(12) United States Patent (io) Patent No.: US 7,159,441 B2 Challoner et al. (45) Date of Patent: Jan. 9,2007 (54) CLOVERLEAF MICROGYROSCOPE WITH FOREIGN PATENT DOCUMENTS ELECTROSTATIC ALIGNMENT AND wo 9745702 4/1997 TUNING (75) Inventors: A. Dorian Challoner, Manhattan Beach, CA (US); Roman C. Gutierrez, OTHER PUBLICATIONS La Crescenta, CA (US); Tony K. Tang, Glendale, CA (US) Geiger, W, et al., New Designs of Macromachined Vibrating Rate Gyroscopes with Decoupled Oscillation Modes, 1997 International (73) Assignee: The Boeing Company, Chicago, IL Conference on Solid-state Sensors and Actuators, Jun. 16, 1997, pp. (US) 1129-1132, vol. 2, Chicago, Illinois. ( * ) Notice: Subject to any disclaimer, the term of this (Continued) patent is extended or adjusted under 35 Primary Examiner-Hezron Williams U.S.C. 154(b) by 234 days. Assistant Examiner-Nashmiya Fayyaz (21) Appl. No.: 10/843,139 (74) Attorney, Agent, or Firmqstrager Chong Flaherty & Broitman P.C. (22) Filed: May 11, 2004 (57) ABSTRACT (65) Prior Publication Data US 200410237626 A1 Dec. 2. 2004 Amicro-gyroscope (10) having closed loop output operation Related U.S. Application Data by a control voltage (Vv),t hat is demodulated by a drive axis (x-axis) signal V,, of the sense electrodes (Sl, S2), (63) Continuation-in-part of application No. 091927,858, providing Coriolis torque rebalance to prevent displacement filed on Aug. 9, 2001, now abandoned. of the micro-gyroscope (10) on the output axis (y-axis) V,-0. Closed loop drive axis torque, V, maintains a (51) Int. C1. constant drive axis amplitude signal, V,. The present GOlC 19/00 (2006.01) invention provides independent alignment and tuning of the (52) U.S. C1. .................. 73/1.77; 731504.02; 731504.04 micro-gyroscope by using separate electrodes and electro- (58) Field of Classification Search ................. 7311.37, static bias voltages to adjust alignment and tuning. A quadra- 7311.38, 514.15, 504.04, 514.29, 1.77, 504.02 ture amplitude signal, or cross-axis transfer function peak See application file for complete search history. amplitude is used to detect misalignment that is corrected to zero by an electrostatic bias voltage adjustment. The cross- (56) References Cited axis transfer function is either VthJVvo r V,.JV,. A quadra- U.S. PATENT DOCUMENTS ture signal noise level, or difference in natural frequencies estimated from measurements of the transfer functions is 4,587,860 A * 5/1986 Audren ......................... 74/5 F used to detect residual mistuning, that is corrected to zero by a second electrostatic bias voltage adjustment. (Continued) 16 Claims, 3 Drawing Sheets 100 I FJ DETECT MISALIGNMENTB Y WAY OF A QUADRATURE SIGNAL AMPLITUDE 'oI I c/ CORRECT MISALIGNMENT BY ai OR 104 Q2 ELECTRODE BIAS ADJUSTMENT DETECT RESIDUAL MlSTUNlNG BY SIGNAL NOISE LEVEL OR TRANSFER CORRECT RESIDUAL MlSTUNlNG BY WAY OF AN ELECTROSTATIC BIAS ADJUSTMENT TO Ti COUPLING ATORQUE COMPONENT OF THE DRIVE AXIS WITH THE OUTPUT AXIS US 7,159,441 B2 Page 2 U.S. PATENT DOCUMENTS OTHER PUBLICATIONS 6,164,134 A * 12/2000 Cargille ................... 73/504.02 Song, H. et al., Wafter Level Vacuum Packaged De-coupled Verticle 6,584,845 B1 * 7/2003 Gutierrez et al. ........ 73/514.15 Gyroscope bY Proceedings ofthe IEEE, 13th Annual International 6,675,630 B1 * 1/2004 Challoner et al. ........... 73/1.77 Conference on Micro Electro Mechanical Systems, Jan, 23, 2000, 6,698,271 B1 * 3/2004 Fell et al. .................... 73/1.37 pp. 520-524, Miyazaki, Japan. 2004/0226370 A1 * 11/2004 Hayworth et al. ....... 73/504.12 * cited by examiner U.S. Patent Jan. 9,2007 Sheet 1 of 3 US 7,159,441 B2 &? 1NPUTAXlS , , f- 'O (PRIOR ART) FIG. 1 29 26 24 -7 / DEMOD 'Out RATE OUT AMP - GAINjPHASE 25 COMPARATOR DETECT COMP I / vr 22 (PRIOR ART) FIG. 2 U, Sheet 2 of 3 US 7,159,441 B2 U.S. Patent Jan. 9,2007 Sheet 3 of 3 US 7,159,441 B2 ' Y ----X - (PRIOR ART) FIG.4 DETECT MISALIGNMENT BY WAY OF 102 A QUADRATURE SIGNAL AMPLITUDE J I CORRECT MISALIGNMENT BY Q1 OR Q2 ELECTRODE BIAS ADJUSTMENT DETECT RESIDUAL MlSTUNlNG BY CORRECT RESIDUAL MlSTUNlNG BY WAY OF 1 AN ELECTROSTATIC BIAS ADJUSTMENT TO T1 NULL IN PHASE BIAS BY ELECTRONICALLY COUPLING ATORQUE COMPONENT OF THE DRIVE AXIS WITH THE OUTPUT AXIS FIG. 5 US 7,159,441 B2 1 2 CLOVERLEAF MICROGYROSCOPE WITH axes so that a single mode at a time can be sensed and driven. ELECTROSTATIC ALIGNMENT AND Electronic tuning is achieved by means of phase adjustments TUNING in an automatic gain control circuit of the output electronics. However, electronic alignment, in which the sense and CROSS REFERENCE 5 control axes are aligned with the mechanical modal axes results in second harmonics and does not correct electronic The invention described herein is a Continuation-In-Part mistuning, or asymmetry of the micro-gyroscope. Tuning is of application Ser. No. 091927,858, filed Aug. 9, 2001, now typically accomplished by AGC phase-adjustment, for abandoned. example. This method has limited tuning range for high Q io resonators and the tuning will change with variations in GOVERNMENT INTEREST damping or temperature. It is known in the art that electro- static tuning and AGC tuning operate by nulling quadrature The invention described herein was made in the perfor- amplitude. However, the quadrature amplitude signal more mance of work under a NASA contract, and is subject to the properly relates to misalignment so that when there is no provisions of Public Law 96-517 (35 U.S.C. 9 202) in which 15 misalignment, there is no quadrature signal, even though the Contractor has elected to retain title. there may still be residual mistuning. Further, inherent in the manufacture of a micro-gyroscope TECHNICAL FIELD are mechanical imperfections that cause mechanical asym- metry and imbalance in the micro-gyroscope. There is a The present invention relates to micro-machined electro- 20 mechanical stiffness, or inertia, imbalance inherent in a m~hanicals ystems, and more Particularly to a MEMS micro-gyroscope that is a result of the way in which the vibratory gyroscope having closed loop output. micro-gyroscope is fabricated. This mechanical stiffness, inertia, or asymmetrical imbalance results in dynamic BACKGROUND ART mechanical misalignment torques. There is a need to coun- 25 teract and correct this imbalance to avoid misalignment and Micro-gyroscopes are used in many applications includ- mistuning of the micro-gyroscope during its operation, ing, but not limited to, communications, control and navi- gation systems for both space and land applications. These SUMMARY OF THE INVENTION highly specialized applications need high performance and cost effective micro-gyroscopes. 30 The present invention is a method for electrostatic align- There is known in the art a micro-machined electrome- merit and tuning of a cloverleaf micro-gyroscope having chanical vibratory gyroscope designed for micro-spacecraft closed loop operation. Bias voltages are applied to the applications. The gyroscope is explained and described in a electrodes to alter the effective spring stiffness governing the technical paper entitled “Silicon Bulk Micro-machined resonator vibration. For closed loop output, a differential Vibratory Gyroscope” presented in June, 1996 at the Solid 35 sense signal (S1-S2) is compensated by a linear electronic State Sensors and Actuator Workshop in Hilton Head, S.C. filter and directly fed back by differentially changing the The prior art gyroscope has a resonator having a “clover- voltages on two drive electrodes (Dl-D2) to rebalance leaf’ structure consisting of a rim, four silicon leaves, and Coriolis torque, suppress quadrature motion and increase the four soft supports, or cantilevers, made from a single crystal damping of the sense axis resonance. The resulting feedback silicon. A metal post is rigidly attached to the center of the 40 signal is demodulated in phase with the drive axis signal resonator, in a plane perpendicular to the plane of the silicon (Sl+S2) to produce a measure of the Coriolis force and, leaves, and to a quartz base plate with a pattern of electrodes hence, the inertial rate input. that coincides with the cloverleaf pattern of the silicon The micro-gyroscope and method of alignment and tuning leaves. The electrodes include two drive electrodes and two of the present invention first detects residual mechanical sense electrodes. 45 imbalance, or misalignment, of the cloverleaf micro-gyro- The micro-gyroscope is electrostatically actuated and the scope by demodulation of the feedback signal with the drive sense electrodes capacitively detect Coriolis induced axis signal and detecting a quadrature signal amplitude. motions of the silicon leaves. The response of the gyroscope Alternatively, the amplitude of a cross axis transfer function is inversely proportional to the resonant frequency and a low from the drive axis control voltage, V,, to the output axis resonant frequency increases the responsivity of the device. 50 sense voltage, V ,, i.e. VthJv,,, or from the output axis Micro-gyroscopes are subject to electrical interference control voltage, V,, to the drive axis sense voltage, Vthn,L e., that degrades performance with regard to drift and scale V,.JV, is indicative of mechanical misalignment. The factor stability. Micro-gyroscopes often operate the drive detected misalignment is corrected to zero by applying an and sense signals at the same frequency to allow for simple electrostatic bias adjustment to at least one electrode rather electronic circuits. However, the use of a common frequency 55 than the electronic signal decoupling that is accomplished by for both functions allows the relatively powerful drive signal electronic alignment methods used in the prior art. After to inadvertently electrically couple to the relatively weak such electrostatic alignment, any residual in-phase demodu- sense signal. lated rate bias may be nulled by electronically coupling a Residual mechanical imbalance, either stiffness or mass component of drive axis torque into the output axis. imbalance, of a cloverleaf micro-gyroscope results in mis- 60 According to the present invention, residual mistuning is alignment or coupling of drive motion into the output axis. detected by detecting a quadrature signal noise level, or a Presently, it is known to correct any misalignment of the mismatch between the drive axis and output axis natural mechanical modal axes by electronically rotating the sense resonance frequencies estimated, respectively from the two and control axes into alignment with the mechanical axes., direct transfer functions, Vth.JV, and VthJv,. These trans- Electronic alignment is accomplished by transform circuits 65 fer functions can be measured open loop or closed loop by in the readout electronics that transform the received elec- summing a pseudo-random noise test signal with the normal trode signal axes and drive axes to the mechanical vibration output or drive axis control signal and correlating the output US 7,159,441 B2 3 4 axis or drive axis sensed motion with this test signal. outer frame 16. The resonator defines a resonator plane and Mistuning is corrected by applying an electrostatic bias the central proof mass 12 is perpendicular to the resonator adjustment to at least one electrode in the electrode plane. plane. The quadrature amplitude is used as an indication of mis- A set of at least four electrodes 18 define an electrode alignment and quadrature noise level, or a natural resonance 5 plane. The electrodes 18 are located under the resonator 14. frequency and amplitude estimates from a transfer function The electrodes function to actuate the resonator and to sense are used as a mistuning indicator for electrostatic adjustment capacitance on the resonator 14. The electrodes are large of alignment and tuning. parallel plate capacitors. The electrodes define an electrode Electrostatic alignment and tuning is accomplished by plane that is separated from the resonator plane by a capaci- applying bias voltages to the electrodes to alter the effective io tive gap. spring stiffness governing the resonator vibration so that the Drive electrodes D1 and D2 actuate movement of the mechanical vibration axes become aligned with the elec- resonator 14 and sense electrodes S1 and S2 sense capaci- trode drive and sense axes. tance. A set of axes are labeled x, y and z to describe the operation of the micro-gyroscope. The x-axis is also known It is an object of the present invention to improve closed loop micro-gyroscope performance. It is another object of 15 as the drive axis. The y-axis is also known as the output, or sense axis. And the z-axis is also known as the input axis. the present invention to improve the accuracy of micro- gyroscope alignment and tuning. The electrodes initiate a rocking motion of the central proof mass 12 about the x-axis that actuates the micro- It is a further object of the present invention to provide gyroscope 10. The rocking motion is accomplished by electrostatic alignment and tuning for closed-loop operation of a vibratory micro-gyroscope. It is still a further object of 20 applying electrostatic forces to petals 1 and 4 by applying a voltage to the drive electrodes, D1 and D2. For a steady the present invention to use the quadrature amplitude or a inertial rate, Q, along the z-axis or input axis, there will be cross-axis transfer function amplitude as an indication of a displacement about the y-axis, or output axis that can be misalignment. It is yet a further object of the present sensed by the differential output of the sensing electrodes, invention to use quadrature noise level, or difference in natural resonance frequencies estimated from direct transfer 25 Sl-S2 or V ., The displacement about the y-axis is due to the influence of a rotation induced Coriolis force that needs function measurements as a tuning indicator. Yet a further to be restrained by a counteracting force. object of the present invention is to provide independent In a cloverleaf micro-gyroscope the resonator 14 that is control of alignment and tuning for a closed loop micro- suspended from the outer frame 16 has a planar structure. gyro scope. 30 The four electrodes 18 define the electrode plane, which is Other objects and features of the present invention will adjacent the resonator plane. The present invention corrects become apparent when viewed in light of the detailed misalignment and mistuning by zeroing the misalignment description of the preferred embodiment when taken in and mistuning using out-of-plane forces, or torques, pro- conjunction with the attached drawings and appended duced by bias adjustments to a particular electrode in the claims. 35 electrode plane. By applying an electrostatic bias adjustment to one of the electrodes in the electrode plane, a torque is BRIEF DESCRIPTION OF THE DRAWINGS generated that counteracts a mechanical cross-coupling spring force that is misalignment caused by the fabrication, FIG. 1 is an exploded view of a prior art vibratory or manufacture, of the micro-gyroscope. micro-gyroscope having four electrodes; 40 In fabricating a micro-gyroscope it is inevitable that FIG. 2 is a block diagram of a prior art closed-loop asymmetry, also called mistuning, and imbalance, also micro-gyroscope; called mechanical misalignment or rocking imbalance stiff- FIG. 3 is an example of a prior art circuit schematic for ness K,,, or inertia J,,, of the resonator will occur. It is not closed loop senseiopen loop drive operation; yet possible to fabricate a micro-gyroscope without FIG. 4 is an exemplary electrode arrangement for the 45 mechanical error. Therefore, in the present invention, elec- method of electrostatic alignment and tuning according to trostatic stiffness is introduced to counteract the inherent mistuning and alignment, by applying an electrostatic bias the present invention, the electrode arrangement includes eight electrodes; and voltage to an electrode in the electrode plane. A bias voltage applied to an electrode in the electrode plane produces FIG. 5 is a flowchart of the method for electrostatic 50 cross-coupling electrostatic spring stiffness, Ken,. This, in alignment and tuning according to the present invention. turn, generates an electrostatic torque, T,, in response to a displacement about the x-axis, caused by the cross coupling BEST MODE(S) FOR CARRYING OUT THE electrostatic spring force, which counteracts the dynamic INVENTION effect of rocking imbalance stiffness K,, or rocking inertia 55 imbalance, J,,. The motion of the post on the y-axis is The method of the present invention is applicable to a thereby nulled. An electrostatic bias adjustment to an elec- closed loop micro-gyroscope. In the preferred embodiment, trode thus creates a stiffness torque that counteracts any the closed loop micro-gyroscope is described in conjunction mechanical stiffness or inertia dynamic imbalance torque. with FIGS. 1 through 3. For example purposes, and for Referring now to FIG. 2, the wide-band closed-loop simplicity, the closed loop control of the preferred embodi- 60 operation of the micro-gyroscope will be described. The ment will be described in accordance with a cloverleaf closed-loop control circuit nulls displacement about the micro-gyroscope having four electrodes. y-axis through linearized electrostatic torques T, and T,. The FIG. 1 is an exploded view of the micro-gyroscope 10. electrostatic torques, T, and T,, are proportional to control The cloverleaf micro-gyroscope 10 has an affixed central voltages V, and V,. The two drive electrodes D1 and D2 proof mass, or post 12 rigidly attached to a resonator 14 65 produce linearized electrostatic torques about the x and y having a cloverleaf shape with petals labeled 1, 2, 3, and 4. axes that are proportional to control voltages V, and V,. D1 The cloverleaf resonator 14 is elastically suspended from an and D2 are defined as: US 7,159,441 B2 5 6 D1 =v,- vw+v, In the above-described closed loop control, if the drive axis creates a disturbance on the y-axis, it is also sensed and using the above described demodulation scheme for the output. The closed loop operation prevents any rocking on D2=V0+ vw+v, 5 the y-axis by feedback 24 applied by differentially feeding D1 and D2. D1 and D2 are responsive to V, as well as V,. where V, is a bias voltage. The linearized electrostatic torques a bout the x and y axes vthx and vth~a re defined by: are defined as: Vth*=S 1+s2 Ty=K,Vw Both V,, and V, are directly proportional to the drive axis rate, i.e. V,=K,-ox and output axis rate, o,=K,O, where the torque constant K, is: where K, is de KT+~,C, vJ[d,l-' 15 Kw=[2r0Cov slrd,l-' r, is the offset from x or y axis to the control, or drive, and R is the transimpedance from the preamplifiers 20. electrode center, C, is the capacitance of one control elec- The cloverleaves of the resonator and the substrate trode, V, is the bias voltage, and do is electrode gap which beneath S1 and S2 electrodes are well grounded at the drive is the separation between the electrode plane and the reso- 20 frequency, capacitive drive feedthrough is reduced and sta- nator plane. bility margins are improved. The control voltage V, provides for automatic gain con- Stiffness is a restorative force typically accomplished by trol of the drive amplitude. The control voltage V, provides applying a spring force. In the present invention, stiffness is for Coriolis torque re-balance. The output axis (y-axis) gain accomplished by applying an electrostatic bias voltage to an and phase compensation are selected based on computed or 25 electrode in the electrode plane. During operation of the v, measured transfer functions, G(s), from to vthy. The micro-gyroscope, Coriolis force causes rocking displace- v, reference signal used to demodulate is vth, which is in ment of the post about the y-axis. The post is perpendicular phase with the drive axis rate signal, ox. to the x-y plane, and also to the electrode plane, as shown in Referring still to FIG. 2, the closed loop operation of the FIG. 1. A cross coupling electrostatic spring force applied to micro-gyroscope of the present invention measures the 30 an electrode offset in the x-y plane generates an electrostatic inertial rate, Q around the z-axis. Signals sl and s2 are torque in response to displacement about the x axis, and output from pre-amplifiers 20 that are attached to the sense nulls motion on the y axis. electrodes S1 and S2. FIG. 3 is an example of a schematic for closed loop The micro-gyroscope is set in motion by a drive loop 22, senseiopen loop drive operation. It should be noted that in that causes the post to oscillate around the x-axis. The post 35 the configuration shown in FIG. 3, the two sense signals S1 rocks and has a rate of rotation about the x-axis. D1 and D2 and S2 are differenced, filtered and amplified. The filter apply voltages in phase therefore, they push and pull the helps to remove residual second harmonics and adjusts loop resonator (not shown in FIG. 2) creating a torque, T,, on the phase to provide stable closed loop operation. The following x-axis. amplifiers serve to combine the closed loop output feedback When there is no inertial rate on the z-axis, there is no 40 signal with the open loop drive signal providing the correct differential motion on S1 and S2. In this case, Vthy=S1- signals to electrodes D1 and D2. Rebalance of the Coriolis S2=0. S1 and S2 are in phase and indicate a rotation around force and robust damping of the output axis resonance is the x-axis. Vthx=S1+S2is amplitude and gain phase com- provided by this wideband closed loop design. pensated in an automatic gain control loop 22, 25, 27 to The method of the present invention is also described drive V,, to V,. An amplitude reference level, V,, is 45 herein with reference to an eight-electrode micro-gyroscope compared with a comparator 23 to the output of the ampli- 100 shown in FIG. 4. The closed loop control is very similar tude detector 22 that determines the amplitude of V,. The to that described in conjunction with the four electrode resulting amplitude error is gain and phase compensated 25 design in FIGS. 1-3. However, in a micro-gyroscope having and applied as a gain to an automatic gain control multiplier eight electrodes, there are obviously four additional elec- 27. A drive voltage V, proportional to V, is thus deter- 50 trodes, Ql,Q2, T1 and S3. D1 and D2 are used differentially mined that regulates the amplitude of the vibration drive. for closed loop control on the y-axis and in common mode When an inertial rate is applied, it creates a difference for x-axis control. S1 and S2 are dedicated to differential between S1 and S2 equal to V,. In the prior art V, was y-axis output sensing. S3 senses the motion of the drive, or merely sensed open loop as being proportional to the rate of x-axis, and T1 is used for tuning on x-axis. Q1 and 42 are the micro-gyroscope. In the present invention V, is gain 55 used to align the micro-gyroscope. and phase compensated based on a computed, or measured, The micro-gyroscope has an inertia matrix J, a stiffness transfer function G(s). The resulting closed loop output matrix, K and a damping matrix D which define the rota- voltage V, generates an electrostatic torque T, to balance tional motion about the x and y axes. In operation, the the torque that results from the Coriolis force, thereby micro-gyroscope is driven about the x-axis in order to sense nulling the motion on the output, or y, axis. 60 inertial rate about the z-axis through Coriolis coupling of the To obtain the micro-gyroscope output signal, V,,,, pro- driven motion to the sense, or y, axis. As described above, portional to an input rate Q, the rebalance torque voltage V, in the preferred embodiment of the present invention, the is demodulated with the drive reference signal V, by an sense axis motion is nulled by a linear feedback torque u,, output axis demodulator 29 and then processed through a where the torque is a measure of the inertial rate Q. demodulator and filter circuit 26. The DC component of the 65 It is also preferred that the micro-gyroscope have closely output signal of the demodulator, V,,,, is proportional to the tuned operation. Closely tuned operation has a drive fre- rotation rate Q. quency that is selected close to the sense axis natural US 7,159,441 B2 7 8 resonant frequency for maximum mechanical gain. Sym- Small angle motion of a rocking mode gyroscope with metrical design and accurate construction of the micro- inertia and stiffness misalignment is governed by: gyroscope are important so that the two rocking mode natural frequencies are similar. A self-resonant drive about the x-axis, for example an AGC loop, will permit large drive 5 motion with small torque controls. It is not presently known how to fabricate a micro- gyroscope with atomic precision. Therefore, it is inevitable where output axis torque Ty=T,+uy+6,T,. The Coriolis that asymmetry and imbalance in the matricies J, D, and K 10 torque is T,=-Jyy2kQs€I,, k is the micro-gyroscope angular will lead to false Coriolis rate indications. The present gain, the wideband control is uy=-G(s)(€Iy+6,€I,) and the invention independently controls alignment and tuning of drive torque T,=D,s€I, is at a drive resonance of oo=(KxJ the micro-gyroscope. Control torque, uy, about the y-axis J,) will be detected with zero inertial rate output. Analysis of the small motion on the y-axis is described The method 100 of the present invention is described with 15 hereinafter. The equation for y-axis motion has the form: reference to FIG. 5. Misalignment is detected 102 by the ~(s)ey+~(s)e~=-G(s)ey-G(s)~~e~+~~(s)e~+~(s))~~~ presence of a quadrature signal amplitude on V,,,. The misalignment is corrected 104 by an electrostatic bias adjustment to electrode Q1 or 42. Misalignment of the 20 cloverleaf microgyroscope is detected by demodulation of the feedback signal with the drive axis signal, thereby detecting a quadrature signal amplitude. In the alternative, the amplitude of a cross-axis transfer function from the drive 25 axis control voltage, V,, to the output axis sense voltage, V,, the transfer function being VthJV,, is indicative of mechanical misalignment. Likewise, the amplitude of the cross-axis transfer function from the output axis control With properly compensated transimpedance buffers, elec- voltage, V, to the drive axis sense voltage, V,, i.e. V,J 30 tronic amplification and biased electrostatic drive (Le., FIG. V,, is indicative of mechanical misalignment. 3), it is possible to provide loop compensation G(s) approxi- The detected mechanical misalignment is corrected to mately equal to sK, so that uy can be expanded as: zero by applying an electrostatic bias adjustment to at least one electrode. After such electrostatic alignment, any 35 residual in-phase demodulated rate bias may be nulled by electronically coupling a component of the drive axis torque into the output axis. Residual mistuning is detected 108 and corrected 110 by way of an electrostatic bias adjustment to electrode T1. The 40 detection 108 is accomplished by noting the presence of a quadrature signal noise level or by detecting a mismatch between the drive axis natural resonant frequency and the output axis natural resonant frequency. This is determined directly from the two direct transfer functions, Vth.JV, and 45 VthJv,. The direct transfer functions can be measured open loop or closed loop by summing a pseudorandom noise test where 6,=DyJK. For steady state drive operation at s=jo,, signal with the normal output or drive axis control signal and the feedback torque becomes: correlating the output axis or drive axis sensed motion with the test signal. Mistuning is corrected 110 by applying, an 50 electrostatic bias adjustment to at least one electrode in the electrode plane. In the present invention, the quadrature amplitude is used as an indication of misalignment and quadrature noise level, 55 or natural resonance frequency and amplitude estimates from a direct transfer function are used as mistuning indi- cators. In the following description of the present invention, the motion about the y-axis is regarded to be infinitesimal, i.e. 60 perfect feedback, and drive axis motion about the x-axis is described as: u,-(l-s,)[(l,+Q,~,)+j(Q,-l,$,)lSe, e,=e,, sin(w,t) 65 where K=K,K,K, can be set by compensator gain, K, to where o, is the operating frequency of the drive and , ,I€ is achieve closed loop bandwidth, o,=KIJyJ2=ooL16,, and the drive amplitude. open loop bandwidth, ooL=DYJJyJ2 US 7,159,441 B2 10 tions VthJV, and V,JV, are nulled, indicating tuning. The frequency at the maximum of each direct transfer function is indicative of the respective axis natural frequency. In the alternative, a pseudorandom test signal may be utilized to 5 generate the transfer functions with either open loop or Demodulation of feedback voltage V,, which is propor- closed loop operation of the microgyroscope. tional to u,, with drive reference V, produces an output For the eight-electrode design, a bias voltage on either Q1 proportional to L2 plus an in-phase rate bias term due to the or 42 will introduce cross axis electrostatic stiffness. To real component of u, and is given by: align the gyroscope, one of these, say Q1 bias, is adjusted io until the quadrature amplitude is nulled. 6,is adjusted, in the n,,=(~,,-s~,-sTo,+$.(-(JY~-~i7K,)~,)I2KJ, absence of input rate, until the rate output bias is nulled. Demodulation of feedback voltage V, with a signal in To independently tune the micro-gyroscope according to quadrature to V,, produces a quadrature rate bias, which is the present invention, the electrostatic tuning bias, electrode given by: T1, is adjusted until closed loop quadrature or in-phase noise 15 in the absence of inertial rate input, or a difference in estimated natural resonance frequencies from direct transfer functions, or another tuning signal, is minimized. Given the above analysis of the small motion on the While particular embodiments of the present invention y-axis, the method of the present invention sets the sensor have been shown and described, numerous variations and misalignment to zero, 6,=0 electronically, and then electro- 20 alternate embodiments will occur to those skilled in the art. statically aligns the micro-gyroscope by introducing an Accordingly, it is intended that the invention be limited only electrostatic cross coupling spring Ken, to cancel the mis- in terms of the appended claims. alignment torque. For example, T,=K “,,~,=(J,,~,’+K,,)~,. The remaining in-phase bias component of QbZ can also be What is claimed is: nulled. This can be accomplished by introducing a relative 1. A method for aligning a cloverleaf micro-gyroscope 25 gain mismatch 6 ~on0 th e control voltage to each of the having a resonator having an affixed central proof mass, the drive electrodes D1 and D2. This compensates for the false resonator being elastically suspended in an x-y plane defin- rate arising from finite modal damping and misalignment of ing a resonator having rocking inertia and rocking suspen- the damping axes, i.e. set D,,-SD,=O. The compensation sion, at least four electrodes in an electrode plane adjacent also applies to any systematic changes in damping affecting 3o the x-y plane, the at least four electrodes for actuating and both axes, for example, as may-be caused by bulk tempera- sensing a rocking motion of the resonator rocking suspen- ture changes. sion, and closed loop control of the resonator rocking motion For a four-electrode cloverleaf micro-gyroscope like the about the x and y axes, said method comprising the steps of one shown in FIG. 1, the cross-coupled electrostatic stiffness detecting mechanical misalignment in rocking vibration can be introduced by applying more or less bias voltage to of the resonator in the x-y plane; and 35 one of the drive electrodes, D1 or D2. Tuning the four- nulling the mechanical misalignment of the resonator to electrode cloverleaf micro-gyroscope The in-phase rate bias zero by applying an electrostatic bias adjustment to an error is also nulled as described above, by applying a relative electrode of the at least four electrodes in the electrode gain mismatch to one of the drive electrodes, D1 or in the plane to produce a cross-coupling spring stiffness, Ken, preferred closed loop operation of the present invention, the and resulting dynamic alignment torques to cancel 4o compensation is set such that G(s)=sK and K is maximized dynamic mechanical misalignment torques caused by to be consistent with loop stability. In such a case, depen- misalignment of the resonator rocking suspension and dence on scale factor and phase shift on the mechanical rocking inertia in the x-y plane. response is minimized. Furthermore, with fully tuned opera- 2. The method as claimed in claim 1 wherein the step of tion, 45 detecting mechanical misalignment further comprises, detecting mechanical misalignment by sensing a quadrature wnx2= K~JJ,=W,~K,JJ,=W,Z signal amplitude obtained by demodulation of a signal of the and there is no closed loop phase error, $,=O. For tuned y-axis using a signal in quadrature to an x-axis rate signal. conditions, maximum mechanical gain and maximum loop 3. The method as claimed in claim 1 further comprising gain occur. Therefore, noise due to input electronic noise is 50 the step of nulling an in-phase bias. minimized. 4. The method as claimed in claim 3 wherein the step of For an eight-electrode design, as shown in FIG. 4, elec- nulling an in-phase bias further comprises electronically trostatic cross-coupled stiffness, Ken, for alignment purposes coupling a torque component of the x-axis with the y-axis. can be introduced by modification of the bias voltage of 5. A method for tuning a cloverleaf micro-gyroscope either Q1 or 42. Electrostatic modification of net K,, for 55 having a resonator having an affixed central proof mass, the tuning purposes can be independently accomplished by resonator being elastically suspended in an x-y plane defin- increasing or decreasing the bias voltage T1 as well. ing a resonator having rocking inertia, mechanical stiffness For example, if o,>o,, then the bias voltage applied to and rocking suspension about the x and y axes, at least four T1 is made larger than the voltage applied to S1 and S2. The electrodes in an electrode plane adjacent the x-y plane, the total stiffness is the elastic stiffness plus the electrostatic 60 at least four electrodes for actuating and sensing a rocking stiffness. The total stiffness about the x-axis is lowered so motion of the resonator in the x-y plane, and closed loop that on,i s also lowered and brought into tune with on,. In control of the rocking motion in the x-y plane, said method this regard, the present invention provides a tuning method comprising the steps of for vibratory micro-gyroscopes in which one of the bias detecting residual mistuning that is a result of mechanical voltages is increased or decreased until a minimum value of 65 asymmetry of the resonator rocking inertia or mechani- the rms noise is obtained or until the drive and output axis cal stiffness by detecting a predefined signal at an resonance frequencies, estimated from direct transfer func- output of the micro-gyroscope; and