Progress In Electromagnetics Research M, Vol. 62, 211–221, 2017

A New Planar Electromagnetic Levitation System Improvement

Method Based on SIMLAB Platform in Real Time Operation

Mundher H. A. Yaseen1, * and Haider J. Abd2

Abstract—Electromagnetic levitation system is commonly used in the ﬁeld of magnetic levitation

system train. Magnetic levitation technology is one of the most promised issue of transportation and

precision engineering. Magnetic levitation systems are free of problems caused by friction, wear, sealing

and lubrication. In this paper, a new prototype of the magnetic levitation system is proposed, designed

and successfully tested via SIMLAB platform in real time. In addition, the proposed system was

implemented with an eﬃcient controller, which is linear-quadratic regulator (LQR) and compared with

a classical controller which is proportional-integral-derivative (PID). The present system has been tested

with two diﬀerent criteria: signal test and load test under diﬀerent input signals which are Sine wave

and Squar wave. The ﬁndings prove that the suggested levitation system reveals a better performance

than conventional one. Moreover, the LQR controller produced a great stability and optimal response

compared to PID controller used at same system parameters.

1. INTRODUCTION

Magnetic levitation technology is a perfect solution to achieve better performance for many motion

systems, e.g., precision positioning, manipulation, suspension, and haptic interaction due to its non-

contact, non-contamination, multi-Degrees-Of-Freedom (DOF), and long-stroke characteristics [1–

4]. Recently, the research on magnetic levitation attracts many researchers, and various types of

magnetically levitated (maglev) motion systems are proposed. Generally, these maglev motion systems

are realized using either Lorentz force or electromagnetic force, and both the moving magnet design

and moving-coil design are proposed for applications with diﬀerent requirements.

In literature, diﬀerent methods and models are suggested to develop electromagnetic levitation

systems and improve the system response [5–17]. However, most of the contributions require data from

measurement devices or observer algorithms. The position and electric current state data are taken

from related measurement devices, but for velocity state data, an observer should be synthesized to

estimate the unavailable signal of the nonlinear dynamical system. Furthermore, it needs a complex

system design and is not cost eﬃcient. In this paper, a new technique is proposed to develop the control

system based on a plate maglev system with the mathematical model. The new system uses a SIMLAB

platform to control the position of electromagnetically levitated system in real time via Matlab/Simulink

environment.

2. MAGLEV SYSTEM CONSTRUCTION

In this section, ﬁrstly, the construction of the magnetic levitation system and its components will be

explained.

Received 13 September 2017, Accepted 31 October 2017, Scheduled 29 November 2017

* Corresponding author: Mundher H. A. Yaseen (mundheryaseen@gmail.com).

1Electrical & Electronics Engineering Department, Gaziantep University, Gaziantep, Turkey. 2Department of Electrical Engineering,

College of Engineering, Babylon University, Iraq.

212 Yaseen and Abd

Levitation system or maglev is a method by which an object is suspended with no support other

than magnetic ﬁelds. Magnetic force is used to counteract the eﬀects of the gravitational acceleration

and any other acceleration. The two primary issues involved in magnetic levitation are lifting forces:

providing an upward force suﬃcient to counteract gravity and stability: ensuring that the system does

not spontaneously slide or ﬂip into a conﬁguration where the lift is neutralized. Maglev trains perform

three diﬀerent parts to operate in high speeds which are: Levitation, Propulsion and Guidance. This

paper focus on the levitation system part.

The proposed experimental magnetic levitation system is shown in Figure 1. The system is made

up 4 electromagnets as actuators for applying magnetic forces to achieve stable levitation and precise

position control, a rigid square plate with 4 permanent magnets on each corner, and 4 Hall eﬀect sensors

for sensing the position of the levitating plate, and Va is coil applied voltage.

Figure 1. Free body diagram of magnetic levitation system.

The electromagnets are 15 mH solenoid coils with 2 Ω internal resistances. The Hall eﬀect sensors

are linear ratiometric Hall eﬀect sensors with 50 V/T. The permanent magnets are N52 neodymium disc

magnets with 12.70 mm diameter and 6.35 mm thickness. The plate is a transparent acrylic plate with

152.4mm×152.4mm×3.175 mm. The frame is constructed by wood. For simplicity and tractability,

the system is modeled using a quarter of the system (similar to a quarter car model). The model of

the quarter-system is shown in Figure 2, where Ris the resistance of the coil, Lthe inductance of the

coil, vthe voltage across the electromagnet, ithe current through the electromagnet, mthe mass of

the levitating magnet plus one-forth of the mass of the acrylic plate, gthe acceleration due to gravity,

dthe vertical position of the levitating magnet measured from the bottom of the electromagnet, Fmag

the force on the levitating magnet generated by the electromagnet, and ethe voltage across the Hall

eﬀect sensor.

3. CASE STUDY

In this section, the mathematical model of maglev system is presented, and the force actuated by the

electromagnet is formulated as [18]

Fmag =Ci(t)

d3(1)

Progress In Electromagnetics Research M, Vol. 62, 2017 213

Figure 2. Electromagnetic levitation system model.

where (t) denotes the current across the electromagnet, dthe vertical position, and Ca constant related

to turn ratio and cross sectional area of the electromagnet. From a force balancing equation, we have

m¨

d=mg −Ci(t)

d3(2)

where mis the mass of the levitating magnet plus one-fourth of the mass of the acrylic plate and gthe

acceleration due to gravity.

In addition, an electrical relation of the voltage supply and the electromagnetic coil can be expressed

by

v(t)=R·i(t)+Ldi

dt (3)

where Rand Lare the resistance and inductance of the electromagnet, respectively. Now consider the

following perturbations with respect to the change of them

i(t)=i0+Δi(t)

d(t)=d0+Δd(t)

v(t)=v0+Δv(t)

(4)

where vois the required equilibrium coil voltage to suspend the levitating plate at do.

Under this perturbation, the dynamics in Eqs. (2) and (3) around an operating point (i0,d

0,v

0)

can be linearized

m¨

Δd=3Ci0

d4

0Δd−C

d3

0Δi(5)

˙

Δi=−R

LΔi−1

LΔv(6)

where Δi,Δv,Δdare linearization of the system about the equilibrium point. After eliminating Δiin

Eq. (6) and applying Laplace transforms, we obtain the transfer function from Δvto Δdgiven as

ΔD(s)

ΔV(s)=

−gR

v0

(Ls +R)s2−3Ci0

md4

0(7)

where ΔV(s)andΔD(s) denote the Laplace transforms of Δv(t)) and Δd(t), respectively.

Hall sensor has an output voltage of the given form [19]

e(t)=α+β

d2+γi(t)(8)

214 Yaseen and Abd

where α, β, γ are constant sensor parameters. A linearization of Eq. (8) around e(t)=

e0+Δeresults in

Δe=−2β

d3

0

Δd+γΔi(9)

where Δeis the sensor voltage.

Applying Laplace transform to Eq. (9) and using I(s)=ΔV(s)/(Ls +R) from Eq. (3) and the

representation in Eq. (7), we obtain a relation between the electromagnet voltage ΔV(s)andasensor

voltage perturbation ΔE(s) as follows;

ΔE(s)

ΔV(s)=

γs2−3Ci0

md4

0+2βRC

md6

0

(Ls +R)s2−3Ci0

md4

0(10)

Equation (10) can be represented also in the state space form after applying the second derivative

of Eq. (5) and ﬁrst derivative of Eq. (6). Thus, the state space representation of the linearized model

of Equation (10) can be represented by followings:

˙x1

˙x2

˙x3=⎡

⎢

⎢

⎢

⎢

⎣

01 0

3C

m

i0

d4

0

0−C

m

1

d3

0

00−R

L

⎤

⎥

⎥

⎥

⎥

⎦x1

x2

x3+⎡

⎢

⎣

0

0

1

L

⎤

⎥

⎦u(11)

y=−2β

d30γx1

x2

x3(12)

The measured output system (y) can be obtained by simpliﬁed Equation (9), where Δe=y,Δd=x1,

and Δi=x3).

Suppose that x=[x1x2x3]=[d˙

di] is the state of the system, where dis the controlled output,

y=ethe measured output, and u=vthe control input.

By substituting system parameters in Table 1 into Eq. (10),

G(s)H(s)= 20.66s2+ 61803

s3+ 132.5s2−1471s−194900 (13)

The numerical values of the state space equations are given below

˙x1

˙x2

˙x3=01 0

1471 0 −9.81

00−133 x1

x2

x3+0

0

66.66 u(14)

y=[−14400.31 ]x1

x2

x3(15)

4. CONTROLLER DESIGN

This section deals with the development of PID based control and LQR controller for magnetic levitation

system

4.1. Linear Quadratic Regulator (LQR) Controller

The Linear Quadratic Regulator (LQR) method is similar to Root Locus approach by inserting the

closed loop poles of the system into the desired location [20]. The EMS linearization dynamic model is

formulated by state space as below:

˙x(t)=Ax(t)+Bu(t) (16)

y(t)=Cx(t)+Du(t) (17)

Progress In Electromagnetics Research M, Vol. 62, 2017 215

Table 1. Proposed system parameter.

Parameter Value Unit

Sensor

β5.64 ×10−4V·m2

γ0.31 V/A

α2.48 V

Operation point

i01 A

d020 mm

Electromagnet

C2.4×10−6kgm5/s2A

R2 Ω

L15 ×10−3H

m=M/40.02985 kg

The x(t) state can be measured, and the cost function of constructing controller can be minimized based

on the formula below:

J(u)=

+∞

0xT(t)Qx (t)+uT(t)Ru(t)dt (18)

where Qand Rvalues can be considered positive deﬁnite weighting matrices. For initial state condition,

the variable x(0) is considered as a steady state based on perturbation of the control system. The ﬁrst

term of the J(u) function is considered as cost subject which is assigned to the energy intransient

response.

The control signal u(t) is considered as linearly proportional to the speciﬁed air gap. It is also

proportional to the clearance of track boundary condition at desired operating point (io,z

o)indesign

stage.

Using the linear state feedback can be expressed by the equation below

u(t)=−[kp(x1(t)−zref)+kv(x2(t)) + ka(x3(t)) (19)

where kpis the steady error, kvthe control suspension damping, and kataken for all stability margins.

The linear controller limitations are considered as the ability to suppress disturbances in the control

loop. The calculated LQR gains are [kp= 32483,k

v=90.4,k

a=−9.4].

4.2. PID Controller

The schematic diagram of PID controller is given in Figure 3. This control system is working based

on the calculations of the error value, trying to reduce the error percentage by adjusting the controller

parameters. The general form of this controller is formulated as below [20].

u(t)=Kp⎛

⎝e(t)+ 1

Ti

t

0

e(τ)dτ +Td

de (t)

dt ⎞

⎠(20)

where u(t) denotes the control signal, Kpthe proportional gain, Tithe integral time, Tdthe derivative

time, and e(t) the diﬀerence between the reference point and the actual plant output. Kp,Tiand Tdare

tuned for better control operation. By placing the closed loop poles at P=[−132.45 38.36 −28.36],

the calculated PID gains are [Kp=10,K

i=4,K

d=0.2].

5. PROPOSED SYSTEM DESIGN AND HARDWARE CONTROL UNIT

In this section, the proposed method and hardware control unit parts are described as in Figure 4. The

SIMLAB contains a set of input representations and output representations. The SIMLAB hardware

216 Yaseen and Abd

Figure 3. Block diagram of PID controller.

Figure 4. Component of the maglev prototype system.

will be connected with both of the maglev prototype and the MATLAB Simulink which enables the

system to control and operate. Proximity sensors are speciﬁc devices that enable the measurement of

the air gap distance. There are many types of sensors such as laser, inductive, resistive, hall-eﬀect

and IR sensors. In the present system, the Hall-eﬀect sensor is used to detect the distance of air gap.

The sensor position in the present maglev system is at the bottom of the coil. The unique feature of

this type of sensors encourages the researchers and producers to use it in many ﬁelds such as aircrafts,

automobile and medical machines.

5.1. Experimental Results and Discussion

In this section, the experimental results are obtained based on diﬀerent tests and parameters according

to the proposed system design in Figure 5. The target is to investigate diﬀerent types of response in

Progress In Electromagnetics Research M, Vol. 62, 2017 217

Figure 5. System implementation.

maglev system which represents the access point to maglev train. The results can be classiﬁed into two

cases of test: signal representation test and load representation test as follows.

5.1.1. Results of Signal Representation Test

The ﬁrst group of tests is the input signal representation. Two kinds of standard signals have been

applied: Sine wave and Square wave. The input signal test was done with variation of diﬀerent tuning

parameters as follows.

I. Eﬀect on One Point

The input of Sine wave signal was applied on one single point in the prototype maglev plate. The

beneﬁt of this test is to show the eﬀect of sudden changes in one point on the maglev plane. The test

signals were implemented with two types of control systems, PID and LQR, and the results are shown

in Figures 6(a)–(b), respectively.

From the results indicated in Figure 6, it is noticed that the system performance is stable, and

the system responses are perfect. Furthermore, the signal response that points x and x3respond

based on the same input wave, while point x1responds oppositely. In this case, the system is able to

convert the force reaction and dynamic moment in the load points (i.e., the discs) based on the load

variation in each point of the plane. Moreover, the experimental results showed that LQR controller

had optimum response and better stability than PID controller under the eﬀect of the same input signal

and parameters.

According to the ﬁndings obtained using input sine wave signal, another investigation was

considered using a square wave signal. The simulation system was also carried out with the same

assumption of the proposed system design. Here, it can be seen that the square wave tests indicate that

the system response is also stable and oﬀers acceptable response. The diﬀerence between square and

sine wave results is the shape of changes in the signal in each point of the plate. The Sine wave signal

revealed better response than the square wave because in the Sine wave, the signal has instantaneous

change with time, and this can reduce the distortion. Also, the ﬁndings conﬁrm that LQR oﬀered better

stability and response even though the input signal is diﬀerent. The results are shown in Figures 7(a)–

(b), respectively.

218 Yaseen and Abd

4

4

4.

4

4.

4

Airgap di st ance

4

4

4.

4

010

0

4

4

.5

010

0

4

.1

15

4

.2

010

0

15

4

.2

010

0

4

4

.5

010

0

4

.1

15

4

.2

0

02000

0

02000

0

02000

0

02000

0

02000

Tim e (ms e

c

3000

refere

n

3000

3000

3000

3000

c

)

4000

n

ce

4000

x0

4000

x1

4000

x2

4000

x3

Air gap dist ance

0500

4.5

5

0500

4.2

4.4

4.6

0500

4.35

4.4

4.45

0500

4

4.5

5

0500

4.2

4.4

4.6

1000 1500

1000 1500

1000 1500

1000 1500

1000 1500

Tim e (m s

e

2000 2500

referen

2000 2500

2000 2500

2000 2500

2000 2500

e

c)

3000

ce

3000

x0

3000

x1

3000

x2

3000

x3

(a) (b)

Figure 6. Sine wave signal applied on one single using (a) PID and (b) LQR controller.

4

4

4

4

4

4

4

4

010

0

4

4

.5

010

0

4

4

.2

4

.4

010

0

4

4

.2

4

.4

010

0

4

4

.5

010

0

4

4

.2

4

.4

0

02000

0

02000

0

02000

0

02000

0

02000

Tim e

(

mse

c

3000

referen

c

3000

x

3000

x

3000

x

3000

c)

x

4000

c

e

4000

x

0

4000

x

1

4000

x

2

4000

x

3

4

4

4

4

4

4

4

4

Air gap dist ance (v)

4

4

4

4

0500

4

.6

4

.8

5

0500

4

.2

4

.4

4

.6

0500

4

.2

4

.4

4

.6

0500

4

4

.5

5

0500

4

.2

4

.4

4

.6

1000 1500

1000 1500

1000 1500

1000 1500

1000 1500

Tim e (m s e

c

2000 2500

referen

c

2000 2500

x

2000 2500

x

2000 2500

x

2000 2500

c

)

x

3000

c

e

3000

x

0

3000

x

1

3000

x

2

3000

x

3

(a) (b)

Figure 7. Square wave signal applied on one single using (a) PID and (b) LQR controller.

From all the results using (single point eﬀect), it can be seen that Sine wave signal revealed better

performance than square wave signal in both stability and response.

5.1.2. Results of Load Representation Test

In this test, the load impact on maglev system is considered. The applied load is equivalent to or mimics

the real use of maglev train when it carries the humans and materials (the goods). This type of test

includes two cases of load experiments. The ﬁrst one is the one point load handling test. It represents

a single load of 10 grams handled with one of the maglev system magnet discs. The second test is the

Progress In Electromagnetics Research M, Vol. 62, 2017 219

Figure 8. Load test applied (one point). Figure 9. PWM results of load test applied one

single point.

Op

p

Load point (x

2

p

osite point (x

1

(x

0

(x

3

PWM

)

)

0

)

)

"

width

Load ch

a

effe

c

a

ng

e

c

t

Figure 10. PWM comparative of coil voltage response.

plane load of the maglev system plate which represents the whole system.

I. Case One: Eﬀect on One Point

In this case, the input actual load of 10 grams is applied on one single point in the prototype maglev

plate. The reason of applying this test is to investigate the eﬀect of unbalance change of load in the

plate based on one point of maglev plane. The test applied on point x2isasshowninFigure8.

The load test is done with LQR control system, and the results are presented in Figure 9. The

results indicate that the system is stable, and the system responds perfectly. It is clear from the

pulse width modulation (PWM) results that the controller power supply of the present maglev system

responds signiﬁcantly as shown in Figure 10. It is seen that the average value of the voltage fed to

the coils diﬀers from point x2which represents the load input point and point x1which represents the

opposite side point.

II.CaseTwo: EﬀectonThreePoint(Plane)

In this case, the eﬀect of load is applied on all plate points (magnet discs) in the maglev prototype.

Figure 11 shows the suspended load on the system plate.

220 Yaseen and Abd

Figure 11. Suspended load on the system plate. Figure 12. PWM results of load applied on a

plane.

The test load is applied using the LQR control system as presented before, as shown in Figure 12.

From this result it can be observed that the system ability to deal with the force reaction and the

dynamic moment in the load line is based on the load variation in four points of the plane.

It is clear from the pulse width modulation (PWM) results that the control power supply of the

present maglev system responds signiﬁcantly. Also, the system responds homogeneously, and all points

respond based on the same input load at the same time of sequence. It means that the system is able

to deal with the force reaction and the dynamic moment of the plane.

6. CONCLUSION

In this paper, an eﬃcient technique of magnetic levitation system is proposed and successfully tested

based on SIMLAB platform in real time operation. Furthermore, the proposed system was described

mathematically and implemented practically under diﬀerent tests and parameters. The present

levitation system was implemented with modern controller which is LQR controller and compared

with classical controller like PID controller under the same tuning parameters. Moreover, the proposed

system has been examined under two tests: signal test and load test. The ﬁndings show that the

LQR controller revealed a signiﬁcant improvement in system performance. It was observed that LQR

controller oﬀered notable stability and better response than PID controller at the same input parameters.

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