The Attitude and Orbit Control System (AOCS) plays an essential role in the flight control of a spacecraft. This system usually contains a minimum of three reaction wheels (often 4-5 wheels are used for optimization and redundancy). By accelerating the appropriate wheels, the system can produce a zero-mean reaction torque about any axis to the spacecraft, which enables the spacecraft to maneuver on orbit. Meanwhile, the momentum generated by acceleration can be stored in the wheels.Lincoln Laboratory. Advanced Concepts Committe

Nejad, Mohammad Imani

Trumper, David L.

Zhou, Lei

DSpace@MIT

HYSTERESIS MOTOR DRIVEN ONE AXIS MAGNETICALLYSUSPENDED REACTION SPHERELei Zhou, Mohammad Imani Nejad, and David L. TrumperDepartment of Mechanical EngineeringMassachusetts Institute of Technology, Cambridge, MA, 02139INTRODUCTIONThe Attitude and Orbit Control System (AOCS)plays an essential role in the flight control of aspacecraft. This system usually contains a min-imum of three reaction wheels (often 4-5 wheelsare used for optimization and redundancy [1]).By accelerating the appropriate wheels, the sys-tem can produce a zero-mean reaction torqueabout any axis to the spacecraft, which enablesthe spacecraft to maneuver on orbit. Meanwhile,the momentum generated by acceleration can bestored in the wheels.[2].As an alternative to the reaction wheels, the ideaof using a single magnetically levitated reactionsphere for satellite attitude control was proposed[3]. In this alternate version, the sphere can beaccelerated about any axis by a spherical motor,making the attitude of the spacecraft in all axescontrollable by a single device. Due to its sym-metry, a sphere can always gives the same iner-tia, independent of its rotational axis. As a result,using a reaction sphere may allow smaller sizeand mass. In addition, when assisted by magneticsuspension, the mechanical friction can be elimi-nated, and thus low steady-state power consump-tion may be possible. This also enables the deviceto work without lubrication and achieve greateroperational lifetime.The idea of reaction sphere was proposed asearly as 1986 [3], however to our knowledge,the current technology is still far from a ready-to-commercialize state. One recent reactionsphere design presents a permanent magnetmotor based reaction sphere designed by ESA[4]. This design uses tiled magnets on the ro-tor surface, which enables simpler angular posi-tion sensing and control. However, its complex-ity of the rotor structure may prevent it from be-ing suitable for small satellites application, and thestrength of the rotor limits its maximum rotationalspeed, which may limit the performance of the ac-tuator.Among many motor driving principles, the hys-FIGURE 1. Design concept diagram of the 1D-MSRS.teresis motor is well known for its simple struc-ture, vibration-free operation, self-starting ability,and constant torque production. Another distinctfeature of this motor is that its rotor can be madeout of a single piece of hard steel, which allowsthe rotor to stand large stresses and thus makesthis motor attractive for high-speed applications.However, to the best of our knowledge, the hys-teresis motor has not yet been used in reactionwheels.Aiming at the dual goal of exploring the designfor a magnetically suspended reaction sphere andevaluating the performance of hysteresis motorsfor reaction wheels application, we focused thisproject on the development of a magnetically sus-pended reaction sphere with one-axis hysteresisdrive (1D-MSRS). The hardware of the 1D-MSRSdemonstrates a solid steel sphere magneticallysuspended in all translation directions, and drivenby a hysteresis motor about one axis. Figure 1shows a diagram of the design concept of the 1D-MSRS.This paper presents the design characteristicsand test results of the 1D-MSRS system. Formore detailed analysis of the design, modeling,and control of the system see [5].HARDWARE DESIGN AND INTEGRATIONThe 1D-MSRS has a magnetically levitated spher-ical rotor that can rotate and store momentumabout the vertical axis. Figure 2 shows the pho-(a) Structure and sensors. (b) stator and rotor.FIGURE 2. Photographs of the 1D-MSRS hardware.tographs of the hardware. In the 1D-MSRS sys-tem, the rotor is a 54 mm diameter sphere of hard-ened D2 steel. Four inductive sensors are placedaround the rotor to measure the sphere’s posi-tion in translational degrees of freedom. The rotorsphere is magnetically levitated in the vertical di-rection by a reluctance actuator placed at its northpole. A stator is arranged around the sphere’sline. It serves both for levitating the sphere in thehorizontal plane and for torque generation simul-taneously via a bearingless motor configuration.A reflective optical tachometer is used for speeddetection of the reaction sphere.The 1D-MSRS consists of several subsystems.They are: a single degree-of-freedom magneticsuspension system for the sphere’s vertical sus-pension, a lateral suspension system for thesphere by mean of the bearingless motor, and ahysteresis motor for driving the sphere about thevertical axis. In the analysis of the 1D-MSRS,these subsystems are considered to be decou-pled, that is, the interaction between the subsys-tems are considered to be negligible. In the fol-lowing these subsystems are introduced.VERTICAL SUSPENSIONThe spherical rotor in the 1D-MSRS is magnet-ically suspended in the vertical direction by anelectromagnet arranged at the north pole of thesphere.In order to reduce the DC current in the actuatorcoil for the sphere’s weight compensation, a thin-disk shape permanent magnet is placed in theFIGURE 3. A cross section of the biased levitationactuation systemmagnetic path of the suspension actuation sys-tem to add a bias DC flux. Figure 3 depicts thesystem for the sphere’s vertical suspension.LATERAL SUSPENSIONIn the design of the 1D-MSRS, a bearingless mo-tor is used to achieve a compact design. Thismotor uses two sets of three-phase windings ona single stator (for 1D-MSRS 4-pole and 2-pole).By correctly configuring and controlling the cur-rents in these motor windings, the machine cangenerate a torque for spinning as well as radialforces for suspension using a single stator. In the1D-MSRS system, the 4-pole winding is the motorwinding, and the 2-pole winding is used for lateralsuspension control.A dynamic model is built to study the lateral sus-pension characteristics of the bearingless motorin 1D-MSRS. Here we only present the high level100 101 102 10310−410−2100Frequency [Hz]Magnitude [mm/A]100 101 102 103−800−600−400−2000Frequency [Hz]Phase [deg]  0.2A0.3A0.4A0.5A0.6A0.7AFIGURE 4. Experimentally measured plant fre-quency response for x-direction sphere suspen-sion with different excitation amplitudes.result, that is, the transfer function from the sus-pension winding current i2a to the rotor’s radialdisplacement x(t) is:X(s)I2a(s)=Kims2 −Ks . (1)Here m is the mass of the sphere, and the valueof Ks and Ki are the negative stiffness [N/m] andthe force constant [N/A] of the lateral suspensionsystem respectively. They can be calculated by:Ks =2piRlµ0N24 (√3/√2Im)2g30[N/m] (2a)Ki =√3√22µ0RlN2N4pig20(√3√2Im)[N/A]. (2b)Here the value Im is the zero-to-peak current am-plitude of the 3-phase current in the 4-pole motorwindings. The meaning of the nomenclatures andthe detailed derivations of these results are pre-sented in [5].Equation 2 shows that the both Ks and Ki inthe bearingless motor system are varying with themotor winding current amplitude Im. This resultcan be verified by measuring the frequency re-sponse of the lateral suspension system of the1D-MSRS under different excitation current am-plitude. The measured Bode plots are depicted inFigure 4. This measurement was taken while un-der closed-loop control of the lateral suspension.10 20 30 40 50 6005001,0001,5001,8002,000Time(s)Speed(rpm)  0.3A0.4A0.5A0.6A0.7AFIGURE 5. Acceleration curves of 1D-MSRSunder different excitation current amplitude.Since the motor excitation amplitude of the reac-tion sphere/wheel needs to vary according to thetorque requirements, the lateral suspension con-troller needs to be able to stabilize the controlloop under all excitation conditions. The detailedcontroller design for the lateral suspension in 1D-MSRS is presented in [5]. With the controller de-sign, the lateral suspension loop of the reactionsphere kept a constant phase margin of 40o, whilethe cross-over frequency varies with the motor ex-citation amplitude.HYSTERESIS MOTOROne goal of this project is to evaluate the per-formance of hysteresis motor for reaction wheelsapplication. A hysteresis motor operates by themagnetic hysteresis effect of its rotor material.Because the magnetization produced in the fer-romagnetic material lags behind the magnetizingforce, a torque is generated due to the rotor andstator field interaction. Although materials withbetter hysteresis properties exists, we selectedD2 steel for the rotor of 1D-MSRS for the proofof our design.Experimental dataThe start up speed curve of 1D-MSRS is mea-sured under different excitation conditions. Fig-ure 5 presents the acceleration curves of the1D-MSRS under different amplitudes of excitationcurrent. Data shows that with 0.7 A excitationcurrent, the sphere can reach the synchronousspeed of 1,800 rpm within 6 seconds. Also, astarting torque of 8.15 mNm is demonstrated un-der 0.7 A exciting current.The maximum synchronous rotational speed thatthe 1D-MSRS can reach is 200 Hz (12,000 rpm) inour lab. We believe that when running in vacuumthe motor has the potential to reach higher speed.FIGURE 6. A comparison of experimental open-loop speed data and the closed-loop speed dataof the 1D-MSRS during starting up.Speed control of 1D-MSRSIn the speed plot shown in Figure 5, a speedfluctuation slightly above and below the referencespeed can be observed when the motor speedfirst reaches the synchronous speed. This motordynamics is known as hunting. It is undesirablewhen a hysteresis motor is used for the develop-ment of a reaction wheel or a reaction sphere, asit will introduce vibrations into the spacecraft.To suppress the motor hunting, a feedback loopon the sphere’s rotational speed is designed andimplemented in the 1D-MSRS. In this control sys-tem, the sphere’s speed is measured by an opticaltachometer, and the control effort is the currentamplitude that we supply to the motor windings.The controller design is introduced in [5] in detail.Figure 6 shows the measured step responseof the reaction sphere’s rotational speed underopen-loop and closed-loop operations, respec-tively. Note the hunting speed ripple in the open-loop speed data (blue). Data shows that the de-signed speed control scheme can effectively sup-press the motor hunting and also enables fasteracceleration.CONCLUSIONS AND FUTURE WORKThe design and development of a hysteresis mo-tor driven magnetically suspended one-axis reac-tion sphere is presented in this paper. Magneticsuspension, bearingless drive and hysteresis mo-tor principles are used in the design for 1D-MSRS.An equivalent circuit model for hysteresis motor isused to analyze the dynamic behavior of the 1D-MSRS, and a speed control loop is built for thesystem to suppress hunting. The 1D-MSRS canrun up to 200 Hz (12,000 rpm) with the existenceof air drag, and a starting torque of 8.15 mNm isgenerated with 0.7 A excitation current amplitude.Future work should consider the design anddevelopment of a three-axis magnetically sus-pended reaction sphere (3D-MSRS). A brief dis-cussion of the possible motor concepts and mag-netic pole configurations for a 3D-MSRS is pre-sented in [5]. The performance of the 1D-MSRSdemonstrates that hysteresis motor has the po-tential for the circumstances where quiet opera-tion and high speed are needed. We believe thatthis motor concept is promising for high speed,low vibration reaction wheel applications.ACKNOWLEDGEMENTSThis work is supported by MIT Lincoln Labora-tory via Advanced Concept Committee. We thankNational Instruments for contributing the real-timecontroller. We also thank Frederick Knight andAndrew Stimac of Lincoln Laboratory for their as-sistance with this project.REFERENCES[1] Budianto IA, Olds JR. Design and deploy-ment of a satellite constellation using collab-orative optimization. Journal of spacecraftand rockets. 2004;41(6):956–963.[2] Bialke B. High fidelity mathematical model-ing of reaction wheel performance. Guidanceand control 1998. 1998;p. 483–496.[3] Isely WH. Magnetically supported andtorqued momentum reaction sphere, USPatent 4,611,863. Google Patents; 1986.[4] Onillon E, Chételat O, Rossini L, Lisowski L,Droz S, Moerschell J. Reaction sphere forattitude control. In: Proc. 13th EuropeanSpace Mechanisms and Tribology Sympo-sium; 2009. .[5] Zhou L. Magnetically suspended reactionsphere with one-axis hysteresis drive. Me-chanical Engineering, Massachusetts Insti-tute of Technology; 2014.[6] Miyairi S, Kataoka T. A basic equivalent cir-cuit of the hysteresis motor. Elect EngngJapan (USA). 1965;85:41–50.[7] Nitao J, Scharlemann E, Kirkendall B. Equiv-alent Circuit Modeling of Hysteresis Mo-tors. Lawrence Livermore National Labora-tory (LLNL), Livermore, CA; 2009.[8] Imani Nejad M. Self-bearing motor design& control. Mechanical Engineering, Mas-sachusetts Institute of Technology; 2013.

Hysteresis Motor Driven One Axis Magnetically Suspended Reaction Sphere

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Hysteresis Motor Driven One Axis Magnetically Suspended Reaction Sphere

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