Abstract:
A micromechanical motion sensor is capable of detecting a deflection imparted to an oscillatably mounted bar spring element excited to a permanent periodic oscillation by an electrostatic oscillating drive to which a periodic drive voltage is applied. To compensate non-linearities of the resonance frequency response of the bar spring element, a sum of a normal drive voltage signal and a compensation drive signal may be applied to a comb drive. In an alternative embodiment, separate compensation comb drive units may be additionally provided to the comb drive units used for the oscillation drive and a compensation voltage signal may be applied to them to compensate for the non-linearity.

Description:
FIELD OF THE INVENTION 
   The present invention relates to a micromechanical motion sensor capable of detecting a deflection imparted to an oscillatably mounted bar spring element excited to permanent periodic oscillation by an electrostatic oscillating drive to which a periodic drive voltage is applied. Such a micromechanical motion sensor which uses bar springs and comb drives among other things is described in U.S. Pat. No. 5,025,346. 
   BACKGROUND INFORMATION 
   Bar springs exhibit non-linear effects when subjected to high deflections. In a yaw rate sensor manufactured by the applicant (Robert Bosch GmbH model MM2R), a rotor is suspended in its center of rotation on an X spring that includes bar springs (see appended  FIG. 3 ). This non-linear effect is clearly detectable even for deflections as small as ±4°. It is manifested in a shift of the resonance frequency of the system. In addition, areas exhibiting a plurality of stable operating states may appear as a result of the non-linearity. If a sudden transition occurs between the stable states during operation due to minor interference, for example, the performance of the yaw rate sensor may be considerably impaired. 
   In the yaw rate sensor (model MM2R) manufactured by the present Applicant and schematically illustrated in  FIG. 3 , due to a centrally mounted X spring  2 , the bar spring element has a centrally mounted and centrally symmetric inertial mass  1  which is excited to a periodic rotary oscillation in a lateral plane x, y having positive and negative deflections i, a of the same magnitude about a rest position O (angle γ designates the deflection angle in positive direction i) by symmetrically acting comb drives. A first comb drive pair has two comb drive units KI 1  and KA 1  opposite one another, which act upon a first drive point P 1  situated on a circular arc-shaped peripheral segment of inertial mass  1 . These two first comb drive units KI 1  and KA 1 , which are provided for a deflection in positive direction i and negative direction a, respectively, are situated parallel to a an imaginary straight line connecting the center of X spring  2  to the rest position of inertial mass  1 . A second pair of comb drive units KI 2 , KA 2  for positive deflections i and negative deflections a, respectively, situated centrally symmetrically to the first pair of comb drive units KI 1 , KA, acts upon a second point of application P 2  diametrically opposite first point of application P 1  on inertial mass  1 . The latter two comb drive units KI 2  and KA 2  are situated parallel to an imaginary straight line connecting the center of inertial mass  1  to point O denoting the rest position. 
   A control unit  3  generates drive voltages U PKI,drive  and U PKA,drive  for comb drive units KI 1  and KI 2  (for excitation in positive deflection direction i) and for comb drive units KA 1  and KA 2  (for excitation in negative deflection direction a), respectively, as shown in appended  FIG. 4 .  FIG. 4  shows in top part A the periodic and, in the ideal case, harmonic excitation function γ(t) of inertial mass  1  in positive direction i and negative direction a, which has the period  2 π. 
   In center  FIG. 4B , a dashed line shows the square pulse-shaped drive voltage U PKA,drive  for comb drive units KA 1  and KA 2  for deflection in negative direction a, while bottom  FIG. 4C  shows drive voltage U PKI,drive  for comb drive units KI 1 , KI 2  for positive deflection in phase opposition to drive voltage U PKA,drive , the positive deflection also having square pulses having the periodicity of periodic excitation oscillation γ(t) shown in  FIG. 4A . 
   In addition,  FIG. 4  shows that the pulses of drive voltage U PKI,drive  for positive deflection i according to  FIG. 4C  are generated symmetrically to the positive zero crossings of periodic oscillation γ(t) of inertial mass  1 , while the pulses of drive voltage U PKA,drive  for negative deflection i according to  FIG. 4B  are generated symmetrically to the negative zero crossings of periodic excitation oscillation γ(t) according to  FIG. 4A . Since the comb drive units (KI and KA) schematically shown in  FIG. 3  are each able to exert a force in one direction only, a plurality of comb drive units are needed to set the rotor in an oscillating motion. 
   For practical reasons, a square-wave voltage is generated for the drive voltage applied by control unit  3  instead of the sinus curve. This is accomplishable using a control logic and a voltage pump in control unit  3 . In principle, a voltage pump is made up of a capacitor which is charged. This allows higher voltages than the operating voltage to be generated for a short period. This voltage is used if needed. 
   The non-linear bending of the bar is describable using Duffing&#39;s differential equation. Since this is a known differential equation, a detailed analysis of the dynamic properties is not necessary. Instead, the two main effects (frequency shift and instability) are briefly explained with reference to appended  FIGS. 1 and 2 . The mechanical non-linearity of the X spring may be described using Duffing&#39;s differential equation
 
 M   drive   =J   z   ·γ+b   t,z   ·γ+k   tz,0 ·(1+ k   tz,NL γ 2 )γ  (1)
 
or
 
 M   drive   =J   z   ·γ+b   t,z   ·γ+k   tz,0   ·γ+k   tz,0   k   tz,NL γ 3   (2)
 
   The parameters are determined via the appropriate finite-element computations. 
   As can be seen from equation (2), this is a second-order differential equation for oscillation, having linear attenuation term b t,z  (velocity-proportional attenuation). γ denotes the angle describing the deflection of the rotor. The only difference with respect to the “standard differential equation for oscillation” is additional non-linear term k tz,0 k tz,NL γ 3 . Term k tz,0  is the linear spring constant (torsion). Term k tz,NL  describes the non-linearity. J z  denotes the moment of inertia of the rotor about the z axis. The rotor oscillation is excited via drive moment M drive . 
   Appended  FIG. 1  shows the resonance curve of the gain in the linear case with attenuation. The gain factor attains its maximum at the exact moment when the system is excited by its intrinsic frequency. In the non-linear case, the maximum of the resonance curve is shifted to the right. As can be seen from appended  FIG. 2 , the resonance curve tends additionally to the right. The one-to-one correspondence between gain and excitation frequency is thus lost. The gain in each individual case depends on the previous history. For example, in the case of a smooth increase in the excitation frequency, there is a slow transition from area I to area II and thus to point  1  in  FIG. 2 . In the case of supercritical excitation and a slower reduction in the drive frequency, the operating state migrates from area III to point  2  in area II. This makes two different states possible for one drive frequency. In general, this is an undesirable effect, because, for example, interference pulses may cause a sudden transition from point  1  to point  2 . The risk of a sudden change exists in the entire area II (shaded in  FIG. 2 ). 
   Only the basic analytical equation in principle is given here as the operating principle of comb drives:
 
 F   x ≈ε 0   ΔU   2 ( h/d   0 )  (3)
 
   The following relationships are discernible from equation 3:
         The greater voltage difference (ΔU) on the capacitor plates of the comb drive, the greater drive force F x .   The greater height h of the comb drive structure, the greater drive force F x .   The smaller distance d 0  between the capacitor plates of the comb drive, the greater drive force F x .       

   These are only the basic relationships. Detailed examination shows that the force is caused by the formation of stray fields. Therefore, in a more accurate analysis, the field lines must be used for computing the force. For more complex geometries, the relationships may be determined using finite element computations. 
   SUMMARY OF THE INVENTION 
   As explained previously, the object of the present invention is to avoid the above-described problems in a micromechanical motion sensor, in particular in a yaw rate sensor equipped with comb drive units or in a linear oscillator due to mechanical non-linearity, and to provide such a micromechanical motion sensor in which non-linearities are compensated. 
   According to an essential aspect, a micromechanical motion sensor for achieving this object according to the present invention is characterized in that electrostatic compensation drive means acting upon the bar spring element are provided, to which a suitable periodic compensation voltage is applied to compensate the non-linearity of the resonance frequency response of the bar spring element. 
   If such a micromechanical motion sensor is configured as a yaw rate sensor on the basis of the aforementioned basic structure of the yaw rate sensor manufactured by the present Applicant, the bar spring element has a centrally symmetric inertial mass (rotor) which is centrally mounted with the help of a centrally situated X spring and is excited by the oscillation drive to a rotary oscillation in a lateral X-Y plane for positive and negative deflections of the same magnitude about a rest position; the oscillation drive has at least one comb drive unit controlled by a control unit using the periodic drive voltage for exciting the inertial mass for positive and negative deflections, whose drive forces act upon the inertial mass tangentially at least one first point of application situated in the same X-Y plane in such a way that they excite, i.e., drive the inertial mass symmetrically about its rest position; and the compensation drive means have at least one comb drive unit for compensating the non-linearities in the positive and negative deflection directions, which acts upon the same point of application and/or upon a second point of application situated diametrically opposite thereto at the same distance from the center of the inertial mass. 
   In one embodiment, the compensation comb drive units may be identical to at least one of the pairs of comb drive units. In another embodiment, at least one additional pair of compensation comb drive units are provided for compensation in addition to the comb drive units used for normal excitation. 
   If a micromechanical motion sensor of this type is configured as a linear oscillator, the bar spring element has a system of a plurality of inertial masses connected by a centrally situated coupling spring and mounted by a symmetric spring suspension so it is able to perform linear oscillations, the system being excited by the oscillation drive to a linear oscillation in a lateral plane with positive and negative deflections of the same magnitude about a central rest position; for exciting the inertial mass system in the positive and negative deflection directions, the oscillation drive has at least one comb drive unit controlled by a control unit, the drive forces of the comb drive unit acting upon the inertial mass system at a plurality of points of application situated in the same lateral plane and opposite one another on each inertial mass of the system in such a way that they excite the inertial masses of the system about their respective rest positions; and the compensation drive means have for each inertial mass of the system at least one comb drive unit which acts upon at least one of the points of application of each inertial mass. 
   Due to the use proposed according to the present invention of comb drive units for compensating the non-linearity, the overall structure made up of bar spring element and comb drive units has a linear characteristic. This eliminates the above-described problems possibly caused by non-linearities. 
   The above and additional advantageous features of a micromechanical motion sensor according to the present invention, in particular of a yaw rate sensor and a linear oscillator, are elucidated in more detail in the subsequent description of preferred exemplary embodiments with reference to the drawing. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  graphically shows the frequency response of the gain (resonance curve) in the linear case with attenuation. 
       FIG. 2  graphically shows the frequency response of the gain in the non-linear case in which, as explained above, the maximum of the resonance curve tends to the right. 
       FIG. 3  shows a schematic top view of the above-described yaw rate sensor configured as a micromechanical motion sensor and indicates at the same time a first exemplary embodiment of the yaw rate sensor (compensated) according to the present invention. 
       FIGS. 4A , B, and C, respectively, graphically show the idealized oscillation curve of the centrally mounted inertial mass according to  FIG. 3 , the drive voltage for the comb drive unit for the negative deflection direction, and the drive voltage for the comb drive units for the positive deflection direction as generated by the control unit according to  FIG. 3 . 
       FIG. 5  shows a schematic top view of a second exemplary embodiment according to the present invention, in which additional compensation comb drive units are provided for compensating the non-linearity. 
       FIGS. 6A-6F  graphically show, in addition to the time diagrams according to  FIGS. 6A ,  6 B, and  6 C already shown in  FIGS. 4A-4C , an oscillation curve of a compensation voltage signal for negative deflection ( FIG. 6D ), an oscillation curve of a compensation voltage signal for positive deflection ( FIG. 6E ), and in  FIG. 6F  a sum of the respective drive voltage signals and the corresponding compensation voltage signal. 
       FIG. 7  shows a schematic top view of a third exemplary embodiment of a micromechanical motion sensor according to the present invention in the form of a linear oscillator in which additional compensation comb drive units are provided for compensating the non-linearity. 
   

   DETAILED DESCRIPTION 
   To compensate for the mechanical non-linearity of the bending bar, in addition to the previous drive signal (see  FIG. 4 ), a compensation voltage is applied to the comb drive, which accurately compensates for the non-linear term of differential equation 2. It must be kept in mind that comb drives are able to apply forces in one direction only due to their operating principle. Thus, in the case of a positive deflection i, comb drive KA is responsible for the compensation, and in the case of negative deflection a, it is comb drive KI. 
   The compensation voltage curve results from the analytical relationships for the yaw rate sensor. The moment to be compensated results from equation 2.
 
M comp =k tZ,0 k tzNL γ 3   (4)
 
   If this moment is to be applied via the available comb drives (KI 1 , KI 2  and KA 1 , KA 2 ), the following equation results: 
                         M   comp     =     2   ⁢           (       U     PKI   ,   PKA       -     U   PCM       )     2     ⁢     ɛ   0     ⁢   h       d   0       ⁢     k   stray     ⁢     n   comb     ⁢     r   eff                   =       k     tz   ,   0       ⁢       k     tz   ,   NL       ·          γ        3                       (   5   )               
where K stray  is a correction factor for taking into account stray field effects; n comb  is the number of combs, and r eff  is the resulting effective radius for calculating the drive moment. U PCM  denotes the common reference potential of all comb drives.
 
   Equation 5 may be solved for voltage U PKI  (voltage applied to comb drive units KI 1 , KI 2 ) or U PKA  (voltage applied to comb drive units KA 1 , KA 2 ), to obtain the compensation voltage 
   
     
       
         
           
             
               
                 
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   Adding drive voltage U PKI, PKA,drive  (see  FIG. 4 ) and compensation voltage U PKI, PKA,comp  computed in equation 6 yields the ideal voltage curve applied to comb drives U PKI,PKA,tot . In practical applications, this curve must be approximated by a stepped graph. 
   Thus, in a first exemplary embodiment, total voltage U PKA,tot  and U PKI,tot  according to  FIG. 6F , formed from the sum of the respective drive voltages U PKA,drive  and U PKI,drive  ( FIGS. 6B  and C) and the respective compensation voltages U PKA,comp  and U PKI,comp  according to  FIGS. 6D  and E, are supplied to the respective comb drive units KA 1 , KA 2  and KI 1 , KI 2  according to  FIG. 3  to compensate the non-linearity. To do so, control unit  3  generates the total voltages U PKA,tot  and U PKI,tot  shown, respectively, in  FIG. 6F  in dashed and solid lines (indicated with dashed lines in  FIG. 3 ) and applies them to corresponding comb drive units KA 1 , KA 2  and KI 1 , KI 2 . 
   In the exemplary embodiment of a yaw rate sensor according to the present invention shown in  FIG. 3 , the oscillation drive has four comb drive units KA 1 , KA 2  and KI 1 , KI 2 , of which a first and second comb drive unit for positive i and negative a deflection form a first pair (KI 1 , KA 1 ), which has a first shared point of application P 1  on inertial mass  1 . A third and fourth comb drive unit KI 1  and KA 2  form a second pair, which act upon the opposite shared point of application on the inertial mass. The two comb drive units KI 1 , KA 1  and KI 2 , KA 2  are situated opposite one another, parallel to an imaginary line which defines rest position O of inertial mass  1  and passes through the center of the very inertial mass. In this way, the drive forces of the comb drive units for positive deflection i and the drive forces of the comb drive units for negative deflection a are added up. 
   According to parts B and C of  FIGS. 4 and 6 , drive voltage signals U PKA,drive  and U PKI,drive  generated by control unit  3  are square voltage pulses in phase opposition; control unit  3  generates square voltage pulses U PKI, drive  for positive deflection i symmetrically to the positive zero crossings of oscillation curve γ(t) shown in  FIG. 4A  and square voltage pulses U PKA, drive  for comb drive units KA 1  and KA 2  for negative deflection symmetrically to the negative zero crossings of oscillation curve γ(t). 
   Compensation voltage signals U PKA,comp  and U PKI,comp  according to  FIGS. 6D and 6E , generated by control unit  3 , are also in phase opposition with respect to one another but are symmetric to the deflection maximums in the positive and negative deflection directions, respectively, of oscillation curve γ(t). Thus, compensation voltage signal U PKA,comp  for negative deflection is delayed by 90° (π/2) with respect to drive voltage signal U PKI,drive  for positive deflection, and compensation voltage signal U PKI,comp  according to  FIG. 6E  is also delayed by 90° (π/2) with respect to drive voltage signal U PKA,drive . 
   To check the practical suitability of a yaw rate sensor compensated as described above, the above equation 6 may be converted into a simulation model using Simulink standard blocks. This simulation model calculates the resulting total voltage from the input signals:
         deflection angle γ of inertial mass  1 ,   reference potential U PCM , and   drive voltage U PKI,drive , U PKA,drive .       

   The simulation results have shown that, in order to achieve sufficient compensation of the non-linearity, the total voltages on the comb drive units shown in  FIG. 6F  and indicated as dashed lines in  FIG. 3  must assume a very high voltage level at which conventional comb drive units no longer operate. The recognition of this fact resulted in the second exemplary embodiment shown in  FIG. 5 , which, in addition to the four comb drive units KI 1 , KI 2  and KA 1 , KA 2  shown in  FIG. 3 , has four compensation comb drive units KIK 1 , KIK 2  and KAK 1 , KAK 2 , which are controlled by control unit  3  exclusively via corresponding compensation voltage signal U PKI,comp  or U PKA,comp  according to  FIGS. 6E  and D. In contrast, comb drive units KI 1 , KI 2  and KA 1 , KA 2  of the drive means receive only drive voltage signals U PKI,drive  and U PKA,drive  shown in  FIGS. 6B and 6C  from control unit  3 , so that the problem of an excessive voltage being applied to a comb drive unit is avoided. 
   In the exemplary embodiment shown in  FIG. 5 , it is apparent that the additional compensation comb drive units KIK 1 , KIK 2 , KAK 1 , and KAK 2  are also arranged in pairs and act upon the same points of application P 1  and P 2  of the inertial mass, situated diametrically opposite one another. The arrangement of four additional compensation comb drive units KIK 1 , KAK 1  and KIK 2 , KAK 2  in pairs used in this exemplary embodiment makes the configuration of this yaw rate sensor completely symmetric. Of course, the non-linearity may also be compensated using only two additional compensation comb drive units, for example, using compensation comb drive units KAK 1  and KIK 1  or compensation comb drive units KAK 2  and KIK 2 . A system having only two compensation comb drive units KIK 1  and KAK 2  or KAK 1  and KIK 2  is also possible. 
   The above-mentioned simulation has also shown that the amplitude of the compensation voltage signal increases approximately linearly with deflection angle γ if, when designing the yaw rate sensor drive, it is ensured that the smallest possible deflection amplitudes are needed. The smallest possible non-linearity must be observed when designing the spring geometry. The additional compensation comb drive units described in the second exemplary embodiment offer the advantage compared to the first exemplary embodiment in the currently used yaw rate sensor technology that the comb drive units provided for the drive means may be designed for lower voltage amplitudes. 
     FIG. 7  shows a schematic top view of a third exemplary embodiment of a micromechanical motion sensor according to the present invention in the form of a linear oscillator in which additional compensation comb drive units are provided for compensating the non-linearity. 
   According to  FIG. 7 , the bar spring element has a system connected via a centrally located coupling spring FC and mounted via a symmetric spring suspension F 1 -F 4  so it is able to perform linear oscillations, the system being composed in this case of two inertial masses m 1 , m 2 , which are excited by comb drive units KI 1 , KA 1 , KI 2 , KA 2  to a linear oscillation in a lateral x-y plane to perform positive and negative deflections i 1 , i 2  and a 1 , a 2  of the same magnitude about their particular rest positions O 1 , O 2 . Accordingly, the bar spring element of  FIG. 7  includes inertial masses m 1 , m 2 , symmetric spring suspension F 1 -F 4 , and coupling spring FC. The oscillation drive thus has four comb drive units controlled by a control unit  3  for exciting the two inertial masses m 1 , m 2  of the inertial mass system, the drive forces of the comb drive units acting upon the two inertial masses at opposite points of application in the same lateral x-y plane in such a way that they excite inertial masses m 1 , m 2  of the system about their particular rest positions O 1 , O 2 . Both coupling spring FC and spring suspension F 1 -F 4  cause oscillation non-linearities, which are compensated according to the present invention. To compensate for non-linearity, the compensation drive means for each inertial mass m 1 , m 2  of the system also have two compensation comb drive units KIK 1 , KAK 1  and KIK 2 , KAK 2 , which act upon the same points of application of each inertial mass m 1  and m 2  as the comb drive units of the oscillation drive. For the drive and compensation voltage signals supplied by control unit  3 , to the latter and to the compensation comb drive units, the same applies in principle as explained above with reference to the second exemplary embodiment illustrated in  FIG. 5 . 
   The control unit is able to advantageously approximate the oscillation curve of the compensation voltage signals via step signals having fine steps. 
   To achieve greater compensation moments with the same voltage, it is advantageous in the exemplary embodiments having separate compensation comb drive units to make the effective radius or effective distance of the compensation comb drive units greater than the effective radius or the effective distance of the oscillation drive comb drive units.