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I......... 2. ..1. . . . 1.. - _ . . 0... out. .¢..a¢. v. ‘5’ .2: ztc .. ..o..0¢1.-P .cvvo ‘0.‘!.! .009. .55Jc.‘1. ‘ 1 u. i I00 Q..| ‘.... 0..., l! 11' 1m i k} This is to certify that the thesis entitled DEVELOPMENT AND CHARACTERIZATION OF AN OPTICAL FEEDBACK CONTROLLED MICROPHONE FOR AEROACOUSTICS RESEARCH presented by Eliott Radcliffe has been accepted towards fulfillment of the requirements for the Masters degree in Mechanical Engineering i L ss/xzxc MW Major Professor’s Signature 9’ /z 6 /20( 0 Date MSU is an Affirmative Action/Equal Opportunity Employer LIBRARY Michigan State University - fi._ ~.—.-.-.- —.—-— -.-.-.---u--u-.- - .0-I-l-l-I_I-1-o-I-I-0-0-I-o-O-’-I-l-o_'-'-!-o-I---Q PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProj/Acc&Pres/CIRCIDateDue.indd DEVELOPMENT AND CHARACTERIZATION OF AN OPTICAL FEEDBACK CONTROLLED MICROPHONE FOR AEROACOUSTICS RESEARCH By Eliott Radcliffe A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Mechanical Engineering ‘20 10 ABSTRACT DEVELOPMENT AND CHARACTERIZATION OF AN OPTICAL FEEDBACK CONTROLLED MICROPHONE FOR AEROACOUSTICS RESEARCH By Eliott Radcliffe This study constitutes a proof of concept of a new feedback-controlled optical mi- crophone for potential use in phased "beamfr)rming" arrays utilized in aeroacoustics research. In the new microphone design. an optical sensor is employed as a means for measuring the center displacement of a stretched thin membrane caused by inci- dent. acoustic I‘n'essure. The membrane is constructed from PVDF (polyvinylidene- fluoride) which exhibits piezoelectric properties allowing; actuation of the membrane in a feedback system. where force feedback is used to nullify the optically detected deflection. The feedback provision was used to actively modify sensor parameters. most notably membrane stiffness. resonant fretpiency, and damping. A theoretical study is presented to examine the viability of two improvements that may be used in future Inicrt‘mhone designs. Inmlementation of one or both of these unprove-‘ments is expected to significantly increase controllability of the feedl)ack-controlled optical microphone documented here. Copyright by Eliott Radcliffe 2010 DEDICATION This thesis is dedicated to family. friends. and anyone else who has helped me along my way, and shaped the person I am today. I‘d like to extend special gratitude to Dr. Naguib who has been absolutely everything that. I could have ever hoped for in a faculty advisor. His combination of genuine understanding and shared wisdom has put me in the best possible position to be successful. Also. to Tony Humphreys for believing enough in the research to spoijisor a GSRP fellowship for two years. and for bringing me to the grand facility that is NASA Langley Research Center. To my parents. you have been there for me every step of the way. and I know will continue to be. For this I am eternally grateful. To N ate and. Terri and my beautiful niece Kaelyn. To Isa and Justin. my nephew Owen. and one more on the way. F inally. to my grandparents and extended family. with special mention to Charles Radcliffe, the patriarch of a. long line of Radcliffe engineers. Lastly. I'd like to thank my closest friends from my college years and beyond. In no particular order, Jesse. Dan. Adam. Ashley. Alan, Dave. Nick. Stacy. Noah. Jenny. Liz, Molly. Godwin. Zach. Jill. Megan. Jess. “ill. and Derek. As many of us are beginning a new chapter in our lives and embarking to distant locales across the country and world. I hope we all rmnember where we came from and return home to Michigan whenever we can find the time. And If I don't see you for a. long while, I'll come and find you left of the dial. -Paul Westerberg iv ACKNOWLEDGMENT This work is generously supported by the NASA GSRP fellowship. grant no NINXOSAOOTH. Additionally, gratitude is extended towards Dr. Allan Zuckerwar at NASA Langley Research Center for his shared expertise in fibre-optic sensing and microphone de- sign. TABLE OF CONTENTS List of Tables ................................. viii List of Figures ................................ ix Key to Symbols and Abbreviations ................... xiii Introduction . 1 1.1 Motivation ................................. 1 1.2 Previous Feedback-Controlled .‘\Iicrophones ............... 5 1.3 Description of Current Research ..................... 6 A Novel Feedback-Controlled Optical Microphone using a Commer- cial Fiber-Optic Sensor . . . . . . . . . . . . . 9 2.1 Microphone Construction and Feedback Sy ste 1n Components ..... 9 2.1.1 PVDF Film Microphone Capsule ................ 9 2.1.2 F iber-Optic Lever Displacement Sensor ............. 11 2.1.3 Feedback System Components .................. 12 2.2 Analytical Modeling ........................... 13 2.3 Experimental Procedure ......................... 19 2.4 Results and Discussion .......................... 22 A Feedback-Controlled Optical Microphone Incorporating a Michel- son Interferometer . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Construction ............................... 32 3.1.1 Microphone Membrane ...................... 32 3.1.2 Michelson Interferometer ..................... 34 3.1.3 Serial Interfaced Controller .................... 38 3.2 Experimental Procedure ......................... 41 3.3 Results and Discussion .......................... 43 3.3.1 Electrical Actuation ....................... 43 3.3.2 Acoustic Calibration ....................... 44 3.3.3 Comparison of Michelson Interferometer to Fiber-Optic Lever Sensor ............................... 48 Theoretical and Experimental Evaluation of Proposed Design Im- provements . . . . . . . . . . . . . . . . . . . . 50 4.1 Displacement Averaging Optical Sensor ................. 51 4.2 Perforated Back Plate .......................... 58 vi 5 Summary and Conclusions . 69 6Appendix............................73 6.1 Appendix A - Electrical Circuits ..................... 73 6.1.1 Phase-Lead Compensator Circuits ................ T3 Compensator Circuit #1 ..................... 74 Compensator Circuit #2 ..................... T4 Compensator Circuit #3 ..................... 75 6.1.2 Michelson Interferometer Control Circuit ............ 80 6.1.3 Other Circuits ........................... 81 Signal Amplifier and Variable Low Pass Filter ......... 81 Third Order Inverse Chebyshev Filter .............. 82 Power Amplifier .......................... 84 6.2 Appendix B — Software Applications ................... 84 6.2.1 FeedbackGUI ........................... 84 Calibration stage ......................... 85 System Identification Stage ................... 86 Closed-Loop Specification Stage ................. 87 Controller Programming Stage .................. 87 6.2.2 MATLAB Software ........................ 88 PhaseLeadGUI .......................... 88 DigitalPot.m ........................... 88 Perforated Backplate GUI .................... 89 PLC_Solver.m ........................... 89 Estimate.\Iembrane.m ...................... 90 Bibliography ..................................................... 91 vii 2.1 3.1 4.1 4.2 6.1 6.2 6.3 LIST OF TABLES Design equations for compensator circuit. Resisters are represented by Rpl. Rpg. Rdg. Rpp and. [Its-um: wlnle potentiometers Hp. RC. It’d control proportional gain. derivative time constant. and derivative gain. A fixed capacitance is represented by C. Microphone parameters for open-loop operation Comparison of sensor parameters between fiber-optic lever and Michel- son interferometer. Average relative displacement of 111cml'1rane vibrational modes over the entire surface of the 111embrane. Known or measured parameters of the acrylic inserts used for verifica- tion of the 111echanical damping model. Calculated parameters of the acrylic inserts used for verification of the 111echanicz—11 damping model. Electrical components used in phase—lead controller circuit depicted in Figure 2.4 Electrical components used in serial interfaced phase-lead controller depicted in Figure 3.7 . Electrical components used in Michelson intcrferometer control circuit depicted in Figure 3.6 . . viii 49 64 "*1 R1 80 1.1 1.2 2.1 5" ca 2.4 2.5 2.6 2.7 LIST OF FIGURES Images in this thesis are presented in color Drawing of a typical connnerciz-il condenst'u‘ 111icropl'1one (p is the acous- tic pressure which causes a proportional 111(‘1vement in the membrane). Drawing of a tv 1ical connnercial electret micro 1hone. C) . Schematic ('lrawing of 1:1.rototype microplmne capsule: exploded (left) and assembly (right) views. Schematic drawing of fiber—optic lever probe. Control block diagram for optical feedln—rck controlled microphone sys— tem. Note that I". 2.». Z(-,~ and I" are the Laplace transforms of the acoustic pressure. actual and reference central Incinbrane deflection. and output voltage respectively. Schematic diagram of circuit used for implementation of the phase—lead compensator. Schematic diagram of the plane wave tube calibration setup. Electrical response of PVDF membrane for variation of internal static pressurization: (top) actuation sensitivity of PVDF membrane; (bot- tom) fum'lamental resonance frerplency of PVDF membrane. Frequency response of PVDF membrane identified using electrical ac- tuation with 1.5kPa internal pressurization: (top) Actuation sensitivity of PVDF membrane; (bip1ttom) Phase response of PVDF mmnbrane 13 17 2.8 2.9 2.10 3.1 3.2 3.3 3.4 3.6 3.7 3.8 3.10 3.11 3.12 Response of microphone in open—loop and closed-loop (’1peration for the design specification of OdB attenuation. 13:950. and f0.(vL:5.1kHz: (top) acmistic sensitivity: (bottom) phase . Response of microphone in open-loop and (i-losed-lii1op operation for the design specificatitm of 3dB attenuation, 13:92.50. and f().(vL=4.8kHz: (top) Acoustic sensitivity; (bottom Phase . Linearity and noise floor for open- and closed-loop operation. . Depiction of 6.35111111 diameter membrane prototype. top: top view. bottom: side view. Front view depiction of 6.35111111 diameter membrane prototype with acrylic channel (PVVT) attached. Depiction of the optical setup for the Michelson interferometer. . Photograph of the optical setup for the Michelson interferometer (Note the placement of a CCD camera. and mirrors which aid in alignment of the laser beam with the center of the microphone membrane). Inteferometer output relative to mirror displacement. Schematic diagram of interferometer circuit. with feedback section. . Schematic diagram of phase-lead controller circuit. . Schematic diagram of serial potentiometer interface. Frequency response of 6.3-5111111 111eml'1rane with .\lich(~1lson interferom— eter. measured using electrical actuation. Frequency response of 6.35111111 membrane with Michelson interferome- ter, measured using electrical actuation. magnified to show frequencies near the fundamental resonance. . Frequency response of 6.35111111 membrane with .\Iichelson interferom— eter, measured using acoustic (i'alilin'ation in a plane wave tube. Linearity of 635111111 111eml‘1rane with Michelson interferometer. mea- sured using acoustic calibration in plane wave tube at. 3kHz and 12kHz. 27 28 29 39 40 43 46 48 4.1 4.2 4.3 4.4 4.5 4.6 4.8 4.9 4.10 6.1 6.3 6.4 6.5 Axi—symmetric mode shapes of a vibrating membrane. . Average relative displacement of membrane \I'ibrational modes over the entire surface of the membrane. Relative average displacement of 111embrane as a function of the sensor probe diameter. Theoretical frequency response of the open-loop when measuring the 111embrane deflection at its center (solid line) compared to when using an optical sensor with (Is/(I 20.37 Theoretical frequency response of the opm1-loop when measuring the membrane deflection at its center (solid line) compared to when using an optical sensor with (lg/(I 20.69 Equivalent circuit of the perforated back-plate and l1ack-chambcr. Schematic drawing of prototype 111icrophone capsule with acrylic insert designed to simulate a perforated back—plate. . Experimental frequency response of 111icrophone 111embrane with per— forated inserts where the number of holes is varied. Experimental frequency response of 111icrophone 111embrane with im— proved perforated insert. Depiction of GUI application used for perforated back-plate design. with “ideal" design of back-plate shown. Schematic diagram of first phase-lead compensator circuit. Photograph of front panel of first phase-lead compensator circuit. Photograph of second phase-lead compensator on a brez‘ulboard. Photograph of third phase-lead cmnpensator circuit. . Exam 1le digital waveform used in 1roe‘rammine‘ a MCP4‘2XXX se- :3 b D ries digital potentiometer. The example. case is for programming po- tentiometer 0 to position 50. where the full 16 bit input is 00010001 00110010. 53 54 57 60 64 CH 6.6 6.7 6.8 6.9 Photograph of Michelson interferometer control circuit... ........ Schematic diagram of signal amplifier and variable low pass filter circuit. Photograph of signal amplifier and variable low pass filter circuit. Photograph of inverse. Chebyshev filter circuit .............. 6.10 Photograph of 386 [xix-ver amplifier circuit. ............... xii 81 83 83 84 85 KEY TO SYMBOLS AND ABBREVIATIONS a S a0.a1.b1 C 0 CO!) (1"). C] ' f 0 ads). 60(3), szp) H(s) lHacf (“Al km. 1‘ 112 K0!) 7 hp Membrane radius Membrane surface area Optical sensor radius Phase lead compensator parameters Damping of fundamental I'PSOllt-tlli mode Damping term added by the perforated back- plate for the zeroth mode " resonant mode Damping of m” Isothermal speed of sound in air Fundamental resonant frequency in Hz Transfer functions of conipt—uisator, optical sensor. and pie7..(_)el(-*ctric system Membrane transfer function Frequency response function of membrane deflection relative to applied voltage Bessel function of the zeroth order Stiffness of fundamental resonant mode \Vave mnnber of mm membrane axi- symme’tric mode Stiffness of mm resonant mode Derivative gain Stiffness term added by back-chamber for the zeroth mode Proportional gain Length of hole. in perforated back-plate xiii 111 film) ]) PWT rk SPL S 1 5 M A Sact SH: 50. 57*» 3P2 Membrane mass (surface density) Inertial mass term added by perforated back— plate for the zeroth mode Number of modes retained in the membrane transfer function Acoustic pressure Plane wave tube Back-chamber pressure vector Acoustic pressure at 11'7”" hole in back-plate Acoustic pressure Laplace transform Number of holes in the perforated back—1;)late Radial coordinate on membrane Radius of hole in perforated back—plate Sound pressure level Complex pole of the closed—loop transfer function I\Iicro1_)hone sensitivity .\Ieml;)rane electrical actuation sensitivity at low frecpienev Sensitivity of membrane. optical sensor, com— iwnsz-rtor, and piezoelectric system Time Membrane tension (force per unit length) Air voltnne velocity vector Air volume velocity at km hole in back—plate Air volume velocity at km hole xiv V(S) N Zb 13 C0 (0th Voltage Voltage Laplace transform Membrane deflection perl‘mndicular to sur- face Membrane deflection averaged over the entire surface of the I‘nembrane Acoustic impedance matrix relating to per- forated back-plate and back—charnber Membrane defle’rction measured at its center Acoustic inmedance of the back-chamber Membrane center deflection reference. l\lembrane center (‘leflection Laplace transform Polar angle of the complex pole of the closed- loop transfer function. measured from the positive real axis Specific heat ratio of air Damping ratio of fundamental resonant mode Damping ratio of fundamental resonant mode in closed—loop operation Angular coordinate on meml'n‘ane VV'avelengtl‘i of light Viscosity of air Membrane surface density (mass per unit area) XV .00 Td Qua (Dee UV’O won I v 1..) WHiWL Density of air Time constant correstmnding to derivative gain cutoff Cross—spectrum between membrane deflec- tion and voltage input and auto—spectrum of voltage input Polar angle of f/(sl )(}'()(s1)GpZ(sl) Angular fretpiency (radians/s) Fundamental natural frequency (radians/s) Fundamental natural frequency in closed- loop operation (radians/s) Half—pmver frequencies (radians/s) xvi Chapter 1 I ntroduction 1 - 1 Motivation A great deal of current research is taking place in the field of aeroacoustics. with Studies being performed to characterize noise sources such as aircraft wings, landing gear -. and jet engines. Tests are. }_)erfori.ned in widely varying environments ranging frorn acoustically treated quiet flow facilities to aircraft fly-overs. One particular teehnOlogy that has been developed for this purpose. is the "beaniforming“ microphone array. These arrays contain large sensor counts, typically ranging from approximately 30 to over 100. The operating principle of these arrays derives from the propagation Clela)’ from a noise source to a given sensor in the array. Knowledge of the delay time for each microphone in the array can be. exploited to resolve the location of an acoustic SOuI-Ce- The classical beamforming method involves discrete time-shifting of each digital 1y acquired microphone signal for localization of acoustic sources. while more Inod er 11 methods use deconvolution and frequency domain based signal processing [11.[2]- Regardless of the method of analysis. it is important to have accurate knowledge of the frequency response of each microplmne in the system. particularly with regard to phase. Typically, IIIiCl‘()[.)ll()Il€S are. calibrated before any experiments such that any Inismat. Ch in the response of individual units may be accounted for. Difficulties arise due to the time consuming nature and equipment required for acoustic calibration. Furthermore, a “alibrat ion perf<_>rmed in a laboratory setting may be rendered invalid vvhen the sensor is used in field testing where it is exposed to effects such as heat and Ilumidity- Various Inicropl'ione technologies are currently implemented. in beamforming arrays. Perhaps most. common is the use of an instrument grade condenser microphcme. A ('1 I‘awing of this type of 111icrt')ph(_)ne is shown in Figure 1.1. The operating principle for the condenser microphone is that the capacitance between a stretched. pressure seI'ISitiVe membrane and ccmductive back-plate varies as a result of membrane mo- t ion_ A typical gap between the back-plate and Inemln'ane is approximately ‘25 pin. \V'hel'l a fixed charge is applied to the back-plate. these changes in capacitance re— Sult in a varying voltage at the back—plate. This charge is maintained by a large (tyDiCally 28V-200V) polarization voltage which is connected to the plate through a reSistor [3]. Additit'mal features include an annular slot around the laugh-plate, in addition to holes to increase damping of the membrane motion. Also, a capillary vent hole is included for equalization of static air pressure in the back—chamber with the a’tnlOSIDhere. Commercial condenser microplmnes are available that are individually Calibl‘élted by the manufacturer and guaranteed to have a high degree of phase uni— formity (:l:10O at 10kHz)l. However. the cost per channel for a high-quality capsule is r \ 81“}; high (approximately $2000)- 1 Da-t-asheet - Briiel 8; Kjaer Type 4958 20kHz Precision Array Microphone 1) Membrane 1 ~ Gap Annular Slot 1 Back-plate H019 Back—chamber Insulator *' I. Capillary Vent ~ ' 7“ if: ”'“W’me Output Terminal Figure l . 1: Drawing of a typical connnercial ctmdenser microphone (p is the acoustic pressure which causes a proportional movement in the membrane). One alternative is to use inex],)ensive electret microplmnes. A drawing of a. “back- electret” type of microphone is shown in Figure 1.2. The operating principle of the P)a.ck-electret is very similar to the condenser microphtme. with the primary distinction being the bonding of a permanently polarim‘d electret material to the surface of the 1)a¢Ck—plate. This method of construction allows for the microphone to operate without a high—voltage power supply. \Vhile these have the advantage of being low-cost, elect ret 111icrophones are known to vary widely with respect to mechanical/electrical Sensitivity and phase. Also, the electret response tends to drift when exposed to environmental elements, and performance tends to degrade over time due to loss of S ‘ . - i 111 face charge l3l Membrane Electret Back-t date [:33 Lift] Em - _ 1 *Capillaiy Vent Figure 1.2: Drawing of a typical commercial electret microphone. e utilization of micro-fabricz—rtion n‘iethods (microelectrornechanical systems. or ZVIE as AIS.) to manufacture microphones based on known transduction methods (such It a- . . . . . . 11on descrlbed above as well as others) seems to hold pronnse 1n reahzmg rm- 3 crophones with the required dynamic range and bandwidth for aeroacoustics appli- cations. While meeting the cost and response-matching requirements of beamforming arrays [4]. A systematic effort to realize this potential has been undertaken over the past few years by the Interdisciplinary l\Iicrosystems Group (IMG) at Univer- sity of Florida. Some of the notable efforts of this group include the development of a. 1VIE1VIS piezm'esistive microphone array [4], piezoelectric microphone [5]. and dual- backplate condenser 111icrophone [6][7]. Other recent MEMS based microphones have been reported by [8]. [0] and [10]. The device discussed in [8] uses a ZnO piezoelec— tric mernbrane and is tested as a micropl’ione as well as a microspeaker. Optical iIlt erferometry using a diffraction-based grating has been incorporated for sensing of I'Ilernbrane displacement in [0] and [10]. The focus of the present thesis is a microphone concept alternative to those discussed i1bOVG. The concept is that of a feetll:)ack-controlled microplume. In this approach. a feedback control loop is integrated into the sensor in order to detect and nullify the IniCerhQne's 111embrane deflection. caused by the sound pressure, using an opposing pres-Sure that is produced by electrostatic, electromagnetic, or other electrical means. The presence of the feedback—control provision in the microphone rn'ovides a means by Vvhich to alter the microphones (’lynamics. giving advantages for aeroacoustic bealnf‘orming measuren'ients that are not attainable in conventional or .\IE1\‘IS—based 111icrophones reported in the literature. For example. the feedback parameters can be tuned to adjust the microphones bandwidth and dynamic range. This enables the Same sensor to be employed in field testing at airports (where the bandwidth required is <20 kHz and maximum Sound Pressure Level (SPL) is less than 120 dB [5]) as ‘Vell as in 1/4—scale model testing in anechoic wind tunnels (where the requirements are 50 kHz of bandwidth and maximum SPL exceeding 160 dB [5]). The tuning of 0Out: JZ‘CJI parameters can also be used to compensate for the modifying influence of 4 environmental factors (e..g temperature. dirt and humidity) 011 the sensors response. In fact, in the limit of sufficiently high feedback gain. the micr01.)hone‘s response is dominated by the dynamics of the feedback circuitry [11]. Thus. the response becomes independent of any envirornnental effects on the mechanical and electrical behavior of the niembrane and deflection transduction scheme (capacitive. piezoresistive, etc). F inally, the actuation scheme used allows for "self-calibration" of the microphone VVit bout the necessity of an amustic caliliu'ation setup. In turn. such capability holds the potential for “self-matching" of microphones in an array application. 1 - 2 Previous Feedback-Controlled Microphones preViOusly, in [12], the response of a fm-ce—feedback 111icrophone was evaluated. This 111icrophone used eltf‘C‘tl‘OSiafiC actuation of a pressure-gradient type microphone cap- Sule, The feedback signal was based on modulation of an LC oscillators frequency Ca“1188(‘1 by the change in the microplmne capsule’s capacitance. In a follow-up study ainling to improve the design of the microphtme. the potential and associated ad— V'antages for uSing a Fabry—Perot i1iterferometer for the feedback sensor were inves— tigated in detail, but no microphone prototypes employing the interferometer were Constructed [13]. Overall the study lacked evidence demonstrating the advantages of f9 . . _, . . ed back microphones (based on Figure 1! 1n the article). Additional published material pertinent to feedback microphones include a patent for a force balance 111icrophone that lists possible transduction and displacement de— tecthn methods, including optical methods [14]. The patent, however. only lists the 111101. Ophone’s concept without giving any experimental data regarding the response Of an actual feedback microphone I‘n‘ototype. More recently, [15] developed a MEMS based microphone that incorporates the displacement sensing method of [9] and [10] for measurement of a. centrally hinged biomimetic membrane with electrostatic actu- at. ion in a feedback system. The construction of this MEMS sensor was motivated by hearing—aid applications. and thus the sensitivity response of the unit was highly non- u niforrn, which renders it unsuitable for aeroacoustic applications. No phase-response data were reported. 1.3 Description of Current Research The uniqueness of the current study derives from the combination of actuation and sensing techniques that are being used for the first time to implement a feedback 111icrophone. In 1')articular. the microplmne prototype (-(mstructed and character— ized here integrates thin film PVDF (polyvinelidine-fluoride) as the pressure sensitive ITlernbrane. The actuation provision is naturally integrated into a microphone con— St I'ucted in this manner by employing the piezrwlectric properties of the PVDF. The Sirnplicity of this constriu‘tion relative to other feei'lback microphones reported in the literature is evident. given that no special means are necessary to construct the ac- t"Jator (such as the back-plate in electrostatic or coils in electromagnetic actuation). In t311is regard, the current prototype has the potential to be simple and inexpensive to fabricate while satisfying the requirement for accurate sensor—response matching in an array application. This is particularly true since the present sensor concept is a1.- - . . 5O dn'renable to ccmstructron uslng MEMS. O tRYDes of optlcal techniques are investigated for sensmg of membrane displace- the - nt 11’1 the prototype mlcrophones developed for tlus research; the fiber-optlc lever and - ._ A’Ilchelson mterferometer. Optical sensors are considered desu'able for their 111- 6 sensitivity to noise; hence decoupling the displacement sensor output from the in- fluence of the actuator signal. The associated trade-offs in sensitivity, noise floor. frequency bandwidth. and linearity are discussed in evaluations of the two sensing t echn i q ues. An integral part of this research is the mathematical analysis necessary for effective design of the control system. Foremost is development of a methodology for sys- tem identification and modeling the dynamics of the inicr‘Ophone memln‘ane. optical Sensor, and electrical components. These models are used in calculation of control I'Jarameters, where the closed—loop response is based on a set of user specified pa- I‘alneters corresponding to a. desired microphone frequency response. Specifically. the research demonstrates that this two-step approach of modeling and control design is IDI‘OInising for "self-matching" of microphones in array where membranes with mis- Illatched open—loop frequency response are forced to the same closed—loop response V’ i a. feedback. The first. prototype microphone. described in Chapter ‘2. used a commercial fiber-optic. leVE-‘I‘ sensor for measurement of the deflection of a 12.7mm diameter membrane. This DI'OtvOtype provided the basis for ('levelopment and testing of modelling and control design of the optical feedback-controlled microphone system. In Chapter 3. results are reported on testing of a second prototype with a sensor diameter of 6.35mm. This Set 1801‘ had the desirable properties of smaller size and higher frequency bandwidth. HOWever, due to the inherent trade-off between n'iembrane resonant frequency and IneClléinical sensitivity (i.e. m/ Pa). the use of an optical sensor with much greater (lisplacement sensitivity (i.e. V / in) was necessary. For this purpose. the Michelson Interferometer setup was implemented. The knowledge gained from these two studies gav ° _ . . . . . . e 1 Ilsrght mto potential design unproy-ements for future prototypes. Chapter 4 gives 7 tilleoretical as well as experimental verification of two of these potential improvements, tllose being (1) an optical sensor that averages (.lisplacement over a large fraction of 1:118 membranes area (both sensors used here. detected the central displacement of the membrane). and (2) a perforated back-plate designed to increase damping of t Ile mechanical resonances of the membrane. A summary of the findings is given in C11 apter 5. along with conclusions and future recmnmendations. Chapter 2 A Novel Feedback-Controlled Optical Microphone using a Commercial Fiber-Optic Sensor 2 - 1 Microphone Construction and Feedback Sys- tem Components 2 - 1 - 1 PVDF Film Microphone Capsule 1‘)er Otype microphone capsule with a memln‘ane diameter of 12.7mm is constructed mg a stretched PVDF membrane as the acoustic pressure sensmg element as illus- t: r d In Figure 2.1. The capsule body and clamping rmg are constructed from r11 1num rod. The membrane, which is metallized with an aluminum layer on both 3 » IS clamped between the body and rlng w1th a rubber gasket air seal. In thls way. 9 t; he body and ring apply tension to the membrane, and also act as electrical conductors to the metallized surface of the PVDF film. At the end opposite to the membrane, an acrylic plate is attached to the capsule body with a rubber gasket inserted in between. The gaskets prevent air leakage from the internal cavity of the microphone caljsule, enabling pressurization of the capsule for reasons that will become clear. The pressurization is achieved through a static pressure tap that is installed in the acrylic plate. The tap couples. via a T connection, to a syringe as well as a pressure gage, 21.1 lowing variation and monitoring of the internal static pressure. 41-40Nylon Screws — ll 3 ll Assembled Capsule l - T :,v 2"}. Clamping Ring __ . l. .m PVDF Membrane — —T'— Rubber Gasket ‘ Capsule Body Rubber Gasket Acrylic Plate Pressure Tap 6—32 Steel Screws F i g1]. re 2.1: Schematic drawing of prototype microphone capsule: exploded (left) and EiS S (a Inbly (right) views. T 1145:; piezoelectric properties of the PVDF can be exploited to electrically induce de- fl '53 C’ t ion of the membrane surface. This is important for two reasons. (1) the membrane CT“ 211‘ I1 aCt as an actuator in a feedback loop, and (‘2) the transfer function and thus fre- q 1‘1 ency’ response of the membrane can be determined through electrical actuation, w i t’ Ilout the necessity of an acoustic calibrator. It is well known that the response of a p VDF membrane while being actuated in this manner (i.e. deflection per unit volt- age} applied across the top and bottom surfaces) is greatly increased when it has some Q 11 I‘ vat ure as opposed to being flat [16]. [17]. [18]. For convenience, this is achieved in 10 t he current prototype by applying static pressurization using the. provisions described above. Of course, although this method is suitable for laboratory characterization of {)1‘ototypes, construction of commercially viable sensors will ultimately have to employ a IIlore practical approach by inducing curvature either through a material treatment or alternate mounting methods. For example. a self-supporting, chime-shaped piezo- electric structure can be manufactured by applying an electric field across the film VV' Ilile stretched over a steel sphere at temperatm'es of 800C. as described by [17]. 2 - 1.2 Fiber-Optic Lever Displacement Sensor A 11 optical sensor is used to measure the ('leflection of the membrane in response to i ncident acoustic pressure. The particular type of sensor employed is a fiber—optic Ie V'er, model Philtec D20. When aimed at a reflective surface, light emitted from a t rarlsmitting fiber is reflected back into l‘nn'ldled receiving fibers. and is detected by ‘c‘L photodetector. Thus. the output of the photodetector will be a "function of the seIDaration distance between the probe tip and the reflective surface [19]. A sensor 118i 11g this setup and seven optical fibers is depicted in Figure. 2.2. In the case of t h 9 sensor used for this research, output voltage increases linearly with the gap size b e t Vveen the probe tip and the membrane. Its linear operation is sustainable over a I 11 aXimum displacement of 23/1111 and frequency bandwidth of 20 kHz with a typical Se nSitivity of 86mV/,um. The latter is obtained from calibraticm using a stationary ta ‘1 - . . C 1“th prlor to taklng I'neasurements. T line fiber- optic lever sensor is aimed at the center of the PVDF membrane. The QC) - mblnation of these two components (Le. sensor and membrane) define the. open- IQ I) Operation of the microphone, where the output voltage of the optical sensor 1s a fu r1 0 - . . “ t 1011 solely of the acoustic pressure acting on the memln‘ane and the membrane 11 F iber-Optic Lever :" Reflective Surface Probe Tip l Figure 2.2: Schematic drawing of fiber-optic lever probe. 2111(1 lever sensor dynamics. Without the feedback, this setup is similar in nature to 1:116) optical 111icrophones reported in [20] and [21]. 2 - 1.3 Feedback System Components T 1 1 e aim of this work is to demonstrate the close(l-l(‘>op operation of the sensor where t: I). e microphone dynamics are modified by a feedback control system as depicted by t h 9 block diagram in Figure 2.3. The two additional blocks that describe the sensors res ponse in closed-loop operation are the c(;)1111.)ensator and piezoelectric system. The CO Inpensator is constructed using (merational anmlifiers. and its transfer function is set 13y precision trim—pots. The piezoelectric system consists of a piezo driver and t 11 E‘ 111embrane itself. The piezo driver used is a ThorLabs model ;\IDT694 which [3 r QViCles a gain factor of 15 for input voltages in the range of O-IOV. Calil'n'ation has b eell performed to show that the unit has a bandwidth of 140kHz with a transfer 1“ L1 notion similar to that of a second-order, slightly under—damped. low—pass filter. rom the plezo drn er in cmnunctlon w1th the p1( zoelet t11( propeit1es of the In mbrane induce an electrical equi 'alent pressure that acts in oppos1t1on to the 1‘) Id ZCI‘ . 7 f 7 . F l PV DF I Z I .__>ll ()ptical Sensor P—axfim—fi Membrane t—‘C‘VE‘Z w V » . l ‘ (10(5) J-f—T ——‘——__—J i l l l F l . i a f l l 1 Piezo Svstem Compensator a Gel-5') ! | l l l | im F igure 2.3: Control block diagram for optical feedback controlled 111icrophone system. N ote that P , ZC, ZCT and V are the Laplacetransforms of the acoustic pressure. actual 8.1:].(1 reference central meml'n'ane deflection. and output voltage respectively. 2 -2 Analytical Modeling T I’le. transfer function relating the voltage output (V) of the optical sensor to acous- t i 4:“: pressure input (P) for the closed-loop system depicted in Figure 2.3 is given by CC; Llation (2.1) below. Here. ”(3) represents the membrane transfer functitm. while 00 (.3), (167(5). and CpZ(.s-) represent the optical sensor. compensator. and piezo— 6) I e(:tric system I'esI.)ectively. each modeled in the Laplace domain. This provides the I )&18 is for analytical design and predit‘rtitm of the frequency response of the closed-loop S_}-’S t. em. lr(8) :: [l(8)(7()(5) (2.1) Ptb") 1+ H(Slaofe‘lGFf-‘lGPZ(3) T fle pllysical plant in the control system is the memln‘ane. For small displz-tcements. t: I). at- are typical in response to acoustic excitation, it is suggested by [22] that the the III }31‘ane deflection can be modeled by the linear wave equaticm for a stretched t he: mbrane given in equation (2.2) with T, 20201). p(r.6.l), and p3 representing r11 <9. “I I”) _ . . . _ ~ I‘ane tens10n. displacement, acoustlc pressure. and surface density. respectn'ely. 13 r and 9 are polar coordinates in the plane of the membrane before deflection, t is tiIIIe and. V2 is the laplacian operator. .4) . d“: TV23+ )2 )-f‘— ‘ .I [v N; III the optical microphone system. (ilisplacement is measured at the center of the 111 embrane, represented by :(.. A simple approximation for the fundamental (lowest C)r(ler) resonant mode of the system can be made by assuming the membrane. to L1 I’ldergo aXi—symmetric. parabolic deflection. This yields equation (2.3). where a. is t. h e membrane radius: .. 4T pszp + 3:33p =1) (2.3) Tllis equation is then transformed into the Laplace domain. where M 2 pg, K0 2 , .) . . s, . _ . ‘—1: T/ a“, and a generalized damping term (.0 is added. Thus. the transfer function I‘e I zlting the center displacement to the acoustic pressure is given by: [1(5) = 248) = . 1 (2.4) . 10(5) AM + (708 + K0 I I"). (l eVeloping the membrane transfer function. it is assun‘ied that the mass term, A], Xed, and is known from the PV DF film s thickness and volume density. The stiff- ID). 9 b‘ “i . . . a . . n :5 {’11 1d damping terms are identified from calibration of the membrane s frequency 1‘6 »~ porlse usmg electrical actuation of the piezoelectric. membrane. Since the mem- 1I::) , » tension T is difficult to directly deteimine, the stiffness term ho is identified I‘D a§ @ ‘ “(I On the observed fundamental resonant frequency tug using: 14 (2.5) ' ‘) [\0 = 4.56/15- T 1 1e damping ratio (0 for the highly underdamped system is identified using equation ( 2 -6) where an” and VJL are the half-power frequencies located on each side of the resonant frequency i110. . ~ “ll! _*'L 1 k“"0 ' I ‘ his allows for the damping ("0 to be calculated as follows: (2.7) ('0 = 240 \/ .11 K0 I 11 I)ractice. multiple resonant peaks are observed at the frequencies predicted for the 21.x i— symmetric modes of the circular membrane. These peaks were determined to be cause of instability in the feedback system. and thus were accounted for in the 21 t: 1‘ 21-nsfer function. A modified membrane transfer function is presented in equation ‘ . 9 -. . 9 , . C 2 - 8) below w1th ( m, = (w‘»n‘,/w0)‘(.0. Ix”, —— (w',,,,/.u0)“l\0. and tum/tug representing resonant. frequency ratios for the higher order modes calculated from membrane 1‘. I). e g” i b 1‘ ation theory. and tabulated. for example. in [23] N—l Z(.(s) ‘ . 1 H s = ’ — -1 m . . ( ) [)(S) 7§)( ) 11152 + (‘mS ‘l‘ I\ In (2.8) E ’ t hat N is the number of modes retained in the model. Here five modes are used c). 1189. these appear in the calibrathm frequency range. Also, The factor ( l)” 111 equation (2.8) is required to obtain the proper phase behavior. To clarify. consider summing two second-order systems to model the leading two resonant frequencies of the membrane. In the limit of infinite fretpiency. the phase angle of the transfer function of each of the two systems composing the model asymptotes to 180 degree. The summation of two complex numbers with 180 degree phase also has a phase of 180 degree. Experimentally. the phase angle experiences 180 degree phase change at every resonance fretpiency. Thus. for the two-resonant-fre(_1uency system. the phase angle should asymptote to (l. and hence the transfer functions should be subtracted rather than added. Once equation (2.8) has been determined for the microphone being tested. the com- pensator C((s) is designed to achieve a desired closed-loop frequency response. This is done using a pole placement method as described by [24]. The compensator used is phase lead. and has a transfer function given by equation (2.9). where (2.1. (10. and b1 are phase-lead parameters to be calculated. KP. Ix'd. and Td represent the ccmipensators proportional gain. derivative gain. and derivative time constant. The electrical circuit ei'nployed to implement this controller is shown in Figure 2.4. Design equations for the circuit are given in Table 2.1. (115' + (If) , [\118‘ : —— : \ —— bls + 1 p Td-S‘ + 1 (2.9) The closed—loop system has a. third-order characteristic equation (denominator of equation 1). To tune the close-loop response to that desired. two of the roots of the characteristic equation are set to correspond to a complex pole .91. The location of this pole. defined by equation (2.10) in terms of polar coordinates. is set as desired in the left half of the complex plane and has a magnitude Is]! and angle 13 relative to 16 _4 R 1 (I) . sz ()Jl'.’ ~70 ‘_ Rf.siini Rdv U' " " """" ' 'U l R” C on 4 +20 ().~ll ' ° -- . - Rd.) .. ‘ 0.13 - ' ° ‘ Rec 12V Figure 2.4: Schematic diagram of circuit used for implementation of the phase—lead conmensator. the positive real axis. Both of these quantities are related to the desired closed-loop fundamental resonance fre( uencv cu . and dam )ine‘ ’ 'v , as 0‘iven by e ua . f).( I. r) U.( L n . (2.11) and (2.12). tions 81 = Isllc‘j‘i (2.10) doc]. = l-S'il (‘3-11) C0.("L = —('080’ (2.12) This pole is plugged into the system's chi-iracteristic equation as shown: 17 Table 2.1: Design equations for compensator circuit. Resisters are represented by Rp1.Rp2,Rd-2,RDC and. [{ffimn. while. potentiometers Rib/1’6. Rd control propor— tional gain. derivative time constant. and derivative gain. A fixed capacitance is represented by (7. Parameter Equation _ R R . - - , P .suni Pro )ortional Gain Ix = TIT— ’ P I.) c “’3 (_. Derivative Gain K I = #32”— (' Rd‘Z Derivative Time Constant rd 2 me Hi . DC‘ Bids "[)(v = 12" Ifufill—Hl- l)(.‘ 1+f](.‘s"1)(f()($1)(i'("(81)(Iypz(81)=0 (2.13) Letting ”(81lG()(-S'i)(fpz(511 = |ll(sl)(;'()(.s-1)(IpZ(s1)|cj“ equation (2.13) can be solved for C(v(sl) to yield equations (2.14) and (2.15) for the controller parameters (1.1 and b1 . Sill ‘3 + (1(7)1[I(.S'l)(r'()(sl )(i’pzfsl )l 8111((3 — L“) . (11 = , v V . . (2.1—l) 151111/1'5'll('()f51l('I’Z(51)l 5111 6" b _ sin(/3 + c") + Helm-91100191101-7131ll Sin-’3 (9 15) 1_ —|sl|SiIIL' w. Note that 0.0 in the above equations can be computed based on the desired DC- response of the closed loop. More specifically. the latter is given by: 1"(w' ——4 O) : $1130 (9 1(5) P(..U —* 0) 1 + Sflib'()S(iiS'}.)Z 18 where each the S terms in equation (2.16) represent the DC sensitivity of the cor- responding system. and they are all known except Sp. Realizing that SC 2 (1.0 (see equation (2.9)). it is then 1,)ossible to calculate (10 based on a desired DC response (or attenuation). 2.3 Experimental Procedure The two primary experiments conducted are calibration of the microphone using electrical actuation. followed by calibration of the 111i<'éi‘<)1_)lioiies acoustic response in a plane wave tube (PVVT). Electrical actuation is used as a means of it'lentifying open-loop membrane parameters based on its measured frequency response (using equations (2.5) through (2.7)). These pare—mieters are subsequently applied using the method described at the end of section 2.2 to the design of the system’s compen- sator. Calibration in the plane wave tube. is then undergone to verify that the actual frequency response for both open- and closed-loop operation conforms to predictions based on the theoretical model. In the electrical actuation calibration. a Hewlett—Packard 33120A function generator is used to produce a harmonic sweep wz-iveform over the frequency range 10Hz-25kHz. This waveform is input to the piezo driver. while simultaneously being recorded us— ing a PC-based. National Instruments POI-60243 12—bit Analog—to—Digital converter. The piezo driver provides a voltage gain factor of 15 producing an amplified output that is applied across the electrodes of the PVDF film membrane. A‘Iembrane deflec- tion is simultaneously measured by the fiber—optic lever sensor. The resulting data are used to obtain the frequency response relating the membrane displacement to the applied voltage from: 19 00:04)) I] . a; = —— 2.1" (I.(f( ) Oi'efw') ( f) where on; is the cross-spectrum between the input voltage to the piezo driver and the membranes deflection. and ow is the auto-spectrum of the former. In this test. 8.192.000 data points are recorded at a sampling frequency of 50kHz. To obtain the spectra. the time series were broken into 2000 records. and the spectra obtained from the individual records were averaged resulting in a random uncertainty of 2.24%. The microphone is placed inside the PW'T which acts as an acoustic waveguide in which sound propagates as plane waves up to a cutoff frequency based 011 the tubes cross-sectional (.lin‘ie’nsions. The tube used for this experiment has a square cross- section with a side length of 31.75mm resulting in a cutoff frequency of approximately 5kHz (which corresponds to an acoustic wavelength of twice the side length [23]). The test I‘nicrophone is mounted in the plane wave tube at the same cross section as a B&K type 4938A 1/4" reference microphone with known manufacturer calibrated response. This configuration ensures that the microplmne under test will be subjected to equal acoustic pressure and phase as the reference microphone. The probe tip of the fiber-optic lever sensor is placed inside the plane wave tube and aimed at the center of the membrane. Fine positioning of the probe is performed using a translation stage with 0.2 [L111 precision. A schematic drawing of the plane wave tube showing positioning of the test microphone. reference 111icrophone. and optical sensor is shown in Figure 2.5. It. is noted here that this "external” placement of the optical sensor is employed for convenience. and is suitable for testing of prototypes. However. in practical microphones. the optical fibers would be integrated into the microphones capsule. and aimed at the back of the. men’ibrane. Top View s B&K § Reference § . \ Microphone § . . § Side View \ . To Syringe § Micrometer B &K § Traverse Table Reference \ . . § [[1 3 _1crophone _ a _ Fibre- L—’ “‘ Prototype Optic ‘ Capsule Lever H To Pressure " Gage F ibre-Optic Lever WWW>WWWW 6" Speaker Figure 2.5: Schematic diagram of the plane wave tube calibration setup. For the acoustic calibration. a Hewlett-Packard 33120A function generator is used to supply white noise signal to a Dayton R815OS—8. 40 Watt speaker that. is powered by Hafler P1000, 110 Watt amplifier. The sound produced by the speaker excites the plane wave tube. The output signal from the B&K reference microphone and the fiber-optic lever sensor are recorded at a sampling rate of 50kHz for a total of 4,096,000 21 samples. The. same analysis procedure described above for obtaining the electrical- actuation response is applied to these signals to obtain the acoustic response, with the additional I.)rovisi0n that the phase response of the reference 111icrophone must be subtracted to yield absolute phase. Two acoustic calibration tests are conducted. First, the acoustic response of the prototype microphone is measured in open-loop operation to verify that its response conforms to that predicted by the parameters identified in electrical actuation. Next. the 111ic1‘()1.)hone system is operated in closed- loop mode. and the response is 111easured. Observation of the. frequency response in open- and closed-lotn) operation is used to validate the theoretical model. 2.4 Results and Discussion Initially, a. set of tests were perfm'med to charau'terixe the change in electrical actu- ation sensitivity (Sud) for variz-itions in internal static pressurization. The results of these tests are shown in Figure 2.6. The figure shows two plots: one depicts the. change in SW, with pressure (top plot). and the other gives the corresponding membranes resonance frequency f0 (bottom plot). The latter is included since it is anticipated that. the increase in internal pressure will increase the membranes tension. and hence the resonance frecpwncy as well. As mentioned luxuriously. it is expected that the induced curvature of the membrane will result. in an increase in the actu- ation sensitivity. obtained here from the a\.-'erage membrane (lis1,)lace1nent per unit applied voltage at frequencies well below resonance. This is consistent with the data in Figure 5 which shows significant increase in actuz‘ition sensitivity, from 1.87 nm / V for the un—pressurized ease, up to 16.8 nm/ V at 3.2kPa. Similarly. the fundamental resonance frequency is raised from 3.61 kHz at OkPa to 4.06 kHz at 3.2kPa. [\D [\J 7 o l 151 0 0 l A I ° | a l O ’ E, 10.“ o l ‘6 l O (U a) o l 5‘“ o 1F o O: . i a s 0 1 2 3 4 Internal Static Pressure (kPa) 4.2--——*~——~—~~— we 7 a 4.1l « 0 4i 0 A O E 3.9l o 5, . .._c 3.8'~ 0 3.7; o o * O 3.6T ° 3.5-—— . ‘ O 1 2 3 4 Internal Static Pressure (kPa) Figure 2.6: Electrical response of PVDF meml’n'ane for variation of internal static pressurization: (top) actuation sensitivity of PVDF membrane: (bottom) fundamen- tal resonance frequtmcy of PVDF membrane. From the static. pressurization results. an internal static pressure of 1.5kPa is chosen for further testing as this provides the desired increase in actuation sensitivity without significantly affecting the characteristics of the membrane from its l111-[.)1‘ess1_1rized 23 condition. An electrical calibration of the membrane for the selected internal pressure is shown in Figure 2.7 across a 100Hz-25kHz bandwidth. The calibration is compared to the analytical membrane model given by equation (2.8). Good agreement is seen between the predicted and measured membranes response. This indicates that the model employed is effective in capturing the resonant peaks of the membrane. though there is some deviation that is believed to be caused by acoustic reflections inside the PVVT (note. that the electrical (v-ilibration is crmducted while the 111icrophone is mounted in the PVV'T‘ in order to maintain the same conditions for both electrical and acoustic calibrations). Open—loop parameters identified using the electrical caliln'ation in Figure 2.7 are given in Table 2.2. where the stiffness and damping terms refer to those identified for the fundamental resonant mode of the 111embrane. Table 2.2: I\licrophone parameters for open-loop operation Parameter Symbol Value Unit — Mass H _—“ WT ill 0.049 kg/ 112.2 Damping ('0 1.5.9 [’0 - s/m. Stiffness K0 26.2 - 10h PU/HI. Damping Ratio (0 7.42 - 10"3 Natural Frequency f0 3.61 HI: .\licropho11e Sensitivity SJ] 3.58 7111/ Pa. After the system pan-uneters are identified using electrical actuation. acoustic testing is performed using the PVVT. Initially. the microphone is tested in open-loop mode to verify the analytical model and to prmide a base-line reference for comparison to closed-loop mode. Then. the closed-loop system‘s DC attenuation and complex pole location are specified. Follmving the prm‘ediu‘e outlined at the end of section 2.2. a MATLAB design program is used to calculate the compensator transfer function re- quired to achieve the user specified parz'mieters. and outputs corresponding values for the phase-lead circuit, (shown in Figure 2.4). Figures 2.8 and 2.9 show the fre - 4 E l 33" -140: m l .0 . ; —160~ 3i : gf-—180* 1 —2ool - ~ .--- . . . e --. 102 103 104 Frequency (Hz) ssoer—u - vevv . ‘ —Calibrated Response; 180g '--- Modeled Response J ES (3 — a) B an —180‘ g .C “- —360~ —540* —720 - ._ 1o2 103 Frequency (Hz) Figure 2.7: Frequency response of PVDF membrane identified using electrical ac- tuation with 1.5kPa internal pressurization: (top) Actuation sensitivity of PVDF membrane; (bottom) Phase response of PVDF membrane of the same microphone capsule. The frequency response predicted by the analytical model for each implementation is also shown on the same plot over a frequency range exceeding the cutoff frequency of the PWT. 25 The implementation shown in Figure 2.8 targets an increase in resonant frequency and damping with ()dB DC attenuatitm (i.e. without affecting the 111icroph(_)ne‘s sensitivity). As seen from the figure. the fundamental resonant frequency has been increased from 3.61kHz in the open—loop system to the design frequency of 5.1kHz in the cl(.)sed—loor;) system. corresptmding to a 41% increase in bandwidth as a result of feedback. Most important. however. is the effectiveness of the analytical model in predicting the closed—loop response. which is a primary aim of the current work with potential applications in "self-calibrz-ition" or "self-matching" of sensor 1.)aramet(—‘rs in lwamforming arrays. as well as for tuning the microphones response to match the needs of different applications (eg. full-scale versus 1/4-model scale airframe noise testing). The second result. shown in Figure 2.9. is for a design that specifies 3dB DC atten- uation in addition to correspomling increase in resmiant frequency. An increase of DC attenuation. or "stiffening“ of the membrane. is desirable if the 111icrophone is to be used for measurement of high SPL as it would result in improved linearity of the SPHSOI‘ . Finally. the sensors linearity and noise floor were determined for open-loop in addi— tion to closed-loop oI.)eration (where the latter was operated at conditions similar to those of Figure 2.9). A sinusoidal sound at lkHz was employed to drive the P\\'T. Power spectrum analysis was then used to measure the rms voltage output of the pro- totype and reference microphone at lkHz for different sound levels. For each sound level. 25 averages were taken with a sampling frequency of 50kHz and a bin width of 1H2 to avoid spectral leakage (since the 1 kHz bin in the power spectrum analysis is an integer multiple of the bin width). The results are shown in Figure 2.10. where the rms output of the prototype sensor is plotted versus the sound pressure level 26 Acoustic Sensitivity (dB RE: 1 V/Pa) Microphone Phase (deg) N O —— Open—Loop- va r O ~ — Closed—Loop (Calibrated) '- ' - ' Closed—Loop (Model) (Calibrate ) - - Open—Loop (Model) l l J -20: _4o~ —60~ -80 ~ * 102 103 104 Frequency (Hz) 270 » . ’-- . . ll — Open—Loop (Calibrated) g 180 ) — - Open—Loop (Model) l — Closed—Loop (Calibrated); 90 " ' ' '9£§9<1-_LOOP_ {Egg}- 3 100 . 0531 - (D p 54-33%} 8 ,,.~‘ifir.e J t .3 E1” 0 “U 2 . .fi‘fi H 3 _2 ; (314 .9- 10 (r s “ 3 3 ’ . 1‘: £1 0 f i ‘4 L . . J 1 A . O 20 4O 60 80 100 SPL (dB Re: 20uPa) Figure 2.10: Linearity and noise floor for open— and closed-loop opr—aration. For both chimed-loop implementations here. the effective cont rollability of the micro- phones. for example using higher values of K], or Kd (see equation (2.9)) than those employed for the cases dennmstrated here. is limited by instability that arises as an effect of higher order resonances. This can be considered to be a. consequence of the relative simplicity of the phase-lead controller conmared to the membrane model with its multiple resonances. Thus. it may be possible to achieve greater increases in closed-loop bandwidth or DC attenuation using more scmhisticz-ited control methods. Alternatively. the effect of the higher—order resonz-mces can be substantially dimin- 29 ished through the use of mechanical damping means (such as the perforz-rtions in the back-plate of condenser microphones). and / or the use of an optical sensor that mea- sures the average. rather than the central. displacement of the membrane. The latter helps in the sense that, unlike the furu'lamental resonance rrrode where the entire mem- brane is moving in phase. higher-order resonances involve nroverrrerrts where parts of the membrane are moving upwards while others are moving downwards. Thus. the average of this motion will be much smaller than the central displacement. and the irrflrre‘rr(1> ()f'lrigglreAr-()r(le3r IT‘S()IIEIII(1‘S ()Il tlreI()1)ti(uil S(‘IlS()f ()rrtlrirt yvill l)(> sirlrstzirrtizrlly' red uced . Chapter 3 A Feedback-Controlled Optical Microphone Incorporating a Michelson Interferometer In Chapter 2. a microphone was discussed that incorporated a filmr—optic lever dis- placement sensor for I‘neasurement of the deflection of the microphones membrane. The sensor was cmnmercially marmfactured and proved simple to use in the develop- ment. of a prototype microphone. However. a. microphmre prototype is desired with a frequency bandwidth that is wide enough to cover the entire human audible range of up to 20kHz. One effective method for increasing the bandwidth of a 111icrophone is to decrease the diameter of the membrane. In fact. assuming surface rrrass density and membrane tension to be constant. halving the diameter of a membrane will dou- ble the resonant frequency as the membrane stiffness ( Pa / m) is increased by a factor of four. For this purpose. a membrane prototype having a 6.3-5111111 diameter mem- brane was fabricated. For convenience. this prototype is physically integrated into the 31 plane wave tube to be used for acoustic calibration. Because of the inherent trade—off between stiffness of the microphone membrane and measurement bandwidth. it is necessary that the optical sensor used with this smaller prototype have a higher sen- sitivity and lower noise floor than the fiber-optic lever sensor. The sensor technology implemented in this study is the Michelson interferometer. 3. 1 Construction 3.1.1 Microphone Membrane To satisfy the desired smaller sensor size and higher bandwidth a 6.35mm diameter microphone membrane was fabricated. While the construction of the new prototype does share certain common clraracteristics with the version described in Chapter 2. there are some notable differemcs which will be described. Similar to the earlier prototype. the membrane is constructed from PVDF. in this case 28 pm thick uni-axial PVDF purchased from Measurement Specialtiesl. The film membrane is stretched and clamped between conductive electrodes. as done pre- viously. In the newer prototype. the bottom electrode is a copper insert that has been embedded in an acrylic base plate. as seen in Figure. 3.1. One notable difference in this design is that the high voltage copper electrode is isolated from the outside. which is important for safety purposes. A rubber O-ring is fitted around the copper electrode. which acts as a compliant surface providing friction to hold the membrane in place. The top electrode is an alurnirnun plate which has been attached to the acrylic plate using screws. This top electrode is electrically grounded. In order to 1http://www.meas-spec.com/downloads/Piezo_Film_Product_Guide.pdf 32 isolate the back side of the membrane from outside acoustic pressure. a second acrylic plate is attached using nuts to plug the back-chamber of the microphone. The prototype discussed in Chapter 2 was acoustically calibrated up to the plane wave tube cutoff frequency. which was approximately 5.3 kHz. Since a higher bandwidth is expected with the 6.35mm prototype. a PWT calibration setup was desired with a higher cutoff frequency. For this purpose. a channel was milled from acrylic with a side width of 7.9mm. When this channel is screwed to the plate upon which the microphone membrane is mounted. it forms a plane wave tube with a cutoff frequency of approximately 21 kHz. Top and side views of the prototype and plane wave tube calibrator are shown in Figure. 3.1 while a front view is shown in Figure 3.2. .. . 7.7553155}J£IT}73’E“'72LL' .‘thflLW-VXT’R l._-£..,"1€’,.~i~'.- .~-..‘- . . ' .7 a 12m~vggarmam~ er.ryztirr'e‘M-rahzay.wwonuserz-xflm "" — ‘ WW” Aluminum PVDF B+K Mp. Acrylic Plate Membrane * ‘ _ Channel - T T _ _ "r -- Tan. T T l T ' i Tl . . ‘7. l T i l T . . l: J , T ' _ '-" I‘ -- 1L- ll ‘- -_ . T-' _ . T- ls Acrylic Plate .{ ._ . g, (\x Copper Insert VI’Z Figure 3.1: Depiction of 6.35mm diameter membrane prototype. top: top view. bot- tom: side view. 33 B+K Mic Acrylic Channel PVDF Aluminum -E Membrane Plate \\ "Tl.niil V- Ill-l .Fl-in Coppc'r Insert. VPZ Figure 3.2: Front view depiction of 6.35mm diameter membrane prototype with acrylic channel (PW T) attached. 3.1.2 Michelson Interferometer The interferometer displacement sensor used here is implemented on an optical ta- ble. Though such implementation is not suitable for realizing compact. and practical microphones. it works well for the purposes of proof of concept and prototype char- acterization. Future integration of the interferometer in practical sensors can be accomplished using fiber optics. A schematic representation of the common Michel- son interferometer is shown in Figure 3.3. while a photograph is shown in Figure 3.4. The setup used for this experiment. uses a Uniphase Model 1135P He—Ne laser with an optical wavelength of 633nm and total output power of 20mVV. The polarized and collimated output from the laser initially passes through a A/4 plate to prevent reflected light from returning into the laser cavity. This beam then passes through a 50/50 beam-splitter (BS) where it is separated into signal and reference arms. The Signal arm is aimed at the. center of the microphone membrane and is reflected back 34 to the lirean‘r-splitter before being directed through a focusing lens to a ThorLabs DSllO photodetector. which has a sensitivity of 0.4 A/VV at the 633nm wavelength. The reference arm is reflected off a mirror that is mounted on a Inezoelectric stack (PZ h‘lirror). The two beams are combined at the photodetector where the measured optical intensity is a sinusoidal function of the difference in phase between the signal ‘dIld I'€f(‘I'(‘ll('9 ‘dl‘lllh‘. H Microphone Membrane A PZ M' ll‘l‘Ol‘ BS Lens PD U ’l: 3 .11.. A/4 He-Ne Laser Figure 3.3: Depiction of the optical setup for the Michelson interferometer. The interferometer's plrotodetector outputs current in 1,)r'oportion to the incident op- tical power. Thus. in order to digitally record this output. it must first be converted to voltage. This is accorrrplished using the "Gain Stage" circuit is shown in Figure 3.6. The photodetector is connected to an input inverting-aunplifier through resistor R1 . The frequency bandwidth of the optical sensor is determined from the value of [1’] 35 icro - hone Figure 3.4: Photograph of the optical setup for the Michelson interferometer (Note the placement of a CCD camera and mirrors which aid in alignment of the laser beam with the center of the microphone membrane). and the diode capacitance C'p D of the photodetector (specifically. the time constant of the photodetector is given by Tp D = I? 1C p D). The output voltage of the inverting amplifier is determined by the current output of the photodetector and the value of the feedback resistor R2 (i.e. VpD = —IPDR‘2). The second op-amp (operational amplifier) in the circuit is a unitv gain inverting amplifier. the output of which is AC coupled with a low frequency cutoff defined bv F I and R5. The voltage ('1 is the microphone output signal and is also the signal fed to the phase-lead compensator. The sensitivity of the interferometer used for the results reported in this chapter was 39 mV/nm at the operating set point (see Figure 3.5) for definition of the operating Point ) . 3 V V 7 TV 1 ‘ Slope = 39 mV/nm 2 - f 2, D O .«3 o» G.) E 9 .92 -1*' (D E -2- x/ _3 . / . . 0 1 00 200 300 400 500 600 Mirror Displacement (nm) Figure 3.5: Intefermneter output relative to mirror displacement. An observation made (hiring the initial setup of the .\Iichelson interferometer is that there was prominent low frequency (sub 1H2) drift that results in the interferometer output signal not maintaining its ('lesired DC set-point and linear operating range. To compensate for this drift. a feedback section is included in the interferometer circuit. (see Figure. 3.6). At the input op-amp of this feedback section, the voltage output from the gain stage is compared to a fixed voltage set by the potentiometer 1736;. The feedback gain is set by the resistance of the trim-pot BC. This output. is then fed to a summation amplifier where a DC bias voltage is added with a value defined by VDC‘ = 12 - Rg/ Rpp. The output is then low—pass filtered using a R—C passive filter with a. cutoff of approximately IHZ at U; and fed to a ThorLabs model MDT691 piezo amplifier. This amplified output is supplied to the piezo mirror in the reference arm of the interferometer. thus maintaining the output of the interferometer at a. constant DC set-point in the sub-1H2 frequency band. A point. of note is that a similar system may be used to extend the interferometers linear range. l’iowever. this would require a piezo stack with a resonant frequency that is much greater than the microphone 37 prototype currently used. Gain Stage Iii 12 138% ,,.,r i -+;2V’ ' _ "*; . ;--- --_v2 ' .. — 12V * C2 Psct ’i '3 Figure 3.6: Schematic diagrz-mi of interfermneter circuit. with fee(_'ll.)a.ck section. 3.1.3 Serial Interfaced Controller In addition to the use of a new optical sensor, the design of the compensator circuit was modified to improve the systems operatitm for the [)111‘1_)(“)S€ of scalability to beamforming array applications. These modifications allow for all of the phase-lead compensator parameters to be adjusted using a serial interface. which in this case is implemented using the digital output of a. National Instruments PC1-6024E general purpose data acquisition (DAQ) board. The added provision allowing to set the parameters of the controller via a computer, when coupled with the open-loop system identification/closed-loop modeling demonstrated in Chapter ‘2 can be used to fully automate the process of tuning the response of microphones in a large array to a desired (“self—matched") response. 38 .> 9 4 R1) , .D‘ RP? “f 0.4; ¢ . ~ a [\p_().\' ‘ I" ‘SO ____ Rfsum C' FTC ' ' am- . R. - . _1__Rdv . “be Du. on . -. D a.” . ~ I Of‘tg 7+ . ‘. , [Minx —- "”96 7 “ fhaa Utes! _ . . . O Rec 1‘2V ‘- Figure 3.7: Schematic diagram of plu—rse—leat’l controller circuit. A schematic of the re-designed com1')ensator circuit is shown in Figure 3.7. The first design modification of the circuit is the replacement of the precision trim-pots used previously with 3—wire serial potent iometers of the RICP42XXX variety Inainifactured by MicroChip Technologies? These are packaged as 14-pin DIP integrated circuits with two on-chip potent iometers. Each of these potentiometers has 256 incremental resistance values. In the conmensator circuit. the two on-board potentiometers are connected in [7)arallel. resulting in a. total of ‘216 possible resistance values. In the micropl‘lone control application the available resistance values are placed in order. and a value is chosen based on a calculation of minimum error from the user's input specifications. The three potentiometers. represented by Hp. Rd. and RC are wired in a daisy chain configuration. as depicted in Figure 3.8. This configuration allows for the resistance values of a large number of serial potentiometer chips to be controlled 2http://wwl.microchip.com/downloads/en/DeviceDoc/l1195C.pdf 39 by only 3 wires. For each chip. a 16 bit serial signal is sent from the DAQ board. where the first 8 bits ('letermines which 1*)otentimneter will be controlled, while the second 8 bits determines the incremental resistance. The chips MCP42050. MCP42100. and MCP42010 corresrmnd to potentiometers with maximum resistance values of SOkQ, 100M? and 10“) which have been chosen because they allow for the controller to produce the necessary proportional gain. derivative gain. and time constant used in control of the microphone. cs : : v+ SC‘KI : 80 SI : ' SHDN (:Nl)‘ : RS I’Bl : I’Bt) P\\'l ‘ . I’\\'H PA 1 ' FAI l 5V Hp Rd Rc 9 9 o ,,, W ,9 o 9 ~ W 9 79 v MCP42050 l\ICP421()() l\ICP4‘2()1() Figure 3.8: Schematic diagram of serial potentiometer interface. The second design modificat ion is the addition of a N-channel MOSFET switching interface. allowing for fast switchng between open- and closed-loop operation. This is done using two separate MOSFETs. one each for the 1')1'()poi'tional gain and derivative gain sections of the circuit. The drain is connected to the negative input of the op-amp while the source connects to grormd. Switching of the proportional and derivative 40 gain sections is controlled by digital connectitms at Kp.()N and 1"d.0.9'\' res1*)ectively. \Vllell both MOSFETS are switched on. the input to the gain and derivative sections is forced to zero and hence. no feedback signal is generated resulting in open-loop orxzration. On the other hand. when one or none of the MOSFETS is turned on. proportional only. derivative only (up to a user-set cut—off frequency). or phase~lead feedback control is implemented. Finally. the circuit has a separate input. west. for function generator signals used in electrical actuation of the PVDF membrane. 3.2 Experimental Procedure The experimental procedure used is largely identical to that used in Chapter 2. with various modifications that arise from prototype and compensator design modifica- tions. Similar to the 1')revious work. electrical actuation is used to determine the transfer function of the membrane across a wide frequency bandwidth. Acoustic calibration is used to verify that the frequency response. due to acoustic. excitation matches that determined through electrical actuation. In tests performed where the microphone membrane is electrically actuated. there are two notable changes in experimental procedure. The first. as mentioned previously. is the addition of the was; input. to the controller circuit. Previously. the output of the function generator was connected directly to the input of the piezo driver. In this new n‘iodification. the function generator connects to a unity gain inverting amplifier at the output of the controller. With this and the other previously described modifications to the control circuit. the microphone can be calibrated in either open- or closed-loop operation without replacing any cable connections. This is expected to provide convenience in a large array application where efficiency in the calibratitm 41 process is essential. Second. there were two considerations that had to be taken into account when the system was operated with the Michelson interferorneter. requiring modification to the calibration process: (1) at resonance the electrical actuation response can eas- ily becon‘ie non-linear due to the small linear range of the Michelson interferometer (approximately 7911111 compared to 28/1111 for the fiber-optic lever sensor) requiring the function generator output to be set to a low voltage amplitude. and (2) when operating at this low voltage anmlitude. the signal-to-noise ratio at low frequency is greatly sacrificed due to much lower sensitivity in this frequency region. A convenient method was developed that allows for accurate calibration of the mem— branes response despite the trade-off between linearity at rescmance at signal-to-noise ratio at low frequency. This method exploits the fact that for a long duration har- monic sweep (i.e. 30s) over a wide frequency band (typically extending from 10Hz to 50kHz). the frequency spectrum of the actuation signal for any single record with short duration (i.e. 30ms) will be dmninated by a. small number of frequency bins located in the vicinity of the function generator frequency. Thus. a. modified cali- brat ion 1')1‘(.)gran.1 was developed using LalNiew where after a sensitivity si.)ectrum is acquired for a single record. only the seven entries nearest the peak in the generator signal are appended to an output matrix. Once the program reaches its completion. this output matrix is sorted by frequency. and entries at it‘lentical frequency bins are averaged and output to a text file. This method is somewhat analogous to tests where measurements are done at a. single fixed frequency. one at a time. while avoiding the inconvenience and lengthy duration of such tests. The method also proves highly ef- fective at maintaining a high signal-to—noise ratio at low excitation amplitudes. 42 3.3 Results and Discussion 3.3.1 Electrical Actuation Electrical actuation was performed on the. new membrane using the methodology described above. with the results for electrical sensitivity shown in Figure 3.9. Using the new Utest input in the controller (see Figure 3.7). the response was tested in both open- and closed—loop operation. _130 D -D--D--. . ......, . D- ——Open-Loop —140~ -— - Closed—Loop — E? —15o~ E f: —160— (D m an -170- $1 €§ —180: , / \ . act /, ,§ S‘ f c ; —190~ V *J —2oo~ _210 r . L 1 . fr.1 . 1 1 #94; 1o2 103 104 Frequency (Hz) Figure 3.9: Frequency response of 6.35mm membrane with Michelson interferometer. measured using electrical actuation. The fundamental resonant frequency of the membrane under test was determined from electrical actuation to be 11.6kHz. It can be seen that. the response of the fundamental 43 mode has the characteristics seen previously with the earlier prototype in Chapter 2. However. the higher order resonant peaks are of much greater magnitude than those seen previously for the 12.7mm prototype (see Figure 2.7). and are in some. cases at. frequencies iruitcmsistent with those predicted for axi-symmetric modes. This renders the system identification 111ethodology described by Equations (2.4)-(2.8) ineffective for the higher order modes. A possible explanation for this behavior is that the forces induced by electrical actuation of the memln'ane are ctmcentrated at its edges due to the clamping 111ethod holding the 111e111brane essentially flat. In contrast. the prototype tested in Chapter 2 had curvature induced by internal pressurization and this would cause electrically induced forces to be near uniformly distributed across the entire surface of the membrane. More important to this rest-)arch is the effect that these large magnitude high order resonant peaks have on controllability. In this experiment. the gain settings 011 the controller were irufreasetl until the system was near its stability limit. In the results. there is negligible DC attenuation resulting from the feedback control. while the resonant frequency has been increased to 12.2kHz in closed-loop operation. a 5% increase. A Iiiagnified plot depicting the change in resonant frequency in closed- loop operation can be seen in Figure 3.10. This is clearly insufficient. for the current prototylm to satisfy the demand for a "self-matching” microphone array. Still. with certain design modifications (see Chapter 4) the smaller diameter prototypes hold promise. 3.3.2 Acoustic Calibration Acoustic calibration was performed in addition to electrical actuation to verify the effectiveness of the latter as a calil'n'ation method. A plot of sensitivity measured up 44 —155 ——Open—Loop 4- —-Closed-Loop -160- - g / .r- E —165L 1/ q“ d g // / \\ % —17or // X . . Z / / ‘ 3. —175~ / ’ 8 . :1_: , —180”// .. / f —185 . . i 1 1.1 1.2 1.3 1.4 Frequency (Hz) x 104 Figure 3.10: Frequency response of 635111111 membrane with Michelson interferom- eter. measured using electrical actuation. 111ag11ified to show fretmencies near the fundamental resonance. to the plane. wave tube cutoff frequency of 21kHz is shown in Figure 3.11. The low frequency sensitivity of the 111icrol.)h(_)ne was measured at 3kHz and determined to be 177 mV/ Pa. It can be seen in the plot that below 2kHz the calibration does not adhere to the flat profile expected. It is possible that this results from the acrylic channel that forms the plane wave tube being significantly shorter (15 cm) than the one used previously. resulting in an 1.11'1predictable acoustic field at low frequency. However. the frequencies of interest are near the fundan‘iental resonant peak. where it can be observed that the behavior is much the same as that of the electrical actuaticm. A second test was performed to characterize the sensors linearity. Based on the 00 O 1 I T T I 1 T r r r I —— Open—Loop - - - Closed—Loop N O _L O O / Acoustic Sensitivity (dB Re: 1 V/Pa) 1 ES ./’ / .fl / -20 J t D/ \ l l \‘~/ / U ( , —30 r —40 1 _50 . 1 1 1 1 1 1 1 1 1o2 103 Frequency (Hz) Figure 3.11: Frequency response of 635111111 111embrane with h‘Iichelson interferometer, measured using acoustic calibration in a. plane wave tube. operating principle of the interferometer. the output voltage is expected to vary si- nusoidally with a period equal to half the optical wavelength with respect to target deflection. The feedback circuit described previously is designed to force the DC setpoint of the interferometer to the highest sensitivity operating region. When the membranes vibrational amplitude becomes very large the voltage output begins to distort in a. manner similar to saturation. To demonstrate the effects of linearity and determine the dynamic range of the sensor. acoustic testing was performed in the plane wave tube setup with the prototype microphone operating in open-loop mode. A harmonic tone was supplied by the function generator to an amplifier and speaker. For each data point an average of ~16 16 spectra was obtained using a sample rate of 50kHz and bin width of 1H2. Data were acquired with acoustic tones generated at 3kHz as well as 12kHz in order to differentiate the performance of the sensor in the low frequency "flat.” region of its response from its performance near resonance. The results are reported in Figure 3.12, where rms voltage of the prototype sensor is plotted versus the sound pressure level (SPL) measured by the reference 111icrophone. A linear trend-line has been fit to the data. corresponding to sensitivity at that frequency. The sensitivities calculated from the slope of these trend—lines were 177111V/ Pa at 3kHz and 1930111V/ Pa at 12kHz, significantly higher than the sensitivity of the previous prototype using the fiber-optic lever sensor. Deviations from the trend-line at high sound pressure levels indicate the onset of non-linearity. It can be observed from Figure 3.12 that for a 3kHz tone the data points begin to deviate from the linear fit as SPL aprn'oaches 110dB (6.3 Pa). The measured values at low SPL for the prototype microphone closely track the linear fit. indicating that the noise floor for the microplmne is very low. perhaps comparable to, or better than that of the BSJK reference 111icrophone. For the 12kHz tone the non-linearity associated with the h-Iichelson interferometer becomes more clearly apparent at lower SPL. The output of the prototype begins to deviate from the linear fit at approximately 90dB (0.63 Pa). before dropping sharply. It was observed at this point that odd-numbered harmonic overtones begin to (‘lominate the signal. This becomes a, matter of practical i11‘1portance when performing "white noise" acoustic calibra—rtirm where it is important to operate the speaker at a high enough level to maximize signal-to—noise without distortion. The smaller linear range of the .\Iichelson interferometer is an important distinction to be made in comparison to the fiber-optic lever sensor. However. it is important to note that. this non-linearity is for the open-loop operation. In closed- loop operation with strong control authority. the sensors linearity should be enhanced 47 10 I I r w —G— 3kHz +12kHz g 102 . ~ 251 / g / 0:) 1O0 . W .8 Q. [A / O / g 10‘2 Vii/26% _ / _ /// /g/ 10'4 c/g . . ' . 4O 60 80 100 120 SPL (dB Re: ZOuPA) Figure 3.12: Linearity of 635111111 111embrane with Michelson interfermneter. measured using acoustic calibration in plane wave tube at 3kHz and 12kHz. subst ant ially. 3.3.3 Comparison of Michelson Interferometer to Fiber-Optic Lever Sensor In con’iparing the performance of the Michelson interferometer to the fiber-optic lever displacement sensor. important trade-offs must be made in regards to sensitivity, res- olution. linear range. and frequency bandwidth. ' "’alues for these parameters for both sensors are given in Table 3.1. where the sensitivity of the fiber-optic lever sensor and all parameters for the Michelson interferometer are experimentally calibrated. while 48 res(,)lution. linear range. and frequency bandwidth of the fiber-optic, lever sensor are taken from its user 111anual. The repm'ted bandwidth of the Michelson interferometer is calculated from the photodetector capacitance and input resistance of the circuit (i.e. Bandwidth 2 l/(‘27r11’1('p])). while the dynamic range of the interferometer is calculated as /\/8 where /\ Z63311111. Table 3.1: Comparison of sensor parameters between fiber-optic lever and Michelson interferonieter. i Sensor Type {SEES—111711?“ Resolution Linear Range Bandwidtlfl , Filt1e1'-O[.)tic. Lever ‘ 86111V/1f1—1i—hifii36 11111 2311111 20kHz E Michelson Interferometer 5 39111V/nm NR 7911111 8MH7. The clearest advantage for using the Michelson interferometer over the commercial fiber-optic lever is the significant increase in sensitivity. The Michelson interfermneter and asst‘x'iated circuitry have shown an increase in sensitivity by a factor of about 450 over the fiber—optic lever sensor. The noise floor is also expected to be a significantly lower. though this is not reported at this time due to the difficulties in achieving a "silent“ experimental setup. The trade-off to the increased sensitixi'ity of the Michelson interferometcr is its much smaller (.lynamic range. Another comment to be made when comparing the two sensors is regarding sim- plicity of use. The fiber-optic lever is very simple to operate, as it requires only a fixture and traverse table for aiming it at a target. More permanent designs can be envisioned where the fiber probe is threaded and attached (.lirectly to the 111icro- phone capsule. The current design of the Michelson interferometer requires careful alignment when setting up. and requires additional electrical circuitry for operation. However. alignment problems could be overcome if future sensors were packaged using fiber-opt ics. 49 Chapter 4 Theoretical and Experimental Evaluation of Proposed Design Improvements In Chapters ‘2 and 3 it was ol_)ser\-'ed from calibration data that several high-order 111embrane resonance modes are excited (luring electrical actuation. These modes have been determined to be a 1')1'i1nary cause of instability that occurs in closed- loop operation. While. the data presented indicates the current design is practical for “self-caliln‘ation" and “self-matching" of 111icroph(_)nes in an array application. it leaves room for improvement in terms of controllability. For this purpose, two ba- sic modifications are suggested. (1) development of an optical sensor that averages displacement over a large fraction of the area of the microphone 111embrane, and (2) modification of the 111echanical 1‘)arameters of the 111icrophone capsule. specifi- cally adding a perforated back-plate to increase damping. Justification for these two methods are given in the sections below. 4.1 Displacement Averaging Optical Sensor As noted previously. the 111icrophone’s (men-loop dynamics can be modeled using the linear wave equation for a stretched thin 111embrane. The wave equation gives rise to an infinite number of axisymmetric and 11(‘111—axisummetric modes of 111embrane vibration. For the case where the optical sensor measures (lisplacemmlt of a point at the center of the 111embr1—1ne. it was determined that the 111embrane could be modeled as a sunnnation of second order systems. with each system representing the transfer function for the correspmn’ling axi-symmetric mode. Non-axisymmetric modes are. neglected. as they have zero magnitude at r = 0. A drawbz-ick of this 111ethod is that the axi—synnnetric modes are prominent in the center measurement and result in instability during closed-loop opera-ition. The proposed alternative is to incorptin'ate an optical sensor that measures the average (lis1.)lac(—‘ment of the 111emln‘ane over a large portion of its area. It is shown in [22] that the axi—synnnetric modes of a circular membrane clamped at its edges take. the shape of Bessel functions of the zeroth order. A plot depicting these mode shapes for the fundamental resonant mode. in addition to the first through third modes is shown in Figure 4.1. The shapes of the higher order resonant modes are notable for the fact that there are regions on the membrz-ine that are 1800 out of phase with the center of the 111embrane. The result is that the displacement for these modes averaged over the surface of the 111embrane is significantly smaller than the displacement measured at the cent er. Mathmnatical analysis can be employed to prove the attenuation of these higher order modes by use of a displacermmt averaging sensor. The average displacement fh relative to rip. 3“,.(1/36. over the area. of the 111embrane for the m mode can be —Mode 0 - - ~Mode1 --'- Mode 2 ------- Mode 3 0.5 z(r)/z —O.5 ‘ ‘ t —1 -O.5 O 0.5 1 Figure 4.1: Axi-symmetric mode shapes of a vibrating 111embrane. calculated by equation (4.1). where (IS/(l. is the optical sensor radius as a fraction of the 111embrane radius. .10 is the bessel function of the zeroth order. 11‘," is the H1 wavenumber associated with the m mode. and r and f) are polar coordinates in the plane of the 111embrane. :(I I“, 1 277 (13 /(1. - i = W [0 /o -111(A'mrll‘drdf9 (4.1) ~(‘ 11 3 By solving equation (4.1) with (Is/(I. = 1 the average relative displacement. magni- tudes of the correspmlding modes over the entire membrane surface is known. The magnitude of this displacement for several of the modes is listed in Table 4.1 and is plotted in Figure 4.2. C}! to Table 4.1: Average relative displacement of 111embrane vibrational modes over the entire surface of the memln'ane. l Model guy/:6 l l 0 i 0.4311 3. 1 ‘ 01234 i 2 0.0627 1 3 - c.0394 ‘ 4 0.0277 .5 -0.0‘208 6 0.0163 7 00133 _ 8 0.0111 J 0.5 l T T T T f i I I O 0.4“ 1 0.3— .1 $0 0.2— ‘ C) 1?: N 0.1 ' ~ T ‘P e e —O.‘| ' 7 —o.2 ..... 1111 012 3 4 5 6 7 8 Mode Number Figure 4.2: Average relative displacement of 111embrane \-'il.)1'atio11al modes over the entire surface of the 111embrane. F urther, this 111ethodology can be extended to design for the optimal probe diameter to maximize attenuation of a particular mode. By selecting as such that 0 < (1.3/a < 1. average displacement. for optical sensors that are a fraction of the total 111embrane r 03 radius can be calculated. It can be shown using equation 4.1 that for certain values of the averaging radius ((13). which are a fraction of the 111icrophone meml'n'ane diameter, individual modes can in fact be cancelled completely (for example. at (1.3/a. = 0.69 the average displacement. of mode 1 is 0). The n'iagnitudes of the average displacement of modes 0-3 for variation in relative probe diameter are. shown in Figure 4.3. Note that as the optical sensor radius approaches the radius of the 111embrane the averaged displacements converge to the values given in Table 4.1 and Figure 4.2. 1 "$5 1 f 1 I \ —Mode 0 - - - - Mode 1 0.8- \_\ \\ ._._ Mode 2 _ '\ \ """"" Modes . \ -_ \ \ .\ \ N” 0.6t ,\ \\ \g, '\ \ N:u \ \\ 0.4- \ \ 4 \ \ .\ \ ' \ \ 0.2— \ \\ - \ /,-\—\.\\ ,”'-“ \ / \ fix," ’__ 1 0 1 1‘\./ l,-'\\/ \:\ ./ I ..... aS/a Figure 4.3: Relative average displacement of membrane as a function of the sensor probe diameter. To demtmstrate the value of using a displacement averaging sensor. the 111agnitudes of average displacement over the area of the optical sensor. illustrated by Figure 4.3. are used to multii1‘1ly the second—order transfer function of their 1‘es1,)ecti\4'e modes in the memln'ane's transfer function (see equation (2.8)). in this example using 111embrane 54 parameters calculated from the prototype used in Chapter 2. For this study. two different sensor sizes were chosen. First, the ratio of (rs/a = 0.37 was chosen. as this corresponds to an optical sensor of 476111111 diameter (which is available commercially; see end of this section) being used for measurement of the 12.7mm prototype capsule. Second. the ratio of (1,1,. / a. = 0.69 was chosen. as this apI_)ears to be an optimal case due to the 2:111ticipated complete cancellatiml of mode 1. Plots of the theoretical frequency response of the open-loop for these two sensor diameters are shown in Figures 4.4 and 4.5. where the sensitivity has been 111,)1'1nalized with respect to the theoretical DC response. Clearly. in both cases controllability would be improved by an increase in gain 111argin resulting from the reduction in magnitude of higher modes. especially in the optimal case where (1.3/a. = 0.69. Also. the phase behavior of the sensor with (Is/(l. = 0.69 should be noted as it appears to asymptote to 1800 at. high frequency. compared with the center 111easurement where there is a 1800 phase transition assm-iated with each resonant peak. As an example of sensors currently available connnercially that measure average dis- placement over an area larger than the. fil'1er-optic lever currently in use. the reader is reffered to models 111a11ufactured by Philtecl. In particular. the Model D169 has a probe diameter of 476111111 with a sensitivity of 40m 1711.111. and 100Hz resolution of 0008/1171. The perfcn'mance of this sensor is comparable to the Model D20 e111ployed here. while having the desired larger diameter. lhttp://www.philtec.com/OQGuideJuly_13.pdf 55 40l t . - . . . .. 1 a i —Center Measurement a 'f._.-.a/a=o.37 £1 .1 S a 20* E a C 6 0. '0 i (D i Q i - (U . r E —20 X11 .1 5 '1 .'\. Z i 1" \ i “ —4o! 1 1 .1.. ‘+ ‘ ** 11 “ J‘ 102 103 104 Frequency(Hz) 'i—Center Measurement 180~l ._.-.aS/a=0.37 i a of a) 3 c1) —180* (D (U .C CL -360r —540% —720 ~ — --.-.1 1o2 103 Frequency(Hz) Figure 4.4: Theoretical frequency response of the open-loop when measuring the membrane deflection at its center (solid line) compared to when using an optical sensor with as/a. 20.37 56 40q__;' .. st. - y ' —Center Measurement 5 31.-.-.a /a=0.69 '3 ll 3 2: 20* E C : e 0e '0 (D 1:1 Tu . E -20~ 5 Z . _40__1 .m. L1. . - . .- 1m 102 103 1o4 Frequency(Hz) l l —Center Measurement 1801y—.—-aS/a=0.69 7 a O (D E a) —180* U) (U .C 0- _350. —540~ —720 * *4 ‘ ***“ 1o2 103 Frequency(Hz) Figure 4.5: Theoretical frequency response of the open-loop when 111easuring the 111embrane deflection at its center (solid line) compared to when using an optical sensor with (1.3/(1. =0.69 57 4.2 Perforated Back-Plate As seen from calibration results. the n'1ic1‘111phcn‘1e prototype tested had very low damp— ing ((20006 for the fundamental mode) resulting in very sharp peaks for each of the resonant modes. An increase in available gain margin and general improvements in cont rollability are expected if a 111echanical damping provision is added to future pro- totype capsules. This would be achieved using a perforated back-plate, similar to what is common in commercial condenser 111icr1'1pl1ones. A 111ethod for analytical design of a perforated lmck-plate is discussed in [‘25]. Equa- tions (4.3)—(4.6). which are taken from this reference. describe the back-chamber pres— sure which resists the membrane motion. These equations are based on the electrical analogy of the "air mass" oscillation through holes in the back-plate. The equivalent circuit for the analogy is shown in Figure 4.6. In the circuit. each hole is represented by an inductance in series with a. resistance. The inductance models the inertia of the air inside the hole. and the resistance represents dissipative effects analagous to damping. The lmck-chamber behind the back-plate acts as a. compliance element. and hence is modeled as an electrical capacitance. Using this electrical circuit model, the pressure drop across hole k can be calculated as follows: (1 pk = Uka + Z UkZ(' (4.2) A‘zl where ZA. is the acoustic impedance of the A” hole. 11k. the acoustic velocity. is equivalent to the electrical current. Z(jv is the acoustic impedance of the back-chamber and 22:1 (1.1. is equivalent. to the sum of all currents passing through the inductance- resistance branches 1‘e1_)resenting holes in the back—plate. Equation (4.2) can be written 58 in matrix form to represent the pressure drop for all holes in the back-plate as given by equations (4.3) and (4.4). Pb = ZbUb (4.3) _ ._ l - 1 pl “1 P2 “‘2 Pl) _ ("b ‘— Pq _l _ Uq _. (4.4) 21 -i- ZC‘ Z(' Z(' Z( Z(‘ 22 + Z(' Z 2,. = C Zq_1 + Z(j,' Z(.‘ ZC - - - ZC' Zq + 2C _J The back—chamber impedance can be coInputed using 9 ’7 ‘1' 1‘("-"~ ’ Jw' 'l‘b where e, is the specific heat ratio for air. pg is air density. of is the isothermal speed of sound through air and Vb is the back-chamber volume. The acoustic impedance of 59 "E 7: [\a '5 ”C .Q U1 2L2 ream ;———— 2’ Q Z 3 Z q Holes (>——\/\/\ J Back- chan'iber ZC Jl lfif 1 Figure 4.6: Equivalent circuit of the perforated back-plate and l’)a.ck-chan1ber. a hole can be calculated using , 81.1; * .1/2 l. _u.". 1.4-171'. ZA-=( #01:) (1+;) +1 100(1 9 l A) (4.6) 7v; 211. 7r)“; where ,11 is air viscosity. 1'1. is the holes radius. and 1;. is the holes length. For purposes of control design. it is desired that Equation (4.3) be such that. it can be integrated into the 111embrane transfer function with ease. Specifically. considering the transfer function of a. second—order system. representing the 111e111brane‘s dynamics through the fundamental resonance. the back—pressure resisting the 111embrane motion (Pk) can be added as a forcing term: (110.92 + Cos + Nazca) = Pa) — 17.15) (1.7) 60 where [’(s) is the Laplace transform of the acoustic pressure acting on the outside sur- face of the membrane and 1’1. is the Laplace transform of the resisting back-pressure. A Simplified transfer function relating I’A.(s) to Z(_.(s) can be obtained if only “piston— like" displacement of the 111embrane is considered. Related to this restriction. it is fur- ther assumed that the air motion through all holes is identical; i.e. p1 2 p2 = = pq and 111 = 11.3 = = uq. “71th these. the current approach departs from the elaborate analysis in [25]. However. the 111ethod used in the latter is too complex to enable the easy incorporation of the back-pressure in the membranes transfer function. \Vith the above simplificatirms. equation (4.2) becomes: P1 = (Zr + (IZ(‘l“k (4-8) where q represents the total munber of holes. The volume velocity can be computed as the volume displaced by the 111embrane motion per unit time. For this analysis. only the air displaced by the first harmonic mode will be considered. The total volume of displaced air (this...) due to the fumlamental mode can be calculated from the average membrane displacement multi1’11ied by surface area A. Taking the ratio saw/3(- for the fundamental mode from Table 4.1. this displaced volume is: 1;“... = 0.4311. :01 (4.9) For harmonic oscillation at angular frequency ed. the amplitude of this volume velocity through a single hole is given by: 61 0.4314 . z .71 11).: q C )0; (4.10) Substituting from equation (4.10) along with ecmaticms (4.5) and (4.6) into equation (4.8) yields an equation for the resisting pressure as a function of center displacement :c and frequency a). After being transformed into the Laplace domain (i.e. letting jw' = 3). this ecmation becomes Pits) = 0.4314 . 24.)..1 Lil/13711192 + QWF; (MW/2 (4.11) QWF; ., 13 (l+%)s + fiv—Ll/M; Substituting equation (4.11) in (4.7). it can be seen that the influence of the resist- ing pressure on the 111embrane dynamics can be modeled as an added inertial mass. damping and stiffness terms that are related to the air layer in the capsule back—plate and back—chamber. These can be represented by equations (412)-(414). In equation (4.13). the 0121/2 term that exists in the numerator has been replaced with the square 1 c) . root of the fundamental resonant frequency .110”. Tlns has been shown to be a rea— sonable approximation as the damping term is dominant only near this frequency. This substitution linearizes the air layer damping term so that its transfer function may be easily used in control system modelling. ’00“). + 1.71%) (1711'; film, = 0.4314 ' ‘4 6‘2 , 81.4.} ' 1/2 I . ' k i 9 TPOPY' [(01) = 0.4314 ' A r 1,. (4.14) These terms can be added into the 111embrane transfer function given in Equation (4.7) yielding 1 (.11 + 1110,.)5‘3 + (CO + ('01))3 + [1'0 + K0,, [1(3) 2 (4.15) To (‘ienicmstrate the effectiveness of the analytical model in predicting the additional damping provided by a perforated back—plate. capsule inserts were machined and tested. These inserts were machined from acrylic rod stock and designed to fit inside the sealed back-cliamber of the 12.7mm [:11‘1'1totype capsule described in Chapter 2 (see Figure 2.1). Holes were drilled in the face of these inserts to enmlate perforations. where their length and the back-chamber volume is known from measured dimensions. A depiction of one of these inserts and the modified capsule prototype is shown in Figure 4.7. A total of five of these inserts were constructed and tested. A list of parameters for each of the inserts is given in Table 4.2. In addition. calculated terms for inertial mass. damping and stiffness added by the air layer are given in Table 4.3. Hole length and back—chamber volume are measured using Vernier calipers. while hole radius is based on the size of the drill bit used. It. should be noted that there is expected uncertainty in this dimension due to vibration while drilling and thermal interactions with the acrylic material (i.e. expansion/ contraction). Also. dimensitms 63 Perforated Insert Assembled Capsule ”t H 1.1-3 ' 1— i l " = d ' y. ((1 Figure 4.7: Schematic (.lrawing of prototype 111icrophone capsule with acrylic insert designed to simulate a perforated back-plate. are not considered “ideal" as they are limited by the geometric scales available in a conventional machining process. as better 1.)erformance is possible with smaller radius holes. Table 4.2: Known or 111easured parameters of the acrylic inserts used for verification of the mechanical damping model. ‘ Inser 7 I'A.(1nm) [((mm) lr§)((:1112)1 _- 1‘34 ”05037—— 3.22‘*71n“1 2 19 0.503 3.23 1.31 3 16 0.503 0.52 1.73 , . 4 1 1 0.503 5.35 1.39 ) ”A 5 ‘13 “0254— 143’ —_—2 171 Initial experiments were conducted using inserts 1-4. where back-chamber volume. hole radius. and hole length were kept nearly constant, and the number of holes were varied. Electrical actuation was performed to determine the frequency response of the modified capsule and verify that it conformed to the model. The frequency response associated with each of the inserts along with their predicted response is shown in Figure. 4.8. 64 Table 4.3: Calculated parameters of the acrylic inserts used for verification of the mechanical damping model. {1114711;.__7,_ 110,.(171/777?) (57941-1777 A. 37/777.) A'0b(71/P77/m')1 i—i . 44 “I "00173—— 0.0?3 5.39 2 I 19 0.0415 0.0332 5.99 3 . 0 0.130 0239 0.09 4 _1 0.717 5 -, 1.529__ 5 73 ffi ___5 4_13__5 _0121 " 0512 _ i‘ 5.11 t 40 —— Experiment Undamped — - Predicted A 44 HOle % 5 19 Holesr > 20- 6Holes . E 1Hole ”At/f s 5 a) 0“¥ “" *‘ i§iJli "V q '0 ' .7 ll '7’ s . l ._= 1 ~\ 5-20— 1; . ‘ L. -\ \‘§ .‘73 . \ \ -404 .\ - \. 1 2 3 4 1O 10 10 10 Frequency (Hz) Figure 4.8: Experimental frequency response of 111icrophone 111embrane with perfo- rated inserts where the mnnber of holes is varied. The first observation to be made from Figure 4.8 is the relation between the munber of holes and the corresponding air layer mass and damping. It can be seen that the desired damping effect increases with fewer holes. as this results in increased fluid velocity through the individual holes. However. inertial mass also increases resulting in an undesirable decrease in natural frequency. A mathematical observation can 65 be made to show that the ratio of inertial air mass to damping of the air layer has only one variable parameter. rk. An approximation for this ratio is given in equation (4.16). where it is assumed ([1. + 1.7171.) z (11‘. +2173) as it is typical that me << 1A:- 1/2 1U ('01) — 240014 Thus. it is inferred that in order to effectively design a. perforated back-plate with 111inimal mass contribution. a very small hole radius, rk, is ideal. After determining this radius, hole length [k and the number of holes. q. can be chosen to achieve the desired open—loop damping. With these ol‘1servations in mind, the improved insert 5 was designed and constructed. Referring to Table 4.3 it can be seen that this insert has a slightly smaller mass contribution than insert 3. while having nearly twice the (.lamping'. The frequcgincy response of the improved insert is shown in Figure 4.9. A GUI program has been developed in .\l.’~\TLAB that incorporates the theoretical model developed in this section and allows the user to vary both meml’1rane and back- plate 1.1arz-11neters and observe the modified frequency response for the fundamental resonant mode. A depiction of this GUI program is shown 011 Figure 4.10. The figure shows a design where significant damping has been added with minimal mass loading. V’Vhile the design satisfies basic geometric requirements, in order to obtain the i1‘1dicate1’l size and number of holes in the back—plate. a micro-fabrication process is likely required. Such an example is a silicon biilk—micromachining process where a (110)—or‘iented silicon substrate is masked and anisotropically etched in KOH-water etchant [‘26]. This process is recommended because it allows for straight-walled holes to be formed, consistent with the desired geometry. 4O ——- Experiment ”mam?“ — — Predicted £5 E a 20 — 3 18 Holes :5) ‘\ C 3 o~ — — — ‘C (D .t’ g —20— L O z —40“ \1 1 1 . 11.11112 . 4 111.1L13 A 1 1.111114 10 1O 1O 10 Frequency (Hz) Figure 4.9: Experimental frequency response of microphone membrane with improved perforated insert. 67 PERFORATED BACKPLATE DESIGN Membrane Parameters Membrane Parameters Diameter: [T12]: mm M: 00“ kgfm’Q Surface Densitytffinflj kglmQ C: 13731? Pa*s/m Damping Ratio: [311155] K: 297500595201 Pafm 7 Edge Tension: '300 N/m 1411 Layer Parameters Back-Piate Parameters M-ai" 002882 kgim’Q Hole Diameter: }__0._1__l mm C_3ifi 571-4057 Pa*Sfm Hole Length: :T:] mm K_air: 25121132927 Palm # of Holes: [5011 l Back. Volume: [Li cm"3 DESIGN! Open Loop Microphone Response A 400 . , ' . . f 063 120 Undamped Membrane E - _ Damped Membrane " T 440 - q § [I] 460 e _ E g '180 "' -200 2 l I I 1 1 1_1 1 l3 1 1 1 4 1 n 1 1 l4 “3 10 111 Frequency Figure 4.10: Depiction of GUI application used for perforated back-plate design. with “ideal" design of back—plate shown. 68 Chapter 5 Summary and Conclusions The present study was undertaken to develop and characterize a. novel design of an optical feedback—controlled microphone. The study was motivated by the ultimate use of an array of such microphones in l'1eamforming array measurements used in experimental aer1‘1acoustics. The 12.7111111 prototy111e presented in Chapter ‘2 provides a proof of concept of a feed- back 111icrophone that is designed using a. unique combination of fiber—optic lever sensing and piezoelectric actuation of a PVDF membrane. The results demonstrate that feedback control is effective at modifying sensor dynamics. Furthermore. cali- bration using electrical actuation of the. piezoelectric membrane is demonstrated to be effective in identifying 1.1arameters required to theoretically model the membranes transfer function. The acoustic frequency response of the I‘nicrophone in open- and closed-loop operation is accurately predicted by the theoretical model. showing a po- tential for an advanced “self-calibrating" / “self-matching" 111icrophone technology. In such a scheme, severally microphones with initially mismatched parameters in open- loop operation (i.e. stiffness. dampintg) would be calibrated and “matched" such 69 that they have identical frequency response in closed-loop operation. Because of the large membrane diameter of the first 111icrophone prototype. the band- width of the microphone was limited to 5.1kHz. Therefore. to construct. a higher bandwidth sensor a smaller 635111111 diameter tin-airbrane is used in a second pro- totype. For 111easurement of the smaller 111enibraries deflection. an optical sensor with higher sensitivity is needed. For this purpose. a Michelson interferometer is implemented for measurenwnt of the riiernbranes deflection due to acoustic pressure. The smaller 111embrane demr1nstrated the expecteril higher frequency bandwidth in open-loop operation. while the .\.lichelson interferometer proved to have significantly higher sensitivity than the commercial fiber-optic lever. However. electrical actuation data showed higher order modes that were significantly more prominent than those reported for the 12.7111111 prototype. These higher order modes reduced the controlla- bility of the 111icr<1phone system as they tended to become unstable even with at. low feedback gain. Another aspect of the modified sensor design that was investigated was the effect of non—linearity due to the sub-wavelength linear range of the interfer- ometer setup. It is apparent that the sensor can be driven into non-linear operation by an acoustic source. especially at frerpiencies near its resonz’ince. Specifically. within the microphones bandwidth. the response became non-linear at and SPL of 110118. The corresponding SPL near resonance was 90118 dB. This effect could eventually be negated by use of feedback. or by modifications to the membrane prototype and optical sensor. In Chapter 4. future improvements to the feedl1ack-controlled 111icrophone were dis- cussed employing theoretical arguments in addition to experimental results. In par- ticular. motivated by increz—Lsing the feedback control authority of future designs. per- formance enhancements from the use of an area averaging optical sensor in addition to 70 a perforated acoustic backplate were described. Both methods are proposed as means for limiting the effect of men‘ibrane resonances that are inherent to the vibrational system. First. an area averaging sensor is described. It is demonstrated that the av- erage displacement of higher order resonant modes is significantly lesser in magnitude than the displacement 111easured at the center of the 111embrane. It is shown that an optical sensor with a radius that. is 0.7 times the membrane radius would provide optimal attenuation of the effect of the first 3 higher order modes. Second, design of a perforated acoustic back-plate was discussed. Acoustic theory was presented to predict the inertial mass. damping. and stiffness contributions that would result from the addition of a. back—plate. Experimental results were presented to show the accuracy of the tl‘ieoretical model when applied to perforated inserts designed for the 1)1‘()t()ty~'1_)(a capsule used in Chapter ‘2. A GUI application based on this model was created in MATLAB to simplify future designs of perforated back-plates. The work presented in this thesis shows that. within the limits of stability of the feedback operation. a desired 111icr1’1phone response (e.g. sensitivity. bandwidth. etc.) can be accoi111‘)lished using the combination of electrical-actuation used for system identification and theoretical modeling used in compensator design. As a result, the feedback 11'1i(,-1'o[_)l'1one concept has several unique advantages: (1) the response of different 111icrophones in a. l.)ea.111forming array can be automatically adjusted to a common desired response. leading to “self-calibrating” / “self—matching” and negating the necessity of an acoustic calibration setup such as a. piston-phone. cavity calibra- tor. or anechoic chamber: (‘2) the. response of the same microphone can be changed to fit different applications by changing the controller parameters; (3) the effects of enviromnental factors on the microphcme‘s membrane (e.g. temperature. humidity. and dirt) can be minimized or eliminated all together through the feedback. Future work 011 the feedback-controlled optical 111icrophone concept will include implementa- 71 tion of the Improvements outlined in Chapter 4 in order to increase the 111ic1'opliones range of ct)ntrollabillity. \Yith these improvements in place. in addition to improved sensor packaging and automated (‘~(’)11t1‘oller design. it. will become practical to scale up the design to a large sensor count array. where the "self-calibration"/"self-matching" properties are truly valuable. -.1 [\D Chapter 6 Appendix 6.1 Appendix A - Electrical Circuits 6.1.1 Phase-Lead Compensator Circuits Three different compensator circuits were built and tested in the course of this re- search. Each used the phase-lead concept, where three independent parameters are adjustable by the user in order to achieve a desired (‘l(.)S(‘(l-l00p response. These parami-‘ters are proportional gain (KP). derivative gain (Kd). and derivative time constant (rd). The circuits are op—amp based. and the three independent parameters are controlled by standard potentiometers in circuits #1 and #2. and by digital po- tentiometers in circuit #3. Descriptions of each Circuit‘s functionality. as well as its construction is given in the following: Compensator Circuit #1 The first iteration of the phase-lead compensator circuit was designed for ease of setup. albeit with minimal precision. The gain factors. K], and [{d. are controlled by a combination of rotary switches which set incremental gain values, and potentiome- ters for variable attenuation. The time constant, Td. is varied by a potentiometer. Additionally. DC bias is variable using a potentiometer. A switch on the front panel can be used to control whether the output signal is inverted. Also, switches allow for proportional gain. derivative gain. and DC bias to be individually switched 011 or off. A schematic diagram of the circuit is shown in Figure 6.1. while a photograph of its front panel is shown in Figure 6.2. Compensator Circuit #2 The second iteration of the phase compensator circuit was designed to have higher precision in selecting phase-lead parameter values. while sacrificing some of the ease of setup of the first version. A breadboard was used for construction of the compensatm‘ prototype. as shown in Figure 6.3. The schematic diagram of this circuit is depicted in Figure 2.4. In this version of the circuit. each of the resistor and capacitor values have been been 111easured and are listed in Table 6.1. The phase lead parameters. K1,. Kay. and Td are set by the trim-pots Hp. 11"). and RC. I'(:‘S[)(‘(‘th()ly. The desired values for these trirn-pots are determined using design software (see later section). and are measured using a multimeter before being placed in the circuit. 74 2’0 f1 1 it " -’\/\/’V Summation v —/vvv\ 4’ -,Dct'\—/‘WV\—/ DC Bias ____/\/‘\\/\/\_/ > EB Proportional \ \ // / .r'/ \ 11. n ft Non-lnvertmg ”WA/Tl lnvertmg VW‘ t t Figure 6.1: Schematic diagram of first phase-lead compensator circuit. Compensator Circuit #3 A third compensator circuit was designed and built that incorporates digital poten- tiometers for setting the three phase-lead compensator parameters. In this way, the 75 Figure 6.2: Photograph of front panel of first phase-lead compensator circuit. Figure 6.3: Photograph of second phase-lead compensator on a breadboard. compensator circuit is automated in such a way that is desirable for large sensor count arrays where it is impractical for the user to individually set the values of standard potentiometers. A photograph of this circuit is shown in Figure 6.4. The digital potentiometers used are of the MCP42XXX variety by Microchip Tech- nologiesl. These chips have two on—board potentiometers each with ‘256 incremental 1http://wwl.microchip.com/downloads/en/DeviceDoc/11195C.pdf 76 Table 6.1: Electrical ctmiponents used in phase-lead controller circuit depicted in Figure 2.4 Symbol Type V Value TLII ' ()p-amp L1220 1 0.42 . ()p-amp . OP27 30.43 : Op-amp . AD827 t ‘ 0.44 Op—amp AD827 le . Resistor 1.49 kQ ' ‘ Hpg Resistor 0.996 kfl ‘ l Hdg Resistor 0.998 kSZ 1 RIM", ' Resistor 9.98 k9 [f[)(' ' Resistor ‘ 23.72 kQ RP : Trim-pot Variable . li’p Trim-pot . Variable 1 Rd . Trim-pot l Variable i _C- ”l Capacitor_ 0.082 it}:J Figure 6.4: Photograph of third phase-lead compensator circuit. resistance settings. The resistance can be programmed using a three wire serial inter- face. The three pins used for programming are SI, SCK, and CS. The SI (signal in) 77 pin is where the 16 bit input is recorded. The first 8 bits. or command byte, of this signal determine which on-board potentiometer will be p1'(,)grammed, where the 8 bit number 17 (00010001) selects potentiometer 0, 18 (00010010) selects potentiometer 1. and 19 (00010011) selects both potentiometers. The command byte is followed by the data byte which selects a resistance increment from 0-256. The signal is clocked in by the SCK (signal clock) pin. where each bit is recorded 011 the rising edge of the. digital clock waveform. The CS (chip select) pin should be asserted low immediately before programming the chip. When the @ pin is asserted high at the end of the programming cycle. the chip will be set to its newly assigned resistance value. An example digital waveform for programming of a MCP42XXX variety chip is shown in Figure 6.5. I11 this example. the user is selecting potentiometer 0 to be programmed to its 50th resistance increment (corresponding to approximately 2kQ for a l\lCP42010 chip). Thus. the full 16 bit signal input at the SI pin is 00010001 00110010. For purposes of the current application the S—H—D: (shutdown) and RS (reset) pins should always be asserted high. and are thus connected to the +5V power supply. An interesting feature of the .\ICF42XXX series of digital potent iometers is the pres- ence of the SO (signal out) pin. Using this pin. multiple chips can be daisy chained in such a manner that a large number of chips can be programmed from a. single three wire interface. This is achieved by wiring the SO pin of one chip to the SI pin of the next. where the SCK and CS connections are shared. In this configuration. when the first chip receives a signal longer than the standard 16 bits. it will pass this first signal to the chip connectml to its SO pin. and record instead the next 16 bits it receives. Using this method. it is assumed that compensator circuits for thirty or more 111icrophones can be ctnitrolled using a single computer interface. In the current circuit. MCP42050 (50kf2). .\ICP42100 (100kf2). and .\IC'P42010 (10k52) 78 a_ r1 r1 7‘1 r1 * 012 3 4 5 6 7 3 9101112131415 T T 1 1 ‘1' Tr T Y 7 I Y Y T T . __.1 8) :1339 ggtmmv nrnrflflflnnnnfl_ 0 1 2 3 4 3 6 i 8 910111W2131415 j (g:_<5871 l T H T T I 1 ‘ §L_ T #17723 4 5 5 7 39101112131415 Bit # Figure 6.5: Example digital waveform used in programming a. .\ICF42XXX series digital potentiometer. The example case is for programming p(,)tentiometer 0 to position 50. where the full 16 bit input is 00010001 00110010. chips were chosen to control KP. Kd. and rd respectively. These values were chosen for the design because they provided a range of gain values that were typical in designs for the first 111icrophone prototype. Future designs may use different components, de- pending if more/ less gain is desired. In the circuit. the two on-board potentimneters ofeach chip are wired in parallel. I11 this configuration. assuming both potentiometers to be identical. each chip will provide over 30.000 unique resistance increments. A table listing components used in the compensator circuit is given in Table 6.2 Calculation of resistance values and determination of required potentiometer settings is performed by a LabView application. to be ('lescribed later. The circuit includes two enhancement mode MOSFETs which are used for switching of the circuit. The source and drain pins of these MOSFETS are connected to the input pins of the T9 Table 6.2: Electrical components used in serial interfaced phase-lead controller de- picted in Figure 3.7 i Symbol T1 Type 1 Value j l ) 0.41 i ()p-amp LM741 ' 0.42 I Op—amp LM741 0.43 Op-amp LM741 0.4-1 Op—amp LM741 Rpl Resistor 1.496 k9 [1’ p2 Resistor 1.808 kQ Rm; 1 Resistor 1.798 kQ Rfvgum Resistor 19.92 kQ Rm...) Resistor 19.92 k9 H00 Resistor 46.8 kg HP Digital Pot MCP42050 RC Digital Pot MCP42010 Rd Digital Pot MCP42100 C Capacitor 0.022 11F fl [1 MOSFET NTE490 .112 MOSFET NTE490 op-amps for the proportional and derivative gain sections. When a high voltage is asserted at the gate of either of these MOSFETS. current will be allowed to flow from the source to the drain. PffOCIlVPly shorting the input pins of the op—amp and. turning it “off". Alternately. when a. low volt-age is asserted no current will be allowed to flow. thus turning that op-amp “on". In total. including power supply. seven wires are used. 6.1.2 Michelson Interferometer Control Circuit During construction of the Michelstm interferometer it was observed that there was a low frequency (sub 1H2) drift in the sensors output. resulting in the sensor drifting out of its desired set-point. In order to 111aintain the output of the sensor at this setpoint. feedback was employed using a mirror mounted on a piezoelectric stack. 80 The schematic shown in Figure 3.6 was designed for the purpose of low frequency fringe-locking of the interferometer signal. A photograph of this circuit is shown in Figure 6.6. and a list of components is given in Table 6.3. Figure 6.6: Photograph of Michelson interferometer control circuit. 6.1.3 Other Circuits Signal Amplifier and Variable Low Pass Filter A signal amplifier was constructed with variable gain and low pass filter options. The circuit is single input / single output. It can be powered either by a 9V battery or by a DC adapter plug. The gain level is controlled by a rotary switch, where the selectable gain values are 1.01, 3.15. 10.2, 39.7, and 100. as determined by experimental cali- bration. The corner frequencies of the low pass filter are also controlled by a rotary switches. and are 340Hz. 620Hz. 3200Hz. 11.700112, and 32.000112. A capacitor is 81 Table 6.3: Electrical components used in Michelson interferometer control circuit. depicted in Figure 3.6 fSymbol 1 Type 1 Value 1 f 0.41 ; Op-amp l TLO72 0A2 : Op-amp 4 TLO72 0A3 ; ()p-amp : TLO72 0.44 1 Op-amp TLO72 RI l Resistor 0.996 kQ H2 ‘ Resistor 2.000 kQ ( Hg ; Resistor 2.004 kn ; H4 1 Resistor 19.92 kQ ‘ R5 1 Resistor 100 k9 . [1’6 ‘ Resistor 0.984 kQ R7 Resistor 1.804 kQ ' R8 Resistor 1.798 M) , R9 l Resistor 0.984 kQ 1 R00 l Resistor 4.64 kn E HG ‘ Trim-pot Variable 1 [’38, i Potentiometer 1 k0 1 Cl ( Capacitor 1 ,uF ‘ .2 ( Capacitor 100 ,uF placed at. the input of the circuit such that the output is AC coupled with a corner frequency of 1.6Hz. A schematic of the signal amplifier and variable low pass filter is shown in Figure 6.7. and photograph of the circuit is shown in Figure 6.8. Third Order Inverse Chebyshev Filter A filter circuit. was constructed for the purpose of sharply cutting off the effect of resonant modes in the microphones response. The type of filter that was constructed for this purpose is the Third order inverse Chebyshev filter. The frequency response of such a filter can be described as having a single sharp notch with a 20dB/ decade roll-off above the notch frequency. The filter is designed using a Texas instruments 82 o—l »——fi lO6pF u—1 318 F Rotary Switches FT 1 p f“ —’ 1. 41—10001061115‘ i ._i i 4» 0.003211}? 1 :1 . HIP—+0.01 F lief) 1 500.52 50k 1 M 100,115” '__— _ T121617 'm_s_, 444 1 . ~.~...~¢ 1 1 (_i + 0 H15“) ‘ ‘ /—l—o ”0 1 259129; + Figure 6.7: Schematic diagram of signal amplifier and variable low pass filter circuit. Figure 6.8: Photograph of signal amplifier and variable low pass filter circuit. UAF 42 Universal Active Filter chip2. The design program FILTER423 can be used to determine the values for the three external resistances that control notch frequency, R p, R p1, and RF'z- Using the same filter chips, a variety of other filter types such as Butterworth, Bessel, and Chebyshev can be constructed. A photograph of the Inverse Chebyshev filter circuit is shown in Figure 6.9. 2UAF42 datasheet - http : //focus . ti . com/1 it/ds/syml ink/uaf42 . pdf 3FILTER42 manual - http : / / f ocus . t i . com/1it/an/sbfaOO2/sbfa002 . pdf 83 l t. I" '2 .1" i a. ».. 1" l 7'.‘-‘ .> .. b I'v .g. I a! ' '\.‘ 3 1" e I _. J',‘ ,1‘, I . . I . , y ‘ "'.‘l 1,;‘7 .. - ' 7“ I:"'~._.-,’:‘:. -. , ’ $1.. ‘ r. r‘ I , . 7. . . . .- ~ _ ‘ - ' , '_ . 1‘ CC ,5 . rt ? l’ 001 1 l .7 o ' l \- I ~ -‘”-._....- _. _.-.._~..__.--._.--’.._.__--_ ._.. ., _ "T’L Figure 6.9: Photograph of inverse Chebyshev filter circuit. Power Amplifier A LM386 chip was used to construct a small power amplifier circuit. The output of this circuit can be used to amplify an audio signal to a speaker, with a peak output power of approximately one watt. The circuit is single input /single output and has a potentiometer providing variable gain. A photograph of the 386 power amplifier circuit is shown in Figure 6.10. 6.2 Appendix B - Software Applications 6.2. 1 FeedbackGUI For simplification of the feedback-controlled optical microphones operation, and for future scalability for large arrays. a single application has been designed to handle 84 Figure 6.10: Photograph of 386 power amplifier circuit. all computational and serial interfacing needs. The program has been written using the LabVIEVV programming environment. The functions of the LabVIEVV application include (1) calibration of the 111icrophone’s frequency response, (2) identification of the open-loop transfer function. (3) calculation of the closed-loop transfer function and compensator settings based on the user‘s desired response. and (4) programming of the compensator through the digital input/output interface of the National Instruments PC I-6024E DAQ board. Two versions of the program exist. In the first variation, FeedbackGUI_V1.vi. the user specifies closed-loop DC attenuation. natural frequency and 1'3. and calculations are performed to determine the required KP, Kd. and Td. In the second variation, FeedbackGULV2vi. the user specifies KP. K d: and rd. and calculations are performed to determine DC attenuation, natural frequency, and 13. Each of the functions of the GUI will be described in detail below. Calibration stage The first. portion of the Feedback GUI application is the calibration section. This is used to calibrate the 1‘1’1icrophone‘s frequency response in an electrical actuation 85 test using a harmonic sweep waveform. The user inputs a sampling frequency, num- ber of records. and munber of samples per record. “hen the program runs, the signal wz-iveform is plotted along with spectra of the signal for the current record. A11 autospectra is performed to get the power spectra of both the reference signal and the 111icrophone actuation signal. Cross spectrum analysis is used to determine the sensitivity and phase of the electrical actuation signal relative to the reference signal. To maximize the signal to noise of the electrical actuation caliln‘a-ition. for each record only the seven frequency bins near the peak of the reference signal are kept. This 111ethodology is practical only when using a long duration hz-n'monic sweep waveform, as this signal will only pass through a small fraction of the calibration frequency range for any single record. After completion of the calibration cycle. sensitivity and phase. for like frequech bins are averaged, and plotted in the front panel. The user also has the option of saving this calibration data in a .txt file, where the data is saved in columns containing frequency. sensitivity. phase. reference spectra. and (_ilectrical actuation spectra. System Identification Stage Using the sensitivity and phase results obtained using electrical actuation. system identification is performed to determine open—loop parameters of the 111icrophone. The system identification is performed using the 111ethodology discussed in Chapter 2. The user specifies a film thickness. which is used to calculate mass. Calculations for damping ratio. stiffness. and electrical actuation sensitivity are performed using a. .\IathScript node. 86 Closed-Loop Specification Stage There are two Feedback GUI applications that have been develo[_)ed, with the differ- ence between the two being the methodology used for calculatimls. In the first version, Feedba(**'kGUI_Vl.vi. the user specifies closed-loop DC attenuation. natural frequency. and angle 13, and the subVI GcSpetleyi computes the required phase-lead param— eters KP. Kd, and Td needed to achieve this closed-loop response. In the second version. F(‘(‘(ll)21('l\'GUI_V‘ZA'l. KP. [{d. and rd are directly specified by the user and DC attenuation. natural frequency. and 13 are ctmiputed in the subVI GcSpec_V2.vi. In both cases. the theoretical frequency response for both open- and closed-loop are plotted. Controller Programming Stage After the phase-lead parameters have been determined. the compensator is pro— grannned using a serial interface. First. the necessary settings for the digital po- tentiometers are determined. Ideal resistance is determined based on the known cmnponent values in the compensator circuit. The program then does a table lookup to determine the digital potentiometIu‘ setting with minimum error from this ideal resistance. The potentiometer settings and cm'responding resistance values are. con- tained in the files RpN’sorttxt. Rd--Vsort.txt. and Rc_Vsort.txt. Once these settings have been ('l(‘l(‘l‘llllll("(l. they are passed to the subVI ProgramChips.vi. This program creates the digital signal waveforms (see Figure 65) for the SI. SCK. and CS wires, and passes them through the digital output of the National Instruments board. Ad- (litionally. the controller can be switched on and off. and re-programmed multiple times from a single calibration. 87 6.2.2 MATLAB Software PhaseLeadG UI I’haseLeadGUI is a MATLAB GUI applicatimi that loads an electrical actuation calibration file and uses this to calculate the phase lead compensator transfer function required to satisfy some user specified closed-loop respcmse. To use this program. open and run the PLC-GUI.111 file. and enter the name of the electrical actuation calibration file that will be used in the field provided. The program allows the user to then input their desired closed—loop parameters. After pressing the DESIGN! button. the program will run computations based on the analytical method described in Chapter 2. The results of these cmnputations are displayed on the right side. and theoretical closed-loop response is plotted (note: the component values output by the program are those that would be required for the circuit used in the second phase-lead compensator design. For different circuits. refer to the phase lead parameters on the upper right and adjust component values as necessary). It should be mentioned that at times the program will output, a negz-rtive value for one or more of the phase-lead parameters. This indicates that particular set of closed- loop parameters cannot be achieved using the basic method outlined in Chapter ‘2. The user should adjust the specified cl(.)se(l-loop response until the program outputs a realistically achievable set of phi-ise-lead parz—uneters. DigitalPot.m DigitalPot is a MATLAB GUI application used to determine the necessary settings of the digital potentiometers used in the third phase—lead compensator circuit. The 88 user inputs values for K1,. K4. and rd. The program then calculates required resis- tance values based on the components used in the compensator circuit given in Table 6.2. Then. based on calibration of the digital potentiometers' incremental resistance. settings are determined that will minimize the. error between the desired resistance and the actual resistance of the digital potentiometer. The frequency response of the desired compensator is then plotted with the the(’)retical response of the actual con1pensat(')r. Perforated Backplate GUI The perforated backplate GUI applicatimi is (_lesigned to simulate the open-loop re- sponse of a microphone where a perforated back-plate has been added to increase damping. Simulations are. based on the analysis described in Chapter 4. To use this progrz-im. open and run the PERF,GUI.m file. The user will then specify values for the unmodified membrane parameters. which by default are set to values similar to those of the 1;)rototype microphone from Chapter 2. Then the user may specify geometric parameters for the back-plate. After pressing the. DESIGN! button. the program will compute the air layer properties and plot the theoretical response of the tin-modified mmnbrane in addition to the response of the membrane with the addition of a perfin'ated back—plate. PLC _Solver.m I’LC_Solver.m is a. MATLAB function file used to calculate pliz-rse-lead parameters based on a set of inputs. The first required input is the ()LParameters vector which includes mass. damping. stiffness. and electrical actuation sensitivity taken from cali- 89 bration data or manually inputted. The other inputs are the user desired cl(_)sed—loop DC attenuation. natural frequency. and angle ,13. The pr(,)gram runs computations based on the analysis (_lescribed in Chapter '2. The program outputs the phase lead parameters KP. lid. and Td. as well as resistor values required for the second com- pensator circuit. EstimateIVIembrane.m Estimate.\lembrane.m is a RIATLAB function file used to estimate the membrane’s mass. damping. stiffness. and electrical actuation seiisiti\~'ity from electrical actuation caliln‘ation data. The program requires a matrix taken from a calibration file as well as a membrane thickness input. The calibration data should be formatted in such a way that its first column is a frequency vector and the second column is sensitivity measured as the output of the lever sensor relative to the signal from the function generator. 90 ll] [3] [4] l0] [Tl BIBLIOGRAPHY Hunmhreys. \V.M.. T.F. Brooks. \V.\V. Hunter, and Kit. Meadows, Design and Use of Microphone Directional Arrays for Aeroacoustz'c Measurements, 368t Aerospace Sciences Meeting 8; Exhibit. 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