A new planar electromagnetic levitation system improvement method based on SIMLAB platform in real time operation

Article (PDF Available)inProgress In Electromagnetics Research M 62:211-221 · January 2017with 31 Reads
DOI: 10.2528/PIERM17091304
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Abstract
Abstract—The 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 it with a classical controller which is proportional-integral-derivative (PID). As well 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 revealed a better performance compared with conventional one. Moreover, the LQR controller produced a great stability and optimal response than PID controller used at same system parameters.
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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)=i0i(t)
d(t)=d0d(t)
v(t)=v0v(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
0ΔdC
d3
0Δi(5)
˙
Δi=R
LΔi1
LΔv(6)
where Δivdare 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)s23Ci0
md4
0(7)
where ΔV(s)anD(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)=
e0eresults 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)=
γs23Ci0
md4
0+2βRC
md6
0
(Ls +R)s23Ci0
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
0C
m
1
d3
0
00R
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=yd=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+ 132.5s21471s194900 (13)
The numerical values of the state space equations are given below
˙x1
˙x2
˙x3=01 0
1471 0 9.81
00133 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 ×104V·m2
γ0.31 V/A
α2.48 V
Operation point
i01 A
d020 mm
Electromagnet
C2.4×106kgm5/s2A
R2 Ω
L15 ×103H
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)+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
4
4
.5
010
4
.1
15
4
.2
010
15
4
.2
010
4
4
.5
010
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: EectonThreePoint(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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    In this paper, we consider the stabilization and trajectory tracking of magnetic levitation system using PID controller whose controller gains are determined via Linear Quadratic Regulator (LQR) approach. Firstly, the nonlinear mathematical model of the system is obtained from the first principles. Then by applying Taylor's series, the non linear equation of motion is linearized around the equilibrium point to implement the stabilizing controller. Finally, the gains of the PID controller to achieve the desired response are determined using the LQR theory. Based on the natural frequency and damping ratio of the closed loop system, a new criterion for selecting the weighting matrices of LQR is proposed in this paper. Experiments are conducted on a Quanser magnetic levitation system to evaluate the performance of the proposed methodology and the experimental results prove that the proposed control strategy is effective not only in stabilizing the ball but also in rejecting the disturbance present in the system. (C) 2013 The Authors. Published by Elsevier Ltd.
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