A Novel Multi-DOF Precision Positioning Methodology Using Two-Axis Hall-Effect Sensors

Transcription

1 5 Amerian Control Conferene June 8-, 5. Portland, OR, USA ThC6. A ovel Multi-DOF Preision Positioning Methodology Using Two-Axis Hall-Effet Sensors Abstrat A novel sensing methodology using two-axis Hall-effet sensors is proposed, where the absolute positioning of a devie atop any magnet matrix is possible. This methodology has the apability of mirometer-order positioning resolution as well as unrestrited translational and rotational range in planar -DOF (degree-of-freedom) motions, with potential apability of measuring all 6-DOF motions. This paper presents the methodology and preliminary experimental results of -DOF planar motion measurements atop a Halbah magnet matrix using two sets of two-axis Hall-effet sensors. This methodology uses the Gaussian least squares differential orretion (GLSDC) algorithm to estimate the relative position and orientation from the Hall-effet sensor measurements. The sensor and its algorithm are implemented to a magneti levitation (maglev) stage positioned atop a Halbah magnet matrix. Preliminary experimental results show its position resolution apability of less than m and position auray of less than. mm. Controllers were designed to lose the ontrol loop for the translational motion using the GLSDC outputs at a sampling frequeny of 8 Hz on a Pentek 8 digital signal proessor (DSP). Calibration was done by omparing the laser interferometers and the Hall-effet sensors outputs to improve the positioning auray. The results exhibit good repeatability. Index Terms Hall-effet sensor, preision positioning, multi-dimensional positioner, Gaussian least squares differential orretion F usuke Kawato and Won-jong Kim, Senior Member, IEEE I. ITRODUCTIO OR high-preision positioning of any devie suh as wafer steppers, surfae motors, magneti suspension stages, or long-range sanning stages, onventional methods use laser interferometers, optial sensors, or apaitane gauges [] []. These sensors have high resolution and low positioning noise, allowing sub-nanometer position measurements. The nonontat nature of these sensors is suitable for maglev appliations. However, these sensors have downsides in ost, design, and limitations in travel range. Components of suh sensors, suh as mirrors, laser heads, and laser interferometers whih Manusript reeived September,. This work was supported in part by the Texas Advaned Tehnology Program under Grant o Kawato is with Department of Mehanial Engineering, Texas A&M University, College Station, T 778, USA (orresponding author to provide phone: ; fax: ; ykawato@tamu.edu). W.-J. Kim is with Department of Mehanial Engineering, Texas A&M University, College Station, T 778, USA ( wjkim@tamu.edu) /5/$5. 5 AACC make up the sensing system add up to be very expensive. For example, the laser interferometry setup for the maglev stage in [] ost approximately $8,. In terms of design, these sensors need a very good surfae finish as a flat referene, where the laser beam will reflet to the laser reeiver. The mirrors may beome very large in order to ahieve long travel range, whih makes the levitated part (namely, the platen) heavy, affeting its performane and design. Another major downside of the use of laser interferometers is the limitation in rotation. Sine the laser beam refleted off the mirror must go into the laser reeiver, even small rotations on the order of a few milliradians an ause the laser beam to stray off the reeiver, whih auses the platen to beome unstable. In a pratial sense, this beomes more problemati when applying large (a few millimeters) step inputs beause this an ause a responsive jerk of the platen, whih may ause the platen to rotate enough to ause instability. It must also be noted that the appliations of maglev devies are not only for photolithography that requires nanometer-preision positioning, but for miroassembly, where nanometer resolution is not a strit requirement. Furthermore, there may be more need for larger angular displaement apabilities, whih annot be met using onventional laser interferometers. Having these onsiderations, we seek for inexpensive sensors with suffiient positioning apabilities allowing large rotations, with absolute outputs with respet to position. We fous on a sensing methodology using Hall-effet sensors in this paper. Hall-effet sensors are used in various fields, for they are ontatless, small in size, reliable, low-ost, and not sensitive to harsh and polluted environmental onditions. However, they are limited in auray due to offset, noise, temperature, and aging effets [5]. evertheless, Hall-effet sensors have been utilized in various measurement tehniques, suh as urrent sensing [6], sensing the movement of ferrous metal targets with Hall-effet proximity sensors, and measuring positions of rotating mahinery [7]. Previous work showed their apability in sensing rotations of less than one degree [8]. In this paper, we propose a novel methodology for 6-DOF positioning atop a magnet matrix, using multi-axis Hall-effet sensors. First, we explain the sensing mehanism and the position-alulation methodology. We demonstrate our onept by using two sets of two-axis Hall-effet sensors

2 : (,, ) Platen.5 in -magnet array S Target Area Sensor B 7.5 in (a) Sensor A (a) -magnet array (,, -) (b) Fig.. Halbah magnet matrix [], []. (a) Coneptual superimposition of the two orthogonal Halbah magnet arrays to produe a onentrated-field magnet matrix. (b) Top view of the onentrated-field magnet matrix : (b) Fig.. Photograph of the experimental setup. (a) Multi-DOF positioner [] with two sets of D-VH-SO Hall-effet sensors mounted on the base. The triangular platen is plaed atop a mirror-finished aluminum plate, and beneath the plate is the Halbah magnet matrix. (b) Close-up view of the mounted Hall-effet sensor A. (Model D-VH-SO by Sentron AG [9]) for -DOF positioning in a plane. Preliminary experimental results are presented. Our approah has many attrative features inluding () very small sensor with unrestrited range in planar (,) and yaw ( z ) motion, () no ostly laser-interferometer setup required (a two-axis Hall-effet sensor is $ apiee), () relatively simple eletroni iruits with no demanding design onstraints, () an be applied in various fields, not limited to magneti fields, and (5) apable of sensing large rotations with sub-degree resolution. II. TWO-AIS HALL-EFFECT SESIG MECHAISM The methodology proposed in this paper is appliable for the positioning of a platen atop various magneti matries, suh as [] []. In this paper, we onsider positioning of a platen on a double-axis Halbah magnet matrix, presented in []. The platen is a magnetially levitated positioner, and is apable of positioning in 6 DOFs with -nm positioning resolution. The platen is urrently suspended using aerostati bearings, and generates fore to move in all 6 DOFs using three planar motors, whih are attahed to the bottom of the platen. Figure (a) shows the platen with two sets of two-axis Hall-effet sensors mounted. The sensor fixture is designed suh that vertial and rotational adjustments an be made. Underneath the platen is the Halbah magnet matrix overed with a mirror-finished thin aluminum plate. A lose-up view of the sensor and the fixture is shown in Figure (b). A. Halbah Magnet Matrix Analysis A oneptual onstrution of the Halbah magnet matrix is shown in Figure. The magnet matrix is a superposition of two orthogonal Halbah magnet arrays with orthogonal magneti fields. Halbah arrays have a stronger fundamental field by a fator of, whih allows a design of a higher power-effiient magneti devie []. The magnet matrix onsists of two kinds of magnets. One is a strong magnet with 9 magnetization (shown with or S in Figure ), where we hose dfeb5 material whih has a remanene of B rstrong =. T. The other magnet used is a weak magnet with magnetization in 5 (shown with arrows). dfeb with a remanene of B rweak =. T was hosen, whih was the weakest dfeb at the time of purhase. The blank areas are non-magneti aluminum spaers. The pith of eah magnet array is 5.8 mm ( ), and the dimension of eah magnet and spaer is.7 mm.7 mm.7 mm ( ). The letters,, and are used for the axes of the magnet matrix, and x, y, and z, the body-fixed axes of the platen. Due to the periodiity of the magnet matrix, the magneti flux density B is modeled using Fourier series. The results for B are shown in Figure. The results for an ideal Halbah array and the fabriated array are presented. The differene results from using weak magnets whih differ from the ideal ase,

3 Fig.. Fourier oeffiients of magneti flux density B at -mm air gap Fig.. Analytial result of magneti flux density B of an ideal Halbah magnet matrix at -mm air gap magnitude (T) B (T) B (a) B y B x platen pith Fig. 5. -D positioning method A z y x A y A x Hall-effet sensor Fig. 6. Representative Hall-sensor setups with minimum number of sensor, (a) for -DOF position sensing in a plane, (b) for 6-DOF position sensing Brstrong Br weak.. () From this analysis, we find that for an ideal Halbah magnet matrix, the fundamental, 5th, 9th, harmonis are non-zero and the other odd harmonis are zero. For the B z B B x ideal atual Harmoni number (n) A z (b) C z A y y C A x x C y atual ase, the fundamental and the 5th-order harmonis have the largest magnitude, and hene we hose these two harmonis as the basis funtions. The urve-fitting model of the magneti flux density at ( i, i, ) is in the form, B ( i, i, ) sin( i) sin(5 i) sin( i) sin(5 i), () B( i, i, ) sin( i) sin(5 i) sin( ) sin(5 ), where,,,, and are the parameters to be urve-fitted. The oeffiients and are inluded to ompensate the sensor misalignment, and is the DC offset. The urve-fitting proedure is presented in Setion III. The -omponent of the total magneti flux density in the target area is shown in Figure. The -omponent is idential, but the axes are reversed. B. Proposed Sensing Method We propose a novel methodology for a 6-DOF positioning of a platen atop a magnet matrix, using multi-axis Hall-effet sensors. This methodology will allow positioning of the platen within the target area in Figure, whih is one pith by one pith (5.8 mm 5.8 mm, ). First, onsider a ase for positioning within one pith in -D, as shown in Figure 5. The platen will move along the -axis where there is a periodi magneti field B that an be modeled as a periodi funtion. On the platen are two Hall-effet sensors whih an detet the magneti flux density at two points along the -axis. If there are two Hall-effet sensors positioned with some phase lag with respet to the pith, it is possible to detet the unique position of the platen within one pith, as well as the diretion of motion. Further, if the Hall-effet sensors are loated pith,,,,... n n () apart, at least one sensor will be loated in a sensitive region where the gradient of B is large. This will allow positioning within the target area to be sensitive at all loations. ext, onsider positioning in a -D plane without rotation. If there are orthogonal magneti fields in a plane and two measurements an be taken for eah axis, we an position the platen. This is preisely the reason we onsider the use of magnet matries. An example of a sensor setup for -D planar positioning is shown in Figure 6 (a). ote that this has only the minimum number of sensors, and having more redundant sensors will improve the resolution and auray of positioning. Further, the fat that the fields B and B are orthogonal brings one more advantage. By having four sensor outputs and two orthogonal magneti fields, it is possible to detet i i

4 Fig. 7. Definition of sensor loations and axes of measurement d the orientation z of the platen as well. This approah an be extended to 6-DOF position sensing, where in that ase, the oeffiients of the urve-fitting (,,, and ) will be modeled as a funtion of the air gap. One possible setup for 6-DOF position sensing is shown in Figure 6 (b). An important part of this researh is to find a way to map the nonlinear relationship between the four sensors outputs to the position and orientation of the platen. Candidate methods for this nonlinear mapping inlude neural networks [5] and the GLSDC [6]. The GLSDC algorithm was implemented due to its more deterministi nature, and resulted in better onvergene. Also, the GLSDC inorporates the ontinuous, periodi model, and the output will be ontinuous even when the platen goes beyond the target area. C. Experimental Setup A photograph of the experimental setup for -DOF positioning is shown in Figure. The platen s axes are defined at the platen s enter of mass, and are not aligned with the magnet matrix s axes. The axes of measurement are shown in Figure 7. The loation of the two sensors A ( xa, y A) and B ( xb, y B) are known in the body-fixed xyz oordinates. A Pentek 8 DSP is used for real-time ontrol, and a Pentek 6 analog-to-digital (A/D) onverter board and a Datel DVME6 digital-to-analog (D/A) onverter board is used for data aquisition and ontrol. The D-VH-SO Hall-effet sensor requires a -ma urrent soure, whih is provided using Vishay s urrent regulator diode CR. The four outputs of the Hall-effet sensors are amplified by y θ z Sensor B (x B, y B ) x a Sensor A (x A, y A ) b times using operational amplifier iruits, and then go through an anti-aliasing filter with a orner frequeny of Hz. The standard deviation of the sensor output noise after filtering is about mv. In Figure 7, the notation a, b,, and d are used for the sensor s outputs after amplifiation and filtering, whih orrespond to the input hannels of the Pentek 6. The GLSDC algorithm is implemented in real-time C odes, and the routine is exeuted every.5 ms (at 8-Hz sampling frequeny). III. SESIG ALGORITHM The objetive of this setion is to show how to resolve the position of the platen { } T z from the sensor outputs { abd } T using the GLSDC algorithm. The tilde represents measured values. A. Bath Least Squares The GLSDC minimizes the error between the measured output and the model, and by doing so estimates the position of the platen. Hene, we must derive an appropriate model of the magneti field for eah sensor output first. The model is obtained using a method of bath least squares prior to the experiment. Consider the ase for output a as shown in Figure 8. First, we obtain measurements as shown in Figure 8 (a). Using the method of bath least squares, we solve for the urve-fitted model shown in Figure 8 (b). The differene between the measured and modeled values is shown in Figure 8 (). The error is found to be less than mv. Possible reasons for this error are () fabriation error of the Halbah magnet matrix, () error in material properties of the magnets, () modeling error of the magnet matrix using bath least squares urve-fitting, () Hall-effet sensor misalignment with respet to the platen s axes, in x, y, and z, (5) error in defining the preise loation of the sensor (the sensitive volume of the Hall-effet sensor is 5 m 5 m m), and (6) external magneti field interferene and sensor noise. Large modeling errors may lead the GLSDC to onverge to inaurate positions, and preise adjustments in alignment must be made along with a low-noise iruit. Having suh a model for eah sensor. Sensor output (V) - Model sensor output (V) - Modeling error (V) (a) (b) () Fig. 8. Bath least squares results. (a) Sensor output a. (b) Curve-fitted model for output a. () Modeling error from urve-fitting 5

5 output, we proeed to the GLSDC algorithm. B. Gaussian Least Squares Differential Corretion The GLSDC solves the nonlinear relation between the position of the platen and the sensors outputs. A flowhart of the GLSDC algorithm is shown in Figure 9. At eah time step, the input signals y { abd } T are obtained, the Jaobian matrix H is solved, and the GLSDC algorithm is exeuted to minimize J, the sum square of the residual errors. J dereases when the GLSDC onverges, and hene an additional loop is added to hek for onvergene. This is a modified algorithm of the onventional algorithm presented in [6], where is a saling fator whih is adjusted to minimize the GLSDC output s osillation. For our experimental setup, the sensor noise s standard deviation is mv, and seleting. resulted in the best onvergene. The GLSDC algorithm takes approximately steps (.75 ms) to onverge when given a step input. IV. EPERIMETAL RESULTS Experiments were onduted to test the performane of the proposed sensing method. To ompare the laser interferometer and our method, the translational and motions are losed using Hall-effet sensor outputs and the GLSDC algorithm, and z motion is losed using the laser interferometers. This is beause when the z motion is losed using our method, the osillation beomes large that the laser interferometers go out of range. This is due to the reasons mentioned in setion III and an be improved by having redundant sensors. Figure shows the experimental result of a zigzag motion. A referene trajetory input to the ontroller is idential to Figure (a), and the platen has been ontrolled to follow the preplanned path very well. However, the atual path of the platen deteted by the laser interferometers outputs is shown in Figure (b). There is a signifiant deviation between the measurements from the laser interferometers and the output of the GLSDC based on the Hall-effet sensors outputs. The maximum positioning error an be as large as. mm, as shown in Figure (). Sensor alibration and using redundant sensors may redue this error. Beause the outputs of the GLSDC are absolute and repeatable, alibration an be done by error-mapping the results of Figure (). The tabulated error is ompensated using linear interpolation with the laser interferometer output as the true measurements. The laser interferometer outputs are shown in Figure for the two ases to a -mm step input. The non-alibrated result shows that the platen atually moved. mm whereas the alibrated results show that it moved mm, hene following the ommand orretly. The GLSDC output for - m steps is shown in Figure. The Hall-effet sensors are apable of deteting the hange Starting estimate x y% x = x, after x = x + α x ES Model fx ( ) Determine f x y =y-f(x % ) J f H = x x xafter = x + x J O T before = yw y ( T T x = HWH) HW y y =y-f(x % ) after < J before Fig. 9. Modified GLSDC algorithm [6] J after after T after = yafterw yafter?...5 x error in error in x - (a) (b) () Fig.. Experimental results of positioning the platen in and using the proposed algorithm. (a) Measured position from the Hall-effet sensors. (b) Measured position from the laser interferometers used for Hall-effet-sensor alibration purpose. () Error between the two measured values. 6

6 in magneti flux density for position hanges of less than m, and hene this method has at least - m position resolution. V. COCLUSIOS AD FUTURE WORK We developed a novel sensing mehanism using two-axis Hall-effet sensors that have the apability to detet the position with mirometer resolution above any type of magnet matrix. The sensing mehanism and experimental results are presented in this paper. A GLSDC algorithm was implemented in real-time C odes at a sampling frequeny of 8 Hz. This sensing mehanism an also be used as a bakup purpose when the sensing signal using laser interferometers beomes undetetable due to large rotation. Using two two-axis Hall-effet sensors are suffiient to estimate the position and orientation. However, there was a signifiant error in positioning whih resulted from the reasons listed in Setion III. Calibration has improved the auray signifiantly. Currently, the translational motions in and are losed using the Hall-effet sensors, and z is losed using laser interferometers so that we an ompare the Hall-effet sensor s performane with the laser interferometers. Closing the remaining z using this sensing method is our future work. Further, we plan to test the GLSDC algorithm with redundant sensors, whih will improve the auray further. ACKOWLEDGMETS The authors would like to thank Tiejun Hu, ikhil Bhat, and Jie Gu, former graduate students of Won-jong Kim, for their ontributions in this projet. REFERECES [] W.-J. Kim, High-preision planar magneti levitation. Ph.D. dissertation, Massahusetts Institute of Tehnology, June 997 [] W.-J. Kim,. Bhat, and T. Hu, Integrated multidimensional positioner for preision manufaturing, Journal of Engineering Manufature, vol. 8, no., pp., Apr.. []. Shan, S.-K. Kuo, J. hang, and C.-H. Menq, Ultra preision 6 x Fig.. Output of the GLSDC when - m steps are applied to the platen motion ontrol of a multiple degrees of freedom magneti suspension stage, IEEE/ASME Transations on Mehatronis, vol. 7, no., pp , Mar.. [] M. Holmes, R. Hoken, and D. Trumper, The long-range sanning stage: a novel platform for sanned-probe mirosopy, Preision Engineering, vol., no., pp. 9 9, July. [5] C. Shott, R. Raz, F. Betshart, and R. S. Popovi, A new two-axis magneti position sensor, Sensors, Proeedings of IEEE, vol., pp. 9 95, June. [6] L. Law, Measuring urrent with IMC Hall effet tehnology, Sensors, vol., no., pp. 9, ov.. [7] P. Driljae, M. Demierre, C. Shott, and R. S. Popovi, onlinear effets in magneti angular position sensor with integrated flux onentrator, Pro. rd International Conferene on Miroeletronis, vol., pp. 6, May. [8] J. Trontelj, Jr,. Funtionality test for magneti angular positioning integrated iruit, Informaije MIDEM, vol., no., pp ,. [9] Sentron AG website. [Online]. Available: [] T. Asakawa, Two dimensional preise positioning devies for use in a semiondutor apparatus, U.S. Patent 55 78, Aug., 995. [] W. Hinds, Single plane orthogonally movable drive system, U.S. Patent 65 57, Mar., 987. [] D. Ebihara and M. Watada, Study of a basi struture of surfae atuator, IEEE Transations on Magnetis, vol. 5, no. 5, pp , Sep [] D. Trumper, W.-J. Kim, and M. E. Williams, Magneti arrays, U.S. Patent , May, 997. [] K. Halbah, Design of permanent multipole magnets with oriented rare earth obalt material, ul. Instrum. Methods, vol. 69, no., pp., Feb. 98. [5]. H. Hu and J.-H. Hwang, Handbook of eural etwork Signal Proessing, st ed. Boa Raton, FL: CRC Press,. [6] J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynami Systems, nd ed. Boa Raton, FL: Chapman & Hall / CRC Press,. 5 x - 5 x - 5 x - from laser interferometer from laser interferometer from GLSDC (a) (b) () Fig.. Laser interferometer output to a -mm step, (a) without alibration, (b) with alibration, and () GLSDC output with alibration 7