Research of Ring MEMS Rate Integrating Gyroscopes

Transcription

1 World Academ of Science, Engineering and Technolog Vol:7, No:4, 013 Reearch of Ring MEMS Rate Integrating Grocope Hui Liu, and Haiang Quan International Science Inde, Electronic and Communication Engineering Vol:7, No:4, 013 waet.org/publication/14443 Abtract Thi paper To get the angle value with a MEMS rate grocope in ome pecific field, the uual method i to make an integral operation to the rate output, which will lead the error cumulating effect. So the rate gro i not uitable. MEMS rate integrating grocope (MRIG will olve thi problem. A DSP tem ha been developed to implement the control arithmetic. The tem can meaure the angle of rotation directl b the control loop that make the enor work in whole-angle mode. Modeling the tem with MATLAB, deirable reult of angle output are got, which prove the feaibilit of the control arithmetic. Keword Rate grocope, Rate integrating grocope, Whole angle mode, MATLAB modeling, DSP control. I. INTRODUCTION EMS vibrator grocope have received increaed Mattention from automotive and conumer electronic indutrie in the pat decade. However, mot commercial MEMS grocope are angular rate meauring enor emploing energ tranfer between the drive and the ene mode. Thee kind of grocope have obviou advantage in bulk, weight and power and the often have lower price while the performance i eligible. MEMS vibrator grocope can be claified into two broad tpe, rate grocope, meauring rotating rate of the tem and rate integrating grocope, meauring the abolute angle of rotation [1]. All the vibrator grocope are baed on Corioli effect, that eploit energ tranfer between the vibration mode. There are man kind of phical tructure of grocope enor, one of which i the ring enor, hown in Fig. 1. The iotrop tructure of the ring enor [], [3] can effectivel weaken the coupling between different mode, o the matching i much eaier. The inherent reonant frequenc i uuall more than 10k Hz, which make the rigidit more than ten time better comparing with other tructure. A a reult, thi kind of grocope will uffer le effect like temperature, acceleration, vibrator, impact and man other effect from environment. Fig. 1 Two mode of a ring rate grocope Almot all the MEMS vibrator grocope are rate grocope o far. Benefiting from the fact that the control arithmetic of thee grocope are imple relativel, and can get the rotating rate, the are being tudied and applied diffuel. Mot MEMS rate grocope have the performance of rate grade, but onl a few lab can reach tactic grade or higher. However, under ome pecific application, like high dnamic environment, range and cale factor are the mot two important parameter. The two parameter are retricted for rate grocope. Man factor like electrode ize and pacing, firt mode amplitude, ring voltage and driving voltage limit the range, and gain of LNA and front end analog circuit, AD tranfer reference voltage will lead to an error in cale factor. V k Y 4k V d C out SF = = = Ω Y c AV 4 n ref n AGC f 1β ( ε HT All of the imperfection are detructive in high dnamic environment. In actual application when the angle information i needed, the uual method i to make an integral operation to the rate output, which will lead the error cumulating effect. A i hown in Fig., Bia Drift, ARW, and the tabilit of SF will be integrated to angle output, and cumulate the error. (1 Hui Liu i with the Beijing Microelectronic Technolog Intitute, P.R. China, (phone: ; fa: ; wukongl@gmail.com. Haiang Quan i with the Beijing Microelectronic Technolog Intitute, P.R. China. Fig. Error cumulating in integrating International Scholarl and Scientific Reearch & Innovation 7( cholar.waet.org/ /14443

2 World Academ of Science, Engineering and Technolog Vol:7, No:4, 013 International Science Inde, Electronic and Communication Engineering Vol:7, No:4, 013 waet.org/publication/14443 MEMS Rate Integrating Grocope (MRIG [4], [5] will olve thee program. Thi kind of grocope can directl meaure the rotating angle of an object, without producing error from both circuit and mechanical tructure after integration. MRIG have ver high preciion of angle gain factor, that promie wonderful performance of cale factor (<1ppm, and their characteritic of freel preceion make their range unlimited. All the advantage provide ver epanive application for MRIG. II. PRINCIPLES All MRIG can be implified to a -dof ma-pring tem, in which there are two principal direction (normal mode ae along which the tem' natural frequencie are lightl different (hown in Fig. 3 (a. One of the main error ource in vibrator grocope arie from the mimatch in natural frequencie of the two vibration mode utilized. The anali of the tem can be applied to all MRIG. (a (b Fig. 3 -dof vibrating model A. Equation of Motion of Generalized Vibrator Gro The model above-mentioned i a ma vibrating in - plane retricted b aimmetric linear pring. In the rotating frame, the - plane i rotating about the z ai with angular velocit Ω, a i hown in Fig. 3 (b. From Newton econd law F = ma = mr, we can get the equation of motion are F m F m = Ω Ω ( Ω = f = Ω Ω ( Ω = f 1 Equation ( contain Corioli Effect, angle acceleration term and centrifugal force term. The component r and f along the - and the '-' ai et are related b the orthogonal tranformation equation (3 = coθ inθ = coθ inθ ( (3 Then we can write the equation of motion in term of - component in the form [6]. 1 1 Ω Ω ( Ω ( coθ in θ = f 1 1 Ω Ω ( Ω ( coθ in θ = f In order to make the equation more intact, angle gain factor k and acceleration factor k are introduced. If we include linear damping with principal-ai time contant 1, the generic equation are 1 k( Ω Ω Δ ( ( coθ in θ k Ω Δ = f ( ( coθ in θ 1 k( Ω Ω Δ( ( coθ in θ k Ω Δ = f ( ( coθ in θ In whichθ i the azimuth of the 1 principal ai ( θ i the azimuth of the principal ai, and (6 are the approimate condition 1 = 1 Δ = = Δ = 1 We call the equation (5 the equation of motion of the Generic Vibrator Grocope [7], [8]. B. Simplifing Model for MRIG All table and figure ou inert in our document are onl to help ou gauge the ize of our paper, for the convenience of the referee, and to make it ea for ou to ditribute preprint. To implement a MRIG, the -dof freel vibrating tem hould approach the ideal condition. Conequentl, we can implif the model when olving the equation above. Auming that the two normal-mode frequencie are identical, and there i no damping, no rate input, no eternal forcing, the equation (5 reduce to = = 0 0 (4 (5 (6 (7 International Scholarl and Scientific Reearch & Innovation 7( cholar.waet.org/ /14443

3 World Academ of Science, Engineering and Technolog Vol:7, No:4, 013 The mot general olution to equation (7 can be written in the form. = acoθ co( t φ qinθin( t φ = ainθ co( t φ qcoθin( t φ (8 International Science Inde, Electronic and Communication Engineering Vol:7, No:4, 013 waet.org/publication/14443 Equation (8 repreent a fact that the trajector of an ideal -dof tem i a tationar elliptical orbit decribed b four parameter aqθ,,, φ, hown in Fig. 4. Fig. 4 Equivalent elliptical orbit When there i no damping and eternal forcing, the orbit of the ideal -dof tem will keep it intrinic hape and prece accordingl following the rotating frame. In a fied period of time, the azimuth of thi orbit relative to the tem above i proportional to the azimuth to inertial frame with a coefficient k. In non ideal environment, the parameter aqθ,,, φ will be varing along with time becaue of frequenc gap, damping and eternal forcing etc. However, for an actual MRIG, thi kind of varing i low on a time cale whoe unit i π /. The anale above provide appropriate baic principle for the Implementation of MRIG. III. CONTROL SCHEME The baic control problem to MRIG are to maintain the amplitude a to a precribed value and to null the quadrature amplitude q. However, in the enor of ring tructure, the vibration i in the form of tanding wave, which i preceing along with the inertial frame (Fig. 5 rather than fied on the driving electrode in rate grocope. A a reult, the control cheme of MRIG i rather different. a Fig. 5 The preceing of a ring enor MRIG Demodulating the ignal of the two normal-mode ae, we can get four pickoff demodulated quantitie c c, which are the baic of all the following ignal proceing work. The relationhip of tranforming between orbit parameter aqθ,,, φ and c c, i different in different working pattern. For whole angle mode, there are a q = c c a q= c c ( cc θ = 1/arctan c c ( c c φ φ = 1/arcin 4( cc ( c c b The equation above are the baic principle for ignal proceing part of control tem. From (9 we know that three cloed loop can tabilize the whole tem. Model the tem [9] uing MATLAB, the block diagram i hown in Fig. 6. Fig. 6 modeling of MRIG with imulink The everal main part of the tem i the enor module, demodulation module, angle calculation module, control module and drive module. Simulating the tem, we get the reult of the important module, which are hown in Fig. 7. (9 International Scholarl and Scientific Reearch & Innovation 7( cholar.waet.org/ /14443

4 World Academ of Science, Engineering and Technolog Vol:7, No:4, 013 the function of the tranformation block i to tranform the demodulation quantitie c c, to the error variable of the controller. 9 9 φ φ (a The AGC model θ θ 9 9 International Science Inde, Electronic and Communication Engineering Vol:7, No:4, 013 waet.org/publication/14443 (b The PID model for tracing (c The angle meauring model Fig. 7 imulation reult with MATLAB The reult indicate that, the control algorithm above can implement the angle meauring function, and make the enor work a rate integrating grocope. IV. CONTROL SYSTEM BASED ON DSP The main work of the ignal proceing part i to accomplih the feedback loop, filter and other compenating arithmetic. Parameter etraction i a proper method to the drive loop. Here we introduce a concept, tatic energ, denoted b E ( E a q =, which i one of the invariant under a tranformation correponding to a rotation pickoff ai et about the z ai. B uing tatic energ E a the error variable of PID controller, we can effectivel olve the problem how to maintain the vibration amplitude when the tand wave i preceing. The whole tem [10] i decribed in Fig. 8. Firt the ening ignal are proceed in DSP from the enor via ADC, and then the driving ignal created b cloed loop are ent back to the driving electrode after digital proceing via DAC. In Fig. 6, Fig. 8 Whole control cheme of MRIG V. HARDWARE CONNECTION The control configuration can be divided into three part. The are analog interface, ignal pretreatment circuit and digital proceing module. The analog interface comprie four LNA and C-V convertor, which tranform the ignal to voltage from capacitance. The ignal pretreatment circuit include amplifier, filter, A/D convertor and D/A convertor chip, and the function i to ene the weak voltage and tranform them to digital ignal. The whole digital proceing module i accomplihed b DSP chip, implementing all the feedback loop and other compenating arithmetic. The tructure frame i hown in Fig. 9. Fig. 9 Hardware platform of MRIG The ignal generation and repone ignal ampling were baed on a codec IC AD1939, which ha 8 channel ADC of 4 bit reolution and 19 khz ampling rate. B emploing an internal digital recontruction filter and an etended ine wave lookup table, the tem can create 4 channel of high qualit ine wave up to 70 khz with a frequenc reolution of 0.01 Hz. Data tranfer between the codec and DSP, and relevant demodulation and control calculation wa interrupt driven with ample baed proceing at a frequenc of 19 khz. The DSP board ha a ver high peed core of ADSP-1469, with intruction eecution time of 0. n. Emploing a hardware circular buffer, addreing all the calculation for ignal International Scholarl and Scientific Reearch & Innovation 7( cholar.waet.org/ /14443

5 World Academ of Science, Engineering and Technolog Vol:7, No:4, 013 generation and meaurement uch a demodulation and low pa filtering can be completed within 5u. International Science Inde, Electronic and Communication Engineering Vol:7, No:4, 013 waet.org/publication/14443 REFERENCES [1] A. M. Shelk, Tpe I and tpe II Micromachined Vibrator Grocope. [] Michael William Putt, A Micro Machined Vibrating Ring Grocope. [3] E. J. Loper and D. Lnch, Vibrator Rotation Senor, Aug. 8, 1990, U.S. Patent 4,951,508. [4] I. P. Prikhodko, S. A. Zotov, A. A. Truov, A. M. Shkel, Foucault pendulum on a chip: Rate integrating ilicon MEMS grocope, Senor and Actuator A 177 ( [5] J. Cho, J. A. Gregor and K. Najafi, Single-Crtal-Silicon Vibrator Clinderical Rate Integrating Grocope (CING, Tranducer 11, Beijing, China, June 5-9, 011. [6] B. J. Gallacher, Principle of a Micro-Rate Integrating Ring Grocope, IEEE Tranaction on aeropace and electronic tem VOL. 48, NO. 1 Januar 01. [7] D.D. Lnch, Vibrator grocope anali b the method of averaging, nd St. Peterburg Int. Conf. on Grocopic Technolog and Navigation, St. Peterburg, Ruia, [8] Z. X. Hu, B. J. Gallacher, J. S. Burde, C. P. Fell, K. Townend, A Parametricall amplified MEMS rate grocope, Senor and Actuator A 167 ( [9] C. Painter and A. Shkel, Eperimental evaluation of a control tem for an abolute angle meauring micromachined grocope, 4th IEEE Conference on Senor, Oct. 31-Nov. 03, 005. [10] J. A. Gregor, J. Cho, K. Najafi, MEMS rate and rate-integrating grocope control with commercial oftware defined radio hardware, IEEE Tranducer 011, Beijing, China, 011. International Scholarl and Scientific Reearch & Innovation 7( cholar.waet.org/ /14443