MANY traditional mechanical stages for positioning,

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1 1254 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998 Modeling and Vector Control of Planar Magnetic Levitator Won-jong Ki, Meber, IEEE, David L. Truper, Meber, IEEE, and Jeffrey H. Lang, Fellow, IEEE Abstract We designed and ipleented a agnetically levitated stage with large planar otion capability. This planar agnetic levitator eploys four novel peranent-agnet linear otors. Each otor generates vertical force for suspension against gravity, as well as horizontal force for drive. These linear levitation otors can be used as building blocks in the general class of ulti-degree-of-freedo otion stages. In this paper, we discuss electroechanical odeling and real-tie vector control of such a peranent-agnet levitator. We describe the dynaics in a dq frae introduced to decouple the forces acting on the agnetically levitated oving part, naely, the platen. A transforation siilar to the Blondel Park transforation is derived for coutation of the stator phase currents. We provide test results on step responses of the agnetically levitated stage. It shows 5-n rs positioning noise in x and y, which deonstrates the applicability of such stages in the next-generation photolithography in seiconductor anufacturing. Index Ters dq theory, linear peranent-agnet otor, agnetic levitation, photolithography, precision position control, vector control. I. INTRODUCTION MANY traditional echanical stages for positioning, such as used in wafer steppers in seiconductor anufacturing, have either crossed-axis-type or gantry-type configurations [1] [3]. The -axis linear stage is typically driven by another -axis stage oving orthogonally to the axis. The echanical bearing tolerance for these precision position control systes ust be very tight, so they are expensive to ake. Soe precision planar positioners also use a piezoelectric fine-otion stage on top of a coarse echanical stage. Vertical ( axis) otions for focusing are generated by additional independent echanical eans. Such Paper IPCSD 98 51, presented at the 1997 Industry Applications Society Annual Meeting, New Orleans, LA, October 5 9, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Coittee of the IEEE Industry Applications Society. This work was supported in part by Sandia National Laboratories under Subcontract AH The work of W. Ki was supported by the Korean Ministry of Education. The work of D. L. Truper was supported by a National Science Foundation Presidential Young Investigator Award. Manuscript released for publication July 9, W. Ki is with SatCon Technology Corporation, Cabridge, MA USA (e-ail: wjki@alu.it.edu). D. L. Truper is with the Departent of Mechanical Engineering, Massachusetts Institute of Technology, Cabridge, MA USA. J. H. Lang is with the Departent of Electrical Engineering and Coputer Science, Massachusetts Institute of Technology, Cabridge, MA USA. Publisher Ite Identifier S (98) systes are coplicated and expensive and have coplex dynaics which liit high-speed operation. It is a trend that the industry has coe to use planar otors for two-diensional positioning applications ore frequently than ever. The Sawyer otor is one of the earliest inventions in this category [4]. Since its otion is tightly constrained to a plane, a Sawyer otor cannot provide focus range or local leveling without using fine-otion actuators. However, the agnetically levitated stage presented herein can generate all six-degrees-of-freedo (6-DOF) otions required for focusing and alignent, and large planar otions for positioning using a single agnetically levitated oving part, naely the platen. This is a significant advance over other existing techniques described previously, thanks to the resulting echanical siplicity. The platen can be designed to have a high natural frequency and, thus, can be oved ore rapidly than ultieleent stages which have ore coplex dynaics. This allows higher speed and, thus, increases achine throughput. Magnetic levitation can also achieve the nanoeter-order position resolution required for deep-subicroeter lithography when appropriate position sensors are used. The actuators for this planar agnetic levitator are threephase surface-wound surface-peranent-agnet linear otors. Error otions due to cogging and nonlinear effects are expected to be inial [5]. The linear otor uses a Halbach agnet array for its power efficiency and low field distortion [6], [7]. Induction otors are avoided, since they dissipate heat in the oving part and are generally hard to control. Variable-reluctance otors, such as stepper otors, have inevitable cogging forces. Multiphase peranent-agnet otors are capable of generating suspension force, as well as drive force [8], [9], so that they do not need any other actuators for suspension and fine position adjustents. We provided a general design and analysis fraework for peranent-agnet achines in a previous paper [10]. There, we derived field solutions, force equations, and an electrical terinal relation for a general class of surface-wound linear peranent-agnet otors. Here, we use these results to derive dynaic equations of otion and a coutation law for the planar agnetic levitator. In this paper, we discuss the odeling and vector control of our planar agnetic levitator. In Section II, we present an overview and the basic working principles of the agnetically levitated stage. A luped decoupled odel using decoposition theory is presented in Section III. We derive in Section IV linearized dynaic equations of otion of the agnetically /98$ IEEE

2 KIM et al.: MODELING AND VECTOR CONTROL OF PLANAR MAGNETIC LEVITATOR 1255 agnetic levitator. To drive the otors, we constructed linear transconductance power aplifiers. Their axiu current and voltage ratings are 1.5 A and 22 V, respectively. The noinal power dissipation per otor is 5.4 W at the 0.5-A noinal peak phase current. The suspension power dissipation coefficient of the agnetically levitated stage is 7.2 W/N. The noinal airgap clearance between the agnet array and the stator is 250. The noinal otor airgap for the capacitance gap sensor is 250 larger than that of the otor airgap, so that the capacitance probes are not touched by the platen in any condition. The detailed electrical and echanical design of the platen and stators and the instruentation structure of the syste are described in [11]. Fig. 1. Planar agnetic levitator. levitated stage. Finally, the real-tie controller design and test results are presented in Section V. II. PLANAR MAGNETIC LEVITATOR Fig. 1 shows a photograph of the planar agnetic levitator [11]. The planar otion coverage of the stage is 50 50, which can readily be scaled to accoodate the next generation wafers. For focusing and alignent, the vertical travel range is 200 and the angular ranges of the stage are 600 rad. We use three channels of laser interferoeters with subnanoeter resolution to easure the position in the plane and three channels of capacitance probes for the stage position out of the plane. Thus, all otions required for photolithography can be supplied by this single stage. The design is also applicable to the newer classes of step-and-scan lithography stages. Fig. 2 is a perspective view of the prototype agnetically levitated stage. The agnetic levitator contains four threephase linear peranent-agnet otors as its actuators. The linear otor is designed to generate suspension (vertical) force, as well as translational (lateral) force, as indicated in Fig. 2. The unpried frae (the inertial frae) is fixed to the stators with its origin at the center of the stators on the plane enclosing the three sensing surfaces of the capacitance probes. The pried frae (the body frae) is fixed to the platen with its origin at the platen center of ass. With an arrangeent of the otors as in Fig. 2, the platen generates all 6-DOF otions for focusing and alignent and large two-diensional step-and-hold and scanning otions for high-precision positioners, as used in wafer stepper stages in seiconductor anufacturing. For exaple, we actuate positive and in Fig. 3 to get a otion in the positive direction. 1 To generate a positive rotation around the axis, we put positive and and negative and. Motions in the four other degrees of freedo are generated in siilar ways. A TMS320C40 digital signal processor is used as a realtie control processor to stabilize and control the planar 1 The capital XY Z frae is fixed to the platen and used as a reference frae for the equilibriu conditions in the Appendix. The X and Y axes are on the sae plane that contains the x 0 and y 0 axes and are rotated by 45 around the z 0 axis. III. DECOUPLED FORCE EQUATIONS For odeling purposes, we easured the echanical and electrical paraeters of the stage. The platen ass is easured as 5.58 kg. The inertia tensor of the platen about the platen center of ass is calculated as kg- (1) The resistance and the self-inductance of one phase of the winding are 14.4 and 3.44 H, respectively; the utual inductance is negligible because the stator is ironless. In the rest of this section, we derive decoupled force equations with a theory. A. Decoposition The decoposition in conventional rotary achines is introduced to isolate the stator current coponent that generates torque [12], [13]. The principal goal of the decoposition is to express the electrical dynaics of the stator and the rotor in a coon reference frae. The direct axis ( axis) and the quadrature axis ( axis) are fixed to the rotor frae and rotate with the rotor. Then, force equations and coutation described in the frae do not contain the position dependence with respect to the stator. Each linear otor in our levitator is designed to generate suspension force, as well as translational force, as indicated in Fig. 2. Decoupling the two orthogonal force coponents should be perfored to control the two degrees of freedo independently. As in Fig. 4, we define the axis as the axis in the platen frae. The axis leads the axis by a quarter of the otor pitch, which is 90 in electrical angle, in the direction. In previous work [10], we defined and as the real and iaginary parts of the fundaental current density coponents in the stator windings. Let and be the quadrature and direct coponents of this current density, respectively. Then, the following transforation fro to holds with the definitions in Fig. 4: (2)

3 1256 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998 Fig. 2. Perspective view. Fig. 4. dq frae fixed to the platen. and (4) In the above equations, is the horizontal displaceent of the frae with respect to the frae in Fig. 4. Fig. 3. Free body diagra for force allocation. where, and is a transforation atrix given by (3) B. Force Equations We derive decoupled force equations in steady-state suspension in a dynaic equilibriu. Using the relationships and, we rewrite the relationship [10, eq. (20)] between the total lateral and vertical forces and and the peak current coponents and. For otors II and IV, this results in (5)

4 KIM et al.: MODELING AND VECTOR CONTROL OF PLANAR MAGNETIC LEVITATOR 1257 For our design, the paraeters have the following values: the agnet reanence is T; the winding turn density is turns/ ; the nuber of active agnet pitches is ; the pitch is ; the absolute value of fundaental wave nuber is ; the agnet array width is ; and the noinal otor airgap is. The agnet array thickness is and the winding thickness is, deterined via the power optial design presented in [7]. The constant contains the effects of the otor geoetry and is equal to [10]. The sae force equation is valid for otors I and III by changing the variable to. Fro (2) to (5), we can decouple the lateral and vertical force coponents in the quadrature and direct current coponents and : (6) (7) where represents otors I IV. With the otor airgap fixed, the lateral and vertical forces are deterined by ultiplication of the constant agnet residual flux density and the stator currents or. 2 Thus, we produce with and with. The quadrature current does not influence the vertical force, and the sae holds for and. Substituting the above paraeter values specific to our otors, Fig. 5. Scheatic diagra of the decoupled lead lag controller. The factor of is introduced to atch the definition of. The transforation is defined by (11) The transforation atrix in the above has different eleents fro the usual inverse Blondel Park transforation [14]. The difference arises fro the phase current convention we are using, and the above representation is consistent with our previous work in [10]. Finally, the coutation law for the three-phase currents and the desired forces becoes N/A (8) yield the otor horizontal and vertical forces. C. Coutation We derive the coutation for the three-phase current densities,, and in the context of the theory (Fig. 4). The stator current density is a function of the lateral position on the stator frae. We can show that The three-phase current densities,,,,, and are located on the stator, the boundaries of which are at, and so forth, and,, and. Then, the inverse Blondel Park transforation holds between and in the balanced three-phase operation [14]. Fro this, it follows that (9) (10) 2 Recall the Lorentz force equation F = J 2 B. Other ters in (6) and (7) are geoetric constants. (12) We now have a relationship between the desired forces and the phase currents. IV. LINEARIZED EQUATIONS OF MOTION In this section, we derive linearized equations of otion for the vertical and lateral dynaics of the stage. They prove to be second-order dynaic equations with a ass and a (positive or negative) agnetic spring. To linearize these force equations, we set,,, and, where is the noinal levitation height, which is 250. Fro (8), the noinal direct current coponent is calculated to be 500 A, which generates 13.9 N per otor, about a quarter of the weight of the platen; four otors support the full platen weight of 54.7 N. The noinal quadrature current coponent is zero, because the platen is in a dynaic equilibriu with. The linearization in ters of the sall-signal quantities with tilde is discussed later in this section. A. Euler Angles We need a transforation between the two coordinate systes the body frae of the platen and the inertial frae of the stator. In other words, we describe the orientation of the body frae with respect to the inertial frae

5 1258 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998 Fig step response in z with perturbed otions in the other five axes. defined in Fig. 2. We follow the convention, which is coonly used in engineering applications, to define Euler angles [15]. Since the angular otions are sall in our case, the Euler angles,, and can be considered as rotations around the,, and axes. B. Equations of Motion Retaining zeroth- and first-order ters, the equilibriu condition for the vertical direction becoes fro (7) So, the equation of increental otion in the vertical direction is (15) When there is no control,, the vertical dynaics are arginally stable. The equation of increental otion in the lateral direction is derived siilarly [16], leading to (13) where is the total vertical force, su of,,, and. The factor of four in (13) results fro assuing that the four linear otors are equally responsible for suspending the platen. When the platen is in dynaic equilibriu, the weight of the platen should be atched by. Now, the force equation becoes (14) (16) When there is no control,, the lateral dynaics show its unstable nature. With the levitator odel in hand, we develop decoupled controllers in the next section. V. DECOUPLED VECTOR CONTROL Classical decoupled lead lag control is applied to stabilize the platen otion. We also provide test results on positioning noise and step responses in this section.

6 KIM et al.: MODELING AND VECTOR CONTROL OF PLANAR MAGNETIC LEVITATOR 1259 Fig rad step response in with perturbed otions in the other five axes. A. Vertical Mode Control By substituting noinal and geoetric paraeters given in Section III into (15), the decoupled vertical translational dynaics can be presented as (17) The phase argin of this controller is 51, and it is fairly robust to force perturbations. Fig. 6 shows a 5- step response in with this lead lag controller. Because of the geoetrical syetry in and of the levitation syste, they have identical controllers. These controllers are The odal force is a su of the decoposed vertical force coponents,,, and. The uncopensated resonant frequency of this platen ass-agnetic spring syste is calculated as 7.85 Hz, which is very close to the easured natural frequency 8 Hz during testing. To eliinate the steady-state error, the following lead lag controller with a pole at the origin is ipleented for : Their gains ust be different fro those in the the nuerical values of the oents of inertia ( kg- ) are different fro those of the ass. (19), since (18) The crossover frequency of this controller is 70 Hz. Fig. 5 is a block diagra of the closed-loop syste with the controller. B. Lateral Mode Control By substituting noinal and geoetric paraeters into (16), the decoupled lateral translational dynaics for the direction

7 1260 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998 Fig. 8. Positioning noises in 6-DOF position regulation with the decoupled lead lag controllers. for otors I and III can be presented as 3 A/D electronics used to saple the capacitance probe outputs is priarily responsible for the poorer positioning noise in. (20) The odal force is a su of the decoposed lateral force coponents and. Here, we again use the lead lag controllers fro (18) with a gain of N/ for and. Siilarly, the controller for has the sae pole zero pattern as before with a gain of N/rad. Fig. 7 is a 50- rad step response in. This copletes the description of the decoupled control design for 6-DOF stabilization of the agnetic levitator. C. Positioning Noise Fig. 8 shows the position regulation under the decoupled lead lag controllers designed above. The positioning noise 4 in and axes is on the order of 5 n in the root-eansquare sense. The positioning noise in is rad rs. The test result in Fig. 8 contains a strong 120-Hz coponent. Laboratory floor vibration due to a large transforer in the laboratory, or heating, ventilation, and air-conditioning (HVAC) equipent located in the next roo is believed to generate this noise. The figure also shows the vertical displaceent and the velocity in the direction. The vertical displaceent shows a 15-n-rs positioning noise in. The noise of the 3 We need to replace x with y for otors II and IV. 4 We use the terinology positioning noise for uncertainty in position due to various disturbance and noise, such as electric noise in position sensors, A/D and D/A quantization, floor vibration, etc. VI. CONCLUSIONS In this paper, we have presented the odeling and vector control of our planar agnetic levitator. All the 6-DOF otions required for focusing and alignent in photolithography and large planar otions for positioning across the wafer surface can be generated by only one agnetically levitated oving part. Thus, the echanical structure of the planar positioner is very siple. The actuators for the levitator are four surface-wound slotless peranent-agnet linear otors which exhibit no cogging force. The otors eploy Halbach agnet arrays for power efficiency and low field distortion. Each of these actuators can generate vertical, as well as lateral, forces; it is a two-degree-of-freedo actuator. We developed a theory for our two-degree-of-freedo actuator to decopose vertical and lateral force and current coponents. With this decoposition and transforations, we derived a coutation law to drive the four otors to stabilize and control the agnetically levitated platen. Linearized equations of otion were derived on the basis of the previous analysis [10]. A vector control was successfully realized for the planar agnetic levitator. We were able to stabilize the platen in 6-DOF, which confired the validity of our odel and coutation law. Decoupled real-tie digital lead lag controllers were designed and ipleented with a digital signal processor. As test results, we presented step responses of the agnetically levitated stage. This levitator shows 5-n-rs positioning noise and consues only 5.4-W power per otor and is suitable

8 KIM et al.: MODELING AND VECTOR CONTROL OF PLANAR MAGNETIC LEVITATOR 1261 for the next-generation photolithography in seiconductor anufacturing. APPENDIX FORCE ALLOCATION To ipleent decoupled digital controllers for 6-DOF stabilization of the platen, we derived force equations and decoupled the platen dynaics in Section IV. Since the current levitation stage is a redundant actuator syste, 5 we need to allocate the odal forces and torques to the vertical and lateral decoposed forces. A. Vertical Force Allocation The force allocation can be derived with a free body diagra (Fig. 3) and dynaic equilibriu. The vertical force coponents should generate three-degree-of-freedo focusing and alignent otions, as well as support the ass of the platen (5.58 kg). So, the noinal vertical forces ust satisfy N (21) By syetry, the two large-signal vertical force coponents and are equal for the suspension purpose. It is arbitrarily chosen that together they carry half of the platen weight. So, (22) These equilibriu conditions are also valid for sall-signal force coponents. Thus, we can use the sae relations for the sall-signal vertical force allocation. (27) Since we do not want any net vertical force perturbation in equilibriu, therefore, (28) Now consider the two other rotational degrees of freedo in the vertical dynaics. The odal torques have the following relationships with decoposed vertical force coponents: By the syetry of the proble for the rotations around and axes, Solving (28) (31) for the force yields (29) (30) (31) Then, and support the reaining half of the platen weight according to (23) Let us use another equilibriu condition for torques around the axis in Fig. 3. Since the oent ars of,,, and are,,,, respectively, If we solve (21) (24) for the force, (24) (32) Thus, the allocation of direct coponents of current is using (8) A/N- (33) (25) where the platen center-of-ass offsets are,, and ( in) is the distance between the centers of two adjacent agnet arrays. Thus, with the force current relationship (8), the noinal direct coponents of the current are A (26) 5 We have eight force coponents as in Fig. 2 in the current agnetic levitator. In fact, six independent force coponents are sufficient for 6-DOF otion control. This copletes the vertical force and current allocation with the odal vertical force and torques. B. Lateral Force Allocation The two relationships for the lateral force coponents are (34) (35) We need to generate the odal torque around the axis with the four lateral force coponents. We have freedo to achieve this, and one choice is (36) (37) So, we generate with and only in the above force allocation. The force coponents, and do not

9 1262 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998 participate in the torque generation. Thus, the otors in the direction will assue an additional task for sall-angle adjustent around the axis, which is also arbitrarily chosen. Solving (34) (37) for the force yields [15] H. Goldstein, Classical Mechanics. Reading, MA: Addison-Wesley, 1980, ch. 4. [16] W.-J. Ki, High-precision planar agnetic levitation, Ph.D. dissertation, Dep. Elect. Eng. Coput. Sci., Massachusetts Inst. Technol., Cabridge, June (38) Thus, the allocation of quadrature coponents of current is using (8) A/N A/N A/N A/N A/N- A/N- (39) This copletes the lateral force and current allocation with the odal lateral forces and torque. REFERENCES [1] G. Van Engelen and A. G. Bouwer, Two-step positioning device using Lorentz forces and a static gas bearing, U.S. Patent , June [2] S. Sakino, E. Osanai, M. Negishi, M. Horikoshi, M. Inoue, and K. Ono, Moveent guiding echanis, U.S. Patent , Aug [3] S. Wittekoek and A. G. Bouwer, Displaceent device, particularly for the photolithographic treatent of a substrate, U.S. Patent , Apr [4] B. A. Sawyer, Magnetic positioning device, U.S. Patent , Apr [5] W.-J. Ki and D. L. Truper, Force ripple in surface-wound peranent-agnet linear otors, in Proc. IEEE Int. Magnetics Conf., Apr. 1996, p. FE-03. [6] K. Halbach, Design of peranent ultipole agnets with oriented rare earth cobalt aterial, Nucl. Instru. Methods, vol. 169, no. 1, pp. 1 10, [7] D. L. Truper, M. E. Willias, and T. H. Nguyen, Magnet arrays for synchronous achines, in Conf. Rec. IEEE-IAS Annu. Meeting, Oct. 1993, pp [8] K. Yoshida, J. Lee, and Y. J. Ki, 3-D FEM field analysis in controlled-pm LSM for aglev vehicle, IEEE Trans. Magn., vol. 33, pp , Mar [9] C. Barthod and G. Learquand, Design of an actuator being both a peranent agnet synchronous otor and a agnetic suspension, in Proc. IEEE Int. Magnetics Conf., Apr. 1997, p. BR 05. [10] D. L. Truper, W.-J. Ki, and M. E. Willias, Design and analysis fraework for linear peranent-agnet achines, IEEE Trans. Ind. Applicat., vol. 32, pp , Mar./Apr [11] W.-J. Ki, D. L. Truper, and J. B. Bryan, Linear-otor-levitated stage for photolithography, Manuf. Technol.: Ann. CIRP, vol. 46, no. 1, pp , Oct [12] A. Blondel, Synchronous Motors and Converters. New York: McGraw- Hill, 1913, pt. III. [13] R. H. Park, Two-reaction theory of synchronous achines, generalized ethod of analysis Part I, Trans. AIEE, vol. 48, no. 3, pp , July [14] A. E. Fitzgerald, C. Kingsley, Jr., and S. Uans, Electric Machinery, 5th ed. New York: McGraw-Hill, 1990, ch. 6. Won-jong Ki (S 89 M 97) was born in Seoul, Korea, in He received the B.S. (sua cu laude) and M.S. degrees in control and instruentation engineering fro Seoul National University, Seoul, Korea, in 1989 and 1991, respectively, and the Ph.D. degree in electrical engineering and coputer science fro Massachusetts Institute of Technology, Cabridge, in In 1997, he joined SatCon Technology Corporation, Cabridge, MA, as a Meber of the Technical Staff. His research interests are analysis, design, and control of electroechanical systes. Dr. Ki received the Grand Prize in the Korean Institute of Electrical Engineers Student Paper Contest in 1988 and the Gold Prize for his doctoral work fro Sasung Electronics Huantech Thesis Prize in David L. Truper (S 84 M 90) received the B.S., M.S., and Ph.D. degrees in electrical engineering and coputer science fro Massachusetts Institute of Technology, Cabridge, in 1980, 1984, and 1990, respectively. In August 1993, he joined the Departent of Mechanical Engineering, Massachusetts Institute of Technology, where he is currently the Rockwell International Career Developent Associate Professor. Following receipt of the B.S. degree, he was with Hewlett-Packard Copany for two years. Following receipt of the M.S. degree, he was with the Waters Chroatography Division, Millipore Corporation, for two years. Following receipt of the Ph.D. degree, he was an Assistant Professor in the Electrical Engineering Departent, University of North Carolina, Charlotte, for three years, working in the Precision Engineering Group. His research interest is in the area of the control of electroechanical systes, with a specialization in agnetic suspensions and bearings. He serves on the Board of Directors of the Aerican Society for Precision Engineering (ASPE). Prof. Truper is a eber of the Aerican Society of Mechanical Engineers, Society of Manufacturing Engineers, ASPE, and Japan Society for Precision Engineering and a corresponding eber of the International Institution for Production Engineering Research. Jeffrey H. Lang (S 78 M 79 SM 95 F 98) received the B.S., M.S., and Ph.D. degrees in electrical engineering fro Massachusetts Institute of Technology, Cabridge, in 1975, 1977, and 1980, respectively. In 1980, he joined Massachusetts Institute of Technology, where he is currently a Professor of Electrical Engineering and Associate Director of the Laboratory for Electroagnetic and Electronic Systes. His research and teaching interests focus on the analysis, design, and control of electroechanical systes with an ephasis on rotating achinery, icro sensors and actuators, and flexible structures. He has authored ore than 120 papers and is the holder of five U.S. patents in the areas of electroechanics, power electronics, and applied control. He is a forer Hertz Foundation Fellow and a forer Associate Editor of Sensors and Actuators. Prof. Lang is the recipient of three IEEE Societies Best Paper Prizes.