150619_244_1_AhmedSalman

RINKO M1 , JUNE 2015 1

Advanced research in state estimation of sensor lessair gap electromagnetic levitation control

Ahmed Salman Student ID 37-145015 , Takafumi Koseki

AbstractThis survey has been conducted to review thelatest advances in the field of sensorless air gap estimation forelectromagnetic levitation control. Sensorless magnetic levitationcan generally be classified into 2 types. 1)Using state observersand 2) Modulation based. This paper highlights some of therecent works in modulation based sensorless air gap estimationand compares the pros and cons for the sub-techniques in themodulation based approach.

Index TermsMagnetic levitation , sensorless , air gap esti-mation , self sensing , active magnetic bearings , current changerate

I. INTRODUCTION

MAGNETIC levitation, Maglev or magnetic suspension,is a method by which an object can be suspended inmid air without any physical support or contacts other thanthe magnetic field. The gravitational pull and other externaldisturbances are countered only by the magnetic force whichis the reluctance force in this case. Magnetic suspensionboasts significant advantages over conventional mechanicalmachines such as high speed ,frictionless, less wear and tearand durability. Magnetic levitation has found its way into theindustrial applications as, most commonly known, the highspeed train. Active magnetic bearings and bearingless motorsare also a significant part of this field. Other applicataionsinclude vibration isolation platforms and conveyer systems.

Magnetic levitation can be classified, generally, into twotypes. 1) Electromagnetic suspension (EMS) and 2) Electro-dynamic suspension (EDS). Though, similar in consequence,they operate under a different mechanism. EMS uses electro-magnets to produce attractive force. This results in an inher-ently unstable system and thus requires active control system(Fig. 1). EDS, on the other hand, uses superconductors toproduce repulsive force for suspension resulting in a relativelystable system (Fig. 2)

This paper reviews some of the recent works related withthe sensor less air gap estimation. Firstly a general overviewof theory of electromagnetic suspension is given in sectionII. Section III describes the fundamental requirements forclosed loop control and explains the motivation for sensor-less air gap estimation. Section IV introduces the basics ofsensorless estimation and its classification, and highlights therecent advances to counter the technical problems in the aforementioned methods. In Section V a comparison between latestestimation techniques is shown and finally in section VI aconclusion is drawn from this review.

Fig. 1. Electromagnetic Suspension

Fig. 2. Electrodynamic Suspension: a) Front view b) Side view

II. THEORY: ELECTROMAGNETIC SUSPENSION ANDRELUCTANCE FORCE

Electromagnetic suspension,as previously mentioned, useselectromagnets to generate force. This force is called reluc-tance1 force. Reluctance force is derived from the energystored in the magnetic field which can be converted to me-chanical energy by principle of virtual work. This force arisesbetween surfaces with different permeabilities for exampleiron core and air. The direction of the force is perpendicular tothe surface of the core and it tends to decrease the reluctanceof the over all system. Fig.3 shows an iron C-I core withcopper wire wound around one of its legs. Voltage is applied

1Magnetic resistance


to the coil resulting in current which produces magnetic fluxin the C-I core. This flux produces reluctance force causingthe I core to be lifted.

Fig. 3. Electromagnet C-I core.

N : Number of Coil turns.

x(t) : Air gap.

l + 2x(t) : Magnetic path.

fmag : Reluctance force

Mathematically, this system can be described by consideringthree terminals 1)Electrical 2) Magnetic energy storage and 3)Mechanical terminal. With each terminal there are associatedvariables which govern its side of the dynamics. Fig.4 showsthe linkages in electromagnetic system. The equations govern-ing the dynamics of an electromagnetic suspension system aregiven as follows:

v(t) = i(t)R+d

dt(1)

v(t) = i(t)R+d((L(x)i(t))

dt(2)

Where L(x) = N2A0

2(x(t)+xg)+ lr

fmag = N2A0

i2

(2(x(t) + xg) + lr )2(3)

Mdx

dt= fmag Mg (4)

Using (1),(3),(4) entire magnetic suspension system is de-fined and analyzed. This set of equations is generally used todesign control system for attaining stable levitation. From theabove set of equations, it is evident that the system is non-linear.

III. CLOSED LOOP CONTROL

Electromagnetic suspension is inherently an unstable systemand that is why it requires an active control system to achievestable levitation. A basic control loop is shown in Fig.III.Key components are a controller, power amplifier and adisplacement sensor. The displacement sensor measures theair gap and feeds this information to the controller which,

Fig. 4. Linkage between electrical, magnetic and mechanical terminals.

according to some predefined control algorithm, computes theoutput voltage. This voltage is fed to the power amplifierwhich amplifies it and inputs it to the coil resulting incurrent and consequently magnetic force. Generally, in anEMS system, current sensor and displacement sensors areused. Displacement sensors are based on different physicalphenomena , such as Inductive Displacement sensors, Eddycurrent sensors, Capacitive displacement sensors, flux sensorsand optical sensors [1].

A. Motivation for sensorless air gap estimation

Over the past few decades, much of the research has beenconducted to achieve stable levitation by applying differentcontrol algorithms. Linear and nonlinear control algorithmshave been applied. Linear control algorithms include conven-tional lag lead, PID, state feedback controllers. Recently moreadvanced and complex controllers, for instance Hinf have alsobeen applied to demonstrate relatively higher performance interms of accuracy, stability, power consumption etc. Being anonlinear system, researchers have also demonstrated the useof nonlinear control algorithms, for instance state feedbacklinearization etc, to compensate magnetic nonlinearity andincrease the operating range for the levitation. To providelogical flow to the conlusion, we turn to a simple example ofstate feedback control which requires the expression of systemdynamic model in state space as shown (5).

x = Ax+Bu (5)y = Cx+Du

The state vector x in (5) has important dynamics variableswhich define the complete system. Some common state vectorsused in magnetic levitation control are given in (6). x air gapx velocity

i current

x air gapx velocityx acceleration

(6)It is important for control algorithms which use state space

model or its variant to estimate the entire state vector. Forthat, system need to be observable i.e from measured output,all the states can be estimated. Unfortunately this is not thecase with every measured output. In designing control system,care is taken in choosing outputs which are to be measuredusing sensors.


Fig. 5. Basic control loop for stable levitation

For the case of EMS, air gap holds that significance ofproviding such facility. By measuring air gap as an output, notonly is the system observable but it also induces robustness.Intuitively it seems more acceptable as the controlled physicalquantity when the final goal is suspension. But as previouslymention, displacement sensors are required to measure air gapwhich add substantial cost to EMS applications. Therefore,drastic reduction in the cost of an EMS system, is a significantmotivation for sensorless air gap estimation.

IV. SENSOR LESS AIR GAP ESTIMATION

Sensorless air gap EMS or self-sensing EMS, as the namesuggests,is a technique that uses the voltage and current his-tories to estimate the air gap without the help of displacementair gap sensors. The function of the displacement sensor isreplaced by some sort of signal processing which can extractair gap information hidden inside the current and voltageof the electromagnetic coil as shown in the Fig. 6. Thereare several advantages of this technique, the most obviousbeing the drastic reduction in expense due to the highercost of the industrial grade displacement sensors. Apart fromthat, this also results in reduced hardware, less wiring , canadd redundancy in case of failure of displacement sensor.Especially for the case of Active magnetic bearings (AMB),no sensor can allow reduced rotor length with the consequenceof higher bending mode and thus higher rotating speeds. Thistechnique can also be used in hostile conditions when themedium of levitation is not air e.g water pumps etc.

Nonetheless, dispensing the air gap sensor comes withcertain technical disadvantages. The EMS becomes less robustdue to the fact that system parameters tend to shift from theirmean values. This makes air gap estimation lose accuracy. Sen-sorless estimation is also computationally demanding becauseof the use of high speed processing units for signal processing.This method is significantly affected by the eddy currents andmagnetic saturation.

As mentioned previously, air gap information is hidden inthe voltage and current of the EMS coil. This can be seen bymanipulating (2) and using expression of L(x). Note that sincethe electrical time constant and mechanical time constants vary

by order of 10s, it is justifiable to neglectdx

dtresulting in (7).

Fig. 6. Changing from a conventionally sensed AMB configuration tosensorless configuration [1]

Fig. 7. Classification of sensorless air gap estimation.

x(t) + xg = N2A0

2(v(t) i(t)R)di(i)

dt l

2r(7)

From (7), if the parameters of the EMS system, the applied

voltage v(t) , coil current i(t) and current slopedi(t)

dtare

known, air gap can be calculated accurately. However, inpractical implementation, much of the system parameters areprone to changes which leads to lose of robustness. Over thepast two decades, research has been conducted to over comesuch problems related to robustness and different techniqueshave surfaced.

A. Classification of sensorless air gap estimation

Sensorless EMS can be classified into two types. 1)UsingState observers and 2) Modulation/Demodulation which isfurther divided into two types. The classification is shown inFig.7.

The first type which uses state observers is demonstratedin [2] in which a hybrid observer is used to show the selfsensing EMS. The results are experimentally proven and showsthe difference between measurements by displacement sensorand estimated air gap. However, it lacks stability and robustanalysis. Such task has been demonstrated in [3] which isbased on the simplified LTI model of the EMS system. This


Fig. 8. Basic closed loop for modulation based self-sensing.

research had concluded the inherent lack of robustness inthe sensorless EMS system when modeled as an LTI system.However research in this field had not stopped because theexperimentally obtained results by contemporary researchesseem to be in contradiction to it. This paradox has been re-cently clarified by a comprehensive robustness analysis of self-sensing EMS system by Eric. H.Maslen in [4]. The researchconducts senstivity analysis for both LTI based observers andlinear periodic (LP) based approach in modelling of system.The results have shown that sensorless EMS shows robustnessif modeled as LP system.

The second category for air gap estimation actually usesthe same approach i.e it involves perturbing the EMS systemcontinuously. Thus making it an LP system and consequentlymore robust. Following is an overview of the different tech-niques employed in the modulation/demodulation approach.

The Modulation approach involves injecting high frequencysignals along with the control current into the coil. This highfrequency signal injection acts as an interrogation signals tothe EMS system. This signal is inherently present in caseswhen the applied voltage is via PWM switching amplifier.The system dynamics of the EMS cause the high frequencysignals amplitude to be changed based on the value of theair gap as shown in Fig.8. This current is obtained via signalprocessing techniques which is in direct proportion to air gap.Further this approach is sectioned into two types based on howthis high frequency signal (current ripple) is obtained.

B. Current ripple extraction: Signal processing usingHPF/LPF

As mentioned, the aim is to some how extract the currentripple which in the frequency spectrum resides at a relativelyhigh frequency. Signal processing concepts are applied to firstremove the control current spectrum by a high pass filter(HPF). Then the remaining spectrum is brought down to lowerfrequencies by demodulation. This process is depicted in Fig.9.This process of strongly dependent on the duty rate of thepower amplifier and the magnetic nonlinearity. Phase delaysare caused by the use of HPF and LPF. The drifting parametersof the EMS also effect the estimation. In the recent trends,these issues have been dealt with. Some recent research onmitigation of these issues follow:

1) New results for self-sensing AMB using modulationapproach [5]: To compensate the duty rate variation, this

Fig. 9. Demodulation of current ripple using HPF and LPF

Fig. 10. Estimation algorithm with permeability compensation.

research proposes the use of voltage and current signalssimultaneously. Fig.10 shows the estimation algorithm. Theapplied voltage is also band pass filtered and demodulated toobtain ud. Equation (8) shows the dependency of demodulatedcoil current on air gap x, magnetic offset lmr and demodulatedvoltage vd (Duty rate). The effects of duty rate and magneticoffset are compensated. The magnetic nonlinearity is compen-sated by estimation of magnetic field from iL and subtractingthis offset from idud .

id =1

Ks(2(x+ x0) +

lmr

)ud (8)

id = (kxx+ kb2B2 + kb1B + kb0)ud

xge =1

kx

idud

The algorithm is implemented on an experimental test rig. Alinear curve between the measured position and estimation po-sition is achieved as depicted in Fig.11. The research concludesby stating that systems robustness can further be improvedby modeling the systems nonlinearities more accurately. Acritical drawback for this technique is the use of an additionalvoltage sensor for compensating duty rate effect.

2) Magnetic displacement of one DOF using simultane-ous actuation and displacement sensing technique[6]: Theresearch deals with demonstration of removing the effect ofvariable duty rate of PWM switching power amplifier fromthe air gap estimation. The concept is based on the the idea ofD.Noh [7]. The concept is similar to the use of state observers.Difference lies in the fact that the instead of the output i(t)and simulated output i(t) to be compared to generate error forobserver, the current ripple is used. The algorithm is shownin Fig. 12.


Fig. 11. Estimator static performance compared with the position sensor.Estimated position (solid)- measured position (dotted)

Fig. 12. Self sensing parameter estimation scheme for determining air gap.

Both the forward path filters consist of a BPF , a full waverectifier and a low pass filter. Its purpose is to generate a signalproportional to the air gap but at a low frequency. The outputsof each forward path filter are subtracted to generate an errorwhich is fed to a controller, Proportional-Integral (PI) in thiscase. The output is the estimated air gap. The controller servesto keep the error e zero. As long as this holds, the estimatedair gap is well within acceptable bounds for stable levitation.

A critical drawback for this method is its dependency onthe simulated model of the EMS. Since actual hardware canshift from mean values of its parameters, the robustness ofthis method is questionable. This can also be attributed tothe simplified EMS model. If EMS system is modeled bytaking the neglected phenomena of magnetic saturation, crosscoupling and eddy currents, as has been done in [8] , thisapproach can be improved. Use of adaptive control algorithmsto compensate the changing parameters can be a good solutionfor this issue.

Fig. 13. Closed loop employed for direct measurement of current slope usingtransformer.

C. Direct Measurement of current ripple change rate

Unlike the demodulation approach which appears mathe-matically challenging, this approach is somewhat simple. Asthe name suggest, it involves direct measurement of the change

of current ripple. It is evident from (7) that measuringdi(t)

dtholds significance in air gap estimation. Since, the current rip-ples frequency spectrum lies at high frequencies, measuring arapidly changing signal demands fast computational processorsand samplers. Nonetheless, due to availability of high speedprocessors, this approach has been pursued by many. Initially,the idea was first proposed and demonstrated by Lichuan Li in

[9]. Current slope(di(t)

dt) is measured by using a transformer

like coil whose output voltage is directly proportional to thecurrent slope as shown in Fig.13. Though the approach is new,it involves yet use of another sensor, (extra coil) , side byside current sensor, which could be used for the purpose ofdisplacement sensing as well. Another drawback stated forthis method is that it required exact timing for sampling thetransformers output. This is attributed to the transient in thecurrent ripple due to the fast switching PWM. An improvementin for this case would be to measure current slope without suchextra hardware. This problem has been addressed the followingway by some recent works.

1) Direct current measurement approach [10]: This is arecent work based on the original work of [5]. However, thisis an improvement from it as it doesnt use extra voltagesensors to eliminate the duty rate effects. The idea is based onthe measurement of current ripple amplitude to approximatecurrent slope and consequently estimate the air gap. Thealgorithm scheme in shown in Fig. 14. The sampled currentis averaged out and subtracted from within itself to extractout the current ripple. The maximum value of ripple is takenwhich is when multiplied with a constant kx gives estimatedair gap. Further magnetic offset is subtracted as had been donein [5].

Since the operating frequency of the PWM switching poweramplifier is high at 20Khz, the nonlinear dependency of the


Fig. 14. DCM Self-sensing approach

Fig. 15. Raw coil voltage and current showing measurement and controlcycles.

air gap estimation on the duty cycle is restricted to be thesame, 0.5 at the time current ripple is measured. This dividesthe PWM cycle into a sensing cycle and a measurementcycle as shown in Fig.15. By doing this, the current controlperformance is degraded or to achieve the same current slopeslew rate, the applied voltage is required to be doubled.

The proposed method is compared with the results of [5]as shown in Figure.16. The position error for the case ofsimulated DCM remains approximately zero for a range ofabout 400s unlike that of Schammass [5]. However, theexperimental results show some odd variation throughout theoperating range. Yet, the error still remains quite low.

2) Detection of current slope using multiple current sam-ples [11][12][13]: This works has proposed a new improvedmethod of direct measurement of current slope by using highspeed ADC to sample current multiple times in one duty cycleas shown in Fig.17. M samples are then used to estimatethe current slope using least square method as given in (9).It should be noted that in the latest work [13], instead of

Fig. 16. Position errors for Simulation and experiment

just rising slope, falling slope is also calculated. This addsadditional advantage which can be inferred from the finalequation (10) derived for the position estimation. The air gapin this case doesnt depend on the resistance of the coil or thevelocity of the levitating rotor. These two quantities have beencanceled out by the use of double detection of current slopes.

in, =

M1j=0 (in,,j in,)(tn,,j tn,)M1

j=0 ((tn,,j tn,)2)(9)

xn =0AN

2

2Udc(i1,n i2,n) (10)

For the rejection of duty cycle effects, this method followsthe same approach of fixing the duty cycle at 0.5. This on onehand doesnt disrupt the current control but it does decrease isperformance in terms of slew rate for current rise and currentfall as shown in Fig.18. Thus a compromise is made betweenthe accuracy of the position estimation and the dynamics ofthe current control.

This estimation method is also experimentally verified byusing it for an Active magnetic bearing. The block diagramfor the control system is shown in Fig.19. The hardwareconsists just of power amplifiers and a current sensor. Thisis a significant edge over the previously mentioned estimationmethods. The experimental results are shown in 20 which areacceptable for the application of AMB.

V. COMPARISON

After a short review of some of the recent works in thefield of sensorless air gap estimation, Table.V sums up thecomparison between different techniques. General trend ob-served is that the modulation approach using filters somewhatlacks good duty rate rejection and often involves an additionalsensor apart from current sensor thus increasing hardware. Themathematical analysis also is relatively complex unlike thedirect current slope measurement which is straight forward.Duty cycle rejection is seen compensated significantly by the


Fig. 17. Principle of multiple sampling [11]

Fig. 18. PWM pattern with split sensing and control cycles.

Fig. 19. Block diagram of the control system

Fig. 20. Estimation performance of step change of the real position in y-axis.a)Position of x-axis during the step change in the y-axis. b)Zoom of a. c)Stepchange of real position in y-axis, d)zoom of c.

[10] and [13]. But this is done at the expense of reducedcurrent control performance.

It should also be noted that comparison is based on thecommonly touched topics between these researches. However,a comprehensive comparison involving additional comparisonparameters for instance stability, current control performanceetc could be incorporated.

Modulation approach using filters is observed to be mathe-matically more complex and involved relatively higher degreeof mathematical analysis e.g the derivation of the currentripple equation after signal processing. Unlike this, the directcurrent slope measurement is straigh forward in sense, the theoriginal equation for air gap estimation is implementedw withan increased effort in calculation of the current ripple slope.

Magnetic saturation is seem to be compensated only in [5]and its improved method [10]. Apart from these, the remainingpresented methods do not explicitly deal with this issue.

In case of hardware complexity, most of the works presentedincluded either additional sensors or filters. The work done by[13] employs just current sensors while most of the algorithmis implemented digitally.

As mentioned before in IV, eddy currents can affect theaccuracy of the estimation. Most of the researches havesufficed by avoiding it by fixed timing or limitation of the dutycycle since the such effects are predominant at the transitiontimes between positive and negative pulses.

VI. CONCLUSION AND FUTURE PROSPECTS

A comprehensive survey in the field of sensorless air gapestimation has been conducted. Two commonly researched ap-proaches, modulation approach using signal processing filtersand direct current slope measurement, have been dealt with.Each approach has its own pros and cons, however the latter


TABLE ICOMPARISON BETWEEN DIFFERENT SENSORLESS AIR GAP ESTIMATION TECHNIQUES

+ Good bad

Signal processing using fil-ters(demodulation)

Direct current slope mea-surement

OriginalIdea

Schammass2005

Tau2011

LichuanLi 2004

Niemann2013

Wang,2014

Duty Cycle vari-ation effects + ++ +++ +++Less Complexity + ++ +++MagneticSaturationCompensation

++ ++

ReducedHardwarecomponents

++ + ++ ++ +++

Eddy currentcompensation

one has been observed to have few technical edges over theformer one. For instance, increased simplicity and reducedhardware. See Table.V.

In section IV, inherent lack of robustness was mentionedas a major disadvantage of sensorless approach. The recentworks have definitely proved otherwise. It has been shown that,though not as robust as the displacement sensor incorporatedcontrol, the sensorless estimation methods when use the highfrequency injected interrogative signal make the over allsystem gain robustness.

It has been observed that the theoretical basis and stabilityanalysis, for the direct current slope measurement is not widelypresented. Most researches extract the sensitivity curves exper-imentally. The author is of the view that a logical and rationaltheoretical basis is a necessity if further knowhow about thebehavior of the such techniques is aimed.

Since, none of the listed works deal with eddy currentcompensation and most have sufficed by avoided it by fixedtimings, this could be a ripe area of research for sensorless airgap estimation.

Generally, industrial EMS system multiple coils whichraises yet another issue of cross-coupling which consequentlyeffects the estimation accuracy. A crude side-solution to thisproblem is presented in [8]. However focused research intothis issue might hold additional possibilities.

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[4] D. T. Eric H. Maslen and T. iwasaki, Robustness limitations in self-sensing magnetic bearings, Journal of Dynamic Systems, Measurement,and Control, 2006.

[5] A. Schammass, R. Herzog, P. Buhler, and H. Bleuler, New resultsfor self-sensing active magnetic bearings using modulation approach,Control Systems Technology, IEEE Transactions on, vol. 13, no. 4, pp.509516, July 2005.

[6] T. M. Lim and S. Cheng, Magnetic levitation of a one {DOF} systemusing simultaneous actuation and displacement sensing technique,Mechatronics, vol. 21, no. 3, pp. 548 559, 2011. [Online]. Available:http://www.sciencedirect.com/science/article/pii/S0957415811000213

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[10] A. C. Niemann, G. van Schoor, and C. P. du Rand, A self-sensingactive magnetic bearing based on a direct current measurementapproach, Sensors, vol. 13, no. 9, p. 12149, 2013. [Online]. Available:http://www.mdpi.com/1424-8220/13/9/12149

[11] J. Wang and A. Binder, Self-sensing magnetic bearings using multiplesampling of currents alone, in Power Electronics and Applications(EPE), 2013 15th European Conference on, Sept 2013, pp. 110.

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