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# ANALOG IC DESIGN ECSE 4962

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This 255 page Class Notes was uploaded by Immanuel Brakus PhD on Monday October 19, 2015. The Class Notes belongs to ECSE 4962 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 147 views. For similar materials see /class/224780/ecse-4962-rensselaer-polytechnic-institute in ELECTRICAL AND COMPUTER ENGINEERING at Rensselaer Polytechnic Institute.

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Mechanical Design Ben Potsaid Control System Design February 26 2003 Mechanical Design Lecture Contents Miscellaneous Components Gears and Belts FleXible Couplings Bearings FiXing Components to Shafts Dynamics Stress and Strain Analysis Heat Transfer Analysis PDE ampThe Finite Element Method Design Studies Flexible Mirror Positioning Robust Design Movies Pendubot Link Design Mass amp Stress Optimized Robot Link Design Controllability Optimized Mechmxcal Design Gears and Belts Mechanical Design Gears and Belts 2 At steady state velocity or ignoring inertia FBD ltgt Thermodynamic ltgt Kinematic F and M balance conservatlon of energy velocity analysis P0wer16i 6 r N T 1 11611262 N 12 r2 T2 r2 91 T TlNt2 N62T 1 6l2N61 l 2 Conservative System Power in Power out Mechanical Design Gearheads Spur Inexpensive Efficient L ow torque Some backlash Motor and Gearhead o en combined Mechanical Design Gearheads Planetary Large reduction in a small and lightweight assembly Large torque capacity Considerable backlash Identical stages can be stacked together Mechanical Design Gearheads Harmonic Flexspline has 2 fewer teeth than circular p ine One tooth advances every rotation Huge reduction in small and lightweight assembly Almost no backlash Aerospace and robotics applications Mechanical Design Gearhead Comparison Type Torque Eiiiciehcy Backlash Cost Spur Low High Low Low Planetary High Low High Med Harmonic Med Med Low High Mechanical Design Bearings l Bearings are usually press fit to the shaft or K Inner race housmg39 N Outer race Correct bearing hole diameter is critical Heat expansion can be used to assist assembly Bearings allow for slight misalignment Mechanical Design Bearings 2 Load conditions determine mounting scheme to prevent bearing creep Creep is when the bearing race rolls on the mating surface Press fit bearing race inner or outer that experiences cyclic loading Belt Drive System gt Shaft sees varying load so press t shaft Centrifuge with unbalanced load 39 y w Housing sees varying load so press fit housing Mechanical Design Flexible Couplings E 1 Pamllel offset misalignment Angular misalignment Coupling is used to transmit torque between two shafts Coupling is rigid in torsion and exible in bending Without exible coupling there would be excessive loads on the shafts and bearings Without exible coupling bearings would fail prematurely and performance would suffer Mechanical Design Fixing Components to Shafts unreliable Method Torque Stress Cost Setscrew Low High Low Clamp High Low Med Pin Low High Low Key Med High Med Spline High Low High Mechanical Design Dynamics Ordinary differential equation M99 C0 139 G09 7 Solution Numerical integration MATLAB ODE solvers Dynamic forces are exerted on the mechanical components Fzmjc39 TJ6l Dynamic forces cause de ections and stresses in the structural components Mechanical Design Stress and Strain l Ultimate l Plastic Region Stress 39 39 39 39 quot 39 39 39 39 quot 39 39 39 elastic animal Limit U Siress 115112 Failure Point if Yield Stress Linear elastic Region Strain elongation In the linear region material acts like a spring F kX Stresses in the components should never exceed the Yield Stress to prevent permanent deformation When would we not design to yield strength Mechanical Design Heat Transfer 1 Heat transfer is energy transfer due to a temperature difference Modes of heat transfer Conduction Convection Radiation Solid No Medium SOhd surface to Fluld Electromagnetic Waves Why are we concerned with heat transfer Mechanical Design Heat Transfer 2 i2R Internal heat generation A Motor Temp small thermalmema i large thermal mama Why is there a max continuous A 100 current for a motor 3 Can we exceed th1s max 2 5 continuous current I 05 1 1 5 2 time s Mechanical Design Partial Differential Equations Stress and Strain 80x BTW ar F 0 8x By 82 x 80y Eer aryz F 0 Equatlons of Equ111br1um 8y 8x 82 y ai 8sz 8T FZ 0 82 8x 8y Heat Transfer Conduction l a aT aT 8T q VT kl j k Fourier s Law k Bx By 82 j q heat ux energy across unit area per unit time T temperature Mechanical Design Solutions to Partial Differential Equations Analytical solutions exist for basic geometry only Stress and Strain Cantilevered beam l P 13x2 7 x 31 3 iii y 6E Heat Transfer 7 1D Conduction Cruskmm lAruA x TxT2 T1ZT1 What if the geometry is complex Mechanical Design Finite Element Method Method to nd an approximate solution to PDE by discretization Solution converges as mesh is re ned S Galerkin Method tress m plston Very time consuming Computation time Vs modeling accuracy What resolution mesh is required Hook Stress Mechanical Design Design Study Flexible Mirror 1 Rapid positioning of laser beam Finite Element Mesh l Lw PD control with actuator saturation ODEPDE High inertia thick mirror increases settling time Vibrations thin mirror increases settling time What mirror thickness minimizes settling time Mechanical Design Design Study Flexible Mirror 2 H 3393 Mirror Settling Time its Mirranhiekness 7 u u u quoti f 3 5 Poss1ble d1mens1onal variation xxquot 39 r EV i With i0010 tolerance ffquot 39 ff 3 quot f 25 f Inertia Jquot Dominates settling time s Vibration 2 f Dominates I I I I I I 005 I11 015 12 025 13 135 04 thickness ineth How would you specify the thickness of the mirror for high performance that is robust against manufacturing tolerances Mechamcal Design Design Study 7 Flexible Mirror 3 x m39nguv Sammy Time vs MmmTlucknsas 5 u 2 u 3 thmkness mch What delity model is required Computation time vs accuracy Mechanical Design Design Study Pendubot Link 1 3 Link 2 0 Free Joint Joint broom on the hand Link 1 is subject to dynamic loading conditions GOAL minimize the mass of link 1 but do not exceed the yield strength of the material Mechanical Design Design Study Pendubot Link 2 Pendubot Balancing Lower Link is subject to dynamic loads Mechanical Design Design Study Pendubot Link 3 Very rough approximation of Tslot hollowing technique 0 9 Design Variables Diaof the holes Material Aluminum 6061T6 Simplified Model Optimal DeSign Deformation I 39t39 1D 39 n11a es1gn ampLoagls Y Forces from simulation FEM lt Mesh Optimization Results THI Mechanical Design Design Study Robot Link 1 Optimal Mechanical Design Design Parameters xi Mass Center of mass location Inertia about x direction Inertia about y direction Optimize for Horizontal Inverted Pendulum l Controllability 2 Small unstable open loop pole Mechanical Design Design Study Robot Link 1 We can t optimize both metrics simultaneously so We get a family of design solutions Mechanical Design Design Study Robot Link 2 ptin39ml h iuclmmiml Dubiiin M 1 Emmy himrmd r EHdUIle Benjamin Pumiil am l39i11i39lquot Wen Ramadanr Pnlylccl mic iII Iriquot39l1llll My 1 EMILE Mechanical Design Conclusion Mechanical Design and Control System Design cannot be done separately when high performance is required Use the latest technologies and design tools to your advantage Don t forget about first principles and the basics ECSE4962 Introduction to Subsurface Sensing and Imaging Systems Lecture 8 More on Waves Their Interactions Kai Thomenius1 amp Badri RoysamZ 1ChiefTechnologist Imaging Technologies General Electric Global Research Center 2Professor Rensselaer Polytechnic Institute BE Global Research Centerfor Subsurface Imaging amp Sensing 7 Slide 1 Outline of Course Topics PULSE ECHO METHODS Examples MRI A different sensing modality 0 THE BIG PICTURE What is subsurface sensing amp imaging from the others Why a course on this topic Basics of MRI 0 EXAMPLES THROUGH MOLECULAR IMAGING TRANSMISSION SENSING What is it X39Ray Imaging PET amp Radionuclide Imaging C mputerT m 9raphy IMAGE PROCESSING amp Intro into Optical Imaging CAD 0 COMMON FUNDAMENTALS propagation of waves interaction of waves with targets 0 I Slide 2 Light propagation Particles or Waves 0 Isaac Newton 7 A particie or corpusciei guy 0 Christiaan Huygens 7 Awave guy introduced the Huygens Principie 0 Thomas Young 7 1801 7 Dou bie siit experiment vaiidated the wave concept 0 Actuaiiy both concepts work and are usetui in understanding different aspects of wave propagation 0 We wiii iargeiy work with wave propagation especiaiiy in acoustic imaging Slide 3 Huygens principle Huygen s principie offers an expianation forwhy ana naw waves bend araimam wnen passing an obstruction e eve Dim an a wave from acts as a source of tiny sphericai Wavelets that travei forward with the some speed asthewave 7 the wave from at a iatertime isthen the iinear superposition of aii the waveiets iii r 4 A ZEIEIEnuteschi 28 uh sicai DDUES um Slide4 Young s double slit experiment o In 1801Thomos Young performed on experiment MWW HW that irrefutobiy demonstrated the wove nature of ig t before this there hod been o iot ofdebote between the porticie Newton ond the wove comps Huygens o IV Ionochromotic fight is first shone through d singie sit this rnokes the iight thot posses through the singie siit coheren we con ovoid thistodoy using iosersi iight from the singie siit is then used to iiiuminote 0 mar doubieesiitwhich produces on interference pattern on 0 screen behind it Mgr 1mme lng ll images a mie mtmc mum mnmsna 5quot marmmmmv whenMIMI o BTW note the interference pattern due to the doubie siit it iooks iike o sine wove Whot is the Fourier Tronsforrn of o quotdoubie siit Sing memnt I m WGWMWMMHUJN 28 physical opticspm Slides Diffraction o The extent to which 0 wove bends when passing around the edge of on opening is related to the ratio MW 28 thsical opticsbm Slides Traveling and Standing Waves Traveling waves Launched waves which propagate in a given direction Most medical imaging uses these Standing waves Wave pattern caused by interference of two traveling Slide 7 Superposition of oppositely traveling wave pulses Constructive Destructive Interference Interference SM Standing Wave 39 PlUCklng the string in A the middle it will T vibrate Note wavelength in the picture is twice the lt string length k2L Standing waves and harmonics Major role 7 the basis for musical tones Clinical Application of Standing Waves NIH Grant Application w RPl Dr Joyce McLaughlin of Math Dept GE Global Research Dr Kai E Thomenius U of Rochester Drs D Rubens amp K Parker Study of prostate cancer using quotcrawling wavesquot These waves are actually traveling beat waves Slide 11 Let s bring this back to imaging Wave theory allows us to develop different propagation models These can be used to develop beamformation technology for radar sonar and ultrasound data acquisition An aperture in this context can be A slit in an opaque screen A transmitting radar antenna A sound source such as a transmitting sonar transducer Goal of Propagation Models Given a known field at the aperture determine what happens to the energy as it travels in the medium of interest Slide 12 Ultrasonic Imaging Ultrasonic Imaging involves the following Generation of acoustic wavelets Control of timing and amplitude ofsuch wavelets 0 We wish to control regions of constructive and destructive interference in other words to form beams 0The ideal imaging beam is a very thin uniform cylinder which interacts with the medium being imaged Reception and processing of the echoes to form the image 0 The rest of the lecture will begin to cover the creation of selected transmit beams Slide 13 Overall Block Diagram of an Ultrasound Scanner Transmit Bearnronnation Transducer Array Receive Bearnronnation 39 g quot ofc quot 39 timing signals for transmit and delays for receive processes 0 Transducers usually multi element arrays or piezoceramic elements 0 Image formation conversion to video raster image processing Acoustic Wave Propagation image Forrnation Slide 14 Example 0 How to determine the field generated from an aperture Start with a general solution to the wave equation Use appropriate approximations to achieve the desired field descriptor Account for propagation related effects leg attenuation Test out the result Slide 15 Anatomy of an ultrasound beam Near field or Fresnel zone For field or Fraunhafer zone Nearetaefar field transitionL RayTeighSommerfelcl Fomlation gt RayleighSommerfeld Formulation e Diffractive component gtgt A 0 Distance to observation plane gtgt 7 39k e r U2xygt Jill man 85877 r 2 gt Implementation e Huygens Fresnel principle An x 0 Direct Integration 5 0 Computational Order 0N4 Ij f h 12 SI i irvi i Ul n Simplifications Example from Radar 0 We will work with the Rayleigh Sommerfeld solution E03 KI Wok where p 1 R2 yix2 2yx x pa 17 o In many applicationspais greater than the aperture esp if R gtgt aperture 0 In such cases the denominator in the integral varies much more slowly than the numerator Simplifications ECVgtRKll Ixejkpdx o If we expand the p in the phase term in a binomial series and keeping the dominant terms we ge l y 390 pl pf 203 l 2 pa Kx pa 2 0 Now the complex field strength is 7 I 2 EyRW J Ixex jk xsi118 x dx Pa 1mg 2pc Slide 19 Simplifications 7 I 2 EyR Wigxx prkbsmSJr 2 J 1 dx 0 Normalizing this expression to the value at 6 0 and setting a sin 6gives us J39 l x2 f zxexpLj xu 2pc de 0 The first term in the integrand is the Fourier kernel expj u This is associated with the Fraunhofer or far eld zone of diffraction theory 0 The second term in the integrand is the Fresnel kernel expljkalZp ll This is associated with the Fresnel or near eld zone of diffraction theory Slide 20 Far field or Fraunhofer Zone rewriergar o If pH is so large that the variation of quadratic term is 1 over the aperture thatterm will have little effect on the field integral 0 If that is the case we can ignore the quadratic term 0 Ourfield expression now becomes a Fourier integral Field due to a circular aperture ll fulaixexpjkxudx share 21 Far field or Fraunhofer Zone fu I ixexpjkxudx o A good rule ofthumb for the transition to far field is a distance of D247r o For analyses beyond this point the above Fourier expression is accurate 0 This is highly desirable consider a uniform line source If iinnlnnnllllllllllllllmlnmuni In this example the aperture function is a rectangle The far eld response is its Fourier Transform the sinc function sirde zz Far field Response amp Fourier Transforms o This is indeed a powerful Interferometer sult 0 Everything we know about Fouriertransforms can be sums A h applied 39 Dismbunun e Linearity 7 add two sources e quot quot quot 39 7 Delay Theorem 7 shift sources Respunse o What is the response of a point source 0 What is the farfield response of a sinusoidal transmit pattern Focused Designs 0 We often work with curved radiations parabolic dishes lenses focused transducers In 1949 O39Neil published a very nice theory for determining the field strength along the axis of a spherical source 0 While the derivation is beyond what we want to cover in this course the result is extremely useful O39Neil HT ThzaxyafFacusmg Radmaxsquot JASAWI 215pp 5157 527 1949 Slide 24 O Neil s Formula 0 O Neil developed the following expression fora focusing radiation 0 p pcuan expjat 7 W where PEsink52 Eix 174 h 5372 M B1lx7h2a2 x272xhb2 c l l Ax l Mr I Dimmsions mtl mmmmim Slide 25 M file for O Neil function p oneilSllambdaaRZl O Neil s expression for axial pressure profile called by p oneilSllambdaaRZl This function returns tne yalue of capital P as giyen by Ea 3 1 in O Neil s paper To get the pressure amplitude one has to multiply P by rno c uO we can ignore tnesefor now wnere lambda is the Wayelengt a is the radius of the aperture R is the radius of curyature 2 is the yector ofdistance along the axis k 2 pi lambda deLz le2 r 211 n R r sarthAZ r ao2 in finle if isemptylin 2in Zlinl 1 0e74 end E2R erZli delta sartllz r n A2 ao2 r 2 p E sinlk delta 2 ifisemptylin 21 Zlin r deL22 E2R Rlei delta sartllzl r n A2 ao2 r 21 p1 E Sli39ilkquot delta 2 22 2in deL22 E2R R722 delta sart22 r n A2 ao2 r 22 p2 E Sli39ilkquot delta 2 Plinlp1 p2l2 displ calculated new yalue for p atroc Slide 26 O Neil Formulation 0 Graph shows a typical result Aperture radius 10 mm Wavelength 077 mm Radius of curvature 50 mm Notice the location of the 39 peak response 7 it does J not coincide with the radius of curvature Why Slide 27 Recap of the Lecture Traveling amp Standing waves Working with the RS formulation derived highly simplified expression as the Fourier transform of the aperture Demonstrated a closed form expression for focused circular apertures Slide 28 Homework 1 Copy oneils function Slide 25 to your matlab mfile folder Write a function call with the following goals a Keeping aperture size constant for transducer in Slide 26 change wavelength from 05 to 10 in 01 mm steps Graphically show the impact of the change in wavelength bl Vary the radius of curvature from 40 mm to 60 mm in 5 mm steps Show the variation in the axial beam profile on a single plot 2 Download and install Field II package from httpserveroersteddtudkpersonal39a39field al In matlab test functionality with command fieldiinit Slide 29 Instructor Contact Information Budri Roysum Professor of Electrical Computer 8 Systems Engineering Of ce JEC 7010 Rensselaer Polytechnic Institute 110 8 h Street Troy Neonrk 12180 Phone 518 2768067 Fax 518 27662612433 Email roysam ecsergiedu Website httg wwwrgieduroysab NetMeeting ID for offcampus students 1281136180 Secretary Loraine Michaelides JEC 7012 518 276 8525 michalrgiedu whynnlzhnQIIIu wmp Slide 30 Instructor Contact Information Kai E Thomenius Chief Technologisl Ullrasound amp Biomedical Of ce KWC3OOA GE Global Research imaging Technologies Niskayuna Neonrk 12309 Phone 5183877233 Fax 518 3876170 Email 1homeniu crdgecom Ihomenius ecsergiedu Secretary Loraine Michaelides JEC 70116181276 43525 michalrgiedu Rensselaer GE Global Research 19 09 42 43 Vfdgfir mfg7957 7quot W W 43 u 43 pie 7 Z P74 6 w f gt 3 9 5ng 9 q 0quot319 2 4374129 1346 as y a a5M a 9amp0 Qc d 39 016 4 M We dgvnazsm W A r 54cm 1 Wff e asc n1670 F F g 03 3 3353516 M V J fgt gt as 5 75 9 54 a 43 4314 52 5g 1 I 26 gag 444 f 039 1 to 1 a mic4 5m out waA69 wSf w7 5w A 99 L u M7quot I4 5quotquot wquot 7412 fin all f f 6 9quot 7791 I 74 0quot 39r l y 39 quota PM ffekJo Mm m Linayyquot W L l WW7 lt w W 1 Wm IV Wagmfnw 39 felt064w EAQi M 9 E 439quot p r v i I y i Isa 8F L g 5 5 a r 400 L aws7 7 a serrer ady a f O 794m 741 7 40quot 7 44 mind WMM fds F fe peeJ acC L ff4626A Ogreyeraoaj a 1 42 a a f quot 7 j 9 116 21 6 5 9 agar6 MQCUZ SSGQ7LampGKJ 05 AX7 67M yc gt o 39 feecv Cort a m4 lade j caor ry 44 44 F face J QOQWJ dSJ o f f 3 ML sz le 434 qu X Q A zv g Ly g gsaaj Qw F 5 l6F LC a My 7 c FQ ECSE 4962 Control Systems Design Final Demonstration Presentation and Report Instructor Professor John T Wen TA Ben Potsaid httpwwwcat rpied uwenECSE496ZSO4 Final Demonstration To be held in CH 2037 at 6pm Could use hallway by moving the interface box and control computer Final demonstration each group has up to 20 minutes including questions and answers Will be part of final presentation grade Send me a demo script by morning of Wednesday April 14 Objective of the project and demo Description of demo Final Presentation Final presentation each group has 25 minutes max including questions and answers General outline Introduction problem statement and motivation Objective and specification Design approach modeling model validation control design design validation and tuning in simulation and experimentation uncertainty analysis Results comparison between performance and speci cation a video here would be great Overall assessment of accomplishments vs objective Conclusion Final Presentation Recommendation Record your demo video camera tripod firewire interface and video editing sw may be checked out from Ben edit the footage into a good short movie and incorporate into your presentation Grading Guideline Attire professional Manner voice eye contact gesture movement Planning organization transition slides understandability Engineering explanation of spec and design approach Performance presentation and analysis of results graphs and charts Questions Relevance of answer clarity Final Presentation and Report Strive to tell a story motivation specification approach modeling model identification and validation linear design nonlinear simulation final tuning results compare achieved performance with original spec and simulated performance evaluation of design step response tracking disturbance rejection motor or amp near saturation Sketch out an outline of the story first and then fill in the details Have writing center do a first level filtering of your writing More detailed guideline online Tomorrow at 6pm in C11 2037 Demonstration Group 1 6pm etc Send me the demo script by tomorrow morning typed description of objective and what will be shown ECSE 4962 Control Systems Design Using MATLAB and Simulink for Control System Simulation and Design Instructor Professor John T Wen TA Ben Potsaid httpwwwcat rpied uwenECSE4962804 Outline Overview review of MATLAB and Simulink Using MATLAB and Simulink for dynamical system analysis and simulation and control design Nonlinear vs linear simulation and analysis Application to PanTilt platform Last Time Equation of motion for dynamical systems 1ink JL NZJmm39L BM NBWL BM NBmCsgn6iL Nrm mg c sin 9L L39L As a control system we may regard rm as the input 0L as the output Today we will see how to use MATLAB and Simulink to simulate the response of the system for a given input trajectory MATLAB A powerful package with builtin math functions array and matrix manipulation capabilities plotting and lots of addon toolboxes eg control image processing symbolic manipulation block diagram programming ie Simulink etc You can install MATLAB 65 Simulink Control toolbox RealtimeWorkshop RTW xPC Target on your laptop httpllwwwrpiedudentarcweblicensesmatlab licensehtml You will use Simulink RTW xPC Target to generate the realtime code for your project MATLAB An interpretive environment may use scripts Vectors thetatheta1theta2 Matrices MM11 M12 M21 M22 Polynomials pa3 a2 a1 a0 Transfer functions Gtfnumden Linear simulation step response stepG impulse response impuseG general response ylsimGut MATLAB Cont Plotting plottx1tx2xlabel time sec ylabel theta deg title thetat legend theta1 theta2 Printing to printer or file print f dltdevice typegt ltfile namegt Using mfiles in MATLAB use any editor or MATLAB builtin editor just type in edit function ffunctxn Getting help in MATLAB help ltfunction namegt orjust help Always label axes include units and include legends in your plots onIine tutorial httpWWWenginumichedugroupctm Nonlinear vs Linear Models Consider input as the motor torques 139 and output as the joint angles link Simulation involves nd the output response for a given input trajectory You will use a the nonlinear simulation to validate your design including nonlinearity friction saturation etc For your control design you will use a linearized model Pan or tilt dynamics Simulation using Simulink PanTili Simulation y Scone ConsIam Moran olllwn Inux Ham Palum llylmnucs Linearization Equation of motion is nonlinear To facilitate control system design we first linearize about an operating point 99 9610 Linearization 1D example Taylor series expansion about 99 2 910 and keep the linear term J9Bv9 Bc sgn9 Ntm mg c sin9 TL sin9 sin9d cos9d9 9d O5sin9d9 902 Linearized system JA9 BvA mg c cos9d A9 Ntm mg c sin 90 Bc sgn EK J J V constant may be cancelled or treated as a disturbance A99 9d Description of LT Systems Inputoutput What does LT mean differential equation Frequency Domain State Space state Input Output Description of LT Systems fy va Cyu InputOutput differential equation Frequency Domain State Space o 1 o x J 1c J IB H J 1 u YS 2 JS2 Bvs C1US E T A G y1 Ox0u ax C E MATLAB Description of LTl Each LTl is treated as an object with a variety of possible description transfer function tfnumden numerator and denominator polynomials polezerolgain zpk zpk zeros poles gain state space 88 ABC D state space parameters Open Loop Linear System Response Impulse response Bode plot yimpulse G ybode G step response poleszerosdampings ystepG pole G zero G dampG general response polezero plot ylsimGut pzmapG gainphase margin robustness margin G Incorporation of Control Interconnection of LT systems Gcl feedbackGKHF Effect of Sampling Most control systems these days are digital in nature so sampling is inherent through AID for sensor which contains a sampler and DIA for actuators which contains a zeroorderhold To analyze the effect of sampling we can find the equivalent discrete time system Gd chGtstssampling period sec Gd is also an LT object and the commands for LT may be applied For your project proposal CI Estimate model parameters estimate load inertia and CG use your motor parameters identify friction CI Use linearize model to develop controller CI Develop a Simulink diagram for your design iteration Test and tune controller in Simulink Desired input should be based on your spec Demonstrate controller meets spec CI Consider sources of error and experimental testing procedure Next Week Real time programming using MATLAB Simulink RTW XPC Target Ben Potsaid Will give the lecture Tomorrow at 6pm Hand in conceptual design memo and prepare to discuss it for 1520 minutes ECSE 4962 Control Systems Design More on Control Design Instructor Professor John T Wen TA Ben Potsaid httpwwwcat rpied uwenECSE496ZSO4 Progress Report Postponed until March 24 Keep CH 2037 clean throw away all trashl Let me know if you notice any unbecoming behavior Progress Report Must contain your control specification and justification Time domain rise time settling time steady state error tracking error Frequency domain bandwidth based on desired trajectory and disturbance rejection robustness Must contain analytical model model based control design and spec verification at least in simulation Progress Report Must contain some experimental results eg friction ID initial control results based on your model Must compare progress against schedule As a good example check out Group 6 s reports and presentations on last year s web page Final Report Final report must contain discussion of societal impact eg similar productsprototypesideas intellectual property manufacturing issues safety economics privacy Today Velocity estimation A bit more on ID Compensation for nonlinearity feedback linearization Trajectory tracking Nonlinear pantilt model Vt Friction ID give a large pulse b initially to break stiction Addition Considerations Velocity Estimation 37 washout filter finite difference low pass filter Kalman predictor state observer based on assumed plant y u Sampling 3to10 times faster than Closed loop bandwidth S nus n1 n15 M Ma n3 n35 n4 More on ID 16 3V9 Bc sgn KV Friction ID BVK BcK KN KIt Ka N Nmotor N extgear KIt motor constant NmA from data sheet Ka 01 AN Ben Potsaid s calibration Double check take off timing belt friction should be close to the values in the motor data sheet How to get the full model 3v BC 9 I 9 I sgn9 I V For a constant voltage V the response is a first order exponential with time constant BV I 91 1 e 0 9 SS Average over different input voltages and time intervals avoid noisy regions How to get the full model Cont Once BV I is found we can find KI mu N m Then Bc I K Now we have the full model for control design B B K 9 V9 Csn92 V I I g I Feedback Linearization c119 a2 sgn9 a3V a4 sine Equation of motIon For pan aXIS a4 O If we have a good model we can just cancel all the nonlinear terms Vi a3 u c119 a2 sgn6I a4 sine Then we get zu If friction not very well known we can just use Viu a4sin6 gt al a2 sgn u a3 Feedback Linearization Cont Pro control design is much simpler only need to deal with two decoupled double integrators Con Model may not be accurate so we ll need to identify them based on experimental data Con longer computation time slower sampling rate Con usually larger torque requirement Trajectory Generation So far all the pointtopoint motions are implemented as steps For smoother motion and lower torque requirement trajectory generation is almost always used GiVen Ytarget Vmax amax find a smooth curve ydt such that for some T yd00 ydTytarget ly39ml s vm S amax Common Trajectory Generation Algorithms Spllneeg MUloMlzt 14 other basis can also be used quot traPEZOid bounded acceleration 2 5 a a 2 a 5 a 5 5 x 1 o 39 5 M i u n 5 m MATLAB code for trapezoid and siquot quotij r c3 i iiquoth e see trajgenm but you must convert them to Simulink if you d like to use them Full Nonlinear Model The code to generate the general equation of motion is posted pantilt m you just have to run it in MATLAB to obtain the expressions for M C G To use pantilt m rst put the mechanism in the zero configuration all angles are zero Choose a coordinate frame Represent pl 1 pi h in this coordinate frame Then run pantiltm For simulation you need to substitute in the parameters m1 m2 110 120 P1 P2 PanTilt Platform The pantilt platform is like a 21ink robot 01 and O2 coincide as hl001T CL h2010T With motors and gears attached First Link Pan massa 0055073 kg moment of inertia about com kgmwz Ill 0001152 112 75938e7 13 4951 Lag 00549quot 22 00007658 123 700001259 33 00007459 43012200 LUZ 39 TLOOEEW p1lca13 ca2 lca3ZIT E L b3 ODUZSm Second Link Tilt 1 mm 7 00 380m Nlcj massib 02035 kg moment of inertla about COM kg mA2 00002701 0 122 957le75 I23 6 931e6 133 0 0003041 7 00m p2lcb1 lcb2 lcb3T Skeletal Pan swam L E A mass 02294 Kg 07 3 79C 03 m moment of inertia V y bout COM kgmquot2 111 00007459 112 00 113 z 2 2 0004750 123 40001031 OOAZSW 133 2 00002978 p1 000125m 00981m 0059OmT Skeletal Tilt Vlr C 7 lt7 00013 p2 0 0003m0T U mass 0 07588 kg moment of inertla about COM kgmquot2 Choice of Motors Gears You will use the design resource page httpWWWcatrpiedupotsaidcsdResourceshtml to find different choices of motors and gears Manufacturers will provide the dimension and mass but not the location of center of mass and inertia Take a guess of Where the center of mass is eg roughly the geometric center and approximate motors and gears as cylinders with uniform density Then you have a guess of the CM location and inertia which you can use in your design iteration Combining Two Bodies CM of combined bodies mc 2mg mb pc mapa mbpbmc 2 1 pacpacT9 paczpc pa pac 2 I mix119 pbc pg pb 1b 0 2 1b mb pr 10 2 la 1bc This is given in a MATLAB program compositebodies m Which requires masscenter m and parallelaxis m Adding Motors Gears to Skeleton For your design you need to obtain m from the manufacturer s datasheet calculate 0 and location of CM based on some simplifying assumptions and the geometry of the part determine p based on Where you will mount the part An Example of Putting Things Together Consider the tilt axis with pulley hub and payload added BC ly B skeleig puHJy payload Putting Things Together Cont First gather part data p 2768 Kgm3 density of Aluminum dhub 00381m diameter of hub d pulley 00630m diameter of pulley dhole 00095m diameter of hole rm 2 00095m thickness of hub tpuuey 00095m thickness of pulley thole 00190m thickness of hole a 1cz 2a 3 00762m 00381m 00095m dimension of payload Putting Things Together Cont Mass and inertia may then be found hole has negative mass m 2 p7 d 22t 2 3 t2 0 0 12 2 For a cylinder 0 m d 2 I 0 33 0 along the y was 2 0 Eb t2 12 2 d d 0 0 12 m For a cube 1 0 dfd 0 12 0 0 d12d22 Putting Things Together Cont Determine Where you are going to put these components thus pin down p for each part Repeatedly apply the composite body formula to nd the overall m 10 p The MATLAB code for the tilt aXis example is online in bodyb m you need to modify it for the pan axis Once you obtain m 10 p for both pan and tilt axes you can substitute the values into the equation of motion Now you are ready to do simulation Overall Dimension OVERALL DIMENSIONS FOR PANTILT E I 2500 27500 00318m 12500 N w 00699m CL 0031 1m EH 32370 00822m 79 I 20 00201 0m link with better pictures I BOXED DIMENSIONS ARE IN INCHES SCALE 1 2 htt wwwcatr iedu otsaidcsdleth modelin lecturez modelin html Next Week Spring break But get ready for your progress report presentation Tomorrow at 6pm in C11 2037 Group 1 6pm Group 2 615pm Group 3 630pm Group 4 645pm Group 5 700pm Group 6715pm Group 7 730pm Prepare to discuss the progress of your project Bring your lab notebook ECSE 4962 Control Systems Design A Brief Tutorial on Control Design Instructor Professor John T Wen TA Ben Potsaid httpwwwcat rpied uwenECSE496ZSO4 Don t Wait Until The Last Minute You got to have a model to work with by now At least a model based on estimated massinertia and your motors and gears very few groups have this in the proposal You should very soon have an identified model If you don t you must seek help Once you have a model start control design in simulation Don tjust tweak the controller with the experiment without some simulation based analysis first Today Review basic control design PID tuning LT System Characterization 139 0 G We ll approximate each aXis as an independent single inputsingleoutput 8180 system 0 G 139 Characterization poles and zeros zpk G frequency response bode G step response step G steady state value evalf r G 0 Closed Loop System nd ed e K T G 0 PID Relevant transfer functions 9K G9d ns 1KG 1KG na 1 KG G 6 961 ns na 1KG 1 KG 1KG Design Objective Stability closed loop poles must all be in left half plane Performance Step response has small overshoot and small settling time Small steady state error Disturbance Rejection Effect of sensor and actuator noises small on 0 Robustness How large an uncertainty acan be tolerated in terms of stability n 9 e PID m if Design Objective Stability closed loop poles must all be in left half plane39 closed loop poles roots of 1 KG Design Objective Performance Step response has small overshoot and small settling time GK 1 GK can sufficiently large g sufficiently close to 1 closed loop transfer function GCL Step Response Intuition based on second order system with no zero under 16 damped 2 H s critically S ZCwns 6tn damped over Ccos I damped 0 i y y i y y y y y y X 0 005 01 015 02 025 03 035 04 045 05 time sec Effect of Zero Zero within system bandwidth strongly affects response Stable zero increases overshoot unstable zero gives rise to undershoot slow stable zero fast stable and unstable zeros asoc1 s2 2Coonsoo2 n HS slow unstable zero 1 l i l v v v i l i l 0 002 004 006 008 01 012 014 016 018 02 time sec Design Objective You want this close to 1 Performance Small steady sta error G0 9 G 0 9 n n ss CL dGKsDC aDC Ga 1 GK X To reduce steady state error You want this close to 0 Cancel na if possible High DC loop gain G0K0 Integral control Design Objective 1 KG G 6 961 Ids 1KG 1KG 1KG na Design KG1KG small over the spectrum of ns and G1KG small over the spectrum of nu Disturbance Rejection Effect of sensor and actuator noises small on 0 S sensitivity T complemen ry sensitivity S T 1 39 i gt Spectrum of nu Spectrum of ns Design Objective Gain margin if ais a real number how far can a be different from 1 before the closed loop system becomes unstable Phase margin if aexpiO a ure phase shift how large can 0 be before the losed loop system becomes unstable Usually expressed in terms of dB or 6 52 means GM6dB Robustness How large an uncertainty acan be tolerated in terms of stability nu ede KwG e f PID L Robustness GainPhase Margins a is nominally 1 Gm19554 dB at 31623 radsec Pm39l1794 deg at 01772 20 Bode Diagrams gain margin 4iradsec Phase deg Magnitude dB l 300 10397 Add phase lead for phase stabilization 10quot 1oU requency r dsec phase margin TH my use margin command in MATLAB Nyquist Diagrams From Um l l I I I I z r l l l 1 Real Axis reduce gain for gain stabilization PID Control quot1 0d e K 139 G PID KSkp kSkDS When does it work PID Control quot1 0d e K T G 0 PID Kskp k1ssz Works well when G is a 2nd order system PID Control Consider Gs1s2 closed loop characteristic polynomial IS 5st2 KDs KP KI For small K I K D governs the damping and K P governs the undamped natural frequency 600 For K I gt 0 DC loop gain is in nite therefore zero steady state error Gain Tuning Intuition P gain increases speed of response but also increases overshoot D gain reduces overshoot but decreases speed of response I gain reduces steady state error but can reduce speed of response and lead to instability Strategy Tune PD gain until desired transient response is obtained Increase I gain until convergence to steady state is satisfactory Retune PD gains increase if necessary Frequency Domain Considerations 0 e 139 0 d K G PID Adjust PID gains to achieve good tracking over the desired bandwidth transfer function from ad to 0 is close to OdB Disturbance Rejection dd 0d e K T G 0 PID K s Adjust controller and possibly add more filtering in K but must be careful to preserve stability and dynamical response so the frequency gain is small over the disturbance frequency Next Week More on control design Tomorrow at 6pm in C11 2037 Group 1 6pm Group 2 615pm Group 3 630pm Group 4 645pm Group 5 700pm Group 6715pm Group 7 730pm Prepare to discuss the progress of your project Parameter Identification 32603 Last Time ARCSIink type in arcslib at MATLAB command prompt to see available blocks Real time Simulink code download pantiltexpmdl from course web page replace PID block with your controller must be discretized with the chosen sampling rate replace set point control with trajectory tracking click on misc block in ARCSlib and use 1D trapezoid Today Friction identification Parameter identification Using ARCS Interactive Development Environment AIDE Friction Overview Friction is constant While COUIOmb FFiCtiOn WW 1 mg the object is moving force 1 F coulomb TN Viscous Friction oil Assume LL 2 LLS 2 uk Friction is proportional velocity velocity F B viscous v Combined Friction F ictl39on Fcoulomb F viscous Sources of Friction Friction comes from Motor Bearings Motor commutator Gearhead gears and bearings Belts and pulleys Joint Bearings We will lump all of the friction sources together and represent their behavior with a combination of Coulomb and Viscous friction models To identify friction we will command a constant torque and then monitor the steady state velocity of the pantilt system Model of Friction 1DOF model 19 Fc sgn 139 ID strategy If t constant A then 03 9 steady state value Fv ss chgnAA A slope FV L r Stribeck friction u s ope FV Friction Identification Input Constant Torque Each line shows the velocity response for that torque veiumiy vs time amiiy nicurves System reaches a steady state velocity No movement for given torque TiO Friction Identification Result victim identi catiun data These are the n ma results for the n ma detno paritilt Coulombpus 00 unit forjomt 1 Viscouspos 146e Viscousneg 156 39E39 m Coulomb friction Slope ofline is Viscous friction 5 1D 15 Au 75 u steady state theta um vads I FV 5 55 772 22l Zw E W Fcil z EH9 Fagra439 C 4 9 aFaaWl A 631 1 E A j Fa V 93934 1 A W xtHWHA 4 W A X a Z 5W dz thr39mfje Axs X ATUV 72gt W Mame quotff1mg ew amma m Parameter Identification 19 Fv chgn6l 2 Multiply by 9 and integrate over 1 sampling period klts klts klts 1 j a39e39d imjme39zd i j W j 939sz as kts kts kts 1 F F 9 913 7v9131 913 ts 709k1 l k 1 ts ES9k1Tkl Qka Write as A x b and solve using least square Consideration condition number of A suf ciency of excitation affected by choice of T ARCS Interactive Development Env AIDE Control and supervision of DSP board Ondemand monitoring and adjustment of DSP variables Realtime data acquisition Remote process configuration and access Today at 5pm Continue with system assembly and programming Next Tuesday 41 5pm Wednesday 42 5pm Programming and initial testing Linearization and Control Design 21203 Today You now know how to incorporate motors and gears into the simulation We ll next review linearization and basic control design Linearization Download pantiltlinm pantilmodel m and put them into your working directory Enter p m Ifor pan and tilt stages and motor and gear parameters motor inertias and gear ratios that you ve obtained into pantiltmodel m In pantiltlinm Choose the joint angles for linearization modify thetald0theta2d0 Modify damping d10 d20 Run pantiltlinm to obtain the linearized model G Open Loop System 139 9 gt G gt This is a 2input2output system We will analyze oneloop at a time G 1 1 pan and G 2 2 pan Characterization G11G 1 1 G22G 2 2 poles and zeros zpkGxx x lor2 frequency response bode Gxx step response step Gxx steady state value eval fr Gxx 0 Closed L00p System 9d e K T G 9 PID MATLAB does not handle improper systems well more zeros than poles a bad situation anyway so let s approximate the derivative term s by ssp1 where p is a large number this is called a washout lter K169 0 K200 KiSkBkliskDissp1 Ks Closed Loop System Cont Q e K 139 G 9 PID Transfer function from ad to 9 GclfeedbackGKeye22 Closed loop poles poleGcl or dampGcl Closed loop frequency response bodeGcl Closed loop steady state value evalfrGcl0 Gain Tuning Intuition P gain increases speed of response but also increases overshoot D gain reduces overshoot but decreases speed of response I gain reduces steady state error but can reduce speed of response and lead to instability Strategy Tune PD gain until desired transient response is obtained Increase I gain until convergence to steady state is satisfactory Retune PD gains increase if necessary Frequency Domain Considerations Q e K 139 G 9 PID Adjust PID gains to achieve good tracking over the desired bandwidth transfer function from ad to 9 is close to OdB good decoupling gain of offdiagonal transfer functions is small Disturbance Rejection dtl 0d e K 1 G 9 PID d S Find transfer function from da to 9 and d3 to 9 Adjust controller and possibly add more filtering in K but must be careful to preserve dynamical response so the frequency gain is small over the disturbance frequency MATLAB Tool K gt G gt Use r1 tool to assist in controller design for SISO only Add poles and zeros corresponding to K1 and K2 Select step response and closed loop Bode plots to guide design process Move polezero locations and gains based on step response and Bode plots Today at 5pm Groups 57 project proposal presentation include both preliminary design and project plan Next Tuesday 218 No meeting Next Wednesday 219 9am Project proposal due Friction and friction identification Next Wednesday 219 5pm Work on final design part sizing controller tuning ECSE4962 Introduction to Subsurface Sensing and Imaging Systems Lecture 8 Propagation of Waves II Kai Thomenius1 amp Badri Roysam2 1Chief Technologist Imaging Technologies General Electric Global Research Center ZProfessor Rensselaer Polytechnic Institute GE Global Research Center for SubSurface Imaging amp Sensing Outline of Course Topics 0 THE BIG PICTURE What is subsurface sensing amp imaging Why a course on this topic 0 EXAMPLES THROUGH TRANSMISSION SENSING XRay Imaging Computer Tomography Intro into Optical Imaging COMMON FUNDAMENTALS propagation of waves interaction of waves with targets of interest PULSE ECHO METHODS Examples MRI A different sensing modality from the others Basics of MRI MOLECULAR IMAGING What is it PET amp Radionuclide Imaging IMAGE PROCESSING amp CAD Recap from last class The basic wave equation i0quotzp 0 1 C32 07t2 PoK Helmholtz equation Vzp at 07 2P PtPOe J II 07 2 k2P0 Homogeneous Z a 2P k2P With excitation 322 fz Recap Useful Relations Equations on right are general Applicable to most probes we discuss in this course For plane acoustic waves 1 C xpoK Please note that c is not a function of frequency As a consequence there is no dispersion all frequencies move at the same velocity 12 k I c k I a 1 3 f Acoustic vs EM Waves Acoustic waves EM waves Wave types longitudinal or shear electromagnetic waves mechanical waves Transmission elastic medium no medium necessary requirements ether Velocity of C 2 1 C 1 propagation 00K 1118 Velocity of 1500 ms in water 30X108 ms in vacuum propagation Characteristic impedance u Zpc Z 8 Amazingly similar for the rstorder wave equation Analytic Solutions to Wave Equations In some simple cases people have found closedform solutions for example Scattered field due to a point source 3 R 2m K K 3 0 3 0 cos6s 3rc K39 2px 0 K is the compressibility or source p is the density of the source In most other cases we need to resort to numerical solution Approximate Analytic Solutions In a general situation it can be very hard to solve the wave equation analytically For some values of wavelengths and distances it is possible to obtain good approximations to the full wave equation Examples Near eld zone Fresnel approximation Farfield zone Fraunhofer approximation We ll get to them in a bit WaveMatter Interactions If a wave passes through a uniform medium we get the same wave unchanged at the other end Not very interesting in practice Medium is transparent to the wave Can t infer anything about the medium Nonuniformities of the medium modify the wave as it passes This is interesting waves interact with the medium We can infer or even map the medium in terms of the wavematter interactions Sensing and0r imaging is possible WaveMatter Interactions Breast path Step Time min us Simple WaveMatter Interactions Attenuation absorption Change in amplitude energy of the wave Re ection Waves bouncing off surfaces echoes Refraction Waves changing direction Diffraction Spreading of waves creating deviation from geometric paths Change in propagation speed Waves change phase Scattering Waves are redirected in many directions 0 Dispersion Different frequency waves traveling at different speeds through the medium 0 Doppler Change in frequency caused by interaction With a moving object Contrast Generation Each of these types of interactions is potentially a source of imaging contrast Changes in properties of the medium as we go from one point to another can be revealed by detectable differences in wavemedium interactions I background Weber39s Contrast Formula 2 background maX min max min Michelson39s Formula Contrast agents These are arti cial substances that we can often inject They produce andor enhance contrast Attenuation Usually measured in units of decibels dB 11 1 Wattcm2 I2 10 Wattscm2 Attenuation 10gtltlog 2 10gtltlog10 l 10dB Attenuation often changes by frequency of the WEIVC The attenuation spectrum is characteristic for a given medium ie a spectral signature Attenuatio L r frequency XRay Absorption Denser materials absorb X rays more strongly 2 Ge M Material Density p gcmz Air 00013 Water 10 Muscle 106 Fat 091 Bone 185 Source Richard Aston s online book Xray absorption Mass attenuation coefficient u cm2 g Xray Photon energy Water Air Bone Muscle keV 10 489 466 190 496 15 132 129 589 136 20 0523 0516 251 0544 30 0147 0147 0743 0154 40 00647 0640 0305 00677 50 00394 00384 0158 00409 60 00304 00292 00979 00312 80 00253 00236 00520 00255 100 00252 00231 00386 00252 150 00278 00251 00304 00276 200 00300 00268 00302 00297 300 00320 00288 00311 00317 Absorption based Contrast Agents l 39 7 i T quotI 139 quot L f 39 r With contrast Normal Difference Xray agent 1nJected into blood vessels httpimagingenguciedu Sample Numbers for Diagnostic Ultrasound Waves Frequency Attenuation coef cient for Imaging Depth MHZ soft tissue dBcm cm 20 10 30 35 18 17 50 25 12 7 5 38 8 100 50 150 7 5 Higherfrequency waves can resolve smaller objects but Penetrate less than lowerfrequency waves Attenuation is not all bad Often we want to attenuate waves deliberately Such highly attenuating materials are called dampers We ll discuss them further when we talk about ultrasound imaging systems Re ections at Interfaces 0 Some poinm on re ection Z 7 IfZ2 21 there is obviously no 0 poc re ection Hence an impedance mismatch is Z Z needed to get a re ecti n R 2 1 7 IfZ2 gtZ1 there is no polarity change Z Z however 1fZ2 lt Z1 the echo W111 be 2 1 inverte This is necessary for there to be continuity in Values at the boundary 7 Upper Video clip 21 ZZ 05 7 Lower Video clip 21 ZZ 20 0 For a nice discussion of this check htggphysicsusaskcaNhirosee o 5 animationre ectionanim re ection htm A o x Practical Application In diagnostic ultrasound there is a large difference between the impedance of air and soft tissue A gel coupling medium helps minimize re ection by bridging the impedance values of air and tissue Impedance matching Transmission at Interfaces 0 Some poinm on transmission 2 Z 7 IfZ2 21 there is100 transmission 1 Hence an impedance mismatch is needed to get a re ection ZZ Zl 7 IfZ2 gt21 there is no polarity change however if Z2 lt Z1 the echo Will be inverted T R 1 This is necessary for there to be continuity in Values at the boundary 7 Upper Video clip 21 ZZ 05 7 Lower Video clip 21 ZZ 20 0 For a nice discussion of this check httpphysics usask caNhiros ee9225 animationre ectionanim re ection trn 1 Refraction at Interfaces 0 Refraction 7 From Latin to turn aside 7 At interfaces of media with differing propagation speeds 7 Only occurs for oblique incidence 7 Changes the direction ofthe wave v1ltv23i1lti2 v1gtv23i1gti2 httglectureonlineclmsuedu7mmgkg213cd372htm Diffraction Diffraction Sommerfeld s 1894 de nition any deviation of light rays from rectilinear paths which cannot be interpreted as re ection or refraction Closedform solutions are available for simple cases In practical complex situations we have to resort to solving the wave equation httplectureonlineclmsuedummpkap l 3cd3 72htm Diffraction Wave Superposition Interference Cnnstrue ve Inte erence Destructive Interference D memoquot D o propaganon Direction W C A Amplllude AW 5 a 7 Wavelenglh AW AMZAI A Ampmune D Resulmnll A a C D Aw39AmAlt 0 6 Wquot M a Path Dl emne o W swam D AR 5 A c A o cgt 180 Z y wavelength ltgt 360 cgt DCSLI IJCUVC Interference Imaging by Phase Differences interferometry Sensing wave Interference pattern Reference wave Basic Idea The object affects the phase of the sensing wave relative to the reference wave If the two waves are brought together and allowed to interfere we can sense the phase change Very small effects fractions of a wavelength can be sensed this way Scattering Backscatter Waves redirected in many directions Usually Scattering intensity is weaker than lt39 re ection Surface Increases W1th frequency Speci c in terms of angular distribution Dependent upon the size and shape f of scatterers relative to L In ultrasound scattering permits imaging of tissue 1 boundaries that are not perpendicular to the incident wave Forward Scatter Refractive index Dispersion speed of the wave is a function of wave frequency Basis for prisms Key to spectral imaging M 2 na dn1 lt 0 611 Refractive index n 04 dense im LaSF9 crown BK 7 crown 06 08 0 12 4 Wavelength 7 pm 6 Doppler Example STATIONARY SOURCE transducer MOVING LISTENER red blood cell vcose Particle passes through em approaching wavefronts v Stationary particle sees cTX wavefronts in time T Moving particle sees cvcoseT7 wavefronts in time T Original transmit frequency EM and Acoustic Waves Classical Acoustic and Electromagnetic wave phenomena are similar Re ection refraction diffraction interference polarization scattering some types etc Differences arise when dealing with quantum phenomena Atomic phenomena are the basis for CT PET and MRI imaging Molecular phenomena are the basis for optical imaging EM and Acoustic Probes Electromagnetic S peclrum 10 5 1oquot Gamma Rays Acoustlc Spectrum 10 2 XRavs 1quot E 7 Infrasound lt20Hz a 1 1 uiiravioiei ID39n E 7 Audlble ZOHZ a l H g inquot Visible 176 E 73 20 E 2 I infrared 5 E 7 Ultrasound gt20kHZ Fa 10 1039 2 i jg Microwaves g a 7 ZOMHZ L l 1quotquot 1quot g g 0 Speed39 a I TV 1o AWFM 10 g 7 Air 330mS Rattle Waves a 103 me E 7 Water 1495 ms 9 m Figure 2 1 7 Bone 4080 ms mm Ugh swim v ukmvinm quotmm mm m am m Figure 1 Physical Interactions of EM waves with Matter Wavelength Range Type of interaction Comment 10m 1meter Change of nuclear spin Nuclear Magnetic Resonance Nucleons absorbemit based on their spin Radio magnetic component of EM Property Frequency wave more important 1 m 1 cm Change of electron spin Electron Spin Resonance Electrons absorbemit based in their spin Radio magnetic component of EM Property Frequency wave more important 1cm 100um Change of orientation rotation Mostly rotational effects Microwaves electric component of EM wave more important 100pm 1um Change of con guration Mostly Vibrations rotations and bending of molecules while Infrared electric component of EM it still remains in its electronic ground state The molecule wave more important must be asymmetric Vibrations need more energy than rotations 20 pm or shorter 1pm 10nm Change of electron Changes in electronic states of atoms in the molecule Visible distribution electric produce changes in electric dipoles of the atoms that ultraviolev component of EM wave interact with the applied wave more important 10nm 7 100pm Change of electron distribution At these shorter wavelengths photons can actually disrupt the Xray absorbing molecule by photodissociation or even produce photoionization of individual atoms 1000angstrom photons will photoionize electrons in the outer shells whereas 100angstrom or shorter photons will photoionize electrons in the inner shells 100pm and smaller gamma rays Change of nuclear configuration Mostly passes through Recap of the Lecture Wave propagation at the heart of sensing and imaging systems Differential wavematter interactions are a primary source of imaging contrast We have noted some parallels between acoustic waves and electromagnetic waves Similar wave equations We ll discuss differences in greater depth later They are the basis for substancespeci c imaging Homework for Lecture 8 Using the data in slides 13 and 14 nd the optimal Xray energies voltages that maximize the contrast between each pair of the materials bonemuscle airmuscle waterair etc Repeat the above exercise keeping in mind that higher energy Xrays are more damaging Assume that damage to tissue is proportional to energy and determine the optimal energy levels for each of the above cases Instructor Contact Information Badri Roysam Professor of Electrical Computer amp Systems Engineering Of ce JEC 7010 Rensselaer Polytechnic Institute 110 8 11 Street Troy New York 12180 Phone 518 276 8067 Fax 518 276 62612433 Email roysam ecseggiedu Website httgWWWggieduroysab NetMeeting 1D for off campus students 1281136180 Secretary Laraine lV chaelides JEC 7012 518 276 78525 michal ggiedu why nut cu m luridquot Instructor Contact Information Kai E Thomenius Chief Technologist Ultrasound amp Biomedical Of ce KW C300A GE Global Research Imaging Technologies Niskayuna New York 12309 Phone 518 3877233 Fax 518 3876170 Email thomenngcrdgecom thomenius ecseIpiedu Secretary LaIaine Michaelides JEC 7012 518 276 525 michal gpiedu Rensselaer GE Global Research w u mquot n rm ECSE4962 Introduction to Subsurface Sensing and Imaging Systems Lecture 11 PulseEcho Imaging Systems Kai Thomenius1 amp Badri Roysam2 1Chief Technologist Imaging Technologies General Electric Global Research Center 2Professor Rensselaer Polytechnic Institute GE Global Research Center for SubSurface Imaging amp Sensing Outline of Course Topics PULSE ECHO METHODS Examples 0 THE BIG PICTURE MRi What IS iUbSUl faCe senSIng 8 A different sensing modality imaging from the others Why a course on this topic Basics of MRI EXAMPLES THROUGH MOLECULAR vAGNG TRANSMISSION SENSING Whatis it XRay Imaging PET amp Radionuclide Imaging Computer Tomography IMAGE PROCESSING amp Intro into Optical Imaging CAD COMMON FUNDAMENTALS propagation of waves ultrasoujd of interest Recap Propagation Models Fresnel or nearfield Fraunhofer or far eld Near to far eld transition distance Starting W RayleighSommerfeld we derived a simpli ed CW far eld expression for the probe eld Fourier transform of the aperture O Neil s eXpression for a circular aperture Basic PulseEcho Imaging 0 Basic Steps 7 Send a pulse of acoustic energy into the patient at a chosen angle 7 Record the intensity echoes from 1 quotED CTR patient s body as a function of time along a line at angle 9 7 Using the known speed of sound and the arrival time of the echo calculate the location x y of each echo 7 Steer the beam to a new angle and repeat 7 From the above data compute and display an image in which the brightness of each pixel is the intensity of the echo at a point in the patient 0 This image has the shape of a slice of a pie ie a sector and is called a 1339 a quot19 5 no1 Brightness Scan or B Scan 7 We can also do linear parallel scans and 3D scans Ultrasound Scanners Most often prescribed modality flustmment sales 4B ever year Gannral Imaninn Variety of Applications gt Portable gt LowCost gt Safe gt RealTime Obrics Vascular Ultrasonic Transducers 39 Rely on the piezoelectric effect piezo means to press in Greek Lead Zirconate Titanate PZT a common piezoelectrical ceramic material Material compresses or expands depends on polarity of voltage Works in reverse as well compressingexpanding the material produces a voltage Can transmit and receive using the same VOItage 1 device PUIse An array ofpiezo elements crystals 7 i provide an array of acoustic sources Each element is roughly 02 1 mm thick 7 7 A o Smaller elements have higher resonance Y frequencies Damping amp Coupling Materials Mixture of metal powder amp epoxy Short Ultrasound Lon Pulse Ultrasound 2393 0370165 Pulse TISSUE The impedance of the solid transducer is 20 times that of tissue 3 90 re ection at surface The matching layers and the gel are of intermediate impedance and they bridge the impedance gap 7 Better coupling Pulse Timing Sequence Pulse 1 us Pulse 1 us i 1 time 4 Listen gt 200 us Pulse repetition frequency PRF lt Listen gt 200 us Number of pulses sent to transducer per second Ranges from 415kHz Listening time must be long enough to receive all echoes from the most recently sent pulse Need to minimize old echoes Deeper imaging requires lower PRF Sound Bea from a Transducer L 4m z2gtlt Nearzone Length v FarField Fraunhofe Zone lt Focal Zone Frequency Width NearZone MHZ mm length cm 20 19 12 3 5 13 10 3 5 19 20 50 6 3 50 10 8 50 13 14 75 6 4 100 6 6 Arrays of Transducers LinearArray 39Arraysarearecumng lllll llllllllll 2322 imagmg By timing the Convex Array W operatlon of array elements we can achieve a large number of useful effects Beam Steering Delay Generator still at llt V V V V V V V V V V V H A Pulses are applied in rapid succession to adjacent transducers The sum of the waves generated by the transducers is a big wavefront The direction of the wavefront can be pointed at any desired angle Beam Focusing Delay Generator I Pulses to the center elements are send ahead of the peripheral lt ddlt tTI EHSducers e sum of the waves generatedbythe lllllllllllllllll transducersisacurved A wavefront with a focus The focal length can be lt5 adjusted dynamically by varying the pulse timing 0 Focus Variable Aperture We can choose to activate any subset of transducers Switches I Small subset gt low aperture Big subset gt large aperture Used to maintain comparable focal beam Width at different depths Low aperture at low depths High aperture at high depths Geometry for Beam Calculations Delay determination simple path length difference reference point phase center Z apply Law of Cosines approximate for ASIC I I rx implementation C To combine steering amp focusing we can split delay into 2 parts beam steering T lLx2 2rxsin6r2 r c dynamic focusing I 2 quotCS If Reception Focusing summing stage 40 3O 20 10 0 1O 20 30 40 We can listen in a focused manner Reception Focusing amp Beam steering before Apodization Voltage Adjusters Switches a a We can choose to apply different voltages to transducers across the array Used to minimize sidelobes in the beam pattern Higher voltages in the middle Set according to a mathematical Window pattern eg Hamming Window Improved PulseEcho Imaging 0 Focus the beam at a speci c distance Z along the line 7 While listening reject all echoes outside the focal zone Takes longer but produces better images by rejecting clutter This is a recurrent idea in imaging systems A 7 We ll see a similar idea in 3 3 quotms no D confocal optical microscopy Ultrasound Transducer Array Element Isolation Cuts Acoustic Lens Acoustic Matching Layers Ground Electrode Piezoceramic Signal Electrode Acoustic Absorber Ground Flex Signal Flex Circuit Ultrasound Probes Linear Convex Intraoperative Vaginal Rectal Linear Scan Transmit Beamforming o o o 0 O Pulser Beamformer o 63 64 127 Channel Number T quot Probe Multiplex rk k k e k k Element Numberola l 63JI JI64 127II l l L91 Transmit Focus 0 O O O Transmit Focus Beam n Weidlinuer Aeeeeiates Flex version 1 h5 materials Hem wen mun mHn back pmt3 5DMH2 1 D linear array beam focused at 5 cm materials HUM WEII39 n et mHn back pmtS Still images from sequence We dlinqcr Associates Flex version 17 h5 5 OMHZ 1 D linear array beam fccllsed at 5 Cm Overall Block Diagram of an Ultrasound Scanner Transmit Beamformation 1 Transducer Array l Receive Image Formation Beamformation Acoustic Wave Scattering Propagation Beamformation generation of coordinated timing signals for transmit and delays for receive processes Probably the most expensive building block Transducers usually multielement arrays or piezoceramic elements Image formation conversion to video raster image processing To Signal Processor Echo Delays AnalogtoDigital Converters Receiver Amplifiers Transmit Receive Switches gt Beam Former Pulse Voltages Pulse Delays IIIIIIII Pulse Generator The heart of the machine Lots of functions Generate voltages to drive transducers Determine PRF frequency intens1ty etc Steer scan focus amp apodize the transmltted beam Amplify received echo voltages Adjust gain to correct for depth dependent attenuation Digitize echo voltages Direct focus and apodize the reception beam Scan Conversion 3mm 0 Vectors from acoustic space must be scan converted to display pixels rastenzed nominal 400 X 400 pixels 8 EBeamformation R 9 t0 XaY I XY to XY HSC Winnipeg 788 BT88 GHEDD285D 14cm 3917 1312 DB FETAL PROFILE TISlt8 4 quot18 2 04439A Sequence of Events in Scanning 0 System processor initiates a scan 7 Beamformer set to appropriate Scan angle Transmit focal location 7 Pulsing voltage applied to array elements in timed sequence 7 Sound emitted from elements 7 Preamplifiers initiate reception of echoes 7 Receive beamformer applies needed delays to optimize energy from desired focus and look angle 7 Data stored scan conversion to video raster begins 0 Process repeats itself 38 8 quot18 5 01 TimeLapse Imaging The entire sequence of events we just discussed can be completed surprisingly fast ltlt 1 sec Once we start to approach 15 30 frames sec for the entire scan the system is considered real time Scanning Modes e ugamcm svsrzn 4cm an39 m my mom VA 39 FROZEN y Ian quot ACUTE RUFTURE SUPRASPINATUS TENDON ROTATOR CLIFF quot18 4 0188 BScan Real Time MMode There are several additional modes mainly involving Doppler These Will be covered in later lectures Typical Commercial Ultrasound System PROCESSED Mn PROCESSORS VECTOR DATA I Q Data SCAN D Pp39e39 sped Converter Color Flow Process Grey 2 RxSyE color 2D amp G M B MOde egg M Controller I Processor i l l I I E Scan Control Bus I E Front End Control Bus E I I l I l l I 39 I I I I TxSync Video Timing gt Scan lt Sequencer I operator System Control Bus VME Bus l Master Controller KERN EL Homework For a lOmm disk transducer What are the beam Widths at the nearzone length and at 2 times the nearzone length Download amp install Field 11 and the User s Guide to your computer htt wwwesoersteddtudkstaffa39 eldindexhtml Execute the rst example om httpWWWesoersteddtudkstaffiai eldexampleshtml the point spread function logo case You should get a strange looking impulse response Don t forget to initialize Field with eldinit command Change the number of transmitted cycles to one cycle three cycles How does the point spread function change Hand in your graphical MATLAB results Summary We have reviewed the major building blocks of an ultrasound scanner Transduction Beamformation Steering Focusing Apodization Scan conversion Next Class We ll learn about the Field 11 MATLAB simulation program 5 FEATURES UL Recognized Component Flexibility lnternal 40pin socketconfigures amp with no soldering Separate current limits Continuous peak and peaktime No integrator windup when disabled 3 LED s for faster setup Normalenable powerOK Fault short or overtemp Fault protections Shortcircuits from output to output output to gnd Overunder vo age Over temperature Selfreset or latchoff modes 3kHz Bandwidth Wide load inductance range 02 40 mH Surface mount technology construction lower part count APPLICATIONS XY stages Robotics Automated assembly machinery Automatically guided vehicles Magnetic bearings THE OEM ADVANTAGE Conservative design for high MTBF No soldering required to change header parts Custom configurations available contact factory Nopots custom headers Models 412 413 421 422 423 432 DC Brush Servo Amplifiers MODEL POWER lCONT lPEAK 412 2490 VDC 10 20 413 2490 VDC 15 30 421 24180 VDC 5 10 422 24180 VDC 10 20 423 24180 VDC 15 30 432 24225 VDC 10 2o FEATURES The 400 series are thirdgeneration amplifiers for dc brush motors from Copley Controls Corp Models operate from 24 to 225VDC unregulated power supplies and output peak currents from 10 to 30A Built using surfacemount technology these amplifiers offer a full comple ment of features for servo motor control All models take industry standard 10V control signals as input and operate motors in three different modes torque velocity and voltage feedback with IR compensation Torquemode finds the widest application for motors used with digital con trol cards that take encoder feedback from the motor for velocity and posi tion control Velocity loops using brushtachometer feedback are used for openloop speed controls or in position control loops requiring superior regulation at low speeds Tachless speed controls can be made using output voltage feedback with IR compensation where lowest cost is required Active logiclevel of Enable Pos Enable and Neg Enable inputs is switchselectable to interface with all types of control cards Groundtoenable or groundtoinhibit are both supported Mosfet Hbridge output stage delivers power in fourquadrants for bidirectional acceleration and deceleration of motors An internal 40pin header socket holds components that configure the vari ous gain and current limit settings to customize the amplifiers for a wide range of loads and applications Individual peak and continuous current limits allow high acceleration with out sacrificing protection against continuous overloads Peak current time limit is settable to match amplifier to motor thermal or commutation limits Header components permit compensation over a wide range of load induc tances to maximize bandwidth with different motors All models are protected against output short circuits output to output and output to ground and heatplate overtemperature With the Reset input open output shorts or heatplate overtemperature will latch off the amplifier until power is cycled off amp on or until the Reset input is grounded For selfreset from such conditions wire Reset to ground and the amplifier will reset every 50ms Three status LED s speed diagnostics during setup or for fault isolation after the unit is in service CO I C coRtTyols com 11 Models 412 413 421 422 423 432 DC Brush Servo Amplifiers TECHNICAL SPECIFICATIONS Test conditions 25 C ambient Load 200uH in series with 1 9 HV maximum normal value MODEL 412 413 421 422 423 432 OUTPUT POWER Peak power i20A i80V i30A i80V i10A i170V i20A i170V i30A i170V i20A i215V Peak time 1 sec at peak power or 2 secs after polarity reversal Continuous power i10A i80V i15A i80V i5A i170V i10A i170V i15A i170V i10A i215V OUTPUTVOLTAGE iVout iHV x 097 Ro gtltlo Ro02 Ro015 Ro04 Ro02 Ro01 Ro02 LOAD INDUCTANCE Selectable with components on header socket 200 pH to 40mH BANDWIDTH Current mode Small signal 3dBfreq Voltagefeedback mode 200Hz max 3kHz with 200pH load at maximum supply voltage varies with load inductance and RH20 CH18 values PWM SWITCHING FREQUENCY 25kHz REFERENCE INPUT Differential 100K between inputs i20V maximum GAINS lnput differential amplifier 10 1 Volt Vot PWM transconductance stage lpeak 6V l peak peak rated output current 6V measured at Current Ref J29 or Current Monitor J28 LOGIC INPUTS Input voltage range 0 to 24V Logic threshold voltage L0 to Hi transition 25V Schmitt trigger inputs with hysteresis Enable S1 OFF S1 ON reverses logic LO enables amplifier Hl disables 50ms delay to enable lt1msto disable POS enable NEG enable S1 OFF S1 ON reverses logic LO enables POSitiveNEGative output currents Hl inhibits lt1 ms delay Reset LO resets latching fault condition ground for selfreset every 50 ms lnput resistance 10K pullup to 5V RC filters to internal logic DIP SWITCHES S1 Enab LOHl Default OFF S1 OFF ground enables open or 5V inhibits Enabe Pos amp Neg enable N open or 5V enables ground inhibits Enabe Pos amp Neg enable 2 Integrator ONOFF Default ON 32 ON torque mode integrator off flatgain OFF velocity mode integrator on tachometer mode POTS Ref Gain Default CW Attenuates Ref input from 100 to 0 controls overall amplifier gain amps volt rpm volt or volts volt Tach Gain Default CCW Tach feedback gain sets basic rpm volt ratio also used as IR comp feedback control Loop Gain Default CCW Servo preamp DC gain increases amps volt gain in torque mode controls bandwidth in velocity mode lnteg Freq Default CCW Integratorfrequency control not used in torque model controls stiffness and speed stability in velocity mode BalanceTest Default center Use to set output current or rpm to zero RH9 10 M9 for Balance function RH9 100k 2 for Test function LOGIC OUTPUTS Faut Normal Hl output voltage HI Overtemp OR out 24V min at 52 mA m put short OR power NOTOK OR NOTEnabled L0 Operating normally AND enabled ax LO output voltage 05V max at 52 mA max Note TTL output do not connect to loads gt5VDC INDICATORS LED s Normal Green ON Amplifier Enabled AND Normal power OK no output shorts no overtemp Power OK Green ON Power OK HV gt22V AND HV lt92V for 41x lt185V for 42x lt230V for 432 Fault Red ON Output shortcircuit or overtemperature condition MONITOR OUTPUTS Current Monitor motor or load current Current Ref current demand signal to PWM stage Voltage Monitor load voltage at output terminals i6V ilpeak 1 k9 33nF RC filter i6V demands ilpeak Vout 10 412 413 Vout 20 421 422 423 432 Bandwidth 200 Hz DC POWER OUTPUTS i5VDC i5 mA PROTECTIVE FEATURES Output short circuit output to output output to ground Overtemperature Undervoltage shutdown lt22V Latches unit OFF Latches unit OFF at 70 C on heatplate Copley 1 2 88 Models 412 413 421 422 423 432 DC Brush Servo Amplifiers COMPONENT HEADER STD VALUES PART FUNCTION NOTE 1 STANDARD VALUE CHANGES WITH DIFFERENT MODELS gt o o RH20 LOAD INDUCTANCE COMPENSATION SEE quotARMATURE INDUCTANCEHCHART BELOW 0 45v 15v o HDR19 HEADER INTERNAL VOLTAGES 47NF O O o CH18 LOAD INDUCTANCE COMPENSATION O RH17 PEAKTIME LIMIT 0 RH16 CONTINUOUS CURRENT LIMIT 0 o RH15 PEAK CURRENT LIMIT RH14 IR COMP FEEDBACK 220 PF O O O CH13 HEADER LOCATION 60 OO RH12 PREAMP DC GAIN HI FREQ ROLLOFF COVER REMOVED 100K O o RH11 AUX INPUT 0 o RH10 OUTPUTVOLTAGE FEEDBACK 10MEG o o RH9 BALANCETEST NOTE DI SWITCI IjhrOIARITYI O 0 CH8 l TACH IN PUT LEAD NETWORK OFF I O o RH7 T 100K o o RH6 TACH IN PUT g REF INPUT LEAD NETWORK J 100K o o RH3 REFERENCE INPUT COMPONENTS IN DOTTED LINES MM O O CH2 INTEGRATOR RC ARE NOT INSTALLED AT FACTORY o 0 RI ARMATURE INDUCTANCE CH18 amp RH20 Model 412 413 421 422 423 432 Load mH C R C R C R C R C R C R 02 to 05 10k 33k 10k 10k 10k 10k 06 to 19 47 499k 47 806k 47 150k 4 7 249k 4 7 464k 4 7 402k 2to 59 150k 100k 30k 62k 100k 82k 6to 19 330k 220k 62k 150k 200k 15 150k 20 to 40 470k 470k 150k 270k 470k 1 300k Note Values in boldamp italics are factory installed standard C CH18 capacitance in nF R RH20 resistance in Q Values shown are for 90V 412 413 180V 421 422 423 and 225V 432 At lower supply voltages RH20 may be increased and CH18 decreased To customize values short CH18 select RH20 for best step response in currentmode next select CH18 for lowest value that does not degrade step response PEAK CURRENT LIMIT CONTINUOUS CURRENT LIMIT lpeak RH15 Q Icont RH16 Q 100 open 1 100 open 1 80 68kQ 80 100kQ 60 33kQ 60 39kQ 40 15KQ 40 15KQ 20 62kQ 20 1k PEAK CURRENTTIME39LIMIT Notes on Current Limits Tpeak S RH17 Q 1Vaues in boldamp italics are factory installed standard 1 open 1 2 Peak times double after polarity reversal O 8 1O Megs 3 Peak current limit should be set greater than continuous 39 current limit If lpeak lt Icont then peak overrides continu 06 22 M999 ous limit and Icont lpeak 04 1 MegQ Minimum setting for peak current is 0 Minimum setting for continuous current is 16 with RH16 0 Q 02 330KQ 4 Continuous current sense is for average current Sym metrical waveforms with zero average value may cause overtemperature shutdown of amplifier or motor damage due to high I2R losses Times shown are for 100 step from 0A co I CZCORtIs 13 lt Corp Models 412 413 421 422 423 432 DC Brush Servo Amplifiers FUNCTIONAL DIAGRAM SWITCHES SHOWN IN ENABLED POSITION FOR S1 OFF USE NORMALLY OPEN SWITCHES TO ENABLE IF S1 ON S1 OFF ENABLE POS ENABLE NEG ENABLE GROUND ACTIVE 5V OR OPEN INHIBITS S1 ON 5V OR OPEN CIRCUIT ACTIVATES ENABLE POS ENABLE NEG ENABLE GND INHIBITS 9 GND 33m G ENABLE INTEGRATOR RESET SWITCHES 1K RH 100K TURN ONVVHENAMPISDISABLED AUXlt W w v vquot 01UF TACH LEAD RH7 CH3 L 2 2quot 2 E V CH13 220 PF lt OFF VELOCITY MODE 39 0 1 1K 0 N CURRENT MODE RH6 100 K L H2 022 UF RH12 lt CW A If n MOMENTARY SVVITCH CLOSURE RESETS FAULT AVAVAW LOOP RE RESET TO GROUND FOR SELFRE 604 K lt GAIN 50K wOPF Ir NF If cURRENTLIMIT J2 SIGNAL CONNECTOR SECTION gt VALUE DEPENDS ON MODEL RH3 100 K RH15 SEE ARMATURE INDUCTANCE TABLE 50K PEAK REF GAIN SERVO lt NTEG RH16 D J1 MOTOR amp POWER CONNECTOR FREAMF FREQ CONT 1K CWlt 500K PEAK RH17 Rm 3 TIME 0 V V V O ltgt 1K MOTOR 5quot lt Voltage gain 1 RH9 STAGE MOSFET BALANCE 10 MEG V CUIRIRPENT quotHquot RH SENSE BRIDGE 15V IR COMP 1K 39GV f r VOLTAGE CUEERENT A A A peak GAIN v v 43 kHz FILTER GV 33NF 10 i K 6V a1 33313 N u v v 43 kHz FILTER RH 33NF 1 OUTPUT Tpu 1K VOLTAGE FEEDBACK VOLTAGE SENSE VOLTAGE m A A MONITOR W 43 kHz FILTER VouI20 421 422 423432 VouI10 412413 5 1 CASE MAY BE GROUNDED AUXILIARY DCDC FOR SHIELDING DC OUTPUTS 20k 15 CONVERTER T l 5 mA max 5 quotv v v 3915 J CASE GROUND 045 150 NOT CONNECTED 142039 A MAX TO CIRCUIT GROUND INTERNAL VOLTAGES PRESENT ON HEADER POWER GROUND AND SIGNAL GROUNDS ARE COMMON OUTLINE DIMENSIONS Dimensions in inches mm IlI III 80 391 gen LU U 1255 MOTOR r N 6 or CCU A 3 gt o 25 mg m mm 2241 gtmgtgtgt 93 mm X F MOTOR 2 G TACH GAI POTS LOOP GAIN Egg 510 W 12 5 2 g 01 4 Crrr mmmzm 222222271 mmbmmgmmmqm 4141 m am 00000 L EIEIEIEIEI 00000 l I 74 2 00 08 222 508 I I 150 381 30 762 14 CO I CORteIIvOIS Corp Models 412 413 421 422 423 432 DC Brush Servo Amplifiers APPUCAWONINFORMAHON IMPORTANT ALWAYS REMOVE POWER WHEN CHANGING HEADER PARTS SETUPSEQUENCE 1 Set RH15 RH16 and RH17 for motor currentlimits to protect motor during setup Disconnect motor and monitor Curr Ref signal at J29 while making settings Set CH18 RH2O on header for armature inductance Connect enable inputs Set S1 for your enable signal polarity Connect motor and if used tachometer Connect amplifier to transformerisolated DC power SUPP39Y 6 Adjust pots and switch S2 according to operating mode PEAK CURRENT LIMIT Amplifiers are shipped with no part installed in RH15 This delivers the amplifiers peak rated current For lower settings use values from the table CONTINUOUS CURRENT LIMIT Choose RH16 based on the motor manufacturers specifi cation for your motor Table values give basic settings This setting keeps the motor within its thermal limits Note that this limit measures average current and will not work on symmetrical waveforms such as might occur during system oscillation Use an external thermal circuit breaker for protection from such overcurrent faults V 2 3 VV 4 5 VV PEAKTIME LIMIT Header component RH17 controls the length oftime for which the amplifier will output peak current When peak currents that are less than the amplifiers peak rated current this time will increase eventually becoming infinite as you reach the continuous current After a polarity reversal the peak time will be twice that of a unipolar current change GROUNDING amp POWER SUPPLIES Connect positive terminal of power supply to J15 negative terminal to J14 For best results do not ground power supply but ground each amplifier with heavy wire from J13 to equipment star ground point If power supply is gt1m from amplifiers add IocaI filter capacitor near amplifiers 250uF minimum per amplifier ENABLE INPUTS With S1 OFF alEnable inputs must be grounded for the amplifier to operate For operation with cards that output 5V to enable the amplifier turn S1 ON Enable active level is now reversed so that grounding inputs will inhibit and 5V or open will enable S1 flips polarity of all enable inputs Note There is a 50ms delay between Enable TRUE and ampli er ON Delay on Pos and Neg enables is lt1ms ARMATU RE INDUCTANCE Values from table work well for most applications To optimize compensation with custom values Turn S2 ON Disconnect tachometer if used Set Ref Gain pot fuy CW Loop Gain pot fuy CCW Replace CH18 with a jumper short Apply 20Hz square wave input to Vref Adjust for i025V at Curr Mon J28 Choose value for RH2O that gives best step response without oscillation Replace CH18 with 47nF If waveform shows gt10 overshoot try larger capacitor until overshoot is 10 or less If no change is seen try smaller value for CH18 until overshoot appears 3 93 3 93 REFERENCE INPUTS Connect both Ref inputs to control card Ref to card output Ref to card ground Using both inputs will reject ground noise between control card and amplifier Use shielded twistedpair cable to minimize noise pickup between amplifier and controller TORQUE MODE For transconductance IoutVref Ipeak1OV 1 Set S2 ON 2 Set Ref Gain fuIIy CW 3 Set Loop Gain fuy CCW 4 To increase gain turn Loop Gain CW To decrease gain turn Ref Gain CCW VELOCITY MODE WITH BRUSH TACHOMETER Disconnect motor from machinery during setup Tachom eter reversal Will cause uncontrolled runaway Set Tach Gain Loop Gain and Integ Freq pots fuy CCW 1 Set S2 ON Connect motor and tach and DC power enable amplifier and spin shaft If motor runs away reverse tachometer connections 2 Apply 5H2 square wave to Ref inputs Adjust for i025V at V Tach input J26 3 Adjust Loop Gain pot CW until oscillation begins then backoff 2 turns If oscillation cannot be eliminated reduce RH12 until adjustment is possible Set S2 OFF Turn Integ Freq CW until overshoot exceeds 10 or oscillation begins Back off for best step response If overshoot is excessive with pot CCW change CH2 to 047uF and retry Use value of CH2 that gives good adjustment range for Integ Freq pot Adjust Tach Gain pot for desired Vtach lVref ratio Repeat steps 24 3 01 V Ref Gain pot will reduce Vtach lVref ratio without affecting tuning If oscillation occurs when motor is connected to load repeat steps 24 VOLTAGE FEEDBACK amp IR COMP Voltage mode with no IR comp is used with position loops that have no D term orthat output a position error signal only IR comp is used mostly with openloop speed control systems COI C Co tls COHl Models 412 413 421 422 423 432 DC Brush Servo Amplifiers 1 Skip this step if no IR comp Jumper J26 to J28 Tach Gain pot now functions as IR comp adjustment fuII CW no IR comp Select RH10 For 41x amplifiers RH1O HV kQ For 42x and 43x models RH1O HV2 kQ Use exact or next larger value Set S2 OFF Ref Gain Integ Freq ampTach Gain pots fuIIy CVV Loop Gain pot fully CCW Connect oscilloscope to J210 Output Voltage monitor Apply 1 10Hz square wave to Ref inputs Check for oscillation If oscillation occurs decrease RH12 to 10kg Oscillation should now be gone Skip this step for no IR comp Turn Tach Gain pot CCW to increase IR compensation Too much will cause oscillation Adjust for best speed regulation under different load conditions If Tach Gain pot cannot produce oscillation decrease RH6 until full range is possible 838 B 9 Ref gain pot can now be used to set overall voltage gain without affecting previous adjustments APPLICATIONS TORQUE MODE ENCODER VELOCITY MODE ENCODER I 4 1 J2 J1 5 2 J2 7 GND 2 GND 2 ENABLE 11 3 ENABLE 11 3 P03 ENABLE 12 J1 4 T GND POS ENABLE 12 J1 4 TGND 1 NEG ENABLE 13 5 J Hv NEG ENABLE 13 5 Jquot HV NOTE NOTE S1 OFF for groundactive S1 OFF for groundactive enables VOLTAGE FEEDBACK with IR COMP REF 4 1 Notes J1 5 J2 2 All amplifier grounds are common J134 amp J227 Caseheatplate is isolated from amplifier circuits T 6 TACH INPUT 2 For groundactive enable inputs set S1 OFF J2 For 5V active enables set S2 ON open inputs wiII GND 2 3 CURR MON OUTPUT enable amplifier via internal puIIups to 5V 3 For best noise immunity use twisted shielded pair cable ENABLE 11 3 for reference and tachometer Inputs P03 ENABLE 12 J1 4 I TGND Twist motor and power cables and shield to reduce m 13 5 I HV radiated electrical noise from pwm outputs NOTE S1 OFF for groundactive nables Copley 1 6 83115rols Models 412 413 421 422 423 432 DC Brush Servo Amplifiers ORDERING GUIDE Model 413 2490 VDC brush motor Model 423 24180 VDC brush motor Model 432 24225 VDC brush motor Notes 1 Add H to model number to specify heatsink option 2 For nopots or custom component con gurations contact factory co I CCoRtls 17 lt Corp 18 cm CO I cases Corporate Of ces 20 Dan Road Canton MA 02021 Telephone 781 8288090 Fax 781 8286547 Email salescopleycontrolscom wwwcopleycontrolscom ECSE4962 Introduction to Subsurface Sensing and Imaging Systems Lecture 10 More on Waves Their Interactions Kai Thomenius1 amp Badri Roysam2 1Chief Technologist Imaging Technologies General Electric Global Research Center 2Professor Rensselaer Polytechnic Institute GE Global Research Center for SubSurface Imaging amp Sensing Slide 1 Outline of Course Topics THE BIG PICTURE What is subsurface sensing amp imaging Why a course on this topic EXAMPLES THROUGH TRANSMISSION SENSING XRay Imaging Computer Tomography Intro into Optical Imaging COMMON FUNDAMENTALS propagation of waves interaction of waves with targets of interest PULSE ECHO METHODS Examples MRI A different sensing modality from the others Basics of MRI MOLECULAR IMAGING What is it PET amp Radionuclide Imaging IMAGE PROCESSING amp CAD Slide 2 Waves at Interfaces 0 Re ection amp Transmission 0 Refraction 7 At interfaces of media with differing propagation speeds 7 Can you have re ection between media w a common propagation speed 0 Diffraction 7 Sommerfeld s 1894 definition 39 any deviation of light rays from rectilinear paths which cannot be interpreted as re ection or refraction htmlecture0nlineclmsuedummgkg213cd372htm S d 3 x e What do we do with the Wave Equation Develop different propagation models These involve an aperture of some sort which de ne an incoming eld Such models permit the calculation of the eld some distance from the aperture An aperture in this context can be A slit in an opaque screen A transmitting radar antenna A sound source such as a transmitting sonar transducer Goal of Propagation Models Given a known eld at the aperture determine what happens to our probe as it travels in the medium of interest Slide 4 What are typical problems we need the Wave Equation for Determine the beam quality given an aperture size wavelength etc Beam quality features l l l Beamwidth often given as a full width half max distance i Sidelobe level given in dB with respect to the main lobe Example Determine the beam quality for ground penetrating radar l l mm l What size targets can we locate What penetration can be achieved For most cases complex simulations needed although good rules of thumb can get you started Slide 5 What are typical problems we need the Wave Equation for Determine the impact of the propagating medium to our eld What happens to our beam quality features Example What is the beamwidth and the sidelobe level of a focused acoustic beam after traveling through tissue Breast path Step 0 Time 100 us Use of simulated propagation gives information for more optimal operating parameter selection Slide 6 Simulated Wavefront Propagation in Breast Stop 1412 Tlmo42 us Step 5585 Time 2158 us Evolution of Wave Equation Maxwells Scalar F1elds Equations 1 Fresnel Helmholtz Green s V Diffraction I Equation Theorem Shadows and Zone Plates Fraunhofer F 1 Conditions General Kirchoff 7gtgtl lesne 39 w K1rchoff Problems Integral r I 1 Four1er Separable Theorem ntegra Transforms Problems Formula 1 Polar S mmet All Scalar y ry quot F1elds Far Wave from A ert re Hankel gt C1rcular Problems p u Transforms Apertures For more details a great reference is Ch 3 of Goodman s Fourier Optics McGrawHill Slide 8 Validity of Scalar Models Full Wave RayleighSommerield Fresnel Fraunhofer Equations amp FresnelKirohott near field far field zgtgtl gtgti kxif yamszz zgtgt k 22 72 Vemor Scalar Approximations J Solutions in 850 nm 966 um 46 nm w 1550 nm 791 um 25 mm Examples 50 um Aperture 200 um Observation kSSO 11m h1550 nm 0 Fraunhofer Approximation Assume planar wavefronts O Fresnel Approximation Assume parabolic wavefronts O RayleighSommerfeld Formulation Spherical wa vefronts gnu Optical Propagation Models 0 Geometric Ray Propagation G Positions and angles 9 No optical signal characterization Gaussian Propagation e 8 scalar parameters 20 x y 7 etc 0 Fast computation no explicit integration at each component a Limited diffraction compensation Scalar Diffraction Propagation G Fraunhofer Fresnel RayleighSommerfeld 9 2D complex wavefront e Propagation by summation of wavefronts Increased Com utation S eed Aoemoov peseemm o FullWave Propagation G Finite Difference Finite Element Rigorous v Coupled Wave Boundary Integral e Computationally intensive Slide 10 Ray Tracing Assumes waves propagate in 7 straight lines ray optics 5 Number of software packages 2 of varying degrees of 3 sophistication available 5 in 25 am m9 mm In example what is the impact of a plate on our focal characteristics What happens to the focal point Do all the lines go through the focus E Relatively straightforward Slide 11 RayleighSommerfeld Formulation O RayleighSommerleld Formulation e Diffractive component gtgt 9 a Distance to observation plane gtgt 7 jkr Z 6 wow l man 2 85877 11 r 0 Implementation 9 Huygens Fresnel principle n 9 Direct Integration iii 0 Computational Order ON4 l quoti r 1 l quotquotquotquotquotquot a Z x r ix Ullt9mgt Simpli cations Example from Radar 0 Let us work with a different version of the R S formulation EyR K I Web line where 0 1 R2 y x2 2yx x2 o 2 2 0 0 o In many applications 00 is greater than the aperture esp if R gtgt aperture 0 In such cases the denominator in the integral varies much more slowly than the numerator A x 1x PyR 0 p R I quotdx Based on Steinberg Principles of Aperture amp Array System Design Simpli cations Wp wdx 1x line If we expand the p in the phase term in a binomial series and keeping the dominant Rx terms we get Py R 2 x x2 0 p2p012p2 0 0 R l 2 p0E x pg 2 Now the complex eld strength is E y R w I Ixexpjkx sin 6 2 de 0 line 0 Slide 14 Simpli cations 6X 39 i x2 EyRkpo IxeX jka sin6 2p de Normalizing this expression to the value at 9 0 and setting u sin 9 gives us fat I z39xex ijkxu 2x Jdx W o The rst term in the integrand is the p Py R Fourier kernel eXpQ39kxu This is associated with the Fraunhofer R I V or farfield zone of diffraction theory 390 The second term in the integrand is the 39 dx Fresnel kernel eXpjkx22p0 This is associated with the Fresnel or nearfield zone of diffraction theory Slide 15 Far eld or Fraunhofer Zone 2 X f Iix eXpjkxu a Field due to a line 200 m I circular aperture 0 If p0 is so large that the variation of quadratic term is ltltl over the aperture that term will have little effect on the eld integral 0 If that is the case we can ignore the quadratic term mm mm Our eld expression now becomes a Fourier integral f I 1xeXPJ 7quot line Slide 16 Far eld or Fraunhofer Zone f I l39 xeXp jkxudx line A good rule of thumb for the transition to far eld is a distance of DZ47t For analyses beyond this point the above Fourier expression is accurate This is highly desirable consider a uniform line source an an mu mammal Hammingan so so we o In this example the aperture function is a rectangle The farf1eld response is its Fourier Transform the sinc functlon Slide 17 Far eld Response amp Fourier Transforms This is indeed a powerful Interferometer result 5 Everything we know about 7 Fourier transforms can be source ed Distribution Linearity add two sources 2quot quot 9 Delay Theorem shift sources 2 i i i Etc A What is the response of a quot Ramon point source V What is the far eld respon of a sinusoidal transmit pattern Slide 18 Focused Designs We often work with curved radiations parabolic dishes lenses focused transducers In 1949 O Neil published a very nice theory for determining the eld strength along the aXis of a spherical source While the derivation is beyond what we want to cover in this course the result is extremely useful O Neil HT Theory of Focusing Radiators JASA V01 215 pp 516 527 1949 Slide 19 O Neil s Formula O Neil developed the quot 7 5quotquot70 following expression for r a focusing radiation l 39 639 e a c o h a p pcuopj expjat kM s b A where 2 25 6 8 7 PEsink52 E 1 4 b G x h xh 5 C 1 z 391 813c h2czz x2 2xhb2 i 39 39 FIG 1 Dimensions and coordinates Slide 20 M le for function p oneilslambdaaRz O Neil s expression for axial pressure profile called by p oneilslambdaaRz This function retums the value of capital P as given by Eq 31 in O Neil s paper To get the pressure amplitude one has to multiply P byrhocu0 where lambda is the wavelength a is the radius of the aperture R is the radius of curvature z is the vector of distance along the aXis k 2 pi lambda delz 202 zll h R sqrtR 2 a 2 in findR 2 if isemptyin zin zin l0e4 end O Neil E2RRz delta sqrtz hquot2 aquot2 z p E sink delta 2 if isemptyin 0 21 zin delz 2 E2RRzl delta sqrtzl hquot2 aquot2 21 pl E sink delta 2 22 zin delz 2 E2RRz2 delta sqrtz2 hquot2 aquot2 22 p2 E sink delta 2 pinp1 p2 2 disp calculated new value for p at roc end Slide 21 O Neil Formulation Graph shows a typical result Aperture radius 10 mm Wavelength 077 mm Radius of curvature 50 mm Notice the location of the peak response it a does not coincide with the focal location Why Slide 22 Recap of the Lecture Overview of scalar diffraction theory W materials from optics acoustics Relation of the solutions to actual problems encountered Working with the RS formulation derived highly simplified expression as the Fourier transform of the aperture Demonstrated a closed form expression for focused circular apertures Slide 23 l a b c 2 a b Homework Determine the neartofar eld transition for the following cases Planar laser wave at 800 nm wavelength that travels through a 1 mm opening in an opaque screen A one THz electromagnetic radiation coming from a 5 mm antenna A 20 mm ultrasound transducer operating at a frequency of 10 MHZ Enter the oneils mfile Keeping aperture size constant for transducer in Slide 25 change wavelength from 05 to 10 in 01 mm steps Graphically show the impact of the change in wavelength Describe qualitatively the changes in the axial pro le How will this affect image data acquisition in terms of sensitivity and the depths at which the imager is likely to work well Slide 24 Instructor Contact Information Badri Roysam Professor of Electrical Computer amp Systems Engineering Office EC 7010 Rensselaer Polytechnic Institute 110 8th Street Troy New York 12180 Phone 518 2768067 Fax 518 27662612433 Email roysamecserpiedu Website httpwwwrpieduroysab NetMeeting ID for offcampus students 1281136180 Secretary Laraine Michaelides EC 7012 518 276 8525 michalrpiedu 39 Rensselaer why nnl change tho world Instructor Contact Information Kai E Thomenius Chief Technologist Ultrasound amp Biomedical Office KWC300A GE Global Research Imaging Technologies Niskayuna New York 12309 Phone 518 3877233 Fax 518 3876170 Email thomeniucrdgec0m thomeniusecserpiedu Secretary Laraine Michaelides EC 7012 518 276 8525 michalrpiedu 39 Rensselaer why not ung Mu world 16 GE Global Research Backup Slides Slide 27 A Few Words about Green s Theorem Key mathematical relationship that relates a volume integral of two functions in space to the associated surface integral Goodman prime foundation of scalar diffraction theory Important aspects to its application Careful choice of the Green s function G below This can be simply an expanding spherical wave from a point source Careful choice of the closed surface S below Some of the integral theorems are derived using these assumptions VI GVZU UVZGdv JG Z Ujds Slide 28

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