Air Gap Control of the Novel Cross (+) Type 4-Pole MAGLEV Carrier System

Abstract

Mechanical non-contact carrier systems based on magnetic levitation (MAGLEV) are used in special transportation areas (clean rooms, chemical areas, etc.). Among these types of carriers, 4-pole hybrid electromagnetic systems (containing permanent magnets and electromagnets) stand out with their low energy consumption. The main problem of maglev carrier systems is their non-linear characteristics and unstable open-loop response. In this study, PID and I-PD controllers are designed for the air gap control of the new cross-type 4-pole mechanical contactless carrier system. Thus, the instability problem was overcome and the desired reference tracking for each degree of freedom was successfully carried out in simulation environments, and the results were compared.

Full text

Air Gap Control of the Novel Cross (+) Type 4-Pole
MAGLEV Carrier System
Enes Mahmut GÖKER
Mechatronics Engineering, Yıldız Technical University, Istanbul, TURKEY
enesgkr@hotmail.com
Ahmet Fevzi BOZKURT
Mechatronics Engineering, Yıldız Technical University, Istanbul, TURKEY
afbozkurt90@gmail.com
Bora BAYKAL
Uskudar American Academy, Istanbul, TURKEY
bbaykal23@my.uaa.k12.tr
Kadir ERKAN
Mechatronics Engineering, Yıldız Technical University, Istanbul, TURKEY
kerkan@yildiz.edu.tr
Abstract – Mechanical non-contact carrier systems
based on magnetic levitation (MAGLEV) are used in
special transportation areas (clean rooms, chemical
areas, etc.). Among these types of carriers, 4-pole
hybrid electromagnetic systems (containing permanent
magnets and electromagnets) stand out with their low
energy consumption. The main problem of maglev
carrier systems is their non-linear characteristics and
unstable open loop response. In this study, PID and I-
PD controllers are designed for the air gap control of
the new cross-type 4-pole mechanical contactless
carrier system.
Thus, the instability problem was overcome and the
desired reference tracking for each degree of freedom
was successfully carried out in simulation
environments, and the results were compared.
Keywords – Magnetic Levitation, Maglev Carrier
System, PID I-PD Controller Design
1 INTRODUCTION
With the developing technology, differences in the
technological needs of people have begun to occur. These
differences have led to innovations in the fields of
production and transportation. Transport of manufactured
materials is of great importance. In particular, the material
produced in clean rooms, chemical areas and high
technology production areas should be away from factors
such as vibration, noise and dust. Existing technologies
are insufficient for such transport environments (Kim et
al. 2011; Jiangheng and Koseki 2001). In the solution of
these problems, the use of electromagnetic forces allowed
the carrier platform to be levitation, enabling contactless
transportation (Atherton, 1980; Han, Kim, 2016; Erkan et
al. 2016). The carrier platforms in the literature are
divided into two types as active rail and passive rail, but
the levitation method is similar in systems where
electromagnetic levitation topology is used (Bozkurt et al.
2018; Ertuğrul 2014). U-type, E-type and 4-pole U-type
hybrid electromagnets are used for levitation. (Tzeng, Y.
and Wang 1998; Lee et al. 2013; Ertuğrul 2014). The
proposed cross-type hybrid electromagnet carrier system
has a multi-degrees-of-freedom control structure. Each
pole produces the electromagnetic force required for
magnetic levitation. Pole terminals energized by closed-
loop controllers keep the carrier platform levitation and
provide the axial or radial movement with internal or
external thrust components. Thus, it can be used in
multiple engineering applications such as transportation
systems, frictionless bearings, and spacecraft design
(Jiangheng L and Koseki T 2001).
The cross-type hybrid electromagnet structure contains
permanent magnets and electromagnets as in the 4-pole U
type electromagnets available in the literature. But due to
its structure, it consists of fewer parts compared to the
convectional 4-pole. While the convectional 4-pole is
formed by the combination of 4 silica sheet metals, the
novel cross-type 4-pole is formed by combining two U-
types. This has been beneficial for the system to reduce
leakage fluxes (Göker E.M. and Erkan K. 2022).
In this article, the model of the novel cross-type 4-pole
maglev carrier system has been developed. Since the
system has an unstable structure, it needs an active
controller. For this, PID and I-PD controllers have been
designed by using canonical structure in analytical model
and analytical model was linearized, simulation studies
have been made. Therefore, by using PID and I-PD type
controller, the carrier system can levitate without steady
state error. When comparing PID and I-PD controllers for
air gap position control, the I-PD controller provides the
best results.
2 MAIN CONTENT
2.1 Levitation Model of Cross Type Hybrid
Electromagnet
Figure 1. The cross-type hybrid electromagnet

The core and coil windings of the cross-pole hybrid
electromagnet are shown in Figure 1.
The dimensions of the cross-type 4-pole hybrid maglev
carrier system and the centralized control geometric
transformation matrices are given (Göker E.M. and
Erkan K 2022).
Controllers are designed on this model by linearizing the
system in the predicted operating range. Ferromagnetic
body resistance, magnetic saturation, hysteresis fuco
losses and flux leakages are neglected in the modelling.
The operating point where the linearization is made is
the point where the axes of rotation are absent. If
balancing is done at this point;
0
0
( , , ) ( ,0,0)
( , , ) ( ,0,0)
z z
z z
i i i i
α β
α β
=
=
(1)
should be. The dynamics of movement in the Z-axis
direction at this point;
( ) ( ( ), ( )) ( )
z z d
m z t f z t i t mg F t
∆ = − −
&&
(2)
If
z
f
, which we express as the gravitational force,
2
2
0
2
0
2 ( ( ))
( ( ), ( )) . .4
2 ( ( ) )
PM z
z z
PM
S E Ni t
B
f z t i t S z t l
µ
µ
+
= = +
(3)
is expressed as. 

denotes the AT value of permanent
magnets, N stands for winding count, i stands for pole
current,
PM
l
magnet thickness, S stands for magnet area,
µ
0
stands for magnetic permeability constant. In Figure 2,
the air gap and the force graph formed by the system
against the currents are given.
Figure 2. Electromagnetic Attractive Force
Characteristic in Z Axis
The linear model for the levitation system of the
electromagnet is found by linearizing the
electromagnetic attraction force by choosing as in the
1rd equation. Minor variations around the linearized
model of the system;
0
0
0
0
( ( ), ( )) ( ( ), ( ))
( , ) ( ) ( )
z z z z
z z A B z
f z t i t f z z t i i t
f z i K z t K i t
= − ∆ + ∆
= + ∆ + ∆
(4)
expression is made. Here;
0
00
2
0
( , ) 3
0
4 ( )
( )
z
PM z
z
A z i
PM
S E Ni
f
Kz z l
µ
+
∂
= −  =
∂ +
(5)
0
00
0
( , ) 2
0
4 ( )
( )
z
PM z
z
B z i
z PM
SN E Ni
f
Ki z l
µ
+
∂
=  =
∂ +
(6)
formula is obtained. If Equation 2 is rearranged;
( ) ( ) ( ) ( )
A B z d
m z t K z t K i t F t
∆ = ∆ + ∆ −
&&
(7)
obtained. m; mass (kg), F
d
; is expressed as the
disturbance input force (N). If the laplace transform of
Equation 7 is done according to the air gap;
2 2
1
( ) ( ) ( )
B
z d
A A
K
Z s I s F s
ms K ms K
= −
− −
(8)
available in the form. Angular displacement axis
dynamics;
0
2
2
0
( ) ( ( ), ( ))
( ( ), ( )) ( , ( ),0, , ( ),0) ( ) ( )
z C D
d t
J T t i t
dt
T t i t T z t i i t K t K i t
α α α
α α α α α
θθ
θ θ θ
=
≅ ≅ ∆ − ∆
(9)
{ }
0
0 0
( ,0)
lim
lim lim ( , )
C
Di
T
K
K T i
i
α
α
θ
α α
θ
α
θ
θ
θ
→
→ →
∂
=∂
∂
=∂
(10)
is expressed as. Since the cross-pole maglev carrier has a
symmetrical structure, the β axis dynamics shows the
same characteristics as the α axis dynamics. For this
reason, the β-axis dynamic equations are not included.
In Equation 8, the control signal is given in the form of a
current source. The coils used in levitation system can be
energized by using a voltage source instead of a current
source. From this point of view, if the dynamic equations
are expressed again;
0
( )
( ) ( ) ( ) ( )
z PM
z z z z
PM
Ni t E
d d
e t R i t N R i t NS
dt dt z t l
µ
+
= + Φ= + +
(11)
is expressed as and this equation is linearized;
. .
( ) ( ) ( ) ( )
A z
z z z z z
B
K L
e t R i t L i t z t
K
∆ = ∆ + ∆ + ∆
(12)
form is obtained. Taking the laplace transform according
to the air gap of the equation;
1
( ) ( ) ( )
A z
z z
z z B
K L
I s E s sZ s
L s R K
 
= −
 
−
 
(13)
is found. The linearized system dynamics for the Z-axis
is given in Figure 3 with block diagrams.
( )
z
E s
1
z z
L s R
−
( )
d
F s
( )
Z s
A z
B
K L
s
K
2
B
A
K
ms K
−
1
B
K
( )
z
I s
Figure 3. Z-Axis Linearized System Dynamics
In Table 1, the model parameters of the cross-pole
electromagnet are extracted.
Table 1. Cross Pole Electromagnet Model Parameters
Size/Unit
Value
Size/Unit
Value
Size/Unit
Value
m
[kg]
10.00 z
0
[mm]
19.30 α
0
,β
0
[rad]
0.00
Jα,β
[kg.m
2
]
0.30 i
z0
[A]
0.00 i
α0
,i
β0
[A]
0.00
S
[A
2
]
12*10
-4
K
A
[N/m]
12473
K
C
[Nm/rd]
79.28
β
[AT/N]
19.85 K
B
[N/A]
9.88
K
D
[Nm/A]
2.38
R
z
,
α,β[Ω]
1.00 L
z,α,β
[H]
0.016 E
pm
[AT]
3970

2.2 Simulations and Results
There are 4 control inputs to control the levitation of the
cross-pole hybrid electromagnet. These control inputs can
be modelled in 3 axes (z and α, β axis) by transforming
them into central control axis matrices. The Z axis model
is similar to the α, β axis models, and the difference only
appears in the relevant parameters. The model of the
voltage input system is given in Equation 14.
2 2
( ) ( ) ( )
( )( ) ( )( )
B z z
d
z z A A z z z A A z
K R L
Z s E s F s
z
R Ls ms K K Ls R Ls m K K Ls
+
= −
+ − + + − +
(14)
2.2.1
PID Controller Design
PID controllers are the most used controllers in the
literature. PID controllers are used in many fields due to
their simple structure, low number of control variables
and easy physical implementation. The PID structure of
the z-axis controller of the cross-pole hybrid
electromagnet is given in Figure 4.
p
K s
s
*
( )
Z s
2
( )( )
B
z z A A z
K
R L s ms K K L s
+ − +
( )
Z s
z z
B
L s R
K
+
( )
d
F s
( )
z
E s
2
d
K s
s
i
K
s
Figure 4. Structure of The System's z Axis PID Controller
When the transfer function of the block diagram is found;
*
2
2 2
( ) ( )
1 ( ) ( )
( )
( ) [ ( ) ]
B d P i
B d P i z z A A z
G s Z s
G s Z s
K K s K s K
K K s K s K s R L s ms K K Ls
= =
+
+ +
+ + + + − +
(15)
obtained. The canonical polynomial approach was used to
calculate the controller coefficients in the closed-loop
transfer function (Mochizuki and Ichihara 2013; S.
Manabe. 1998).
Table 3. PID and I-PD Controller Coefficients
Kp
Kd
Ki
1756
32
3088
The Matlab-Simulink model is given in Figure 5. In this
simulation, the response of the system against the entered
air gap reference value is observed.
Figure 5. PID Controller Simulink Model
Looking at Figure 6, it is seen that the PID controller
creates an overshoot by exceeding 1.5 millimetres against
the 0.5 mm reference signal given in the 1st second. In
the real system, this overshoot causes the system to
become instability (mechanical constraints and non-linear
characterism). This problem can be solved by using the I-
PD controller instead of the PID controller.
Figure 6. Step Reference Input PID Controller z Axis
Response
2.2.2
I-PD Controller Design
Significant changes in the reference signal input in the
PID controller produce large input signals as a result of
proportional (P) and derivative (D) coefficients. This
causes overshoots in the system, that is, saturation. Since
the integral (I) block is used first in the I-PD controller, it
integrates the first effect on the error signal. Thus, it
limits the input signal to be applied to the system.
Proportional and derivative expressions are integrated
into the system as feedback from the closed loop.
(Mochizuki and Ichihara 2013).
When the transfer function of the block diagram is found;
* 4 3 2
( )
( ) ( ) ( ) ( ) ( )
B i
z z B d P B A z B i
K K
Z s
Z s s mL s mR s K K s K K K R K K
=+ + + − +
(16)
is expressed.
Figure 7. I-PD Controller Simulink Model
Figure 7 shows the simulation study of the I-PD
controller. In this simulation study, a reference air gap
value was entered and the system was controlled in this
air gap with the I-PD controller.
The model was carried out using the parameters used in
PID. Looking at Figure 8, it is seen that the I-PD
controller responds more smoothly to the 0.5 mm
reference signal given at 1 second, without creating an
overshoot.
Figure 8. Step Reference Input I-PD Controller z Axis
Response

Figure 9 shows the comparison of PID and I-PD
controllers. Looking at this comparison, it is seen that
using the I-PD controller instead of the PID controller is
better in terms of control.
Figure 9. Comparison of Step Reference Input I-PD
Controller with PID Controller's z Axis Response
3 CONCLUSION
In this study, the air gap control of the maglev carrier
system, which contains a novel cross-shaped 4 pole
hybrid electromagnet, was carried out. Analytical model
was linearized, PID and I-PD controllers were designed
by using canonical structure in the analytical model and
controllers were compared in simulation environment.
The successful realization of simulation provides
opportunities for future studies.
For future studies, it is aimed to perform the experimental
setup and to improve the system performance by studying
different controllers.
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