Patent Publication Number: US-10767992-B2

Title: Gyro sensor system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2017-059892, filed Mar. 24, 2017, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to a gyro sensor system. 
     BACKGROUND 
     When an attempt to detect an angle by using a gyro sensor is performed, normally, angular velocities detected by the gyro sensor are integrated. For this reason, there may be a case in which sufficient angle detection accuracy is not obtained. 
     The angle can be directly detected by means of the gyro sensor. In this case, however, there are not only various restrictions, but also is difficulty in performing the angle detection with high accuracy. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram showing a basic configuration of a gyro sensor system according to an embodiment. 
         FIG. 2  is a plan view schematically showing a configuration of a gyro element in the gyro sensor system according to the embodiment. 
         FIG. 3  is a plan view schematically showing a configuration of a modified example of the gyro element in the gyro sensor system according to the embodiment. 
         FIG. 4  is a diagram showing an example of α(Δf) according to an embodiment. 
         FIG. 5  is a diagram showing a first specific example of an amplitude detection operation for adjustment and an amplitude detection operation for measurement according to an embodiment. 
         FIG. 6  is a diagram showing a second specific example of the amplitude detection operation for adjustment and the amplitude detection operation for measurement according to the embodiment. 
         FIG. 7  is a diagram showing a third specific example of the amplitude detection operation for adjustment and the amplitude detection operation for measurement according to the embodiment. 
         FIG. 8  is a diagram showing a fourth specific example of the amplitude detection operation for adjustment and the amplitude detection operation for measurement according to the embodiment. 
         FIG. 9  is a diagram showing a basic configuration (concept) of a gyro sensor system according to a first modified example of the embodiment. 
         FIG. 10  is a diagram showing a basic operation of the gyro sensor system according to the first modified example of the embodiment. 
         FIG. 11  is a diagram showing a first operation example of the gyro sensor system according to the embodiment. 
         FIG. 12  is a diagram showing a second operation example of the gyro sensor system according to the embodiment. 
         FIG. 13  is a diagram schematically showing a configuration used for a second method of the second operation example of the gyro sensor system according to the embodiment. 
         FIG. 14  is a diagram showing a third operation example of the gyro sensor system according to the embodiment. 
         FIG. 15  is a diagram showing a fourth operation example of the gyro sensor system according to the embodiment. 
         FIG. 16  is a diagram showing a basic configuration (concept) of a gyro sensor system according to a second modified example of the embodiment. 
         FIG. 17  is a diagram showing a basic configuration (concept) of a gyro sensor system according to a third modified example of the embodiment. 
         FIG. 18  is a diagram schematically showing a first configuration example of a gyro sensor system having a damping coefficient adjustment mechanism according to an embodiment. 
         FIG. 19  is a diagram schematically showing a second configuration example of the gyro sensor system having the damping coefficient adjustment mechanism according to the embodiment. 
         FIG. 20  is a diagram schematically showing a third configuration example of the gyro sensor system having the damping coefficient adjustment mechanism according to the embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In general, according to one embodiment, a gyro sensor system including at least one gyro sensor unit is disclosed. The unit includes a movable body, a spring mechanism, a detector, an adjuster and a rotation angle acquisition unit. The spring mechanism vibrates the movable body. The detector detects an amplitude of vibration of the movable body wherein the vibration is due to a Coriolis force acting on the movable body. The adjuster adjusts a first resonance frequency of vibration of the movable body in free vibration and a second resonance frequency of vibration of the movable body wherein the vibration is due to the Coriolis force acting on the movable body so that the first resonance frequency and the second resonance frequency are to coincide with each other, based on the amplitude of the vibration due to the Coriolis force detected by the detector. The rotation angle acquisition unit acquires a rotation angle of the movable body, based on the amplitude of the vibration due to the Coriolis force detected by the detector in a state in which the first resonance frequency and the second resonance frequency are adjusted by the adjuster so that the first resonance frequency and the second resonance frequency are to coincide with each other. 
     Hereinafter, embodiments will be described with reference to the accompanying drawings. 
       FIG. 1  is a block diagram showing a basic configuration of a gyro sensor system according to an embodiment. 
       FIG. 2  is a plan view schematically showing a configuration of a gyro element in the gyro sensor system (gyro sensor unit) according to the embodiment. The gyro element is formed on a substrate by means of a micro-electromechanical systems (MEMS) technology. 
     As shown in  FIG. 1 , a gyro sensor system  200  (gyro sensor unit  100 ) comprises a gyro element (MEMS element)  110 , an amplitude detection circuit  120 , an adjustment signal generation circuit  130 , and a rotation angle acquisition circuit  140 . 
     As shown in  FIG. 2 , the gyro element (MEMS element)  110  includes a movable body  111 , a spring mechanism  112 , an anchor  113 , a catch and release mechanism  114 , a drive and monitor mechanism  115 , a detection mechanism  116 , and an adjustment mechanism  117 . 
     The movable body  111  includes a movable portion (movable mass)  111   a  and a movable portion (movable mass)  111   b , and can be vibrated in an x direction (first direction) and a y direction (second direction) perpendicular to the x direction. The movable portion  111   a  is a movable portion for drive and can be mainly vibrated in the x direction (first direction). The movable portion  111   b  is a movable portion for sense and can be mainly vibrated in the y direction (second direction). As shown in  FIG. 2 , the movable body  111  has an x-direction pattern and a y-direction pattern that are different from each other. In the more strict sense, when the movable body  111  is rotated by 90° with respect to an axis that is perpendicular to the x direction and the y direction and passes through a center of the pattern of the movable body  111 , the pattern of the movable body  111  before the movable body  111  is rotated and the pattern of the movable body  111  after the movable body  111  is rotated do not coincide with each other. 
     The spring mechanism  112  includes a spring portion  112   a  and a spring portion  112   b  and vibrates the movable body  111  in the x and y directions. The spring portion  112   a  is connected to the movable portion  111   a  and is provided to mainly vibrate the movable portion  111   a  in the x direction. The spring portion  112   b  is connected to the movable portion  111   a  and the movable portion  111   b  and is provided to mainly vibrate the movable portion  111   b  in the y direction. In the example shown in  FIG. 2 , the spring mechanism  112  includes eight spring portions  112   a  and four spring portions  112   b . If a rotational motion is applied to the movable body  111  that is in free vibration in the x direction by the spring mechanism  112 , a Coriolis force acts on the movable body  111 , such that the movable body  111  is vibrated in the y direction. 
     The anchor  113  is provided to support the spring portion  112   a  and is fixed to an underlying area. In the example shown in  FIG. 2 , eight anchors  113  are provided corresponding to the eight spring portions  112   a.    
     The catch and release mechanism  114  serves to catch the movable body  111  and release the caught movable body  111  to set the movable body  111  in the free vibration in the x direction. The catch and release mechanism  114  includes an electrode portion  114   a  and a stopper portion  114   b . An electrostatic attraction is applied between the electrode portion  114   a  and the movable body  111  by applying a predetermined voltage between the electrode portion  114   a  and the movable body  111 . As a result, the movable body  111  stops with being in contact with the stopper portion  114   b  and the movable body  111  is caught by the catch and release mechanism  114 . The voltage applied between the electrode portion  114   a  and the movable body  111  is lower to reduced the electrostatic attraction, thereby releasing the movable body  111  from the catch and release mechanism  114 , and thus the movable body  111  starts free vibration in the x direction. 
     The drive and monitor mechanism  115  includes an electrode portion  115   a  and an electrode portion  115   b  and has a drive function and a monitor function for the movable body  111 . The drive function serves to forcibly drive the movable body  111  in an initial state immediately after turning on a power supply of the gyro sensor system. That is, the movable body  111  is not caught by the catch and release mechanism  114  in the initial state immediately after turning on the power supply. In such an initial state, the electrostatic attraction is applied between the electrode portion  115   a  and the electrode portion  115   b  by applying a predetermined voltage between the electrode portion  115   a  and the electrode portion  115   b . As a result, the movable body  111  is driven, such that the movable body  111  can be caught by the catch and release mechanism  114 . The monitor function serves to monitor an x-direction position of the movable body  111  that is vibrating in the x direction. The x-direction position of the movable body  111  can be monitored by detecting a capacitance between the electrode portion  115   a  and the electrode portion  115   b . In the example shown in  FIG. 2 , two drive and monitor mechanisms  115  are provided, in which one drive and monitor mechanism  115  can be used for drive and the other drive and monitor mechanism  115  can be used for monitor. 
     A detection portion including the detection mechanism  116  and the amplitude detection circuit  120  (see  FIG. 1 ) detects amplitude of the vibration in the y direction of the movable body  111  based on the Coriolis force acting on the movable body  111  that is in the free vibration in the x direction by the spring mechanism  112 . Hereinafter, the detection mechanism  116  and the amplitude detection circuit  120  will be further described. 
     The detection mechanism  116  detects a predetermined physical quantity based on amplitude of the vibration in the y direction of the movable body  111  and includes an electrode portion  116   a  and an electrode portion  116   b . In the present embodiment, the predetermined physical quantity is a physical quantity that is based on a capacitance Ca between the electrode portion  116   a  and the movable body  111 , and a capacitance Cb between the electrode portion  116   b  and the movable body  111 . As described above, if the rotational motion is applied to the movable body  111  that is in the free vibration in the x direction, the Coriolis force acts on the movable body  111 , such that the movable body  111  is vibrated in the y direction. As a result, the above-described capacitances Ca and Cb are changed in accordance with the vibration. Since the electrode portions  116   a  and  116   b  are fixed to the underlying area, if one of the capacitances Ca and Cb is increased due to the vibration of the movable body  111  in the y direction, the other of the capacitances Ca and Cb is decreased. 
     The amplitude detection circuit  120  shown in  FIG. 1  is connected to the electrode portions  116   a  and  116   b  of the detection mechanism  116 . The amplitude detection circuit  120  detects the amplitude of the vibration in the y direction of the movable body  111  based on the predetermined physical quantity (capacitances Ca and Cb) detected by the detection mechanism  116 . As described above, if one of the capacitances Ca and Cb is increased, the other one of the capacitances Ca and Cb is decreased. Therefore, the amplitude detection circuit  120  can detect the amplitude of the vibration in the y direction of the movable body  111  based on a difference between the capacitance Ca and the capacitance Cb. 
     An adjustment portion including the adjustment mechanism  117  and the adjustment signal generation circuit  130  (see  FIG. 1 ) performs predetermined adjustment based on the amplitude of the vibration in the y direction of the movable body  111  detected by the detection portion (the detection mechanism  116  and the amplitude detection circuit  120 ). Specifically, as will be described later, the adjustment portion performs the predetermined adjustment so that a resonance frequency (first resonance frequency) of the vibration in the x direction of the movable body  111  coincides with that (second resonance frequency) of the vibration in the y direction of the movable body  111 . Hereinafter, the adjustment mechanism  117  and the adjustment signal generation circuit  130  will be further described. 
     The adjustment signal generation circuit  130  generates the adjustment signal to coincide the first resonance frequency and the second resonance frequency with each other, based on the amplitude of the vibration in the y direction of the movable body  111  detected by the detection portion (detection mechanism  116  and amplitude detection circuit  120 ). Specifically, amplitude information from the amplitude detection circuit  120  is input to an adjustment value acquisition circuit  131 . The adjustment value acquisition circuit  131  calculates an adjustment value (correction value) based on the amplitude information, and acquires the adjustment value. The adjustment value information from the adjustment value acquisition circuit  131  is input to the voltage generation circuit  132  and a voltage for coinciding the first resonance frequency and the second resonance frequency with each other is generated. 
     The adjustment mechanism  117  receives the adjustment signal generated from the adjustment signal generation circuit  130  to perform the predetermined adjustment on the movable body  111 . Specifically, the voltage generated from the voltage generation circuit  132  is applied to an electrode portion  117   a  of the adjustment mechanism  117  as the adjustment signal. A voltage signal (adjustment signal) generated from the voltage generation circuit  132  is applied to the adjustment mechanism  117  to adjust a direction (angle in an xy plane) of the movable portion  111   b  of the movable body  111  with respect to the movable portion  111   a , such that the first resonance frequency and the second resonance frequency can coincide with each other. In the example shown in  FIG. 2 , four adjustment mechanisms  117  are included in the gyro element  110 , and voltages V 1 , V 2 , V 3 , and V 4  are respectively applied to the four adjusting mechanisms  117 . 
     The rotation angle acquisition circuit (rotation angle acquisition portion)  140  acquires (calculates) a rotation angle of the movable body  111 , based on the amplitude of the vibration in the y direction of the movable body  111  that is detected in a state in which the adjustment portion (adjustment mechanism  117  and adjustment signal generation circuit  130 ) adjusts the first resonance frequency and the second resonance frequency so that the first resonance frequency and the second resonance frequency coincide with each other. As will be described later, the amplitude of the vibration in the y direction of the movable body  111  is detected in the state in which the first resonance frequency and the second resonance frequency are adjusted so that the first resonance frequency and the second resonance frequency coincide with each other, thereby capable of directly acquiring the rotation angle of the movable body  111 . 
       FIG. 3  is a plan view schematically showing a modified example of the configuration of the gyro element in the gyro sensor system (gyro sensor unit) according to the embodiment. Since a basic configuration of the gyro element of the present modified example is similar to the configuration of the gyro element shown in  FIG. 2 , the description of the items already described will be omitted. 
     In the gyro element (MEMS element)  110  shown in  FIG. 2 , the movable body (movable mass)  111  mainly includes the movable portion  111   a  which can be mainly vibrated in the x direction and the movable portion  111   b  which can be mainly vibrated in the y direction. As shown in  FIG. 3 , a gyro element (MEMS element)  110  of the present modified example has a movable body (movable mass)  111  in which a movable portion vibrated in an x direction and a movable portion vibrated in a y direction are integrated. For this reason, even a spring mechanism  112  includes only a spring portion  112   a . In addition, even positions of a detection mechanism  116  (electrode portions  116   a  and  116   b ) and an adjustment mechanism (electrode portion  117   a )  117  are different from those in the case of  FIG. 2 . 
     The basic functions and operations of the gyro element  110  of the present modified example are the same as those of the gyro element  110  shown in  FIG. 2 . Therefore, by applying the gyro element  110  of the present modified example to the gyro sensor system  200  (gyro sensor unit  100 ) shown in  FIG. 1 , it is possible to perform the same operations as in the above embodiment. 
     Next, the principle of the gyro sensor system according to the present embodiment will be described. 
     A gyro sensor capable of directly detecting a rotation angle is based on the principle of the Foucault pendulum. A movable body (mass) that is held by a spring mechanism and can be vibrated in x and y directions is assumed. It is assumed that a resonance frequency in the x direction and a resonance frequency in the y direction are equal to each other and an angular resonance frequency is ω. 
     In the system as described above, equations of the motion when the movable body (mass) is rotating at an angular velocity Ω(t) are expressed as follows.
 
 {umlaut over (x)}+ω   2   x= 2Ω( t ) {dot over (y)} 
 
 ÿ+ω   2   y=− 2Ω( t ) {dot over (x)} 
 
     The right sides of the above formulas represent contributions of the Coriolis force. 
     Initial Condition 
     A solution satisfying the initial condition 
     x(0)=A 
     {dot over (x)}(0)=0 
     y(0)=0 
     {dot over (y)}(0)=0 
     is as follows. 
     
       
         
           
             
               ( 
               
                 
                   
                     x 
                   
                 
                 
                   
                     y 
                   
                 
               
               ) 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Φ 
                       
                     
                     
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Φ 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           sin 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Φ 
                       
                     
                     
                       
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Φ 
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         A 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                     
                   
                   
                     
                       
                         Ar 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Where Φ(t) and r are as follows. 
     
       
         
           
             
               Φ 
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 ∫ 
                 0 
                 t 
               
               ⁢ 
               
                 
                   dt 
                   ′ 
                 
                 ⁢ 
                 
                   Ω 
                   ⁡ 
                   
                     ( 
                     
                       t 
                       ′ 
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             r 
             ≡ 
             
               
                 Ω 
                 ⁡ 
                 
                   ( 
                   0 
                   ) 
                 
               
               ω 
             
           
         
       
     
     Φ is obtained by integrating an angular velocity Ω, that is, an angle. 
     Therefore, a rotation angle in an xy plane of the movable body (mass) that is in the free vibration is obtained by the following formula, 
     
       
         
           
             Φ 
             = 
             
               
                 tan 
                 
                   - 
                   1 
                 
               
               ⁡ 
               
                 [ 
                 
                   - 
                   
                     y 
                     x 
                   
                 
                 ] 
               
             
           
         
       
     
     the angle Φ can be directly obtained. 
     Since the above-described method can directly obtain the rotation angle, it is possible to greatly improve the accuracy as compared with the method for obtaining the rotation angle by integrating the angular velocity. However, the above-described method has the following problems. 
     Firstly, the resonance frequency in the x direction and the resonance frequency in the y direction are difficult to coincide with (match) each other. Specifically, even if the influence of manufacturing variation is compensated and temperature is changed, it is difficult to make the resonance frequencies coincide with each other. Secondly, the above-described scheme is established only in a period during which the movable body (mass) is in the free vibration. Since the free vibration is necessarily attenuated due to an energy loss such as a damping effect, it is difficult to perform the continuous measurement over a long period of time. 
     In the present embodiment, the above-described problems are solved in the following manner. 
     First of all, as a premise of the present embodiment, it is assumed that a value of ω is sufficiently large and r&lt;&lt;1 is satisfied. In addition, when a time t of the free vibration is small and the angle Φ is small,
 
 y ( t )=− AΦ  cos ω t  
 
     is established. 
     Therefore, the angle Φ can be obtained by setting the movable body (mass) in the free vibration in the x direction and monitoring the amplitude in the y direction. When the time t is large, a nonlinear effect appears and therefore the amplitude is not proportional to Φ, but there is no problem if the amplitude is caught and ends to be monitored before it comes to such a state. 
     The equation of motion of the movable body  111  of the present embodiment can be expressed as follows. 
     
       
         
           
             
               
                 ( 
                 
                   
                     
                       
                         
                           m 
                           x 
                         
                         ⁢ 
                         
                           x 
                           ¨ 
                         
                       
                     
                   
                   
                     
                       
                         
                           m 
                           y 
                         
                         ⁢ 
                         
                           y 
                           ¨ 
                         
                       
                     
                   
                 
                 ) 
               
               + 
               
                 ( 
                 
                   
                     
                       
                         
                           b 
                           x 
                         
                         ⁢ 
                         
                           x 
                           . 
                         
                       
                     
                   
                   
                     
                       
                         
                           b 
                           y 
                         
                         ⁢ 
                         
                           y 
                           . 
                         
                       
                     
                   
                 
                 ) 
               
               + 
               
                 
                   K 
                   M 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         x 
                       
                     
                     
                       
                         y 
                       
                     
                   
                   ) 
                 
               
             
             = 
             
               ( 
               
                 
                   
                     
                       2 
                       ⁢ 
                       
                         m 
                         x 
                       
                       ⁢ 
                       
                         Ω 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ⁢ 
                       
                         y 
                         . 
                       
                     
                   
                 
                 
                   
                     
                       
                         - 
                         2 
                       
                       ⁢ 
                       
                         m 
                         y 
                       
                       ⁢ 
                       
                         Ω 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ⁢ 
                       
                         x 
                         . 
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Where m x  represents a mass of the movable body in the x direction and m y  represents a mass of the movable body in the y direction. It should be noted that in the case of the structure in which the movable body in the x direction and the movable body in the y direction are integrated as shown in  FIG. 3 , m x =m y . In addition, K M  is the following spring matrix. 
     
       
         
           
             
               K 
               M 
             
             = 
             
               ( 
               
                 
                   
                     
                       k 
                       xx 
                     
                   
                   
                     
                       k 
                       xy 
                     
                   
                 
                 
                   
                     
                       k 
                       yx 
                     
                   
                   
                     
                       k 
                       yy 
                     
                   
                 
               
               ) 
             
           
         
       
     
     Although it is preferable that off-diagonal components k xy  and k yx  of the spring matrix are small, the off-diagonal components are usually not zero because they are affected by the manufacturing variation or the temperature dependence. In the following description, for simplicity, damping coefficients (attenuation coefficients) b x  and b y  are zero. If a Q value is large, an approximation thereof is reasonable. In addition, even when the b x  and b y  are not zero, the essence of the following discussion remains unchanged. 
     In  FIG. 2 , V 1 =V 3  and V 2 =V 4  and adjustment voltages V 1  and V 2  are applied to the adjustment mechanism  117 . In this way, by applying the adjustment voltage to the adjustment mechanism  117 , it is possible to change an effective spring constant by the electrostatic attraction. An amount of change in the effective spring constant by the electrostatic attraction is represented as follows. 
     
       
         
           
             
               K 
               E 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             V 
                             1 
                             2 
                           
                           - 
                           
                             V 
                             2 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             V 
                             1 
                             2 
                           
                           - 
                           
                             V 
                             2 
                             2 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       q 
                       ⁡ 
                       
                         ( 
                         
                           
                             V 
                             1 
                             2 
                           
                           + 
                           
                             V 
                             2 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Where p and q are constants which depend on a dielectric constant, an inter-electrode gap, or the like [Yunfang Ni, Sensors 2014, 14, 20419-20438]. 
     /K M , /K E , and /K are defined by the following formulas. 
     
       
         
           
             
               K 
               _ 
             
             = 
             
               
                 
                   
                     K 
                     _ 
                   
                   M 
                 
                 + 
                 
                   
                     K 
                     _ 
                   
                   E 
                 
               
               ≡ 
               
                 ( 
                 
                   
                     
                       
                         μ 
                         2 
                       
                     
                     
                       
                         
                           ( 
                           
                             κ 
                             ′ 
                           
                           ) 
                         
                         2 
                       
                     
                   
                   
                     
                       
                         κ 
                         2 
                       
                     
                     
                       
                         ω 
                         2 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               
                 K 
                 _ 
               
               M 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         1 
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         
                           m 
                           x 
                         
                       
                     
                     
                       0 
                     
                   
                   
                     
                       0 
                     
                     
                       
                         1 
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         
                           m 
                           y 
                         
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 K 
                 M 
               
             
           
         
       
       
         
           
             
               
                 K 
                 _ 
               
               E 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         1 
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         
                           m 
                           x 
                         
                       
                     
                     
                       0 
                     
                   
                   
                     
                       0 
                     
                     
                       
                         1 
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         
                           m 
                           y 
                         
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 K 
                 E 
               
             
           
         
       
     
     Where μ is the angular resonance frequency in the x direction (drive direction), and ω is the angular resonance frequency in the y direction (sense direction). In this case, the equation of motion is represented by the following formula. 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       x 
                       ¨ 
                     
                   
                 
                 
                   
                     
                       y 
                       ¨ 
                     
                   
                 
               
               ) 
             
             + 
             
               
                 K 
                 _ 
               
               ⁡ 
               
                 ( 
                 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           Ω 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           y 
                           . 
                         
                       
                     
                   
                   
                     
                       
                         
                           - 
                           2 
                         
                         ⁢ 
                         
                           Ω 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           x 
                           . 
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     When a solution for the above equation of motion is obtained by perturbation (with respect to Ω and κ 2 ), the solution satisfying the above initial condition is as follows.
 
 x ( t )= A  cos μ t 
 
     
       
         
           
             
               
                 
                   
                     y 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     2 
                     ⁢ 
                     A 
                     ⁢ 
                     
                       μ 
                       ω 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           
                             I 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                         - 
                         
                           
                             J 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                       
                       } 
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 Where 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       ∫ 
                       0 
                       t 
                     
                     ⁢ 
                     
                       
                         dt 
                         ′ 
                       
                       ⁢ 
                       
                         
                           Ω 
                           ~ 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             ′ 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
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                         ) 
                       
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                       ⁢ 
                       
                           
                       
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
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                     J 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       ∫ 
                       0 
                       t 
                     
                     ⁢ 
                     
                       
                         dt 
                         ′ 
                       
                       ⁢ 
                       
                         
                           Ω 
                           ~ 
                         
                         ⁡ 
                         
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                       ⁢ 
                       
                           
                       
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                       ⁢ 
                       
                           
                       
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                       ⁢ 
                       
                           
                       
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                       ω 
                       ⁢ 
                       
                           
                       
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                       ~ 
                     
                     ⁡ 
                     
                       ( 
                       t 
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                           Ω 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         2 
                       
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                           2 
                         
                         
                           4 
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                             μ 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
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                         1 
                       
                     
                     ⁡ 
                     
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                             ⁡ 
                             
                               ( 
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                       ] 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     In case of μ˜ω and κ˜0, y is as the follows.
 
 y ( t )˜−α(Δ f ) A {tilde over (Φ)}( t )cos ω t  
 
Where
 
{tilde over (Φ)}( t )=∫ 0   t   dt ′{tilde over (Ω)}( t ′)
 
     Δf is the difference between the resonance frequency in the x direction and the resonance frequency in the y direction. α(Δf) becomes a maximum value 1 if Δf=0 (μ=ω), and is a function quickly approaching zero if Δf deviates from zero. A specific form of α(Δf) is determined by Ω(t). 
       FIG. 4  is a diagram showing an example of α(Δf). Specifically,  FIG. 4  shows an example in the case in which the angular velocity input is given only for a fixed period. 
     In case of μ=ω and κ 2 =0, y is as follows.
 
 y ( t )=− A Φ cos ω t  
 
     This is the same form as the above-described Formula, which means that the angle Φ is obtained from the amplitude of the vibration in the y direction. In order to extract the angle Φ, the vibration in the y direction is monitored, and a high frequency component (contribution of ω) is reduced by a low pass filter. The angle Φ may have time dependence. 
     From the above, it can be seen that in order to calculate the angle Φ from the amplitude of the vibration in the y direction, there is a need to establish that μ=ω and κ 2 =0. This means that a matrix /K needs to be represented in the following form. 
     
       
         
           
             
               K 
               _ 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         ω 
                         2 
                       
                     
                     
                       
                         
                           ( 
                           
                             κ 
                             ″ 
                           
                           ) 
                         
                         2 
                       
                     
                   
                   
                     
                       0 
                     
                     
                       
                         ω 
                         2 
                       
                     
                   
                 
                 ) 
               
               ≡ 
               
                 
                   K 
                   _ 
                 
                 J 
               
             
           
         
       
     
     It should be noted that (κ″) 2  need not be zero. 
     In the present embodiment, the matrix /K as described above is obtained by adjusting the voltages V 1  and V 2  to an appropriate voltage and changing a matrix /K E . Since there are two parameters V 1  and V 2 , it is possible to obtain the matrix /K as described above. 
     There is no need to extremely increase a symmetry of the structure of the movable portion (extremely increase the identity between the x-direction pattern and the y-direction pattern of the movable portion) by adopting the above-described method. Therefore, it is possible to manufacture the gyro sensor element at low cost by using the normal MEMS manufacturing process. In addition, it is possible to always maintain the matrix /K in the above form (/K=/K J ) by appropriately adjusting the voltages V 1  and V 2  even when the operating environment such as temperature is changed. That is, it is possible to adaptively adjust the matrix /K. 
     Next, a method for obtaining the above-mentioned condition (/K=/K J ) will be described. That is, a method for determining V 1  and V 2  will be described. 
     
       
         
           
             
               
                 d 
                 ⁢ 
                 
                   
                     Φ 
                     ~ 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
               
               dt 
             
             = 
             
               
                 
                   
                     
                       Ω 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     2 
                   
                   + 
                   
                     
                       κ 
                       2 
                     
                     
                       4 
                       ⁢ 
                       
                         μ 
                         2 
                       
                     
                   
                 
               
               ≥ 
               
                 Ω 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
             
           
         
       
     
     First of all, when the above formula is considered,
 
 y ( t )= A   m ( t )cos ω t  
 
 A   m ( t )=−α(Δ f ) A {tilde over (Φ)}( t )
 
     In the above formula, if V 1  and V 2  are determined so that a slope (dA m (t)/dt) of amplitude A m  is minimized, κ 2 =0 is established. In addition, if α(Δf) is maximized, Δf=0 (μ=ω). Therefore, if the V 1  and V 2  are determined so that the amplitude A m  is maximized, the condition that Δf=0 (μ=ω) can be obtained. 
     From the above, it is important for the gyro sensor of the present embodiment to satisfy the following two conditions. 
     The first condition is that “μ=ω” is established. That is, the angular resonance frequency p of the vibration in the x direction of the movable body  111  and the angular resonance frequency ω of the vibration in the y direction of the movable body  111  coincide with each other (the first resonance frequency of the vibration in the x direction of the movable body  111  and the second resonance frequency of the vibration in the y direction of the movable body  111  coincide with each other). Specifically, the adjustment portion (the adjustment mechanism  117  and the adjustment signal generation circuit  130 ) adjusts the first resonance frequency and the second resonance frequency to coincide each other based on the amplitude of the vibration in the y direction of the movable body  111  that is detected by the detection portion (the detection mechanism  116  and the amplitude detection circuit  120 ). In addition, in order to establish such a condition, the amplitude A m  of the vibration in the y direction of the movable body  111  is set to be maximized. Specifically, the adjustment signal generation circuit  130  generates the adjustment signal (the adjustment voltages V 1  and V 2 ) so that the amplitude A m  of the vibration in the y direction of the movable body  111  is maximized. 
     The second condition is that “κ 2 =0” is established. That is, in the spring matrix defining the vibration in the x and y directions of the movable body  111  by the spring mechanism  112 , the component κ 2  defining the motion of the movable body  111  in the y direction among the off-diagonal components in the spring matrix is zero. Specifically, the adjustment signal generation circuit  130  generates the adjustment signal (adjustment voltages V 1  and V 2 ) so that the off-diagonal component κ 2  in the spring matrix is zero. In addition, to establish such conditions, the adjustment signal generation circuit  130  generates the adjustment signal (the adjustment voltages V 1  and V 2 ) so that a temporal variation in the amplitude A m  of the vibration in the y direction of the movable body  111  is minimized. That is, the adjustment signal generation circuit  130  generates the adjustment signal so that the slope (dA m (t)/dt) of the amplitude A m  is minimized. 
     Obtaining the V 1  and V 2  that satisfy the first condition (μ=ω) and obtaining the V 1  and V 2  that satisfy the second condition (κ 2 =0) may be performed at the same time and may also be performed by shifting time. In case of shifting the time, in order not to destroy an optimum value first determined, the following conditions shall be satisfied. 
     In the case of determining the condition that satisfies μ=ω after determining the condition satisfying κ 2 =0, a value of V 1   2 −V 2   2  is maintained to be a constant value (value first determined) while the V 1  and V 2  satisfying μ=ω are searched. Meanwhile, in the case of determining the condition that satisfies κ 2 =0 after determining the condition satisfying μ=ω, a value of V 1   2 +V 2   2  is maintained to be a constant value (value first determined) while the V 1  and V 2  satisfying κ 2 =0 are searched. 
     Next, timing at which the detection operation is performed by the detection portion (the detection mechanism  116  and the amplitude detection circuit  120 ) will be described. 
     As described above, the detection portion (the detection mechanism  116  and the amplitude detection circuit  120 ) performs the amplitude detection for performing the adjustment satisfying the above-described first and second conditions and the amplitude detection for performing the actual measurement (for acquiring the rotation angle). Basically, both the amplitude detection operation for adjustment and the amplitude detection operation for measurement are performed in the middle of a release period during which the movable body  111  is released from the catch and release mechanism  114  and thus is in the free vibration. Hereinafter, this will be described in detail. 
       FIG. 5  is a diagram showing a first specific example of an amplitude detection operation for adjustment and an amplitude detection operation for measurement. In this case, a catch period and the release period are repeated at a constant cycle, and the release period ranges from time t 0  to t 2 . The same goes for even second to fourth specific examples shown in  FIGS. 6 to 8 . 
     In the first specific example, an adjustment period (t 0  to t 1 ) and a measurement period (t 1  to t 2 ) are separately provided in a release period (t 0  to t 2 ). In the adjustment period, the adjustment voltages V 1  and V 2  satisfying the first condition (μ=ω) and the second condition (κ 2 =0) described above are simultaneously searched. In the measurement period, the adjustment operation is performed in the state in which the adjustment voltages (V 1  and V 2 ) determined during the adjustment period are maintained. It should be noted that point P is a point at which the slope (dA m (t)/dt) of the amplitude A m  in the y direction is minimized. 
       FIG. 6  is a diagram showing a second specific example of the amplitude detection operation for adjustment and the amplitude detection operation for measurement. 
     Even in the second specific example, an adjustment period (t 0  to t 1 ) and a measurement period (t 1  to t 2 ) are separately provided in a release period (t 0  to t 2 ). However, in the present specific example, the adjustment period is divided into a first adjustment period (t 0  to t 0   a ) and a second adjustment period (t 0   a  to t 1 ). For example, the adjustment voltages (V 1  and V 2 ) satisfying the first condition (μ=ω) are searched in the first adjustment period, and the adjustment voltages (V 1  and V 2 ) satisfying the second condition (κ 2 =0) are searched in the second adjustment period. Conversely, the adjustment voltages (V 1  and V 2 ) satisfying the second condition (κ 2 =0) may be searched in the first adjustment period, and the adjustment voltages (V 1  and V 2 ) satisfying the first condition (μ=ω) may be searched in the second adjustment period. In the measurement period, the adjustment operation is performed in the state in which the adjustment voltages (V 1  and V 2 ) determined during the adjustment period are maintained. 
       FIG. 7  is a diagram showing a third specific example of the amplitude detection operation for adjustment and the amplitude detection operation for measurement. 
     In the third specific example, there are provided a first adjustment period (t 0  to t 1 ), a second adjustment period (t 0  to t 2 ), and a measurement period (t 1  to t 2 ). For example, the adjustment voltages (V 1  and V 2 ) satisfying the first condition (μ=ω) are searched in the first adjustment period, and the adjustment voltages (V 1  and V 2 ) satisfying the second condition (κ 2 =0) are searched in the second adjustment period. Conversely, the adjustment voltages (V 1  and V 2 ) satisfying the second condition (κ 2 =0) may be searched in the first adjustment period, and the adjustment voltages (V 1  and V 2 ) satisfying the first condition (μ=ω) may be searched in the second adjustment period. In the present specific example, the second adjustment period is provided even during the measurement period. For this reason, the adjustment operation is performed even in the middle of the measurement period. Therefore, when the optimum condition is changed during the measurement period, the method of the present specific example is effective. 
       FIG. 8  is a diagram showing a fourth specific example of the amplitude detection operation for adjustment and the amplitude detection operation for measurement. 
     In the fourth specific example, an adjustment period (t 0  to t 2 ) and a measurement period (t 1  to t 2 ) are provided. In the adjustment period, the adjustment voltages (V 1  and V 2 ) satisfying the first condition (μ=ω) and the second condition (κ 2 =0) are simultaneously searched. In addition, in the present specific example, since the adjustment period is provided even during the measurement period, the adjustment operation is performed even in the middle of the measurement period. Therefore, when the optimum condition is changed during the measurement period, the method of the specific example is effective. 
     In the first to fourth specific examples described above, after the movable body  111  is caught by the catch and release mechanism  114 , the vibration in the y direction of the movable body  111  may be forcibly attenuated. In the example shown in  FIGS. 5 to 8 , the amplitude of the vibration in the y direction is forcibly attenuated during a catch period after time t 2 . Such an operation can be realized by tuning the voltages V 1  and V 2  based on a force feedback that makes the amplitude A m  in the y direction zero. In this way, it is possible to prevent the sense vibration in the y direction from continuing until a next release period starts by forcibly attenuating the vibration in the y direction. It should be noted that the forcible attenuation may be realized by a damping coefficient adjustment mechanism to be described later. 
     Next, a first modified example of the gyro sensor system according to the present embodiment will be described. It should be noted that since the basic matters are similar to those of the above embodiment, the description of the matters described in the above embodiment will be omitted. 
       FIG. 9  is a diagram showing a basic configuration (concept) of a gyro sensor system according to the present modified example. In the present modified example, a gyro sensor system  200  includes two gyro sensor units  100   a  and  100   b  that have the same configuration as that of the gyro sensor unit  100  shown in  FIG. 1 . 
       FIG. 10  is a diagram showing a basic operation of the gyro sensor system according to the present modified example. 
     As shown in  FIG. 10 , each of the first gyro sensor unit  100   a  and the second gyro sensor unit  100   b  alternately has a release period during which a movable body  111  is in the free vibration in an x direction and a catch period during which the vibration of the movable body  111  is stopping. In addition, the release periods of the gyro sensor units  100   a  and  100   b  are sequentially and continuously generated. In other words, the release period of the gyro sensor unit  100   a  and the release period of the gyro sensor unit  100   b  are set to be complemented to each other. 
     In addition, in the present modified example, the release period of the first gyro sensor unit  100   a  and the release period of the second gyro sensor unit  100   b  overlap each other. In the overlap period, angle information of the first gyro sensor unit  100   a  and angle information of the second gyro sensor unit  100   b  may also match each other. In addition, the adjustment period as described above may be provided during the overlap period. 
     In the examples shown in  FIGS. 9 and 10 , the gyro sensor system  200  includes the two gyro sensor units  100   a  and  100   b , but the gyro sensor system  200  may include three or more gyro sensor units  100 . 
     In addition, the amplitude detection circuit  120 , the adjustment signal generation circuit  130 , and the rotation angle acquisition circuit  140  that are shown in  FIG. 1  may be shared by a plurality of gyro sensor units  100  included in the gyro sensor system  200 . 
     As described above, in the present modified example, the gyro sensor units  100  are provided, and each of the gyro sensor units  100  alternately has the release period during which the movable body  111  is in the free vibration in the x direction and the catch period during which the vibration of the movable body  111  is stopping, such that the release periods of the gyro sensor units  100  are sequentially and continuously generated. In this way, since the release period is continuously set, it is possible to perform the continuous measurement without interruption. By doing so, the detection accuracy of the rotation angle can be improved. 
     In addition, in the present modified example, the gyro sensor units  100  are provided, and therefore it is possible to shorten the release period of one gyro sensor unit  100 . If it is assumed that the gyro sensor system  200  is constituted by a single gyro sensor unit  100 , there is a need to set the release period of the single gyro sensor unit  100  to be long. When the angular velocity is constant, the amplitude of the vibration is monotonically increased, if the release period is set to be long, the amplitude becomes excessively large. In the present modified example, the release period of one gyro sensor unit  100  can be set to be short, such that it is possible to prevent such a problem. For example, if the angular velocity is set to be 1000 deg/sec, the movable body  111  is rotated by 1 deg at 1 ms and therefore is rotated by 10 deg at 10 ms. Therefore, the rotation range can be limited to a range in which a linear approximation of “sin Φ˜Φ” can be established. 
     In the present modified example, it is preferable that the directions of the movable bodies  111  included in each of the gyro sensor units  100  are aligned with each other. That is, it is preferable that the x directions (first directions) in each of the gyro sensor units  100  are the same as each other and the y directions (second directions) in each of the gyro sensor units  100  are the same as each other. By adopting such a configuration, the drive vibrations by the gyro sensor units  100  become the same direction. For this reason, it is possible to prevent noise due to the drive vibration of the movable body  111  included in one gyro sensor unit  100  from adversely affecting the sensing operation of the other gyro sensor units  100 . 
     Further, the gyro sensor units  100  may be provided in the same chip or may be provided in separate chips. 
     Next, various operation examples of the gyro sensor system  200  according to the present embodiment will be described. 
       FIG. 11  is a diagram showing a first operation example of the gyro sensor system  200  according to the present embodiment. 
     It should be noted that the present operation example can be mainly applied to the gyro sensor system shown in  FIG. 9 . 
     In the present operation example, when the amplitude of the vibration in the y direction of the movable body  111  of one gyro sensor unit  100  is increased to be larger than the predetermined value, the vibration in the x direction of the movable body  111  of the other gyro sensor unit  100  starts.  FIG. 11  shows that when the amplitude of the vibration in the y direction of the movable body  111  of the first gyro sensor unit  100   a  becomes larger than a predetermined value (Amax), the vibration in the x direction of the movable body  111  of the second gyro sensor unit  100   b  starts. In addition, in the present operation example, after the overlap period has elapsed, one movable body  111  is caught to stop the vibration. By using the control method as in the present operation example, it is possible to prevent the amplitude of the vibration in the y direction of the movable body  111  from being excessively increased. 
     In addition, if a predetermined maximum release period has elapsed before the amplitude of the vibration in the y direction of one movable body  111  becomes larger than the predetermined value (Amax), the vibration in the x direction of the other movable body  111  starts after the predetermined maximum maximum release period has elapsed. That is, in the present operation example, if the release period during which the movable body is actually vibrating is TR, the predetermined maximum release period is TRmax, and the period until the amplitude of the vibration in the y direction of the movable body  111  reaches the predetermined value (Amax) is TAmax, then TR becomes the smaller of the TRmax and TAmax. That is,
 
 TR =min{ TR max, TA max}
 
       FIG. 12  is a diagram showing a second operation example of the gyro sensor system  200  according to the present embodiment. It should be noted that the present operation example can be mainly applied to the gyro sensor system shown in  FIGS. 1 and 9 . 
     In the present operation example, when the amplitude of the vibration in the y direction of the movable body  111  is increased to be larger than the predetermined value, the amplitude detection for acquiring the rotation angle is performed. In  FIG. 12 , when the amplitude of the vibration in the y direction of the movable body  111  is increased to be larger than the predetermined value (Amin), the measurement period for acquiring the rotation angle starts. When the rotation angle is very small, the value of the angle Φ is almost zero and the amplitude A m  is a very small value. When the amplitude A m  approaches a noise level of the measurement system, the measurement accuracy deteriorates. In the present operation example, since the measurement period starts when the amplitude of the vibration in the y direction of the movable body  111  is larger than the predetermined value (Amin), it is possible to prevent the measurement accuracy from deteriorating. 
     In the present operation example, as described below, the amplitude of the vibration of the movable body  111  may be forcibly increased. 
     In the first method, in the adjustment period, the value of κ 2  is adjusted so that the amplitude of the vibration in the y direction of the movable body  111  becomes larger than the predetermined value (Amin). If κ 2 &gt;0, the following formula is established.
 
{tilde over (Φ)}( t )&gt;Φ( t )
 
     Therefore, it is obvious that the present method is possible. It should be noted that the condition of the voltages V 1  and V 2  at which κ 2 =0 are found beforehand and stored in a register. 
     In the second method, as shown in  FIG. 13 , the rotation mechanism  150  is provided to forcibly rotate the gyro element  110 . In this way, the amplitude of the vibration in the y direction of the movable body  111  becomes larger than the predetermined value (Amin) by forcibly rotating the gyro element  110  by the rotation mechanism  150 . 
       FIG. 14  is a diagram showing a third operation example of the gyro sensor system  200  according to the present embodiment. It should be noted that the present operation example can be mainly applied to the gyro sensor system shown in  FIG. 9 . 
     In the present operation example, when the amplitude of the vibration in the y direction of the movable body  111  of one gyro sensor unit  100  is decreased to be smaller than the predetermined value, the vibration in the x direction of the movable body  111  of the other gyro sensor unit  100  starts.  FIG. 14  shows the case in which when the amplitude of the vibration in the y direction of the movable body  111  of the first gyro sensor unit  100   a  becomes smaller than the predetermined value (Amin), the vibration in the x direction of the movable body  111  of the second gyro sensor unit  100   b  starts. In addition, in the present operation example, after the overlap period has elapsed, one movable body  111  is caught to stop the vibration. By using the control method as in the present operation example, the measurement can be prevented from being performed in a state in which the amplitude of the vibration in the y direction of the movable body  111  is excessively small, and thus the measurement accuracy can be prevented from being deteriorated. 
     In addition, if a predetermined maximum release period has elapsed before the amplitude of the vibration in the y direction of one movable body  111  becomes smaller than the predetermined value (Amin), the vibration in the x direction of the other movable body  111  starts after the predetermined maximum release period has elapsed. That is, in the present operation example, if the release period during which the movable body is actually vibrating is TR, the predetermined maximum release period is TRmax, and the period until the amplitude of the vibration in the y direction of the movable body  111  is smaller than the predetermined value (Amin) is TAmin, then TR becomes the smaller of the TRmax and TAmin. That is,
 
 TR =min{ TR max, TA min}
 
       FIG. 15  is a diagram showing a fourth operation example of the gyro sensor system  200  according to the present embodiment. It should be noted that the present operation example can be mainly applied to the gyro sensor system shown in  FIGS. 1 and 9 . 
     In the present operation example, the amplitude A m  of the vibration in the y direction is controlled to be constant with respect to the movable body  111  of the gyro sensor unit  100 . Specifically, a feedback control is performed so that the amplitude of the vibration in the y direction is constant. By using such a control method, the sensing operation can be performed at the optimum amplitude level, such that it is possible to perform the measurement with high accuracy. It is should be noted that as a method for keeping an amplitude A m  in a constant value, there are a method for adjusting a value of K 2 , a method for using a rotation mechanism  150  as shown in  FIG. 13 , or the like. In the former method, it is possible to perform an inversion on the information on the angle Φ from the value of K 2  for keeping the amplitude A m  in the constant value. 
     Next, a second modified example of the gyro sensor system according to the present embodiment will be described. It should be noted that since the basic matters are similar to those of the above embodiment, the description of the matters described in the above embodiment will be omitted. 
       FIG. 16  is a diagram showing a basic configuration (concept) of a gyro sensor system according to the present modified example. In the present modified example, a gyro sensor system  200  includes gyro sensor units  100   a ,  100   b , and  100   c . Both of the gyro sensor units  100   a  and  100   b  have the same configuration as the gyro sensor unit  100  shown in  FIG. 1 . That is, in the gyro sensor units  100   a  and  100   b , the rotation angle of the movable body is directly acquired. The basic operation of the gyro sensor units  100   a  and  100   b  is the same as the operation of the first modified example shown in  FIGS. 9 and 10 . The second gyro sensor unit  100   c  acquires the angular velocity of the movable body included in the second gyro sensor unit. 
     It is possible to calculate the angular velocity Ω by differentiating the angle Φ acquired by the gyro sensor units  100   a  and  100   b , but the second gyro sensor unit  100   c  can directly detect the angular velocity Ω to decrease the computation. It is also possible to improve the accuracy of both the angle Φ and the angular velocity Ω by acquiring both the angle Φ and the angular velocity Ω and by matching them. 
     It should be noted that a plurality of the second gyro sensor units may be provided or a triaxial gyro sensor may be used as the second gyro sensor unit. 
     Next, a third modified example of the gyro sensor system according to the present embodiment will be described. It should be noted that since the basic matters are similar to those of the above embodiment, the description of the matters described in the above embodiment will be omitted. 
       FIG. 17  is a diagram showing a basic configuration (concept) of a gyro sensor system according to the present modified example. In the present modified example, a gyro sensor system  200  includes three gyro sensor units  100   x ,  100   y , and  100   z . The gyro sensor unit  100   x  includes gyro sensor units  100   ax  and  100   bx , the gyro sensor unit  100   y  includes gyro sensor units  100   ay  and  100   by , and the gyro sensor unit  100   z  includes gyro sensor units  100   az  and  100   bz . All of the gyro sensor units  100   ax ,  100   bx ,  100   ay ,  100   by ,  100   az , and  100   bz  have the same configuration as the gyro sensor unit  100  shown in  FIG. 1 , and the rotation angle of the movable body is directly acquired. The basic operation of each of the gyro sensor units  100   x ,  100   y , and  100   z  is the same as the first modified example shown in  FIGS. 9 and 10 . 
     The gyro sensor system according to the present modified example is used as a triaxial gyro sensor. That is, the gyro sensor unit  100   x  detects a rotation angle about an x axis as a rotation center, the gyro sensor unit  100   y  detects a rotation angle about a y axis as the rotation center, and the gyro sensor unit  100   z  detects a rotation angle about a z axis as the rotation center. In other words, in the three gyro sensor units  100   x ,  100   y  and  100   z , the first directions defined in the above embodiments are perpendicular to each other, and the second directions defined in the above embodiments are perpendicular to each other. 
     In the present modified example, a triaxial gyro structure (for example, a pantograph type triaxial gyro structure) connected to each other may be adopted. In this case, a frequency fd of a drive vibration and frequencies fsx, fsy, and fsz of three sense vibrations may be equal to each other. That is, it may be set to be fd=fsx=fsy=fsz. 
     In the above embodiment, when the damping coefficients (attenuation coefficients) b x  and b y  are not zero, each of the amplitudes in the x direction and the y direction is attenuated based on exp (−b x t/2) and exp (−b y t/2). When the angle information and the angular velocity information are acquired, such the attenuation effect may be corrected. For example, if the correction is performed on the measurement value y obs  of the amplitude in the y direction as follows,
 
 y   obs ( t )→ e   b     y     t/2     y     obs ( t )≡ y   c ( t ),
 
     a value yc(t) from which the attenuation influence is removed can be obtained. In addition, in the above embodiment, it is known that an angle drift occurs if an asymmetry of the damping coefficients (attenuation coefficients) b x  and b y  exists [Igor P. Prikhodko, et. al., “Foucault pendulum on a chip: Rate integrating silicon MEMS gyroscope”, Sensors and Actuators A 177 (2012) 67-78]. Therefore, in order to suppress the angle drift, a damping coefficient adjustment mechanism may be provided as below. 
       FIG. 18  is a diagram schematically showing a first configuration example of a gyro sensor system having a damping coefficient adjustment mechanism. 
     In the first configuration example, one variable capacitor  118  (electrode pair  118   a  and  118   b ) having capacitance C 1  and the other variable capacitor  118  (electrode pair  118   a  and  118   b ) having capacitance C 2  can be connected to each other via a variable resistor R. The variable voltage V can be supplied to the two variable capacitors  118  via a switch SW 1 . If both of the switch SW 1  and a switch SW 2  are turned on to charge the two variable capacitors  118  with the variable voltage V and then only the switch SW 1  is turned off, the two variable capacitors  118  are connected to each other via the variable resistor R. If the movable body (mass)  111  is displaced, the capacitances C 1  and C 2  are changed, charges accumulated in the variable capacitor  118  move through the variable resistor R. As a result, the variable resistor R generates heat energy and serves as the damping. 
     The capacitances C 1  and C 2  can be represented by as follows using a position x of the movable body  111 .
 
 C   1   =α+βx  
 
 C   2   =α−βx  
 
     If the switch SW 1  is turned off and then movable body  111  is displaced by Δx during a period of Δt, the moving charge amount is as follows.
 
Δ Q=ΔC   1   V=βΔxV  
 
     At this time, the energy consumed by the variable resistor R is as follows. 
     
       
         
           
             
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     Therefore, a damping force by the variable resistor R is as follows. 
     
       
         
           
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     This means that the damping force having the damping coefficient
 
 b   R =β 2   V   2   R  
 
acts. This damping coefficient can be changed by the variable voltage V and the variable resistor R. Therefore, it is possible to eliminate the asymmetry of the damping coefficient by adjusting the values of the variable voltage V and the variable resistor R.
 
     It should be noted that there is a relationship of τ=2 m/b between the damping coefficient b and a damping time constant τ, where m is the mass of the movable portion. Therefore, adjusting the damping coefficient b is the same as adjusting the damping time constant τ. 
       FIG. 19  is a diagram schematically showing a second configuration example of the gyro sensor system having the damping coefficient adjustment mechanism. 
     In the second configuration example, the damping coefficient adjustment mechanism is adopted even for both the x direction and the y direction. If either a switch SWx 2  or a switch SWy 2  is turned off, the damping influence due to the variable resistor can be eliminated. By doing so, for example, it is possible to suppress unnecessary vibrations from occurring by operating the damping mechanism only during the catch period. Specifically, in the release period during which the measurement is performed, switches SWx 1   a , SWx 1   b , SWy 1   a , and SWy 1   b  are in a turned on state and switches SWx 2  and SWy 2  are in a turned off state. During the catch period, the switches SWx 1   a , SWx 1   b , SWy 1   a , and SWy 1   b  are in a turned off state and the switches SWx 2  and SWy 2  are in a turned on state. In order to suppress unnecessary vibrations from occurring immediately after the release period, the same switch state as the switch state during the catch period may be continued in a fixed period after the release period. 
       FIG. 20  is a diagram schematically showing a third configuration example of the gyro sensor system having the damping coefficient adjustment mechanism. 
     In the third configuration example, the variable resistor R is connected to a capacitor C having a fixed capacitance. That is, the variable resistor R is connected between a variable capacitor  118  whose capacitance is changed according to a displacement of the movable body  111  and the capacitor C having the fixed capacitance. When the movable body  111  is displaced, a part of the charges accumulated in the variable capacitor  118  passes through the variable resistor R. Due to the energy loss at this time, the damping coefficient of the movable body  111  is adjusted. 
     It should be noted that a fixed resistor may be adopted instead of the variable resistor and the damping coefficient may be adjusted only by the variable voltage V. In this case, the variable capacitor is connected to a variable voltage source via the switch, and the accumulated charge amount of the variable capacitor is controlled by adjusting a voltage value of the variable voltage source. By doing so, it is possible to adjust the damping coefficient. 
     In the above embodiments, the amplitude of vibration of the movable body in the second direction is detected to acquire the rotation angle of the movable body, however the amplitudes of vibrations of the movable body in the first and second directions may be detected to acquire the rotation angle of the movable body. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.