HARNESS THE LAG: PRECISION MOTION WITH HYSTERESIS …web.mit.edu/leizhou/~lei/publications/ASPE_2020_hyst... · 2020. 4. 18. · duction motor. The third hysteresis motor being tested,

HARNESS THE LAG: PRECISION MOTION WITH HYSTERESISMOTORS

Lei Zhou1, David L. Trumper21 Mitsubishi Electric Research Laboratories, Cambridge, MA, USA

2 Massachusetts Institute of Technology, Cambridge, MA, USA

INTRODUCTIONIn precision motion systems, hysteresis in ac-tuators is typically a detrimental effect, and anumber of research efforts have studied meth-ods to compensate it. However, the hysteresiseffect is not always harmful. When building mo-tors with secondaries made of magnetically semi-hard materials, the hysteresis effect of the sec-ondaries can generate a spacial lag between thesecondary’s magnetization and the external mag-netic field, and thus generate thrust force/torque.Such motors are called hysteresis motors. Inrecent years, the hysteresis motor is receivingincreasing research attention due to its advan-tages of simple construction, vibration-free oper-ation, constant torque/force in transient, and self-starting [1]. The most distinct feature of a hystere-sis motor is that its secondary can be made of amonolithic piece of magnetically semi-hard alloy,which has high strength, stiffness, and thermalrobustness. This fact makes the hysteresis mo-tor attractive to many special precision devices,such as in-vacuum drives [2], miniature pumps[3], high-temperature/high-speed drives [4], andspace devices [5].

In contrast to the motor’s good potential, the re-search on hysteresis motors until today remainslimited. To our knowledge, hysteresis motors aretypically operated in open-loop, and there was nodeveloped method to control the motor’s torqueor position with high bandwidth before our work.As a result, the hysteresis motor has been almostignored in precision applications in the past. Thisgap between the motor’s great potential and theexisting technology motivated our study for meth-ods to control the hysteresis motors with highbandwidth, and therefore enable them for preci-sion applications in the future.

This paper introduces the research efforts at thePrecision Motion Control Lab at MIT on the pre-cision positioning using hysteresis motors. Thepaper includes two parts. In the first part, weintroduce the modeling and field-oriented control

(FOC) for hysteresis motors, and presents the ex-perimental tests of the proposed method on threerotary hysteresis motors with different rotor mate-rials. Test results show that all three motors canreach a position control bandwidth of 130 Hz withthe proposed methods. The second part brieflyintroduces the design, building, and testing of amagnetically-levitated linear stage driven by lin-ear hysteresis motors, targeting at the in-vacuumtransportation application in semiconductor man-ufacturing systems. To the best of our knowl-edge, our work demonstrates the first experimen-tal study on position control for hysteresis motors,and the first linear version of hysteresis motors. Italso first demonstrates the use of hysteresis mo-tor in precision motion stages.

POSITION CONTROL FOR ROTATY HYSTERE-SIS MOTORSHysteresis Motor Operating PrincipleIn this section we briefly discuss the operatingprinciple of hysteresis motors. We first limit ourdiscussion to rotary hysteresis motors. A hys-teresis motor consists of a regular poly-phasestator and a rotor made of solid semi-hard mag-netic material. The magnetic hysteresis effect ofthe rotor material causes a lag angle betweenthe rotor magnetic field and the air-gap magneticfield, and a hysteresis torque can be generated.Hysteresis motors can be operated either syn-chronously or asynchronously. When the motoris under asynchronous operation, eddy current isinduced in the rotor, which also contribute to themotor’s torque generation. Under this operationmode, the motor can be regarded as a hysteresis-induction-hybrid motor. When the motor is op-erated synchronously, the motor behaves like aweak permanent magnet motor. When operatedsynchronously, the rotors of hysteresis motors areoften pre-magnetized or over-excited for torqueand efficiency improvement [6].

Rotor Field Orientation EstimationThe challenge of controlling a hysteresis motor isbecause the magnetization can move on the ro-

D

Q

isq

idsiqs

isD

isQωd

θ

Φ"

FIGURE 1. Hysteresis motor field-oriented con-trol vector diagram.

tor surface. Fig. 2 shows a vector diagram of thehysteresis motor’s field-oriented control. Here,D-Q is the stationary two-phase frame, d-q isthe rotor flux-oriented frame, where the d-axis isaligned with the rotor flux linkage. Vector is rep-resents the stator phase currents, and Φr is therotor flux vector. Under this case, the motor’storque is proportional to iqs. It can be seen thatthe key of hysteresis motor’s control is to achievean accurate estimation to rotor flux vector’s ori-entation, i.e. the field angle θ. With such fieldorientation information, one can control a hys-teresis motor in the same way with a PM ma-chine. In the rest of this section, we discuss twodifferent rotor field orientation estimation meth-ods for both synchronously- and asynchronously-operated hysteresis motors.

Asynchronous OperationFor asynchronously-operated hysteresis motors,we propose to use a model-based rotor flux ob-server for real-time field-orientation estimation.A model that describes the hysteresis motor’stransient-time dynamics is required to constructsuch estimator. The challenge of constructingsuch model for hysteresis motors is mainly dueto the fact that the hysteresis effect and the eddycurrent effect need to be modeled in different co-ordinate frames. Fig. 2 shows such separation inreference frames. In a hysteresis motor, the hys-teresis effect of the rotor generates a constant lagangle between the rotor flux and the air-gap flux,and this relationship should be modeled in thestator-fixed frame. On the other hand, the eddycurrent effect should be modeled in the rotor-fixedframe, since the eddy currents are generated inconductors fixed on the rotor. This fact preventsus from modeling the rotor flux using unified vari-ables as in an induction motor model.

Hysteresis

Eddy current

FIGURE 2. Hysteresis motor circuit diagram withhysteresis effect and eddy current effect in differ-ent coordinate systems.In this work, we developed a transient-time dy-namic model for hysteresis motors with eddycurrent effect considered. The model is basedon the elliptical hysteresis loop assumption [7],where the the B-H curve of the rotor mate-rial is approximated by an ellipse, as B =Bm cos θ, H = (Bm/µ) cos(θ + δ), where Bm isthe maximum flux density amplitude, µ is the ro-tor material permeability, and δ is the lag an-gle between B and H. This model consid-ers only the fundamental harmonics for B- andH-fields. Based on such simplified hysteresismodel, we listed the motor’s eddy current andhysteresis dynamic dquations in their different co-ordinates, and selected a set of state variablesas x = [isD, isQ,ΦHrD,ΦHrQ,ΦErD,ΦErQ]>, astate-space model for the hysteresis motor canbe derived. For more details about the hysteresismotor model, see equations (9-14) in [8].

Given the hysteresis motor state space model, afull-order Luenberger state observer can be de-signed to estimate the rotor’s field orientation.The derived hysteresis motor model is fully ob-servable even when the motor is operating at zerospeed, and therefore asymptotically convergingobserver designs are available. This flux observermethod provides good rotor flux angle estimationaccuracy over a large speed range. Note thatthe estimation performance of this method signifi-cantly depend on the model parametric accuracy.

Synchronous OperationFor synchronously-operated hysteresis motorswith or without pre-magnetization, one can usemodel-free methods to estimate the rotor’s field

orientation for control purpose, as discussed inthe following:

(a) Approximate with Rotor Mechanical Angle:The most simple method for estimating the ro-tor flux angle is to directly use the measured ro-tor angular position. This method assumes thatthe magnetization is fixed on the rotor surface.Pre-magnetizing the rotor by a large d-axis cur-rent can help improve the performance of this fluxangle estimation method.

(b) Back-EMF method : The second method usesthe back-electromotive force (EMF) in the statorcoils to estimate the rotor flux orientation. Whenthe magnetized rotor is rotating, the change of therotor field induces voltages in the stator windings,which is the back-EMF. The back-EMF in the sta-tionary D-Q frame can be calculated as

eD = usD −RsisD − Llsi̇sD, (1)

eQ = usQ −RsisQ − Llsi̇sQ. (2)

An estimate for the flux linkage in the stationarytwo-phase frame can be calculated by

Φ̂rD =

∫eDdt, Φ̂rQ =

∫eQdt. (3)

Finally the estimated flux angle θ̂ can be calcu-lated. This method provides good rotor flux ori-entation estimation performance when the motorspeed is relatively high. However, when the mo-tor is standing still or operating at low speed, theback-EMF signals are small and therefore the an-gle estimation is not accurate.

(c) Combination of Mechanical Angle and Back-EMF Methods: To improve the rotor field orien-tation estimation performance over a large motorspeed range, we can use a combination of usingback-EMF based estimation when the rotor speedis high, and using rotor’s mechanical angle whenthe rotor speed is low. One implementation of thecombined flux orientation estimation is

θ̂ = (1− S(|ωr| − ωswr ))θr + S(|ωr| − ωsw

r )θ̂EMF ,

where ωr is the rotor speed, ωswr is a thresh-

old rotor speed for estimation method switching,θ̂EMF is the back-EMF method estimated an-gle, θr is the rotor’s mechanical angle, and θ̂ isthe resultant rotor flux angle estimation. S(x) =1/(1 + e−x) is the sigmoid function, which is asmooth transition function from 0 to 1 at x = 0.

Squirrel Cage IM rotor

FeCrCo alloy (CROVAC 12)HM rotor

D2 steelHM rotor

FIGURE 3. Custom-made rotors for hysteresismotors. Left: D2 hysteresis rotor for Motor I. Mid-dle: FeCrCo alloy hysteresis rotor for Motor II.Right: the original squirrel cage rotor for the in-duction motor.

Rotary Hysteresis Motor TestsThree different rotary hysteresis motors aretested to validate the proposed control method.Motor I and Motor II are custom-made hystere-sis motors, which are fabricated by replacing thesquirrel cage rotor in a regular three-phase induc-tion motor with rotors made of different semi-hardmagnetic materials. Motor I has a rotor made ofD2 tool steel, and Motor II has a rotor of FeCrCoalloy. Fig. 3 shows the custom-made rotors forMotor I and II and the original rotor for the in-duction motor. The third hysteresis motor beingtested, Motor III, is a commercial hysteresis mo-tor from Elinco Inc.

The proposed field-oriented control scheme istested with all three hysteresis motors. For Mo-tor I and Motor II, the full-order state observermethod is used for the rotor flux orientation es-timation. For Motor III, rotor flux orientation is es-timated through the combination of the mechan-ical angle and back-EMF method. Fig. 4 showsthe measured plant frequency responses of theposition control plant for the three hysteresis mo-tors, where the input signal is the q-axis current,and the output signal is the measured rotor an-gular position. Fig. 4 shows that all three mea-sured Bode plots demonstrate -2 (or -40 dB/dec)slope at high frequency, which follows the torque-to-position relationship in a motor. This obser-vation indicates that the q-axis current is roughlyproportional to the torque of the motor. The threeplots in Fig. 4 all demonstrate zero slope at lowfrequency, which is due to the spring-like behav-ior of bearing friction.

Fig. 5 shows the measured close-loop Bode plots

100 101 102-80-60-40-20

02040

D2 steel motorFeCrCo alloy motorElinco Inc. Motor

100 101 102-270

-180

-90

0

90

FIGURE 4. Measured Closed-loop Bode plots forthree hysteresis motors. Input: reference posi-tion; output: measured position. The -3 dB inmagnitude plot is shown as the dashed line.

100 101 102-20

-10

0

10

20

100 101 102-270

-180

-90

0

90

D2 steel motorFeCrCo alloy motorElinco Inc. Motor

FIGURE 5. Measured Closed-loop Bode plots forthree hysteresis motors. Input: reference posi-tion; output: measured position. The -3 dB inmagnitude plot is shown as the dashed line.for the position control systems for the hysteresismotors. Fig. 5 demonstrates that the position con-trol for all three hysteresis motors are successfulwith a bandwidth of above 130 Hz.

HYSTERESIS MOTOR DRIVEN MAGNETI-CALLY LEVITATED LINEAR STAGEThe second part of this paper discusses the de-sign and tests of a magnetically-levitated linearstage driven by linear hysteresis motors. The tar-get application of this linear stage is for the in-vacuum transportation in semiconductor manu-facturing systems, for example reticle transporta-tion in EUV photolithography scanners. Hystere-sis motors do not require permanent magnets(PM) on the moving stage. This feature of themotors is highly-desirable for in vacuum environ-ment, since the magnets can out-gas in vacuum

Air-gap sensor PCB

Biasing magnets

Motor stator

Yaw control stator

Stage back iron Hysteresis secondaryEncoder array

x

y

z𝜃𝑧𝜃𝑥

𝜃𝑦

Bias flux collector

FIGURE 6. Cross-section CAD model of thehysteresis-motor-driven magnetically-levitatedlinear stage.

xy

z

FIGURE 7. Photograph of the magnetically-levitated linear stage prototype.

and thus need to be encapsulated. Using mo-tor secondaries made of solid magnetically-semi-hard steel will allow a much simpler stage design.The major disadvantage of using hysteresis motoris that their thrust force is relatively low comparedto other motor types. However, this is acceptablefor the reticle transportation application, since itsacceleration requirement is relatively low and isachievable with linear hysteresis motors. To ourknowledge, this work demonstrates the first linearversion of hysteresis motors.

Fig. 6 shows a cross-section CAD model for thelinear stage design, and Fig. 7 shows a photo-graph of the linear stage prototype. The coordi-nate system is also shown in Fig. 6 and Fig. 7.Here, the stage is driven along the y-axis via lin-ear hysteresis motors, and is magnetically levi-tated in all other degrees of freedoms. Here, thestage is passively suspended in the z-, θx-, andθy-directions via the reluctance forces betweenthe stage and stator assemblies using a linearbearingless slice motor design, and is levitatedactively using feedback control in the x- and θz-DOFs.

Fig. 8 shows the magnetic fluxes and the suspen-sion forces/torques generation principle for ourlinear stage. There are three kinds of magnetic

fluxes in the system. The black lines in Fig. 8aand Fig. 8b show the PM bias magnetic fluxes,which generate passive suspension force/torquein the z-, θx-, and θy-DOFs. The blue lines inFig. 8a and Fig. 8b represent the yaw controlfluxes, which are distributed approximately sinu-soidally in the air gaps, and is synchronous withrespect to the moving stage. This flux steers thePM bias flux (black lines) for yaw (θz) suspen-sion control torque generation. The red lines inFig. 8a and Fig. 8c show the motor fluxes. Thecommon-mode of the two motor fluxes generatesthrust force on the stage in the y-direction by in-teracting with the hysteresis secondaries on themoving stage. The differential of the two mo-tor fluxes generates lateral-directional reluctanceforces, which is used to control the stage’s levi-tation in the x-direction. With all three magneticfluxes, we are able to stabilize all five suspen-sion DOFs of the moving stage, either actively orpassively. More detailed suspension force/torquegeneration mechanism as well as the hardwaresystem design are discussed in [9].

The thrust force generation of our linear stageuses short-secondary linear hysteresis motors,where D2 tool steel is used as the motor sec-ondary material. We operate the linear mo-tors synchronously with the secondaries pre-magnetized to improve the thrust force capabil-ity of the linear stage. The linear hysteresis mo-tors are operated synchronously for two reasons:First, reluctance force can be generated in themotor due to the end effects, which is oscillatoryif the motor is driven asynchronously and thusgenerate an undesirable vibration. Second, syn-chronous operation of the motors reduces hys-teresis and eddy current losses in the secon-daries. This is especially important for in-vacuumoperation, since cooling of the moving stage ischallenging when the stage is in vacuum, whereconduction and convection heat transfer are notpossible.

The position control of our linear stage uses thefield-oriented control method assuming the sec-ondary’s magnetization fixed in the stage co-ordinate. Fig. 9 shows the measured closed-loop step response of the moving stage’s posi-tion in the motion direction. Here the 10%-90%rise time of the step response is 0.012 s, whichcorresponds to a position control bandwidth of30 Hz. Fig. 10 shows the measured tracking per-formance of the stage to a second-order polyno-

xy

z

Stage

Motor stator

Yaw control statorBiasing PM

Hysteresismotor secondary

Bias flux collectorYaw control flux

PM bias flux

Motor flux

Stator backiron

(a)

44

T"x

y

z

PM bias flux

Yaw control flux

x

y

z

𝐹"

𝐴 − δ𝐴 𝐴 + δ𝐴

𝐹'

(b) (c)

FIGURE 8. Magnetic fluxes and the suspensionforces/torques generation in the magnetically-levitated linear stage. (a) Cross section diagramof the stage. (b) Top view of the permanent mag-net bias fluxes (black) and the yaw control fluxes(blue) in the air gaps. (c) Top view of the motorfluxes (red) in the air gaps.

mial reference trajectory, including the referenceand measured position (top plot), y-directionaltracking error (middle plot), and the stage’s x-and θz-directional displacements (bottom plot).The trajectory’s maximum acceleration and veloc-ity are 500 mm/s2 and 250 mm/s, respectively,which are the acceleration and velocity require-ments for the reticle transportation application inEUV photolithography scanners. The middle plotin Fig. 10 shows that the maximum position con-trol tracking error is about 50 µm, and the trackingerror demonstrates a periodic pattern, where thespatial period of the tracking error matches withthe motor stator tooth pitch. To our understand-ing, this error is caused by the cogging force inthe pre-magnetized linear hysteresis motors. Thebottom plot in Fig. 10 shows that the stage’s max-imum deviation from center in the x-direction isalso approximately 50 µm. Such data show thatthe stage’s active magnetic suspension are suc-cessful during the stage in transportation.

CONCLUSIONS AND FUTURE WORKIn this work, we discussed the position con-trol method for rotary hysteresis motors, and acase study of using linear hysteresis motors inmagnetically-levitated linear stages. Experimentsshow the proposed field-oriented control methodis able to achieve high-bandwidth position servo

-0.05 0 0.05 0.1 0.15 0.2Time (s)

0

0.05

0.1

0.15

Dis

plac

emen

t (m

m)

Measured PositionReference

FIGURE 9. Measured closed-loop position stepresponse of the linear stage in the y-axis motiondirection.

yerror

x-error𝜃"-error

FIGURE 10. Measured tracking performance ofthe stage while tracking an S-shaped trajectorywith amax = 500 mm/s2 and vmax = 250 mm/s.Top plot: reference and measured stage displace-ment. Middle plot: position tracking error. Bottomplot: measured stage displacements in x- and θz-directions.

for hysteresis motors, and the linear motor is ableto demonstrate satisfactory performance for thein-vacuum transportation stage. To this point, itis fair to say that this series of work has enabledthe hysteresis motors for being used in precisionmotion systems for special applications.

Given the hysteresis motors’ good potential, fu-ture work should consider further use of thesemotors in precision mechatronic devices. Thestudy on vector hysteresis models with improvedaccuracy is also suggested to further improve themotor’s performance.

ACKNOWLEDGMENTThe authors thank ASML for supporting thiswork. We thank Dr. Ruvinda Gunawardana and

Dr. Minkyu Kim at ASML for valuable discussionsthroughout the project. We thank Dr. WolfgangGruber and Gereon Goldbeck at JKU, Linz, Aus-tria for their help with the hysteresis propertymeasurements.

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