration isolation table  3  may be isolated from vibration even at a low frequency with accuracy in the six-axis direction. 
     Ninth Embodiment 
     Next, a description will be given of a vibration isolation device according to a ninth embodiment of the present invention.  FIG. 13  is a schematic view illustrating the configuration of the vibration isolation device of the present embodiment. In  FIG. 13 , the same elements as those in the aforementioned embodiments shown in the preceding figures are designated by the same reference numerals, and thus, the explanation thereof will be omitted. A vibration isolation device  90  of the present embodiment employs a reference body system  91  that is capable of performing six-axis measurement as shown in  FIG. 13  as the reference body system disposed on the vibration isolation table  3 , and isolates the vibration of the vibration isolation table  3  in the six-axis direction.  FIGS. 14A to 14C  are schematic diagrams illustrating the configuration of the reference body system  91 . In particular,  FIG. 14A  is a side view of the reference body system  91 ,  FIG. 14B  is a bottom plan view of the reference body  93  facing the base  92 , and  FIG. 14C  is a top plan view of the base  92  facing the reference body  93 . The reference body system  91  includes one own-weight compensation unit  94 , six actuators, and six displacement sensors, all of which are disposed between the base  92  and the reference body  93 . The own-weight compensation unit  94  is disposed at the center of the reference body  93 , and supports the reference body  93  from the base  92  by imparting a force balancing the own-weight of the reference body  93  to thereby compensate the own-weight of the reference body  93 . The own-weight compensation unit  94  may be provided in plurality. The six actuators are constituted by three Z-axis drive actuators  95   a  to  95   c,  one X-axis drive actuator  96 , and two Y-axis drive actuators  97   a  and  97   b  in order to drive the reference body  93  in six axes with respect to the base  92 . Six displacement sensors are measuring units configured to measure the position of the reference body  93  relative to the base  92  in the six-axis direction. The six displacement sensors are constituted by three displacement sensors  98   a  to  98   c  for the Z-axis direction, one displacement sensor  99  for the X-axis direction, and two displacement sensors  100   a  and  100   b  for the Y-axis direction. 
       FIG. 15  is a block diagram illustrating a method for controlling the vibration isolation device  90 . Firstly, a control device acquires position information  300  ( 300   a  to  300   f ) from six displacement sensors described above. Next, the control device converts the six-position information  300  into six-axis position information  302  ( 302   x,    302   y,    302   z,    302 θ x,    302   θy,  and  302 θ z ) about the center of gravity of the reference body  93  by a non-interference matrix  301 . Next, the control device calculates deviations  304  ( 304   x,    304   y,    304   z,    304 θ x,    304 θ y,  and  304 θ z ) from the differences between the six-position information  302  and preset target values  303  ( 303   x,    303   y,    303   z,    303 θ x,    303 θ y,  and  303 θ z ). Next, the control device subjects these six deviations  304  to the compensator  305  to thereby determine six drive signals  306  ( 306   x,    306   y,    306   z,    306 θ x,    306 θ y,  and  306 θ z ) about the center of gravity of the reference body  93 . In this case, while a PD compensator is employed as the compensator  305 , any one of the compensators shown in the aforementioned embodiments may also be employed. Next, the drive signals  306  are converted into the drive signals  308  ( 308 _ 95   a,    308 _ 95   b,    308 _ 95   c,    308 _ 96 ,  308 _ 97   a,  and  308 _ 97   b ) of the six actuators  95   a  to  95   c,    96 ,  97   a,  and  97   b  using a thrust distribution matrix  307 . Then, the actuators  95   a  to  95   c,    96 ,  97   a,  and  97   b  drive the reference body  93  in the six-axis direction based on these six drive signals  308 . 
     Furthermore, the control device executes control similar to that in the eighth embodiment using another control system  310  disposed therein. In other words, firstly, a control system  310  calculates six deviations  103  from the differences between six-position information  302  about the center of gravity of the reference body  93  and preset target values  102  of the vibration isolation table  3 . Next, the control system  310  subjects these six deviations  103  to the compensator  104  to thereby determine six drive signals  105  about the center of gravity of the vibration isolation table  3 . Next, these six drive signals  105  are converted into the drive signals  107  of the six actuators  81   a  to  81   c,    82 ,  83   a,  and  83   b  using a thrust distribution matrix  106 . Then, the actuators  81   a  to  81   c,    82 ,  83   a,  and  83   b  drive the vibration isolation table  3  in the six-axis direction based on these six drive signals  107 . In this way, according to the present embodiment, the vibration isolation table  3  may be isolated from vibration even at a low frequency with accuracy in the six-axis direction as in the eighth embodiment. 
     (Exposure Apparatus) 
     Next, a description will be given of an exposure apparatus employing the vibration isolation device of the present invention.  FIG. 16  is a schematic view illustrating the configuration of an exposure apparatus according to the present embodiment. An exposure apparatus  400  includes an illumination optical system  401 , a reticle stage  402  that holds a reticle, a projection optical system  403 , and a substrate stage  404  that holds a substrate to be treated. The exposure apparatus  400  of the present embodiment is a scanning projection exposure apparatus that exposes the pattern formed on the reticle to a wafer, i.e., a substrate to be treated, employing a step-and-repeat system or a step-and-scan system. The illumination optical system  401  includes a light source unit (not shown), and is a device that illuminates the reticle. At the light source unit, the light source uses a laser, for example. Available lasers include an ArF excimer laser with a wavelength of about 193 nm, a KrF excimer laser with a wavelength of about 248 nm, an F2 excimer laser with a wavelength of about 157 nm, and the like. The reticle is, for example, an original plate made of quartz glass. The circuit pattern to be transferred is formed on the reticle. Also, the reticle stage  402  is a stage that is moveable in the x-y direction, and is a device that holds the reticle. The reticle stage  402  is held on a reticle stage base  405 . The projection optical system  403  projects and exposes the pattern on the reticle, which has been illuminated with exposure light from the illumination optical system  401 , onto the substrate with a predetermined magnification (e.g., 1/4). As the projection optical system  403 , an optical system consisting only of a plurality of optical elements or an optical system (catadioptric optical system) consisting of a plurality of optical elements and at least one concave mirror can be employed. The reticle stage base  405  and the projection optical system  403  are supported by a lens barrel plate  407  including the vibration isolation device of the present invention on a floor (base ground surface)  406 . A substrate (substrate to be treated) is an object to be processed such as a silicon wafer or the like. A photosensitizer (resist) is applied on the surface thereof. The substrate stage  404  is a stage that is movable in the X, Y, and Z directions. The substrate stage  404  is disposed on a stage plate  408  that is placed on the floor (base ground surface)  406 . In the exposure apparatus  400 , the diffracted light emitted from the reticle passes through the projection optical system  403  and is projected on the substrate. The substrate is in a conjugated relationship with the reticle. In the case of a scanning type projection exposure apparatus, the pattern of the reticle is transferred onto the substrate by scanning the reticle and the substrate. In the case of a stepper (step-and-repeat type exposure device), exposure is performed while the reticle and the substrate are held stationary. Here, the lens barrel plate  407  includes the vibration isolation device according to the aforementioned embodiments, and thus excellent vibration isolation performance is achieved even at a low frequency. 
     (Device Manufacturing Method) 
     Next, a method of manufacturing a device (semiconductor device, liquid crystal display device, etc.) as an embodiment of the present invention is described. The semiconductor device is manufactured by a front-end process in which an integrated circuit is formed on a wafer, and a back-end process in which an integrated circuit chip is completed as a product from the integrated circuit on the wafer formed in the front-end process. The front-end process includes a step of exposing a wafer coated with a photoresist to light using the above-described exposure apparatus of the present invention, and a step of developing the exposed wafer. The back-end process includes an assembly step (dicing and bonding), and a packaging step (sealing). The liquid crystal display device is manufactured by a process in which transparent electrodes are formed. The process of forming a plurality of transparent electrodes includes a step of coating a glass substrate with a transparent conductive film deposited thereon with a photoresist, a step of exposing the glass substrate coated with the photoresist to light using the above-described exposure apparatus, and a step of developing the exposed glass substrate. The device manufacturing method of this embodiment has an advantage, as compared with a conventional device manufacturing method, in at least one of performance, quality, productivity and production cost of a device. 
     While the embodiments of the present invention have been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2010-184616 filed Aug. 20, 2010 which is hereby incorporated by reference herein in its entirety.