MEMS-FABRICATED GYROSCOPES WITH FEEDBACK COMPENSATION

Transcription

1 MEMS-FABRICATED GYROSCOPES WITH FEEDBACK COMPENSATION Yonghwa Park*, Sangjun Park*, Byung-doo choi*, Hyoungho Ko*, Taeyong Song*, Geunwon Lim*, Kwangho Yoo*, **, Sangmin Lee*, Sang Chul Lee*, **, Ahra Lee*, **, Jaeang Lim**, Seongoo Hong*, Kunoo Huh***, Jahng-hyon Park***, and Dong-il "Dan" Cho*, **, *School of Electrical Engineering and Computer Science, Seoul National Univerity, San 56-, Shinlim-dong, Kwanak-gu, Seoul 5-7, Korea **SML Electronic, Inc., Seoul, Korea ***School of Mechanical Engineering, Hanyang Univerity, Seoul, Korea Abtract: Thi paper preent a lead-lag compenator deign for a MEMS-fabricated microgyrocope. The microgyrocope i baically a high Q ytem, thu the bandwidth i limited to be narrow. To overcome the open-loop performance limitation, a feedback controller i deigned to improve the reolution, bandwidth, linearity, and bia tability of the microgyrocope. The feedback controller i applied to the -axi microgyrocope fabricated by SBM proce. In MATLAB imulation, reolution, bandwidth, input range, and bia tability of cloed-loop ytem are improved from 0.00 deg/ec to deg/ec, from.8 H to 5 H, from ±50 deg/ec to ±00 deg/ec, and from 0.09 deg/ec to deg/ec, repectively. Copyright 005 IFAC Keyword: Gyrocope, Performance limit, Feedback control, Modelling, Simulation. INTRODUCTION Micro-fabricated gyrocope have received much commercial attraction due to the mall ie, low power conumption, rigidity, and low cot. Application area of the microgyrocope include automotive afety and tability control ytem, video camera tabiliation, and 3-D input device for computer and peronal data aitance (PDA) ytem (Song, 977; Gripton, 00). The feedback controller i applied to the -axi microgyrocope fabricated by the Sacrificial Bulk Micromachining (SBM) proce. The performance of thi open-loop gyrocope are repreented in the literature (Lee, et al., 000; Cho, et al., 000; Park, et al., 00). The non-linear output characteritic and mall bandwidth are main problem of thi microgyrocope. Becaue the reonant frequencie of the decoupled microgyrocope hould be matched identically and the ytem ha a very high Q, the gyrocope operate at a narrow bandwidth near a pecific reonant frequency. In the open-loop ytem, if the bandwidth of the ytem can be increaed by increaing the difference of two reonant mode, but then the enitivity of thi ytem become poor. To ameliorate thi trade-off problem, we deign a feedback controller in thi paper. The cloed-loop ytem feed the control ignal from the ened output ignal back to the feedback control electrode. Thi make a diplacement of the moving part very mall, and the bandwidth of the ytem i increaed without lowering the enitivity. Furthermore, becaue the diplacement of the moving part i controlled to be mall, the linearity of the output ignal can be improved.. WORKING PRINCIPLE Figure how the -axi microgyrocope fabricated by acrificial bulk micromachining (SBM) proce. The tructural thickne i 0 µm, and the acrificial gap i 0 µm. The SBM proce ha the added benefit of a large acrificial gap when compared to conventional SOI proce (Lee, et al., 999; Lee, et al., 000; Cho, et al., 000). Correponding author, Phone: , Fax: , dicho@ari.nu.ac.kr

2 The chematic of the fabricated microgyrocope can be repreented a hown in Figure. The outer and inner mae are driven together in the x- direction at the mode. If an angular rate i applied in the -direction, then the inner ma move in the y-direction by the Corioli force. That i, the microgyrocope etimate the input angular rate by ening the diplacement of the inner ma induced by the Corioli force. ocillate in inuoidal motion by force, and Ω i input angular rate. To vibrate the gyrocope in mode, a inuoidal voltage i applied to the -comb electrode. Thi voltage generate the electrotatic force. The force i given by F e Nε tvoff Va (3) d d Act- ACTSEN- Act SEN- CONT- CONT SEN Act- ACTSEN Act where N, ε, d d, t, V off, and V a are number of comb, permittivity, gap between comb, tructural thickne, offet voltage of carrier ignal and ac voltage of carrier ignal, repectively. The value of calculated F e i.6-7 V a N. W F c k m b y x b a Fig.. Fabricated microgyrocope comb for ening motion pring for motion F e v a m a k a Fig. 3. Modeling of microgyrocope. comb pring for ening motion comb for ening motion comb ening comb Fig.. Schematic diagram of microgyrocope. 3. Microgyrocope 3. DYNAMIC MODELLING y ening mode x mode angular rate input The dynamic of the microgyrocope can be modelled a two orthogonal ma-damper-pring ytem a hown in Figure 3. The motion equation of plant dynamic are given by Driving part: ( m a m ) x ba x k ax F () e Sening part: m y b y k y F m Ω v () where m a, b a, k a are ma, damping and pring coefficient of the part, repectively; m, b, k are ma, damping and pring coefficient of the ening part, repectively; F e i force, Fc i corioli force, v x i velocity of the ma which c x The value of m, b, and k can be obtained from the tructure of the microgyrocope and the equation of relation between the reonant frequency, quality factor, and damping coefficient. The reonant frequency and quality factor are given by k f () π m µ Aβ Q coh βd co βd mk inh βd in βd 3 µ Ac β µ tw 3 coh βdc co βdc d mk mk inh βdc in βdc (5) where µ, β, A, A c, d, d c, d, and W are abolute vicoity, momentum propagation velocity, area of plate, area of inter-comb, acrificial gap, lateral gap between comb, gap between tructure and comb, and width of comb, repectively (Cho, et al., 993). Becaue the fabricated microgyrocope i teted in vacuum environment, the vacuum level i alo important. The damping coefficient i given by mk b. (6) Q The calculated ma, m a and m, are 78.3 µg and.6 µg, repectively. By ANSYS imulation, the firt mode reonant frequency of the mode i 5.0

3 kh. The reonant frequencie of the and ening mode hould be matched to achieve a enitivity of the ytem. The ening mode reonant frequency i tuned to be H higher than the mode, that i, 5.05 kh. From Eq. (), the value of k a and k are. N/m and.85 N/m, repectively. From Eq. (5) - (6) and the vacuum level, the value of b a and b are kg/ and.35-6 kg/, repectively. Therefore, from Eq. () - (3), the tranfer function of the part and the ening part become X( ) Td () 9 V () a Y( ).35 T () F () c 9 7 (7). (8) The movement of the ening-comb in the y- direction by the Corioli force compel the gap of the ening-comb to vary, and thi variation produce the capacitance change. So, C/Y gain, that i, the ratio of the capacitance change to the movement of the ening-comb i given by C / Y Gain N ε A c ( d y) ( d y) (9) where N i number of ening-comb and d i lateral gap between ening-comb. When the value of y i very mall, Eq. (9) become 3N ε A C/ Y Gain. () c d The calculated C/Y gain i C/m. 3. Meaurement Circuit Figure how the meaurement cheme in the open-loop. To vibrate the gyrocope in mode, a volt peak-to-peak inuoidal voltage with a 0.5 volt offet i applied to the -comb electrode. When an angular rate i applied in the -direction, the ening-comb electrode move in the y-direction by the Corioli force. The capacitance change due to the motion of the ening-comb electrode are detected by a charge-to-voltage converter. To pa only modulated high frequency ignal, a high-pa filter i ued. After the high-pa filtering, the ignal i demodulated uing an analog multiplier. After the demodulation, the high frequency component of the ignal are removed uing low-pa filter, and the angular rate ignal i obtained The tranfer function of the charge amplifier T C () i given by VC ().05 TC() V ref () C () 9 where C() i capacitance change, V C () i output voltage of the charge amplifier, and V ref i reference voltage. The tranfer function of the high-pa filter T H () i given by T H () () Alo, the gain of the differential amplifier i 5.7 V/V. - actuation electrode Gyro tructure actuation electrode Sening electrode C 0 C _ C0 C Sening electrode V t V t C C R R high pa filter high pa filter Fig.. Meaurement cheme of the open-loop.. CONTROLLER DESIGN diff. amplifier Figure 5 how the block diagram of the cloedloop ytem. The cloed-loop ytem feed the control ignal from the modulated output ignal back to the feedback control electrode. The plant G() conit of the ening dynamic of the microgyrocope, the charge amplifier, the highpa filter, and the differential amplifier a hown in Figure. Thi plant G() i modeled a a 5th-order tranfer function. Thi plant G() i given by G () ( )( ) V ou t (3) If the output voltage of the controller i applied to the feedback control electrode, the electrotatic force i exerted on the inter-comb. The F/V gain, that i, the ratio of the electrotatic force to the control output voltage i given by Nε AV F / V Gain. () d c ref The calculated F/V gain i N/V. The nd order bandpa filter B() in Figure 5 reject the noie except the operating frequency. The magnitude and bandwidth of the bandpa filter deigned are 0 db and kh, and the center frequency of the deigned bandpa filter i matched with the reonant frequency of ening mode, that i, 5. kh. So the bandpa filter B() i given by 683 B ( ). (5)

4 The deigned lead-lag compenator K() i given by kl ( K( S) ( p lead lead )( )( p lag lag ) ) (6) where k l i the controller gain; lead and p lead are ero and pole of the lead compenator; and lag and p lag are ero and pole of the lag compenator. rate input F() Ω m v - G() Plant k vf F/V Gain a Amp K() Controller B() BPF Fig. 5. Block diagram of cloed-loop. d() output voltage V() n().36 rad/ec and 7. rad/ec, and the bandwidth of the cloed-loop ytem i H. So, Eq. (6) i given by 5(.36 )( 7. ) K ( S). (9) ( 9 )(.5 ) Figure 7 how the Bode diagram of the open-loop and cloed-loop ytem. The bandwidth of the cloed-loop ytem i improved to H from 5 H of the open-loop ytem at the reonant frequency. The % ettling time of the cloed-loop ytem i decreaed to 0.0 ec from 0.6 ec of the openloop ytem. Alo, the diplacement of the eningcomb electrode of the cloed-loop ytem i decreaed a hown in Figure 8. The reonant frequencie of the open-loop and cloed-loop ytem hould be matched. From thi condition, the below term i given by k lead lag. (7) m The magnitude of the open-loop and cloed-loop ytem hould be alo matched at the reonant frequency. From thi condition, the below term i given by b ( a ) lead lag (8) ak k k vf cv l where a i proportional coefficient of feedback loop, k vf i F/V gain, and k cv i proportional coefficient of charge-to-voltage converter. The value of k cv i V/C. Fig. 7. Bode diagram of open-loop and cloed-loop. Fig. 8. Step repone for diplacement of eningcomb electrode. Fig. 6. Bandwidth of cloed-loop, when value of a and k l are varied. Firt of all, the uitable value of p lead and p lag are elected in the neighbourhood of the reonant frequency. When the value of p lead and p lag are 9 rad/ec and.5 rad/ec, Figure 6 how the bandwidth of the cloed-loop ytem a the value of a and k l are varied. The bandwidth increae when the value of a increae, but the noie of ytem alo increae. If the value of a and k l are and 5, then the value of lead and lag can be obtained from Eq. (7) and (8). The value of lead and lag are 5. SIMULATION RESULTS We ue the Matlab imulink a the imulation program. Figure 9 how the imulink block diagram of the cloed-loop ytem. When the input angular rate i deg/ec, 5 H, Figure how the frequency repone of the modulated output ignal. The noie equivalent angular rate reolution of the cloed-loop ytem i improved from 0.00 deg/ec to deg/ec, when compared to the open-loop ytem. At thi time, the average output ignal level and the noie floor of open-loop ytem are.8 db

5 and 95.5 db, and the average output ignal level and the noie floor of cloed-loop ytem are.3 db and 88.3 db. tability of the cloed-loop ytem i improved from 0.09 deg/ec to deg/ec. Fig. 9. Simulink block diagram of cloed-loop. (a) Open-loop ytem (a) Open-loop ytem (b) Cloed-loop ytem Fig.. Bandwidth of output ignal. (b) Cloed-loop ytem Fig.. Frequency repone of modulated output ignal. Figure how the bode diagram of the demodulated output ignal. Thi output ignal i obtained by increaing the period of input angular rate. The bandwidth of the cloed-loop ytem i improved from.8 H to 5 H. Figure how the demodulated output ignal when the magnitude of input angular rate varie. The cale factor of the cloed-loop ytem i increaed to 0. mv/deg/ec from mv/deg/ec of the open-loop ytem. The input range i improved from ±50 deg/ec to ±00 deg/ec a hown in Figure, and thu, the dynamic range i improved from 87.5 db to 3.7 db. Alo, the linearity of the cloed-loop ytem i improved from 7.5 % to 0 % in the ±50 deg/ec range. Finally, the bia tability tet are performed. The output ignal without applied the input angular rate i obtained a hown in Figure 3. The bia (a) Open-loop ytem (b) Cloed-loop ytem Fig.. Linearity of output ignal.

6 (a) Open-loop ytem (b) Cloed-loop ytem Fig. 3. Bia tability of output ignal 6. CONCLUSION Thi paper deigned a lead-lag compenator for a MEMS microgyrocope. The deign feedback controller greatly improve the bandwidth, linearity, dynamic range, and bia tability of the microgyrocope without acrificing reolution, by feeding the control ignal from the ened output ignal back to the ening-comb electrode. Thi controller can maintain the matched tate of the and ening mode, and therefore the expanded bandwidth can be achieved without lowering the enitivity. A a reult, the bandwidth of the cloed-loop ytem i improved from.8 H to 5 H, the input range i improved from ±50 deg/ec to ±00 deg/ec, and the dynamic range i improved from 87.5 db to 3.7 db. The linearity i alo improved from 7.5 % to 0 % in the ±50 deg/ec range, and the bia tability i improved from 0.09 deg/ec to deg/ec. Thee performance improvement are achieved without acrificing the reolution, which alo improve from 0.00 deg/ec to deg/ec. Lee, S., S. Park, and D. Cho (999). The Surface/Bulk Micromachining (SBM) proce: a new method for fabricating releaed microelectromechanical ytem in ingle crytal ilicon. IEEE/ASME Journal of Microelectromechanical Sytem, vol. 8, no., pp Lee, S., S. Park, J. Kim, S. Yi, and D. Cho (000). Surface/Bulk Micromachined Single-crytalline Silicon Micro-gyrocope. IEEE/ASME Journal of Microelectromechanical Sytem, vol. 9, no., pp Cho, D., S. Lee, and S. Park (000). Surface/Bulk Micromachined High Performance Silicon Micro-gyrocope. 000 Solid-tate Senor and Actuator Workhop (Hilton Head). Park, S., S. W. Lee, J. Kim, S. Lee, and D. Cho (00). Tactical Grade MEMS Gyrocope Fabricated by the SBM Proce. International MEMS Workhop 00, pp Gripton, A. (00). The Application and Future Development of A MEMS SiVSG for Commercial and Military Inertial Product. Poition Location and Navigation Sympoium, 00 IEEE, pp ACKNOWLEDGMENTS Thi reearch wa upported in part by KOSEF Development of Telematic-baed Integrated Sening and Monitoring Sytem Project (R ). REFERENCES Cho, Y. H., B. M. Kwak, A. P. Piano, and R. T. Howe (993). Vicou energy diipation in laterally ocillating planar microtructure: A theoretical and experimental tudy. Proc. IEEE Workhop on Microelectro-mech. Sy., pp Song, Cimoo. (997). Commercial Viion of Silicon Baed Inertial Senor. Proceeding of Tranducer '97, vol., pp