机械设计制造及其自动化毕业设计外文文献资料二.pdf

Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 Complete decoupling rebalance loop design of a micromachined electrostatically suspended gyroscope XIAO Qi? jun 1, 2, C HEN Wen? yuan1, CUI feng1, LI Sheng? yong1, LIU Chao? ying2, ZHANG Wei? ping1 肖奇军, ? ?陈文元, ? ? 崔? 峰, ? 李胜勇, ? ?刘超英, ? ?张卫平? ( 1 . N ationa lKey Laboratory ofNano /M icro Fabrication Techno logy , K ey Laboratory forThin Fil m andM icrofabrication ofM inistry of Education , Institute ofM icro and Nano Science and Technology, Shangha i Jiaotong University, Shanghai 200240 , China , shawq j126 . com; 2 . Faculty ofElectronic Infor mation m icro?gyroscope ;rebalance loop ;co mplete decoupling CLC nu m ber : U666?1? ? ? Docu m ent code : A? ? ? ? Article ID: 1005?9113( 2010) 05?0672?07 ? W ith the development of inertial technologies , man focus on the fiber?optics gyroscope and the m i? cromachined gyroscope based on MEMS technology . The vastmajority of all reportedMEMS gyroscopes are vibratory gyroscope , which detect the rotation induced Coriolis acceleration of a vibrating proofm ass to meas? ure rotation .It requires the matching of the drive and sense mode resonant frequencies , which makes the gy? roscope sensitive to the manufacture tolerances.The fabrication i mperfections can also introduce an i mbal? ance in the gyroscope suspension resulting in amechan? ical cross?talk between the drive and sensemodesof the device leading to the so?called quadrature errors. Alter? native approaches have been raised ,one of the most prom ising concepts is a m icromachined electrostatically suspended gyroscope (MESG), which e mploys the e? lectrostatic force to suspend a proofmass from the sub? strate to m ini m ize the mechanical friction . So the long? ter m stability and sensitivity of the device is i mproved and it is able tomeasure the input two axis rate velocity and three axis linear acceleration si multaneously . When an angular rate orthogonal to the spinning axis is ap? plied ,a torque applied by the levitation control returns the rotor to the null position .In real application ,the rebalance loop controls the rotor to keep the tilt angles nul, l and the performance of the rebalance loop plays an i mportant role in deter m ining the accuracy and the operation range of aMESG.In strap?down system,the torque required to maintain the null condition is propor? tional to the inertial rate that is applied to the MESG when the tilt angles are kept smal.l Therefore ,a good rebalance loop ,which keeps the tilt angle sm all in transient state,is dispensable to reduce the transient dynam ic errors and to obtain aw ide operation range and high accuracy . There are two reported attempts to developMESG, one in Japan by TakaoMURAKOS H I 1, and a si m ilar concept is being developed inUK led byM. Kraft 2- 5. A sigma?delta control strategy is applied byM. Kraft to realize the rotor to m ini m ize the tilting anger about the t wo in?plane axes , while Japanese adopt the PI D con? trol strategy to control the tilt of the anger . They all ig? nore the coupling phenomenon between the axes . Vari? ous authors have proposed different approaches to de? sign a good rebalance loop . Briggs suggested a si mple rule to design a stable rebalance loop for a general two? degrees?of?freedom gyroscope based on the classical control theory 6 .Byung Su Chang etc designed and Received 2009- 04- 12 . Sponsored by the Pre? weapons Research Fund ( GrantN o . 9140A09020706J W 0314) andN ew TeacherR esearch Fund for the Doctoral Program ofH igher Education ofChina ( Grant No. 200802481026). ?672? Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 analyzed themultivariableH controller am i ing at a kind of digital rebalance design for aMEMS gyro ,and design the controller by electronic components and DSP 7. A designed structure of the levitated m icrogyro , based on LIGA or LIGA?like fabrication process ,was presented by our research group 8, as shown in Fig . 1 ( a).The sandwich?like suspended levitated gyroscope consists of three main parts ,the upper stator ,the rotor and the lower stator .The rotor is levitated by electro? static force through axial and radial electrodes and driv? en to rotate by the rotation electrodes to produce angular momentu m in order to detect the input angular rate . The fabricatedm icrogyrow ith a nickel rotor ,employing glass as top and bottom stator substrates then bonding together by soldering ,is shown in Fig. 1( b) 8. Based on ourm icrogyro ,decoupling control is in? troduced to eli m inate the coupling bet ween the orthogo? nal axis and the complete decoupling rebalance loop is designed to i mprove the perfor mance of the MESG in this paper . ( a) Schematic view of the gyroscope ( b) the fabricated chip on PCB Fig . 1? M ESG based on LIGA?like technology 1?The Dynam ic Analysis of theMESG The torque applied on the MESG mainly consists of gyroscope torque from the shell transferring to the ro? tor ,the feedback toque from the rebalance loop and the electrostatic disturbing torque acting on the ro? tor 9. The torque equation can be expressed as : - Ie!?- bx?+ kd?+ H ?= MX- Ie! X- H ? Y Ie!? + by? - kd? + H ?= MY- Ie! Y+ H ? X ( 1) ? ?In Eq . ( 1), Ieis themom ent of inertia about the in?plane axes, bx, byare the damping coefficient rotate about theX and Y axes ,respectively. kdis the out?of? plane electrostatic stiffness coefficien, t H is the angular momentum,and ? , ?are the angles rotate by theX and Y axes of the rotor relative to the shel, lrespectively . X, Yare the input angle from the shell ofX and Y axes,respectively. MX, MYare the feedback control torque to rebalance the input torque from theX and Y axes,respectively , which reflect the input angular rate from the shel. l From Eq . ( 1), we can see that the left of the equation includes the gyroscopic effect item as H ?andH ? , which indicate the precession characteris? tic ,while other items indicate non?gyroscopic effec, t which indicate the angular acceleration characteristic . The right of the equation is the control torque subtracts the input torque from the shell transfer to the rotor . As? sume the gyro works under the idea condition . Neglec? ting the disturbing torque and the da mping force to si m? plified torque equation ,the dynam ic equation is con? structed as: - Ie!?+ H ?= MX- Ie! X- H ? Y Ie!? + H ?= MY- Ie! Y+ H ? X ( 2) ? ? After Laplace changing ,it can be expressed as : - Ies 2?(s) + H s? (s) = M X( s) - Ies!X(s) - H!Y(s) Ies 2? ( s) + H s?( s) = M Y(s) - Ies!Y( s) + H !X( s) ( 3) It can be transfor med as thematrix: ?( s) ? ( s) = 1 Ie( s 2 + 4! 2 ) - 2! Ies( s 2 + 4! 2 ) - 2! Ies( s 2 + 4! 2 ) - 1 Ie( s 2 + 4! 2 ) ? ? MX( s) MY(s) - 1 s !X( s) !Y( s) .( 4) In Eq . ( 4), ! is the rotate speed of the rotor . From a? bove equation ,it can be seem that the torque acts on one axis not only produce the angle rotate by the or? thogonal axis, which is the precession item or themain transfer ite m, but also produce the rotation by the same axis called high frequency nutation item.It is the cou? pled ite m andmust be eli m inated to apply in the close? loop contro. l There are t wo ways to realize the close? loop control of theMESG.It can be see m that the de? coupling control combined w ith the compensation loop has the high accuracy and fast response speed from the si mulation resul. t Furthermore ,the digital decoupling helps to eli m inate the coupling of the output voltage . ?673? Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 2? Rebalance Loop Design In order to realize the close?loop control of the ro? tor ,two torque rebalance loops are introduced. 2?1? The Design of Rebalance Loop Adopting PID and Compensation Loop W hen inputted angular velocity is integral to be changed into the angle ,it is sensed by the capacitive sensing uni, tfollow ing by the rebalance loop to pro? duce the control signal to act on the axial control plate and apply torque on the rotor to produce precession to trace the inputted angular velocity .The leading com? pensation is applied in the compensation loop .In order to stabilize the syste m,the integral segment should be added to make the steady state errors to be zero and low?pass filter measure is taken si multaneously .After opti m ization ,the transfer function of the compensation loop is expressed as : G ( s) = 10( 0?25s+ 1) ( 0?045s+ 1) s( 0?1s+ 1) ( 0?002s+ 1) ( 5) In Eq . ( 6),the output angles of the gyro are ? and v. G ( s) is the compensation loop transfer func? tion . Kuis the sensitivity of the test circui. t KTis the voltage?torque transfor m ation coefficien. t Gc(s) is the transfer function of PI D controller . According to Eq . ( 6),the control sche m atic diagram can be constructed as shown in F ig. 2 . - Ies 2?(s) + H s? (s) = K TKuGc( s)G ( s)?(s) - ? Ies!X( s) - H !Y(s) Ies 2 ? ( s) + H s?( s) = KTKuGc(s)G( s) ? ( s) - ? Ies!Y(s) + H !X(s) ( 6) Fig . 2?Sche m atic diagram of rebalance loop adopting PID and com pensation 2?2? TheRebalance Design of the DecouplingCon? trol Co mbined with Lead Co mpensation In order to eli m inate the coupling between the ax? es ,a decoupling way is applied in the rebalance loop . The decoupling network is placed between the compen? sation and the PI D controller , which is also placed be? yond the control device to realize the single output cor? responding to single inpu. t The output is controlled by the input correspondingly . The transfer function is rela? tive to the control device and it isneeded to choose ap? propriate lead compensation loop to stabilize the sys? te m.The a mplitude frequency response characteristics analysis shown in Fig . 3 indicates that the amplitude in the rotation frequency should attenuate to zero and the phasemargin is about 50 degrees . Fig . 3?Bode diagram of the decoupling syste m ?674? Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 ? There are two types of decoupling network to real? ize the decoupling contro.l In the type system, ow ing to the adding of integral loop in the forward channe, l when angular velocity is inputted ,the deflection angle of the rotor is zero ,and when the constant angular ac? celeration is inputted ,the deflection angle of the rotor is constan. t While to the type # system, when the an? gular velocity is inputted,the deflection angle of the rotor is constan, t andwhen the constant angular accel? eration is inputted ,the deflection angle of the rotor is increasing linearly . 10 For the reason that the type system has the small rotation deflection angle , which is considered the superior perfor mance compared w ith the type# system. So in practical application ,the type syste m decoupling net work is applied to make it be? come orthogonalm atrix . ? ? Let the control decoupling matrix to be : D (s) = - 1- 2! s 2! s - 1 ( 7) ? The si mulation sche m atic diagra mis constructed as shown in F ig. 4 . Fig . 4?Sche m atic diagram of rebalance loop adopting decoupling network ? The output angle can be deduced as: ?( s) ? (s) = KPKPC( s)KTGc( s) ? ? 1 Ie( s 2 + 4! 2 ) - 2! Ies( s 2 + 4! 2 ) - 2! Ies( s 2 + 4! 2 ) - 1 Ie( s 2 + 4! 2 ) ? ? ? D ( s) ?( s) ? ( s) - 1 s !X( s) !Y( s) = ? KPKPC( s)KTGc( s) - 1 Ies 2 0 0- 1 Ies 2? ? ? ?(s) ? ( s) - 1 s !X( s) !Y( s) ( 8) where, Kpis the sensitivity of the test circui, t Kpc( s) is the compensation loop transfer function ,andGc( s) is the transfer function of the PID controller .It can be deduced as : ?( s) ? ( s) = - 1 s !X( s) !Y( s) 1 1+ KPKPC(s)KTGc(s) Ies 2 1 0 0 1 ( 9) ? ?It can be seem that after realization of control de? coupling,theX axis input producesX axis output and the Y axis input producesY axis outpu. tIt is that the coupling component is completely eli m inated to realize the decoupling contro.l But the coupling of the feed? back voltage still exists asEq . ( 10) shows. UX( s) UY( s) = - 1 sK PKPC(s)Gc( s) - 1- 2! s ? 2! s - 1 ? ? ? 1 1+ KPKPC( s)KTGc( s) Ies 2 !X(s) !Y( s) ( 10) It is unable to realize the control decoupling and the output decoupling using the single decoupling network . So it is needed to realize the output decoupling of the output voltage by digital ways to achieve the complete decoupling of the rebalance loop .The output decou? pling matrix is : F(s) = ? 2! s 2 + 4! 2? s s 2 + 4! 2 - s s 2 + 4! 2? 2! s 2 + 4! 2 = F1( s) F2(s) - F2( s) F1( s) ( 11) ?675? Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 Then the output voltage is : UX 0( s) UY0( s) = 1 s ?KPKPC( s)Gc( s) ?0? 1 s - 1 s ? 0? ? ? 1 1+ KPKPC( s)KTGc( s) Ies 2 ? !X(s) !Y( s) (12) ? The difference equation can be directly got by the computer asEq . ( 13) shows . UXX(K ) = 2cos( 2!T )UXX(K - 1) - ? ? UXX(K - 2) + sin(2!T )UX(K - 1) UXY(K ) = 2cos( 2!T )UX Y(K - 1) - ? ? UXY(K - 2) + UY(K ) - cos( 2!T )UY(K - 1) UYY(K ) = 2cos(2!T )UYY(K - 1) - ? ? UYY(K - 2) + sin( 2!T )UY(K - 1) UY X(K ) = 2cos( 2!T )UY X(K - 1) - ? ? UY X(K - 2) - UX(K ) + cos( 2!T )UX(K - 1) UX 0(K ) = UXX(K ) + UXY(K ) UY0(K ) = UYY(K ) + UY X(K ) (13) In Eq . ( 13), T is the feedback voltage sa mpling peri? od . UX(K ), UY(K ) are the sa mpling data of the feed? back voltage of the Xand Y axes, correspondingly . UX 0(K ), UY0(K ) are the output voltage data without the coupling segm en. t For the syste m exists a pair of conjugate i maginary roo, tit is in the status of critical stabilization .So the decoupling networkF ( s) can be compensated to form a stable decoupling network sys? tem and the compensation network is introduced asEq . ( 14) shows . W( s) = T( s). F( s) = s 2 + 4! 2 s 2 + 4 !s + 4! 2? ? ? 2! s 2 + 4! 2? s s 2 + 4! 2 - s s 2 + 4! 2? 2! s 2 + 4! 2 = ? ? 2! s 2 + 4 !s + 4! 2? s s 2 + 4 !s+ 4! 2 - s s 2 + 4 !s+ 4! 2? 2! s 2 + 4 !s+ 4! 2 ( 14) When 1 0 ,system is stable.It can be directly shown as : UXX(Z) = 1 1- 2 e - 2 !T sin( 2!1- 2T )Z- 1 1- 2e - 2 !T cos(2!1- 2T )Z- 1 + e - 2 !TZ- 2. UX (Z) UX Y(Z ) = 1- e - 2 !T cos( 2!1- 2T )Z- 1 - 1- 2e - 2 !T sin(2!1- 2T )Z- 1 1- 2e - 2 !T cos(2!1- 2T )Z- 1 + e - 2 !TZ- 2 . UY(Z ) UYY(Z) = 1 1- 2 e - 2 !T sin( 2!1- 2T )Z- 1 1- 2e - 2 !T cos( 2!1- 2T )Z- 1 + e - 2 !T Z - 2. UY (Z) UYX(Z ) = - 1- e - 2 !T cos(2!1- 2T )Z- 1 - 1- 2 e - 2 !T sin(2!1- 2T )Z- 1 1- 2e - 2 !T cos(2!1- 2T )Z- 1 + e - 2 !TZ- 2 . UX(Z) UX 0(Z) = UXX(Z ) + UXY(Z ) UY0(Z ) = UYY(Z) + UYX(Z ) ( 15) ? The dynam ic character of t wo?order system is re? lated to the damping coefficien. t From the theory of the dynam ic response of the two?order response ,the transi? tion ti me of the t wo?order system is the shortest when = 0?707 . 3? The Si mulation ResultAnalysis and theRealiza? tion of the Co mplete Decoupling W hen the input step angular velocity of theX axis is 1 rad/s,theY axis is2 rad/s . F ig . 5 shows the con? trol inputs voltage for step inputs .It can be seen that the overshoot of the decoupling control is less than 20%. The ti me of the rotor returning to its null place is 0?4 s, which has superiority over the rebalance loop a? dopting PID controller combined w ith the compensation loop . F ig. 6 shows the tilt angles for step inputs . Under the step angular velocity,the rotor departure from the null place a certain angle in proportional to the input angular velocity ,then the rotor trace the shell by the control torque to m ini m ize the relative angle .It can be seen that the angle of rotor departure from the null place w ith decoupling is less than the rebalance loop w ithout decoupling and the ti me is shorter either . Ow? ing to the rebalance loop w ithout decoupling does not eli m inate the cross coupling,it is easy to surge .The outputs of complete decoupling for step inputs are shown in F ig. 7 . The output voltage ofX axis (UX 0) is 1?24 mV while the output voltage of Y axis (UY0) is 0 . 62 mV,which is proportional to the input angular velocity .So the digital cross complete decoupling is ?676? Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 completed . The output voltage reflects the input angu? lar velocity . Fig . 5?Control inputs for step inputs Fig. 6? The tilt angles for step inputs Fig . 7?The outputs of complete decoupling for step inputs ? ?The control decoupling circuit includes the com? pensation loop and decoupling loop . The compensation loop adopts the T?shape net work proportional?differenti? al compensation structure ,and the parameter is deter? m ined by the circuit para m eter . The decoupling circuit includes the integral and additive operation uni. t The digital output decoupling is realized by floating type DSP C33PS through difference equations .Fig . 8 shows the control system of the MESG of the two degree of freedom ( DOF ) of theZ?displacem ent and rotate by theX ?ax is .In order to detect the multi?axis displace? ment signa,l the frequency multiplex way is applied in the signal detection, which consists of the multi?chan? nel signalgenerator ,the front amplifier ,the demodula? tion and the low?pass filtermodule . The controlmodule includes the control combining module , DSP controller and the decoupling module .It produces control signal plus the carrier v1, v2and bias voltageVrefto m ake the rotor s rotation angle and displacement along Z axis being zero. Vfb1reflects input linear acceleration ,and Vfb2reflects input angular velocity rotate by theY?ax is . Fig . 8?Control sche m atic diagram for theMESG ?677? Journal of Harbin Institute of Technology (New Series), Vol. 17 , No. 5 ,2010 4?Conclusion The dynam ic model of the two?degree MESG is constructed . Under the idealwork situation ,two types of rebalance loop are introduced . The complete decou? pling loop is applied in theMESG to realize the fast re? sponse speed and small overshoo. t The circuit realiza? tion is proposed .In order to rea