Modeling and Control of the Electrical Actuation System of

1 Copyright © 2014 by ASME

MODELING AND CONTROL OF THE ELECTRICAL ACTUATION SYSTEM OF AN ACTIVE HYDROMAGNETIC JOURNAL BEARING (AHJB)

Michael G. Farmakopoulos Machine Design Laboratory

Department of Mechanical Engineering and Aeronautics

University of Patras, Patras-26504, Greece

Eleftherios K. Loghis School of Electrical and Computer Engineering

National Technical University of Athens Athens, Greece

Pantelis G. Nikolakopoulos

Machine Design Laboratory Department of Mechanical

Engineering and Aeronautics University of Patras, Patras-

26504, Greece

Nikolaos I. Xiros School of Naval Architecture and

Marine Engineering

University of New Orleans, New Orleans, United States

Chris A. Papadopoulos Machine Design Laboratory Department of Mechanical

Engineering and Aeronautics University of Patras, Patras-

26504, Greece

ABSTRACT The architecture of the electrical actuation module driving a

magnetic-hydraulic bearing system is presented. The bearing is

intended to be scaled for use in applications of all sizes in

industries like shipboard for support of the engine-propeller

shaft or in power-plants for the shaft through which the prime

mover, e.g. steam or gas turbine, is driving the electric

generator. The benefits of this new bearing is first and foremost

its superb performance in terms of low down to practically no

friction losses since there is no direct contact between the

supporting bearing surface and the rotating shaft supported.

Other benefits include the potential of active, inline, real-time

balancing and alignment. To implement such concept of a

magnetic-hydraulic bearing, the following tasks need to be

carried out. First, identification of mechanical,

electrodynamical and circuit properties of the bearing’s

electromagnets in the system is necessary. Toward such

identification, a series of experiments needed to be carried out.

To be able to carry out these experiments, a specific power

electronic converter is developed to drive each electromagnet.

The power electronic drive is a quad MOSFET circuit based on

full-bridge converter topology and outfitted with appropriate

sensory instrumentation to collect and record measurements of

all the physical variables of interest. Special care has been

taken to compensate for magnetic hysteresis of the

electromagnets, mitigate any induction heating effects and

maintain operation within the material’s linear region i.e.

without significant saturation occurring. The use of a power

transistor bridge allows rapid changes to be applied on the

electromagnet’s load force which could compensate disturbance

or misalignment developed on the shaft supported. The data

series from these experiments are useful for formulating a

possibly nonlinear model of the electromagnetical and

electromechanical processes involved in the bearing’s

operation. Such a model can then be employed to help design a

digital microcontroller system which could effectively drive the

power electronics and electromagnets to perform their required

tasks as part of the bearing. Besides, the model could also be

used for the synthesis of the nonlinear, sampled-data (discrete-

time) control law which will be programmed on the

microcontroller system board.

INTRODUCTION A specific value of current in the coil of an electromagnet

produces specific electromagnetic force. This electromagnetic

force is applied to a rotor to levitate it in a bearing. Every

different position of the rotor and every different load that the

bearing carries need different current to levitate the rotor.

Levitating a rotor in a bearing provides advantages such as low

friction and almost maintenance-free operation. A patent for an

active hydromagnetic journal bearing by Papadopoulos et al

was presented in (1). The patent referred to a journal bearing

that is capable of operating as an Active Magnetic Bearing

(AMB), a Hydrodynamic Journal Bearing or a Hybrid Bearing.

There are several ways presented to model an AMB.

Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-38346


Antila et al (2) presented a nonlinear two-dimensional finite

element method (FEM) to predict the performance and estimate

the load capacities of radial magnetic bearings, while Khoo et

al (3) presented a study concerning the specific load capacity of

radial-flux radial magnetic bearings, and provided some

insights into what values are achievable and how these values

depend on various parameters such as air-gap thickness,

allowable temperature rise in the coils, certain heat-transfer

coefficients, and certain de-rating factors associated with the

distribution of the bearing load in time and space. Ren et al (4)

presented in their work using the FEM that in order to increase

the carrying capacity and to reduce the weight and the size of

AMBs, it is necessary to use a ferromagnetic material with high

magnetic flux density, which can make AMBs run in the non-

linear region. Farmakopoulos et al (5) presented an analytical

study to calculate the magnetic field forces and the

hydrodynamic field forces of the bearing patented in (1). They

also calculated the stiffness and damping properties of the

bearing operated under active magnetic, hydrodynamic and

hybrid mode, respectively. Besides, Farmakopoulos et al in (6)

presented a PID control model of an AMB operated under the

influence of unbalance and gyroscopic forces.

Lei et al (7) presented an analysis and design of magnetic

suspension systems with large flexible rotordynamics models

using FEM. They concluded that the large order of the rotor

model and high spin speed of the rotor present a challenge for

magnetic suspension control.

Arredondo et al (8) presented a model and a basic control

design process of a rotary flexible spindle hovered by Active

Magnetic Bearings (AMB). They took into account the rigid

dynamics, the flexible dynamics, the rotating unbalanced

motion and the gyroscopic coupling. They compared their

numerical predictions with the actual measured experimental

results from laboratory set-up based on the MBC500 Rotor

Dynamics.

Guojun et al (9) presented an application for the helium

turbine and generator system of a 10MW high-temperature gas-

cooled reactor (HTR-10GT). They chose active magnetic

bearings instead of ordinary mechanical bearing, to support the

rotor in the HTR-10GT. They studied extensively the effects of

AMB stiffness on the critical speeds of the rotor using

numerical and experimental techniques.

Štimac et al (10) presented a modeling strategy for a

flexible rotor/active magnetic bearing system using the non-

collocation method. They paid special attention to the vibration

reduction and the stable passage through the first critical speed.

Antila (11) presented the effects of some none ideal

properties of the electromagnetic actuators in radial active

magnetic bearings such us the eddy currents effects in the

laminations, the magnetic hysteresis, etc.

Zimon et al (12) presented a non-symmetrical twelve poles

active magnetic bearing actuator. They included the control

system in their computer simulations. They used the field-

circuit modeling method under various speed of the rotor. They

solved the electromechanical equation system, taking into

account the integral parameters obtained from finite element

analysis of the magnetic field. They verified their calculations

by the measurement tests under various rotational speed of the

AMB rotor.

In this paper, comparisons between experimental and

simulation results of the required current applied to one of the

bearings’ electromagnets for rotor levitation under different

loads and rotor positions are presented. The proposed

methodology and the data series obtained from the experiments

can be used to formulate a possibly nonlinear model of the

electromagnetical and electromechanical processes and help

design a digital microcontroller system which could drive the

power electronics and enable the electromagnets to apply the

required force to the bearing system.

NOMENCLATURE A Cross-sectional area of each electromagnetic pole

Fy Magnetic force of one horseshoe-shaped electromagnet

g Magnetic air gap

ga Gravity acceleration

Iy Current in Y-axis

m Mass of the shaft

Nw Number of windings per pole

y Rotor’s displacement from the centre position in the Y-

axis

μο Magnetic permeability of vacuum (4π10-7

N/A2)

THE ROTOR-BEARING SYSTEM SETUP The rotor-bearing system and the AHJB used in this paper is

presented in Fig. 1 (a) and Fig. 1 (b), respectively. The rotor

and the active hydromagnetic journal bearing are designed to fit

the RK4-Rotor Kit of the former Bently Nevada.

(a)


(b)

Figure 1: (a) The RK4 Rotor Kit of GE (former Bently-Nevada)

with (b) the AHJB on the right, constructed by the design team of

the Machine Design Lab.

The cylindrical magnetic bearing rotor (Fig. 2 part R), on

which the magnetic forces act, is fixed to the rotor at a length of

L from the left end of the rotor. Under normal conditions, the Z

and the K-axes are aligned. But in reality, there is always a

difference. In Fig. 2 (b), the K-axis is inclined by an angle θΥ

which respect to the Z-axis and a moment MY is applied around

the Y-axis. Along the X-axis, the angle coming from the Z-axis

is defined as θX and the moment around the X-axis is defined as

MX, as shown in Fig. 2 (c). The dimensions of the rotor are

shown in Fig. 2 (d).

Z

X

Y

Ω

XYZ – Stationary coordinate system

IJK – Rotating coordinate system

I

J

K

View-1

View-2

Z

X

YΩ

KL

Z

Y

Ω

KL

View-2

View-1

X

MY

MX

x

y

θΥ

θX

Lub

La

mga

FextY

LFextY

a

b

c

R

20

10

210 15

60

25

28

35

25

40

d

R

Figure 2: The rotor used a) at Y-Z axes, b) at X-Z axes, c) at Y-Z

axes, d) dimensions.

The mass of the shaft at the bearing position is m = 0.820

kg. The magnetic force Fy acting on the shaft from the magnets

of the AHJB can be expressed as,

2

2

0

y

y W

IF N A

g y

(1)

The number of coils WN and the area A in Eq. (1) referred

to one pole of each horseshoe shaped electromagnet.

The Active Hydromagnetic Journal Bearing has the

following operational characteristics: four horseshoe

electromagnetic poles, permeability of vacuum μ0 = 4π10-7

N/A2, 500 coil windings per pole, the cross-section area of each

electromagnetic leg is 191.81 mm2 and the air gap denoted by g

is 800 μm. The bias current in both X and Y-direction is zero

Ampere.

MEASUREMENT METHODOLOGY MEASUREMENT OF VERTICAL POSITION SENSOR OUTPUT

Two of the most critical sensors of the proposed system are

the X and Y position sensors. Thus, some tests had to be

performed on them in order to decide their suitability for the

application. In addition, the dynamics of their coupling with the

overall system and the corresponding response is obtained.

Fig. 3 shows the measurement setup used for the results

reported in this as well as the following sections. As shown in

the figure, the two position sensors are located close to the

bearing. The output of the sensors is then decoded and

amplified by the position sensor amplifier. We picked the Y-

sensor to monitor and record the amplifier’s output by an

oscilloscope.


Y P

os

Senso

r

X Pos S

ensor

IN1 IN2 IN3 IN4

Amplifier Power Supply

OSCILLOSCOPE

Y Pos Sensor Amplifier Out

Position Sensor Amplifier

Shaft

Motor

Bearing

Figure 3: Measurement setup for position sensors.

The measurements were performed in a lab environment of

17oC. The voltage supplied to the sensor amplifier was -17.9V.

During noise signature recording, the electromagnets were not

driven by current.

At the lowest position of the shaft the unfiltered sensor

amplifier output was -8.79V (average value).

In order to get an estimation of the noise injected to the

unfiltered signals, the oscilloscope persistence mode was

used. For the same rotor position, a voltage fluctuation of

-8.48V to -9.12V was observed.

For the upper shaft position (manual lift), the sensor

amplifier output was -5.618V on average with 480mV pp

noise.

The above measurement methods created a 3.51V voltage

output deviation for the two positions of the shaft (about 200μm

apart). Repeating the measurement with an accurate micrometer

and an accurate multimeter, the result was that the amplifier

output changes by 14mV per μm the shaft moves.

The first measurement reveals the need of filtering the

amplifier output because a 480mV pp noise means about

34.286μm position measurement error. Since the target

accuracy is at least 1μm, such high level noise has to be

suppressed. Besides, the fact that the noise levels of the A/D

conversion system employed in the measurement might be

totally different also need to be taken into consideration.

Nevertheless, although the need for filtering the collected signal

is apparent, the final results from the filter's output have to be

evaluated based on the practical situations of the rotor bearing

system rather than an oscilloscope.

DEPENDENCE OF SENSOR AMPLIFIER OUTPUT ON SUPPLY VOLTAGE

For the evaluation of the amplifier output, the effect of the

regulation of the power supply that is used for the operation of

the position sensor amplifier needs to be investigated.

Our tests showed that any glitch in the power supply is

passed almost intact to the amplifier output. For example, using

-17.9V as supply -8.38V was measured for a certain position.

When the supply was changed to -16.9V under the same

position, the output moved to -7.49V.

This means that tight regulation must be applied to power

supply. The final specification will be determined by the

deviations and errors introduced by the rest of the

instrumentation and electronics involved in position sensing.

The objective for the moment remains to achieve 1μm

accuracy.

POSITION SENSOR RESPONSE

The purpose of our electromechanical systems used as a

bearing is to achieve shaft position regulation. To design a

control algorithm for this purpose, we first have to evaluate all

system components that influence the dynamics of the system.

The position sensor is our key element in the control loop.

Ideally, its bandwidth should be much greater than the

maximum frequency emerged in the shaft’s dynamics.

The test scenario was to measure the sensor response and

reading a gear in Bently-Nevada RK4 that controls the rotor’s

speed. The figures below show the position sensor’s response at

560rpm and at 1500rpm.

Figure 4: Sensor response at 560rpm. Sensor volts vs. time

Figure 5: Sensor response at 1500rpm. Sensor volts vs. Time


Figs. 4 and 5 are screenshots from an Agillent DSO3202A

oscilloscope. The X-axis for these figures is time, set to 500us

per division. Τhe Y-axis is voltage set to 1V per division. Since

the specific voltage is the output of the position sensor, it

actually means distance from sensor tip. The constant that

relates voltage to distance for these sensors is 14mV/um. Thus

the Y-axis units of these figures are 71.43um per division

EFFECT OF TEMPERATURE TO POSITION SENSOR’S OUTPUT

To evaluate the sensitivity of the sensor to temperature, we

increased the ambient temperature of the sensor using a

thermogun, while maintaining the shaft at its rest (lower)

position. The results were as follows:

Temperature

(oC)

Amplifier Output

(Volt)

19.1 -8.92

30 -9.183

39.15 -9.457

60 -9.654

Table 1: Output of position sensor at different ambient

temperatures.

Considering these values, the first conclusion is that besides

the effect of temperature to the sensor’s output, thermal

expansion of the shaft has to be also measured in real time. This

leads to the decision that, in order to regulate the shaft’s

position with sufficient robustness, the shaft has to be measured

differentially. This means that two instead of one sensor per

position measurement should be employed, located on opposite

sides of the shaft. Thus the evaluation of temperature sensitivity

of the position sensor can be postponed until the second

position sensor is mounted and operated.

DETERMINATION OF ELECTROMAGNET’S MAXIMUM SAFE OPERATING CURRENT

Figure 6: Thermocouple readings vs. time.

It is of critical importance, prior to engaging in the

development of electronic systems and control algorithms, to

have a clear picture of the operational limits of the main

system’s actuators - the electromagnets. A major objective is to

decide the maximum safe operating current for the

electromagnets. This maximum current determines the

maximum forces that the bearing can handle.

Maximum current determination was based on the

incurrence of the electromagnet’s thermal effect. Out of the

four electromagnets of the bearing, we selected the upper one

as our test subject. During the test, we applied test currents to

that particular magnet and measured temperatures at the

following system points:

1. Upper electromagnet.

2. Lower electromagnet.

3. Left electromagnet.

4. Right electromagnet.

5. Position sensors’ ambient (1cm close to the Y position

sensor).

Assuming that a temperature increase of 50oC at the

electromagnet is acceptable, we ought to find the current that

would result in such effect. The temperature increase range was

based on the assumption that the maximum lab environment

temperature is 40oC. This means that with a 50

oC increase of

system temperature, we would have a bearing working at 90oC.

At the time of measurement, the ambient temperature was

17oC. The following table summarizes the system’s thermal

response under different test currents. Fig. 6 shows the

temperature change versus time at each measurement point,

which is helpful in understanding the content of table 2. In table

2, besides temperature measurements, the electromagnet’s coil

resistance is also measured.

Current

(mA)

Start

time

(sec)

End time

(sec) Comments

100 0 400 Initiating test. Coil

resistance 15.7Ω.

200 401 800 17.8

οC at 400sec with

resistance 16.05Ω.

300 801 1300 20.14

οC at 1220sec with

resistance 16.26Ω.

800 1301 1700 20.29

οC at 1300sec with

resistance 17.125Ω.

1000 1701 2400 35.5οC at 1700sec.

1020 2401 2535

64.56οC at 2535sec.

Current driving is

terminated at 2535sec to

protect the system from

overheating.

1020 2716 2842

1.2A is applied again to

reheat the system and

come faster to the point

of thermal stability of

°C

20

30

40

50

60

Channel 1: Y magnet (upper)Channel 2: Y magnet (lower)Channel 3: X magnet (left)

Channel 4: X magnet (right)Channel 5: Sensors Ambient

0 1000 2000 3000 4000 5000

Sec


the system for 1A.

1000 2843 4915

66.90οC at 4915sec. The

thermal equilibrium is

estimated to be reached

at 70οC.

Table 2: Temperature rise under different experimental currents.

Under 66.5

οC, the coil resistance was found to be 22Ω.

From the data above, it is concluded that the safe operating

current is 1A. Besides, some useful conclusions about the

thermal coupling between all electromagnets can also be

derived from Fig. 6. For example, one conclusion is the ratio of

the increase of temperature of each electromagnet and the time.

When all electromagnets are in operation, each electromagnet's

temperature will be higher than the one measured in our

experiment (under the same current).

ELECTROMAGNET PERFORMANCE UNDER MAXIMUM SAFE OPERATING CURRENT

After obtaining the maximum safe operating current, the

performance of the electromagnet was measured under the

operating limits. The purpose of this measurement was to prove

that the currently available electromagnets are suitable to apply

forces to the shaft (a future experiment will be carried on to

investigate their magnetic force response times).

E

E

DDDD

AB

C

Y

Figure 7: The way and the position of the applied force onto the

rotor.

To evaluate the forces generated by the electromagnets, we

applied a range of certified weights (denoted by D in Fig. 7) at

the center position of the shaft (denoted by B in Fig. 7) through

using a metallic rod weighting 365.44gr (denoted by E in Fig.

7) without rotating the shaft. Then we provided drive current to

the coil of the electromagnet under test and checked whether it

could lift the shaft along with the weights. Due to the

mechanics of the system, the additional load at the bearing's

position (denoted by C in Fig. 7) is exactly half of the one we

applied at position B in Fig. 7. This is because the additional

load was applied at the center of the shaft and the shaft can

rotate around position A. The left four columns of table 3 list

the weights we applied to the shaft at position B; the force

required by the upper electromagnet of AHJB located at

position C and the currents needed to lifting the shaft from its

lowest position (-120μm) as well as to lifting it from its highest

position (+120μm). In table 3, “DW” stands for Default

Weight, which stands for the weight that must be lifted by the

electromagnet when the system is unloaded. This default

weight is equal to the mass of the shaft at the bearing position,

which is located in position C in Fig. 7 and is equal to 0.820 kg.

To get an estimation of the force generated by the

electromagnet and the corresponding position of the shaft, the

output of the position sensor was recorded every time the

electromagnet lifted or released the shaft. The recordings of the

position sensor are shown in a later section.

CROSS-VALIDATION OF MEASURED FORCES WITH AHJB MODEL USING FEM

The 2-D magnetostatics analysis, using the Multiphysics

module of ANSYS, was used for the finite element simulation

(5). In this model the deformation of the shaft is not taken into

account. The PLANE53 element which is suitable for 2-D

models (Planar and axisymmetric) of magnetic fields is used.

The element is defined by 8 nodes and has up to 4 degrees of

freedom per node: z component of the magnetic potential vector

(AZ), time-integrated electric scalar potential (VOLT), electric

current (CURR), and electromotive force (EMF). The element

has nonlinear magnetic capability for modeling B-H curves or

permanent magnet demagnetization curves. The B-H data as

given in ref. (13) are used, for pure iron annealed.

In Figs. 8 and 9 the finite element magnetic field (B) and the

direction of the magnetic lines of force of the radial AHJB are

shown, respectively.

Figure 8: Finite element magnetic field (B) plot of the radial

AHJB.


Figure 9: Direction of the magnetic lines of force of the radial

AHJB.

The experimental and simulation results concerning the

current demanded to support the shaft, which carries a specific

load, along Y direction are presented in table 3 below.

Weight

applied

at

position

B in Fig.

7

(kg)

Force

required

by the

upper

electrom

agnet of

AHJB at

position

C in Fig.

7

(kg)

Y

Positi

on of

the

rotor

(μm)

Y

current

-

experi

mental

results

(mA)

Y

current

-

simulati

on

results

from

Ansys

(mA)

Devia

tion

(%)

No Load DW -120 330 332.62 0.79

+120 240 254.44 5.68

7.36544 DW +

3.6827

-120 750 779.13 3.74

+120 580 595.55 2.61

10.36544 DW +

5.1827

-120 860 899.62 4.4

+120 670 687.6 2.56

14.36544 DW +

7.1827

-120 1020 1038.82 1.81

+120 800 794.12 0.74

Table 3: Experimental and simulation results

A very well agreement between the experimental the

simulation results is observed, which means the above detail

described design methodology is valid and can be used for a

specific micro - controller design and construction.

POSITION SENSOR DATA SERIES UNDER DIFFERENT ELECTROMAGNET SETTINGS

The following figures show data series obtained from the

position sensor when the electromagnets were active or inactive

(and therefore lifting or releasing the shaft), respectively. These

data series were collected to investigate the dependence of the

electromagnet's force on the distance from the shaft to its core.

Such data could be useful for design and validation of the

suitability of Eq.1 in systems similar to ours.

Figure 10: Magnet lifting the unloaded shaft. Sensor volts vs. time

Figure 11: Magnet releasing the unloaded shaft. Sensor volts vs.

time


Figure 12: Magnet lifting the shaft with 7 kg test load. Sensor volts

vs. time

Figure 13: Magnet releasing the shaft with 7 kg test load. Sensor

volts vs. time

Figure 14: Magnet lifting the shaft with 14 kg test load. Sensor

volts vs. time

Figure 15: Magnet releasing the shaft with 14 kg test load. Sensor

volts vs. time

Figs. 10 to 15 are screenshots from an Agillent DSO3202A

oscilloscope. The X-axis for these figures is time, set to 10ms

per division. Τhe Y-axis is voltage set to 500mV per division.

The voltage measured is the output of the position sensor. The

constant that relates voltage to distance for these sensors is

14mV/um. This means that for these figures Y-axis units are

500mV/14mV = 35.7um per division.

CONTROL SYSTEM ARCHITECTURE

Based on the initial findings, presented earlier in this work,

for transient response and performance of the bearing under

development, a full state feedback controller is envisioned.

Such controller will be probably have to include some degree

of nonlinearity, a partial state observer (Luenberger) or even

state estimator (Kalman filter) as well as employment of

integral control elements regarding several state integrals like

e.g. that of X and Y shaft positions to eliminate steady-state

error that can still occur in several full state feedback schemes

see e.g. [14].

Before the control system detailed design can be carried out,

the development of the bearing needs to be completed. In this

end, now that performance data of the electromagnets involved

are available, design and development of the electrical

actuation subsystem to drive the electromagnets has to be

conducted.

This is no trivial task. A first approach, based on the energy

balance analysis performed on the grounds of the

measurements performed is presented in Fig. 16. This is the

driving system for one of the four electromagnets of the

bearing.


AC

LPFLPF LPF LPF

A/D A/D A/D A/D

MIXED SIGNAL

(ANALOG & DIGITAL)

CONTROL

SYSTEM

D/ALPF

Vout Setting

220V~

DC

X-Pos Sensor

Rsense

Y-Pos Sensor

Magn

et C

urr

ent S

ense

Magn

et V

oltage S

en

se

Y-P

OS

sig

nal

X-P

OS

sig

nal

220V~

DC

Figure 16: Electrical actuator topology intended to drive each

bearing electromagnet In this setup, one can identify the control system, shown as

a single block at the bottom framed by three types of signal

transducers: analog inputs being fed to the control system

through anti-aliasing filters and Analog-to-Digital converters

(A/D), analog outputs generated by the control system to drive

the process through Digital-to-Analog converters (D/A) and

smoothening filters and finally Pulse Width Modulation (PWM)

that are discrete-amplitude continuous-time signals with

periodic high-frequency triggering capable of driving solid-

state switches used in power electronics like e.g. the power

MOSFET through appropriate drivers.

The control system regulates the voltage on the DC bridge

connecting the full-wave rectifier block with the MOSFET

block. Then power and current flow to each individual

transistor is regulated by the control system in order to achieve

the required current profile required to drive the magnet.

The force of each electromagnet is a complicated function

of the current through each coil as well as the relative position

and velocity of the metallic mass it drives, i.e. the shaft as has

been seen in [15, 16]. Finally, the important aspects of the

nonlinear state-feedback control strategy derived from the

Volterra-Wiener theories are presented in [17-20] as pertaining

to electromechanical motion control systems driven by

electromagnets or power electronics.

CONCLUSIONS

The following conclusions can be drawn based on tests

performed so far:

1. A very good agreement of the proposed experimental

methodology with simulation results is found. Thus simulation

will be used as an alternative method to experiments during the

stage of system response identification.

2. The results obtained from the experimental device

patented in ref. (1) prove that the method proposed by the

present paper has the ability to develop the required digital

microcontroller system.

3. The simulation and experimental results have established

a solid knowledge about the maximum magnetic force the

bearing could generate.

4. The fundamental experiment of rotor lifting monitoring

will be used as the bases to create timing specifications for our

control algorithm and electronic hardware.

5. The position sensor's limitations have been partially

understood by the acquisition of its dV/dt curve. A new

experiment must be designed to verify the presence of the pure

delay element in the position sensor's response.

6. Further research will be performed to control the rotor

bearing system in X direction and finally in both X and Y

directions simultaneously.

7. All the above work and conclusions will be extended and

adapted in the hybrid operating mode of the bearing, promoting

its beneficial operation as referred in (1).

REFERENCES 1. C. A. Papadopoulos, P. G. Nikolakopoulos and M. G.

Farmakopoulos, “Hybrid Journal Bearing,” Patent: WO

2012/032362 A1 / 15-03-2012.

2. M. Antila, E. Lantto and A. Arkkio, 1998, “Determination

of forces and linearized parameters of radial active magnetic

bearings by finite element technique,” Ieee Transactions on

Magnetics, 34(3), pp. 684-694.

3. W. K. S. Khoo, S. D. Garvey and K. Kalita, 2007, “The

specific load capacity of radial-flux radial magnetic

bearings,” Ieee Transactions on Magnetics, 43(7) pp. 3293-

3300.

4. S. Ren, C. Bian and J. Liu, 2008, “Finite element analysis

on the electromagnetic fields of active magnetic bearing,”

Journal of Physics: Conference Series, 96(1).

5. M. G. Farmakopoulos, P. G. Nikolakopoulos and C. A.

Papadopoulos, 2013, “Design of an active hydromagnetic

journal bearing,” Proceedings of the Institution of

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