A cascaded sliding mode control for magnetic levitation systems. A disturbance observer-based sliding mode controller is designed for the electrical loop while a state and disturbance observer-based sliding mode controller is designed for the electromechanical loop. The overall stability of the system is rigorously established. The performance of the proposed scheme is compared with a conventional linear quadratic regulator combined with a proportional-integral controller by simulation as well as experimentation on a magnetic levitation setup in a laboratory

1. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Precise Position Control of a
Magnetic Levitation System using
Different Control Techniques
Guided By : Dr. P.D. Shendge
Presented By : Chandrashekhar Gutte
MIS No.: 121216017

2. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Outline I
1 Introduction
2 Mathematical Modeling
3 State Feedback Control
4 SMC
IDO
LQR Design
IDC
5 Simulation Result
6 Exprimental Result
7 MAGLEV Train
8 Electromagnetic Levitation System
9 Conclusion
10 References

3. College Of
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Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Introduction
Figure: Lab experimental system

4. College Of
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Modeling
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Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Modeling of MAGLEV system
Vc
Vs
Vb
rb Fc
Fg
Ic
Rc
Lc
Mb
Tb
x1
2.rb
x y
Electromagnet
Rs
Figure: Schematic of magnetic levitation system

5. College Of
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SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Electical System
The voltage Vc across coil, can be expressed as,
Vc = RcIc (1)
Using Kirchhoff’s voltage law, the expression of voltage across
the coil can be written as,
dIc
dt
=
(Rc + Rs)
Lc
Ic −
1
Lc
Vc (2)
where
Ic is the current through the coil,
Rc is the coil resistance
Lc is the inductance of the coil

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IDO
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Simulation
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Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Electro-mechanical system
The attraction force Fc generated by the electromagnetic coil
and acting on the ball can be expressed by
Fc =
KmI
2
c
2Mbx2
1
(3)
where,
x1 > 0 is the air gap between the ball and the face of the
electromagnet,
Km is the electromagnetic force constant
Mb is the mass of the ferromagnetic ball
The gravitational force Fb experienced by the ball is expressed
as,
Fg = Mbg (4)
The equation of motion (EOM) using newton’s second low of
motion along (3) and (4) as,

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IDO
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IDC
Simulation
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Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
content...
¨x = −
kmI2
c
2Mbx2
+ g (5)
We can write the state space equations using (2) and (5) as,
˙x1 = x2
˙x2 = −
Kmx2
3
2Mbx2
1
˙x3 = −(Rs +Rc )
Lc
x3 + 1
Lc
u



(6)
It is observed that the second channel contains non-linear
terms and act as input to the electro-mechanical subsystem.
Simplify (6) further
˙x1 = x2
˙x2 = −a1x1 − a2x2 + x3 + d1
˙x3 = −a3x3 + bu + d2



(7)

8. College Of
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IDC
Simulation
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Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
where a1, a2, a3 and b are the constants assumed by the
designer. The disturbances d1 and d2 are expressed as,
d1 = a1x1 + a2x2 − x3 −
Kmx2
3
2Mbx2
1
(8)
d2 = ∆a3x3 + ∆bu + (b + ∆b)e (9)
where ∆ represent the parametric uncertainties and e is the
external disturbance injected into the control input.

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IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Parameters of magnetic levitation setup
Symbol Description Value Unit
Mb Steel Ball Mass 0.068 kg
Tb Steel Ball Radius 0.014 mm
Rc Coil Resistance 10 Ω
Rs Current Sense Resistance 1 Ω
Lc Coil Inductance 413 mH
Ic max Maximum Coil Current 3 A
V Voltage 24 V
Nc No. of Turns of Coil 2450
Lc Coil Length 0.0825 m
g Gravitational Const. 9.81 m/s2
µ0 Mag. Permeability Const. 4π × 10−7 H/m
Km Electromag. Force Const. 6.580 × 10−5 Nm2/A2
KB Sensor Sensitivity 2.83 × 10−3 m/v

10. College Of
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IDO
LQR Design
IDC
Simulation
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Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
State Feedback Control
0 5 10 15 20
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20
−2
−1
0
1
·10−3
time in sec
x2
(b)
0 5 10 15 20
0
0.1
0.2
time in sec
u(V)
(c)
0 5 10 15 20
0
2
4
6
·10−3
time in sec
current(A)
(d)
Figure: Simulation result of state feedback controller

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IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
0 5 10 15 20
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20
−0.2
−0.1
0
0.1
time in sec
x2
(b)
0 5 10 15 20
−10
0
10
20
time in sec
u(V)
(c)
0 5 10 15 20
0
1
2
time in sec
Current(A)
(d)
Figure: Experimental result of state feedback controller

12. College Of
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Introduction
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SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Inertial Delay Observer Based SMC
Consider the dynamics of electro-mechanical system as
˙x1 = x2
˙x2 = −a1x1 − a2x2 + x3 + d1
(10)
We can write the system dynamics in compact form as,
˙x(t) = A x(t) + B v(t) + B d(x, u, t) (11)
y(t) = Cx(t) (12)
and the matrix form are given as
A =
0 1
−a1 −a2
; B =
0
1
; C = 1 0
and the states x(t) = x1 x2
T
, the input is v(t) = x3.

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Simulation
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MAGLEV
Train
Electromagnetic
Levitation
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The observer dynamics can define as,
˙ˆx(t) = Aˆx(t) + Bv(t) + Bˆd(ˆx, v, t) + L (y(t) − ˆy(t))
ˆy(t) = Cˆx(t)
(13)
ˆd is estimation of lumped disturbances. and if all states are
available then it can expressed as,
d(x, v, t) = B+
˙x(t) − Ax(t) − Bv(t) (14)
where B+ = (BT B)−1BT is the pseudo inverse of the matrix
B.
Unfortunately all the states are not available, so
¯d(ˆx, v, t) = B+
(˙ˆx − Aˆx − Bu) (15)

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LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
To estimate the lumped disturbance,
ˆd(ˆx, v, t) = Gf (s) ¯d(ˆx, v, t) (16)
Simplifying (16) using (13) and (15) gives,
˙ˆd(ˆx, v, t) =
1
τ
B+
L(y(t) − ˆy(t)) (17)
The observer estimation error is given as,
˜x(t) = x(t) − ˆx(t) (18)
˜d(t) = d(x, v, t) − ˆd(ˆx, v, t) (19)
The estimation error dynamics are given as,
˙x(t) = (A − LC) ˜x(t) + B ˜d(t) (20)
˙˜d(t) = −
1
τ
B+
LC˜x(t) + ˙d(x, u, t) (21)

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LQR Design
IDC
Simulation
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Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
The observer dynamics can be written in compact form as,
˙z(t) = Hz(t) + G ˙d(x, u, t) (22)
where,
z(t) =
˜x(t)
˜d(t)
; H =
A − LC B
−
1
τ
B+LC 0
; G =


0
0
1



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IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Linear Quadratic Regulator
To obtain the optimal gain of the parameters using LQR the
following cost function should be minimize
J =
∞
0
xT
Qx + uT
Ru dt (23)
and control input as,
u = −R−1
BT
Px (24)
where, P is symmetric positive definite solution of the
Continuous Algebraic Riccardo equation and is given as,
AT
P + PA − PBR−1
BT
P + Q = 0 (25)
The weighting matrix Q is a symmetric positive definite and
the weighting factor R is a positive constant. In general, the
weighting matrix Q is varied, R fixed to obtain the optimal
control signal for linear quadratic regulator.

17. 0 2 4 6 8 10
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
0 2 4 6 8 10
−1
−0.5
0
0.5
1
·10−4
time in sec
x1-r
0 2 4 6 8 10
15
20
time in sec
voltage(V)
0 2 4 6 8 10
0
1
2
3
time in sec
current(A)
0 2 4 6 8 10
0
0.2
0.4
0.6
time in sec
x2
Figure: Simulation Result of LQR Design

18. 0 2 4 6 8 10
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 2 4 6 8 10
−0.4
−0.2
0
0.2
0.4
time in sec
x2
(b)
0 5 10 15 20
0
10
20
time in sec
voltage(V)
(c)
0 2 4 6 8 10
0
1
2
3
time in sec
current(A) (d)
Figure: Experimental Result of LQR design

19. 0 2 4 6 8 10
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 2 4 6 8 10
−2
0
2
4
6
8
·10−4
time in sec
x1-r
(b)
0 2 4 6 8 10
0
5
10
15
20
time in sec
u(V)
(c)
0 2 4 6 8 10
0
0.5
1
1.5
time in secCurrent(A)
(d)

20. 0 2 4 6 8 10
0.8
1
1.2
1.4
·10−2
time in sec
x1andˆx1
(e)
0 2 4 6 8 10
0
0.5
1
·10−2
time in sec
x2andˆx2
(f)
0 2 4 6 8 10
−2
−1
0
time in sec
eandˆe
(g)
0 2 4 6 8 10
0
1
2
·10−2
time in sec
sigma(σ) (h)
Figure: Simulation result of Inertial delay observer based SMC
.

21. 0 2 4 6 8 10
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 2 4 6 8 10
0
2
4
·10−3
time in sec
x1-r
(b)
0 2 4 6 8 10
0
10
20
time in sec
u(V)
(c)
0 2 4 6 8 10
0
0.5
1
1.5
2
time in seccurrent(A)
(d)

22. 0 2 4 6 8 10
0.8
1
1.2
1.4
·10−2
time in sec
x1andˆx1
(e)
0 2 4 6 8 10
−0.4
−0.2
0
0.2
0.4
time in sec
x2andˆx2
(f)
0 2 4 6 8 10
−2
−1.5
−1
−0.5
0
time in sec
ˆe
(g)
0 2 4 6 8 10
−0.15
−0.1
−5 · 10−2
0
5 · 10−2
time in sec
sigma(σ)
(h)
Figure: Experimental result of Inertial delay observer based SMC

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MAGLEV
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System
Inetial Delay Control For Current loop
Consider the dynamics of current loop as,
˙x3 = −a3x3 + bu + d2 (26)
Selecting the control input u as,
u = ueq + un (27)
ueq = −
1
b
[ −a3x3 + kl1 x3 + ks1 sat(x3) ] (28)
where kl1 > 0, ks1 > 0

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MAGLEV
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sat(x3) =
sign(x3) if absx3 >
x3/ if absx3 ≤
(29)
where is a small positive number.
The lumped uncertainty can be expressed using (26), (27) and
(28) as,
d2 = ˙x3 + kl1 x3 + ks1 sat(x3) − bun (30)
Estimate lumped uncertainty using broadband filter.
Gf (s) =
1
τs + 1
(31)
where τ > 0 is the filter time constant, which decides the
accuracy of estimation of uncertainties

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The estimation of lumped uncertainty is given by,
ˆd2 = Gf (s) d2 (32)
Selecting un as,
un = −
1
b
ˆd2 (33)
Simplify (32) using (30), (31) and (33) as,
˙ˆd2 =
1
τ
[˙x3 + kl1 x3 + ks1 sat(x3)] (34)
or
ˆd2 =
1
τ
x3 +
1
τ
t
0
kl1 x3 + ks1 sat(x3) dt (35)
Estimation error is defining as,
˜d2 = d2 − ˆd2. and the dynamics of x3 becomes,
˙x3 = −kl1 x3 − ks1 sat(x3) + ˜d2 (36)

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MAGLEV
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Simulation Result of LQR Design
Case: I
0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
−0.5
0
0.5
1
1.5
·10−3
time in sec
x1-r
(b)
0 5 10 15 20 25
14
16
18
20
22
24
time in sec
voltage(V)
(c)
0 5 10 15 20 25
0
1
2
3
time in sec
current(A)
(d)

27. 0 5 10 15 20 25
0
0.2
0.4
0.6
time in sec
x2
(e)
Figure: Case I. Simulation result of LQR control design
Case: II
0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
−0.5
0
0.5
1
1.5
·10−3
time in sec
x1-r
(b)

28. 0 5 10 15 20 25
14
16
18
20
22
24
time in sec
voltage(V)
(c)
0 5 10 15 20 25
0
1
2
3
time in sec
current(A)
(d)
0 5 10 15 20 25
0
0.2
0.4
0.6
time in sec
x2
(e)
Figure: Case II. Simulation result of LQR control design

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MAGLEV
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Levitation
System
Simulation Result of IDO with IDC based SMC
Case: I
0 5 10 15 20 25
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
0
2
4
6
·10−4
time in sec
x1-r
(b)
0 5 10 15 20 25
0
10
20
time in sec
u(V)
(c)
0 5 10 15 20 25
0
0.5
1
1.5
2
time in sec
current(A)
(d)

30. 0 5 10 15 20 25
1
1.2
1.4
·10−2
time in sec
x1andˆx1
(e)
0 5 10 15 20 25
−2
−1
0
1
·10−3
time in sec
ˆx2
(f)
0 5 10 15 20 25
−2
−1
0
time in sec
dandˆd
(g)
0 5 10 15 20 25
0
1
2
·10−2
time in sec
sigma(σ)
(h)
Figure: Case I. Simulation result of IDO with IDC based SMC

31. Case: II
0 5 10 15 20 25
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
0
2
4
6
·10−4
time in sec
x1-r
(b)
0 5 10 15 20 25
0
10
20
time in sec
u(V)
(c)
0 5 10 15 20 25
0
0.5
1
1.5
2
time in sec
current(A)
(d)

32. 0 5 10 15 20 25
1
1.2
1.4
·10−2
time in sec
x1andˆx1
(e)
0 5 10 15 20 25
−2
−1
0
1
·10−3
time in sec
ˆx2
(f)
0 5 10 15 20 25
−2
−1
0
time in sec
dandˆd
(g)
0 5 10 15 20 25
0
1
2
·10−2
time in sec
sigma(σ)
(h)
Figure: Case II. Simulation result of SMC with IDO and IDC

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Exprimental Result of LQR Design
Case:I
0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
0
2
4
·10−3
time in sec
x1−r
(b)
0 5 10 15 20 25
−10
0
10
20
time in sec
voltage(V)
(c)
0 5 10 15 20 25
0
0.5
1
1.5
2
time in sec
current(A)
(d)

34. 0 5 10 15 20 25
−0.1
−5 · 10−2
0
5 · 10−2
0.1
time in sec
x2
(e)
Figure: Case I. Experimental result of LQR control design
Case: II
0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
0
2
4
·10−3
time in sec
x1−r
(b)

35. 0 5 10 15 20 25
0
10
20
time in sec
voltage(V)
(c)
0 5 10 15 20 25
0
0.5
1
1.5
2
time in sec
current(A)
(d)
0 5 10 15 20 25
−0.1
0
0.1
time in sec
x2
(e)
Figure: Case II. Experimental result of LQR control design

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MAGLEV
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Electromagnetic
Levitation
System
Exprimental Result of IDO and IDC based SMC
Case: I
0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
0
2
4
·10−3
time in sec
x1-r
(b)
0 5 10 15 20 25
0
10
20
time in sec
u(V)
(c)
0 5 10 15 20 25
0
1
2
time in sec
current(A)
(d)

37. 0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andˆx1
(e)
0 5 10 15 20 25
−4
−2
0
2
4
·10−2
time in sec
ˆx2
(f)
0 5 10 15 20 25
−2
−1.5
−1
−0.5
0
time in sec
ˆd
(g)
0 5 10 15 20 25
−0.15
−0.1
−5 · 10−2
0
5 · 10−2
time in sec
sigma(σ)
(h)
Figure: Case I. Experimental result of SMC with IDO and IDC

38. Case: II
0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andr
(a)
0 5 10 15 20 25
0
2
4
·10−3
time in sec
x1-r
(b)
0 5 10 15 20 25
0
10
20
time in sec
u(V)
(c)
0 5 10 15 20 25
0
1
2
time in sec
current(A)
(d)

39. 0 5 10 15 20 25
0.8
1
1.2
1.4
·10−2
time in sec
x1andˆx1
(e)
0 5 10 15 20 25
−4
−2
0
2
4
·10−2
time in sec
ˆx2
(f)
0 5 10 15 20 25
−2
−1.5
−1
−0.5
0
time in sec
ˆd
(g)
0 5 10 15 20 25
−0.14
−0.12
−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
time in sec
sigma(σ)
(h)
Figure: Case II. Experimental result of SMC with IDO and IDC

40. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Development of MAGLEV Train
Hardware components required for MAGLEV train:
A train track and train car body frame
Four magnetic strip of 1000 × 30 × 20 mm3
Four strong neodymium disk magnets as part of the
propulsion system
Four weak neodymium disk magnets for
levitation/stabilization
Ball bearings and rubber spaces for each of the four disk
magnets used for levitation/ stabilization
AC Drive to provide the variable 3-phase current source

41. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Technical Specification
Table: Specification of MAGLEV train
Criteria Design Specification
Height of train (along rail) 45 mm
Height over LSM 4 mm(optimal) - 6 mm (Max)
Table: Specification for Magnet array
Criteria Design Specification
Material NdFeB Grade N32
Max B value 3000 Gauss; 0.3 Tesla
Magnets φ 30 mm & 5 mm width
Bearing φ 30 mm outer & φ 10 mm internal

42. Table: Specification for LSM
Criteria Design Specification
Class of motor Linear Synchronous
Primary 3∅ winding embedded in track
Secondary 4 disc magnet array
Drive Current –
Drive Frequency –
Table: Specification for Train Track
Criteria Design Specification
Topology Linear Track
Material Acrylic, Glue
Dimension 45 mm ×1000 mm × 500 mm
Train car weight 559 gm

43. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Figure: Drawing of MAGLEV train

44. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Figure: Drawing of train car

45. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Proposed Train Model

46. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Developed hadware of MAGLEV train
(a) MAGLEV plant:Front view (b) MAGLEV plant:Back view

47. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Figure: Actual train car

48. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Electromagnetic Levitation System
Figure: Electromagnetic levitation system

49. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Design of Analog Circuit
Figure: System Schematic

50. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Parameters of Electromagnetic levitation system
Parameter Value Unit
Max. Coil Current 3 A
Voltage to Coil 23.5 V
Core Length 7 cm
Core Radius 1 cm
Wire Gauge of Coil 23
Total Coil Inductance 195 mH
Total Coil Resistance 3.39 KΩ
Material of Object NdFeb magnet
Mass of Object 3 gm
Gravitational constant 9.81 m/s2
Magn. Permeability Const 4π × 10−7 H/m
Electromag. Force Const 6.580 × 10−5 N − m2/A2
Sensitivity of Hall Sensor 2.83 × 10−3 m/v

51. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Force Equation
The force of attraction generated by an electromagnet acting
on the object can be expressed by,
fe =
KmI2
2d2
(37)
where,
d is the distance between the object
Km is the electromagnetic constant, I is the required current.
The force due to gravity acting on the object is given by,
fg = Mg (38)
The total force acting on the object is given by,
ftotal = −fe + fg (39)
ftotal =
KmI2
2d2
+ Mg (40)

52. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Experimental Analysis
Table: Parameters of magnetic levitation setup
Position of Object Vref Vs Verror Comparator O/p
Below reference position Vref >Verror +Vsat
Above reference Vref <Verror −Vsat
At reference position Vref = Verror +Vsat

53. (a) Object below the reference
position
(b) Object above the reference
position

54. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Figure: Object at reference position

55. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Developed Electromagnetic Levitation setup

56. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Conclusion and Future work
The Different control techniques are implemented for the
precise position control of a magnetic levitation system
which is inherently nonlinear in nature. IDO is designed to
estimate states and disturbances occurred in system. IDC
is implemented for current loop to estimate the lumped
uncertainty. All control techniques are compared with
LQR techniques and observed that proposed control
technique gives significantly improved results.
The Low cost and simple electromagnetic levitation
system using analog circuit is successful developed.
The development of remaining MAGLEV train work is
carried out for next year.

57. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
Prof. Shrivijay B. Phadke, Professor Emeritus,
Department of Instrumentation and Control Engineering,
Pune.
Dr. P. D. Shendge, Associate Professor, Department of
Instrumentation and Control Engineering, Pune.
Mr. Divyesh Ginoya, PhD Student, Department of
Instrumentation and Control Engineering, Pune.
All my Control Lab friends
Team MAGLEV.
My brother Anurath Gutte.

58. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
References
[1] W. Barie and J. Chiasson, “Linear and nonlinear
state-space controllers for magnetic levitation,”
International Journal of systems science, vol. 27, no. 11,
pp. 1153–1163, 1996.
[2] A. Charara, J. De Miras, and B. Caron, “Nonlinear control
of a magnetic levitation system without
premagnetization,” Control Systems Technology, IEEE
Transactions on, vol. 4, no. 5, pp. 513–523, 1996.
[3] A. El Hajjaji and M. Ouladsine, “Modeling and nonlinear
control of magnetic levitation systems,” IEEE
Transactions on Industrial Electronics, vol. 48, no. 4, pp.
831–838, 2001.

59. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
References
[4] S. Joo and J. H. Seo, “Design and analysis of the
nonlinear feedback linearizing control for an
electromagnetic suspension system,” Control Systems
Technology, IEEE Transactions on, vol. 5, no. 1, pp.
135–144, 1996.
[5] A. E. Rundell, S. V. Drakunov, and R. A. DeCarlo, “A
sliding mode observer and controller for stabilization of
rotational motion of a vertical shaft magnetic bearing,”
Control Systems Technology, IEEE Transactions on, vol. 4,
no. 5, pp. 598–608, 1996.

60. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
References
[6] J. Yang, A. Zolotas, W.-H. Chen, K. Michail, and S. Li,
“Disturbance observer based control for nonlinear maglev
suspension system,” in Control and Fault-Tolerant
Systems (SysTol), 2010 Conference on. IEEE, 2010, pp.
281–286.
[7] H. Katayama and T. Oshima, “Stabilization of a magnetic
levitation system by backstepping and high-gain
observers,” in SICE Annual Conference (SICE), 2011
Proceedings of. IEEE, 2011, pp. 754–759.
[8] E. Vinodh Kumar and J. Jerome, “Lqr based optimal
tuning of pid controller for trajectory tracking of magnetic
levitation system,” Procedia Engineering, vol. 64, pp.
254–264, 2013.

61. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
References
[9] J.-D. Lee, S. Khoo, and Z.-B. Wang, “Dsp-based
sliding-mode control for electromagnetic-levitation
precise-position system,” Industrial Informatics, IEEE
Transactions on, vol. 9, no. 2, pp. 817–827, 2013.
[10] H.-W. Lee, K.-C. Kim, and J. Lee, “Review of maglev
train technologies,” Magnetics, IEEE Transactions on,
vol. 42, no. 7, pp. 1917–1925, 2006.
[11] R. F. Post and D. D. Ryutov, “The inductrack: a simpler
approach to magnetic levitation,” Applied
Superconductivity, IEEE Transactions on, vol. 10, no. 1,
pp. 901–904, 2000.
[12] D. Funk and K. Getsla, “Magnetic levitation train final
report,” 2006.

62. College Of
Engineering,
Pune
Introduction
Mathematical
Modeling
State
Feedback
Control
SMC
IDO
LQR Design
IDC
Simulation
Result
Exprimental
Result
MAGLEV
Train
Electromagnetic
Levitation
System
References
[13] P. Friend, “Magnetic levitation train technology,” progress
report, Bradley university, 2004.
[14] S. C. Paschall II, “Design, fabrication, and control of a
single actuator magnetic levitation system,” Ph.D.
dissertation, Texas A&M University, 2002.
[15] K. H. Lundberg, K. A. Lilienkamp, and G. Marsden,
“Low-cost magnetic levitation project kits,” Control
Systems, IEEE, vol. 24, no. 5, pp. 65–69, 2004.
[16] N. Black, B. James, G. Koo, V. Kumar, and P. Rhea,
“Small-scale maglev train,” 2009.