MEV


 

 

Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

Mechatronics, Electrical Power, and 

Vehicular Technology 
 

e-ISSN:2088-6985 

p-ISSN: 2087-3379 

Accreditation Number: 432/Akred-LIPI/P2MI-LIPI/04/2012 

 

 

www.mevjournal.com 
 

© 2014 RCEPM - LIPI All rights reserved 

doi: 10.14203/j.mev.2014.v5.17-26 

DESIGN AND IMPLEMENTATION OF A MAGNETIC LEVITATION 

SYSTEM CONTROLLER USING GLOBAL SLIDING MODE CONTROL 
 

Rudi Uswarman
 a,

*, Adha Imam Cahyadi 
a
, Oyas Wahyunggoro

 a
 

a
Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada 

Jl. Grafika 2, Yogyakarta 55281, Indonesia 

 
Received 12 March 2014; received in revised form 16 June 2014; accepted 19 June 2014 

Published online 23 July 2014 

 

Abstract 
This paper presents global sliding mode control and conventional sliding mode control for stabilization position of a 

levitation object. Sliding mode control will be robusting when in sliding mode condition. However, it is not necessarily robust at 
attaining phase. In the global sliding mode control, the attaining motion phase was eliminated, so that the robustness of the 
controller can be improved. However, the value of the parameter uncertainties needs to be limited. Besides that, the common 
problem in sliding mode control is high chattering phenomenon. If the chattering is too large, it can make the system unstable due 
the limited ability of electronics component. The strategy to overcome the chattering phenomenon is needed. Based on simulation 
and experimental results, the global sliding mode control has better performance than conventional sliding mode control. 

 
Keywords: magnetic levitation system, global sliding mode control, conventional sliding mode control, chattering.  

 

I. INTRODUCTION 
Magnetic levitation systems (MLS) have been 

widely applied in various fields that aims to help 
people, such as biomedical [1], maglev train [2], 

maglev wind tunnel [3], and micro-robotic [4]. 

Several techniques have been implemented to 

control the magnetic levitation system, for 
examples using gain scheduling [5], high-gain 

observers [6], and passivity based control [7, 8]. 

These controllers do not consider the parameter 
uncertainties of magnetic levitation system. 

However, some researchers have used nonlinear 

controllers considering mass parameter 

uncertainties of magnetic levitation such as using 
gain scheduling [5], and sliding mode control [9]. 

The uncertainty of parameters other than mass is 

not considered. In this paper, not only uncertainty 
of the mass but also uncertainties of the other 

parameters are considered. 

Linear controller is not suitable for control 
magnetic levitation because the dynamic of 

magnetic levitation is highly nonlinear. Nonlinear 

controller is needed to overcome the nonlinearity 

of magnetic levitation. Besides that, general 

problem in MLS is uncertainties of the system. 
The uncertainties are a very challenging task for 

researchers. These problems can be overcome 

with robust controller. Robust controller are 

composed of a nominal part, similar to a 
feedback linearization or inverse control law, and 

of additional terms aimed at dealing with model 

uncertainty [10]. 
Sliding mode control technique will be 

investigated to control position object of MLS. 

Sliding mode control is precise controller to solve 
the problems of the system, because this 

technique are nonlinear controller and robust 

from disturbances and parameter uncertainties. 

Sliding mode control technique was initially 
proposed in the early 1960s. The ideas did not 

appear outside Russia until mid 1970s [11]. 

The MLS consists of an object suspended in a 
voltage controlled magnetic field. The magnetic 

field is used to against gravity effect. To adjust 

the desired position of the object, we can use a 
controller to change appropriate magnetic field. 

Model of MLS is shown in Figure 1. 

* Corresponding Author.Tel: +62-81227632318 

E-mail: uswarman@yahoo.com 

http://ugm.academia.edu/Departments/Department_of_Electrical_Engineering_and_Information_Technology
http://dx.doi.org/10.14203/j.mev.2014.v5.17-26


R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

18 

II. DYNAMICS OF THE MLS 
The Lagrangian will be presented to find the 

mathematical model of a MLS. Lagrange 
equations of motion can be written as: 

𝑑

𝑑𝑡
 

𝜕𝐿

𝜕 𝑥 𝑖
 −

𝜕𝐿

𝜕 𝑥𝑖
= 0 , 1 ≤ 𝑖 ≤ 𝑛. (1) 

We now define 𝐿 = 𝑇 − 𝑉; 𝐿  is called the 
Lagrangian, 𝑇 is kinetic energy and 𝑉 is potential 
energy.  

The generalized coordinates to be chosen such 

that 𝑥1 = 𝑥 , 𝑥 1 = 𝑥 , 𝑥 2 = 𝑖 . 𝑥  represent the 
object position, 𝑥  represent the velocity, and 𝑖 
represent the current. The kinetic energy and 
potential energy can be written as: 

 𝑇 =
1

2
𝐿 𝑥 𝑖2 +

1

2
𝑚𝑥 2 ,

𝑉 = −𝑚𝑔𝑥,
  (2) 

where coil inductivity 𝐿(𝑥)  is a nonlinear 
function of the ball’s position, 𝑔  is the 
gravitational constant, and 𝑚  is the mass of a 
levitated object. 

The Lagrangian formula can be written as: 

𝐿 =
1

2
𝐿 𝑥 𝑖2 +

1

2
𝑚𝑥 2 + 𝑚𝑔𝑥. (3) 

The approximation coil inductance 𝐿(𝑥) can 
be written as:  

𝐿 𝑥 = 𝐿𝑖 +
𝐿0𝑥0

𝑥
 , (4) 

where 𝐿0 𝑥0 = 2𝑘, 𝐿𝑖  is a system parameter, and 
𝑘 is the magnetic force constant. 

Thus, the general form of Lagrangian 
equation can be written as:  

𝑥 =
𝑓

𝑚
+ 𝑔 − 𝑘

𝑖 2

𝑚𝑋 2
 ,and (5) 

𝑑𝑖

𝑑𝑡
=

𝑢

𝐿
−

𝑖𝑅

𝐿
+ 𝑖

2𝑘

𝐿𝑥 2
𝑥 . (6) 

Taking 𝑥1 = 𝑥, 𝑥2 = 𝑥 , 𝑥3 = 𝑖, 𝑢 = 𝑒. Then, 
we can get state space model of a MLS as: 

 

𝑥 1 = 𝑥2 ,

𝑥 2 = 𝑔 −
𝑘 𝑥3

2

𝑚𝑥1
2 ,

𝑥 3 = −
𝑅𝑥3

𝐿
+

2𝑘𝑥2 𝑥3

𝐿𝑥1
2 +

𝑢

𝐿
.
 
 
 

 
 

 (7) 

Consider the nonlinear change of coordinates. 

The nonlinear change in coordinates is presented 

in Equation (8). 

 

𝑛1 = 𝑥1 − 𝑥1𝑑 ,
𝑛2 = 𝑥2 − 𝑥2𝑑 ,

𝑛3 = 𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2 . where 𝑥1 > 0 and 𝑥3 > 0.

  (8) 

In the new coordinates, we can get: 

 
𝑛 1 = 𝑛2 ,
𝑛2 = 𝑛3 ,

𝑛 3 = 𝑓 𝑛 + 𝑔(𝑛)𝑢.
  (9) 

Differentiating Equation (9), then substituting 

Equation (7) into 𝑛 3: 

𝑛 3 = −
4𝑘 2𝑥2𝑥3

2

𝑚𝐿 𝑥1
4 +

2𝑘𝑅𝑥3
2

𝑚𝐿 𝑥1
2 +

2𝑘𝑥3
2𝑥2

𝑚 𝑥1
3 −

2𝑘𝑥3𝑢

𝑚 𝑥1
2𝐿

.  (10) 

The function 𝑓 𝑛  and 𝑔(𝑛)  are 
correspondent to the original coordinates: 

 
𝑓 𝑥 = −

4𝑘 2𝑥2𝑥3
2

𝑚𝐿 𝑥1
4 +

2𝑘𝑅 𝑥3
2

𝑚𝐿 𝑥1
2 +

2𝑘 𝑥3
2𝑥2

𝑚 𝑥1
3 ,

𝑔 𝑥 = −
2𝑘𝑥3

𝑚 𝑥1
2𝐿

, where 𝑥1 > 0.
  (11) 

.  
Figure 1. Model of MLS 

 



 R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

 

19 

III. CONTROLLER DESIGN 
Sliding mode control was first proposed by 

Emel’yanov and Barbhasin in the early 1960s 

[11]. The major advantages of this technique are 
completely insensitive to variation in system 

parameters, external disturbances, and modeling 

errors. The methodology of sliding mode control 

consists of three components. The first is 
designing a sliding surface in the state space. The 

second is designing high switching control law to 

reach the sliding surface. The third is designing 
equivalent control law to maintain the system 

state trajectory on the sliding surface for all 

subsequent times. 
 

A. Conventional Sliding Mode Control 
The first step in conventional sliding mode 

control (CSMC) is designing the switching 
surface. The sliding surface is defined as: 

𝑠 = n  1 + 𝛼𝑛  1 + 𝛽𝑛 1 , (12) 

substituting Equation (8) into Equation (12): 

𝑠 = 𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2 + 𝛼(𝑥2 − 𝑥2𝑑 ) + 𝛽(𝑥1 − 𝑥1𝑑 ). (13) 

The switching control law can be written as: 

𝑢𝑠 = −𝐴 𝑠𝑖𝑔𝑛 (𝑠), (14) 

where 

𝑠𝑖𝑔𝑛 𝑠 =  
 1, 𝑠 > 0,
 0, 𝑠 = 0,
−1, 𝑠 < 0.

  (15) 

The sliding mode control technique generally 

experiences chattering phenomenon, which is an 

oscilation around sliding surface as an effect of 
high switching. The saturation function can be 

used to overcome chattering phenomenon. The 

technique can be written as: 

𝑢𝑠 = −𝐴 𝑠𝑎𝑡 (𝑠), (16) 

where 

𝑠𝑎𝑡  
𝑠

𝜑
 =

 
 
 

 
  1,

𝑠

𝜑
> 1,

𝑠

𝜑
,  

𝑠

𝜑
 = 1,

−1,
𝑠

𝜑
< 1.

  (17) 

The equivalent control design to maintain the 

system state trajectory is: 

𝑠 = 𝑛 1 + 𝛼𝑛 1 + 𝛽𝑛 1. (18) 

substituting Equation (9) and (11) into Equation 

(18): 

𝑠 = 𝑓 𝑥 + 𝑔 𝑥 𝑢𝑒𝑞 + α  𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2 + 𝛽(𝑥2 −

𝑥2𝑑 ), (19) 

and we get equivalent control: 

𝑢𝑒𝑞 =
1

𝑔 𝑥 
(−𝑓 𝑥 − α(𝑔 −

𝑘 𝑥3
2

𝑚 𝑥1
2) − 𝛽(𝑥2 − 𝑥2𝑑 )).

 (20) 

Finally, we can get the CSMC controller as: 

𝑢 =
1

𝑔 𝑥 
(−𝑓 𝑥 − α(𝑔 −

𝑘 𝑥3
2

𝑚𝑥1
2)  − 𝛽(𝑥2 − 𝑥2𝑑 )) −

𝐴𝑠𝑎𝑡(
𝑠

𝜑
)). (21) 

The stability of a controller can be analyzed 
by Lyapunov function. Lyapunov function 

candidate is defined as: 

𝑉 =
1

2
𝑆2 > 0, (22) 

and 𝑉 = 𝑠𝑠   

𝑉 = 𝑠(𝑓 𝑥 + 𝑔 𝑥 𝑢𝑒𝑞 + α(𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2)  + 𝛽(𝑥2 −

𝑥2𝑑 )), (23) 

Substituting Equation (21) into 𝑢𝑒𝑞  in Equation 
(23): 

𝑉  = 𝑠𝑠 = 𝑠(𝑓 𝑥 + 𝑔 𝑥 
1

𝑔 𝑥 
(−𝑓 𝑥   

 −α(𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2)  − 𝛽(𝑥2 − 𝑥2𝑑 )) − 𝐴𝑠𝑎𝑡(

𝑠

𝜑
))  

 +α(𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2)  + 𝛽(𝑥2 − 𝑥2𝑑 )). (24) 

It can be simplified as: 

𝑉 = 𝑠𝑠 < 0  

 = 𝑠(𝑓 𝑥 + 𝑔 𝑥 
1

𝑔 𝑥 
 −𝑓 𝑥  − 𝐴𝑠𝑎𝑡(

𝑠

𝜑
)). (25) 

We ensure the stability of our system by 
choosing A to be large enough so that stable in 

the sense of Lyapunov. 

 

B. Global Sliding Mode Control 
The robustness of sliding mode control to 

disturbances and parameter uncertainties exists in 

sliding mode condition, and not necessarily 
robust at attaining phase. In the global sliding 

mode control (GSMC), the attaining motion 

phase was eliminated, so that the robustness of 
the controller can be improved [12-14]. 

The first step is designing the switching 

surface. The sliding surface is defined as: 

𝑠 = 𝑛 1 + 𝛼n 1 + 𝛽𝑛1 − 𝑟(𝑡), (26) 

substituting Equation (8) into Equation (26): 

𝑠 = 𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2 + 𝛼 𝑥2 − 𝑥2𝑑  + 𝛽 𝑥1 − 𝑥1𝑑 −

𝑟(𝑡). (27) 

The additional function 𝑟(𝑡) should be satisfied: 

𝑟 0 = 𝑒 0 + 𝛼𝑒 0 + 𝛽𝑒0, (28a) 

𝑟 𝑡 → 0 as 𝑡 → ∞, (28b) 

𝑟(𝑡) ∈ ℝ′ , (28c) 



R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

20 

where 𝑒0 = 𝑒 𝑡 = 0 , 𝛼 > 0, and 𝛽 > 0. 

Equation (28a) represents the initial states on 

the sliding surface, Equation (28b) represents 
asymptotic stability, and Equation (28c) 

represents the existence of sliding mode (GSMC 

improved design for a brush). From three 

conditions to Equation (28a), (28b), and (28b), 

𝑟(𝑡) can be designed as: 

𝑟 𝑡 = 𝑟(0)e−𝑘𝑡 . (29)  

The switching control law can be written as: 

𝑢𝑠 = −((
1

∆𝑔 𝑥 
(−∆𝑓 𝑥 − α(𝑔 −

𝑘 𝑥3
2

𝑚 𝑥1
2)  −

𝛽 𝑥2 − 𝑥2𝑑  − 𝑟 )) + 𝐷)𝑠𝑎𝑡
𝑠

𝜑
 . (30) 

The equivalent control to maintain the system 
state trajectory can be written as: 

𝑢𝑒𝑞 =
1

𝑔 𝑥  
(−𝑓 𝑥  − α  𝑔 −

𝑘 𝑥3
2

𝑚𝑥1
2  −

𝛽 𝑥2 − 𝑥2𝑑  + 𝑟 ), (31) 

where 

 

𝑅 =
𝑅𝑚𝑎𝑥 +𝑅𝑚𝑖𝑛

2
,

∆𝑅 =
𝑅𝑚𝑎𝑥 −𝑅𝑚𝑖𝑛

2
,

𝐿 =
𝐿𝑚𝑎𝑥 +𝐿𝑚𝑖𝑛

2
,

∆𝐿 =
𝐿𝑚𝑎𝑥 −𝐿𝑚𝑖𝑛

2
,

𝑚 =
𝑚 𝑚𝑎𝑥 +𝑚 𝑚𝑖𝑛

2
,

∆𝑚 =
𝑚 𝑚𝑎𝑥 −𝑚 𝑚𝑖𝑛

2
,

𝐷 > 0,

𝑓(𝑥) = −
4𝑘 2 𝑥2𝑥3

2

𝑚 𝐿 𝑥1
4 +

2𝑘 𝑅 𝑥3
2

𝑚 𝐿 𝑥1
2 +

2𝑘𝑥3
2𝑥2

𝑚 𝑥1
3 ,

𝑔 𝑥  = −
2𝑘 𝑥3

𝑚 𝑥1
2𝐿 

,

𝑓 𝑥 = −
4𝑘 2 𝑥2𝑥3

2

∆𝑚 ∆𝐿𝑥1
4 +

2𝑘 ∆𝑅𝑥3
2

∆𝑚 ∆𝐿𝑥1
2 +

2𝑘 𝑥3
2𝑥2

∆𝑚 𝑥1
3 ,

∆𝑔 𝑥 = −
2𝑘 𝑥3

∆𝑚 𝑥1
2∆𝐿

.
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 

 (32) 

Finally, we can get the GSMC controller: 

𝑢 =
1

𝑔 𝑥  
(−𝑓 𝑥  − α(𝑔 −

𝑘 𝑥3
2

𝑚𝑥1
2) − 𝛽 𝑥2 − 𝑥2𝑑   +

𝑟 ) − ((
1

∆𝑔 𝑥 
(−∆𝑓 𝑥 − α(𝑔 −

𝑘 𝑥3
2

𝑚 𝑥1
2) −

𝛽 𝑥2 − 𝑥2𝑑  − 𝑟 )) + 𝐷)𝑠𝑎𝑡
𝑠

𝜑
 . (33) 

Lyapunov function candidate is defined as: 

𝑉 =
1

2
𝑆2 > 0, (34) 

and 

𝑉 = 𝑠𝑠 = 𝑠(𝑓 𝑥 + 𝑔 𝑥 𝑢𝑒𝑞 + α(𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2)  +

𝛽 𝑥2 − 𝑥2𝑑  − 𝑟 ). (35) 

Substituting Equation (33) into 𝑢𝑒𝑞  in 
Equation (35): 

𝑉 = 𝑠(𝑓 𝑥 + 𝑔 𝑥 
1

𝑔 𝑥  
(−𝑓 𝑥  − α(𝑔 −

𝑘 𝑥3
2

𝑚 𝑥1
2)  −

𝛽 𝑥2 − 𝑥2𝑑  + 𝑟 ) − ((
1

∆𝑔 𝑥 
(−∆𝑓 𝑥  −

α(𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2) − 𝛽 𝑥2 − 𝑥2𝑑  −)) + 𝐷)𝑠𝑎𝑡

𝑠

𝜑
 +

α(𝑔 −
𝑘 𝑥3

2

𝑚 𝑥1
2) + 𝛽 𝑥2 − 𝑥2𝑑  − 𝑟 ). (36) 

It can be simplified: 

𝑉 = 𝑠𝑠 < 0 = 𝑠(𝑓 𝑥 + 𝑔 𝑥 
1

𝑔 𝑥  
(−𝑓 𝑥  )  −

((
1

∆𝑔 𝑥 
 −∆𝑓 𝑥 − 𝑟  + 𝐷)𝑠𝑎𝑡

𝑠

𝜑
). (37) 

We ensure the stability of our system 
choosing D to be large enough so that stable in 

the sense of Lyapunov. 

 

IV. SIMULATION RESULTS 
The robustness of the CSMC and GSMC from 

parameter uncertainties and disturbance are 

proposed. Furthermore, the chattering 

phenomenon will be investigated. The parameters 
of the magnetic levitation system are the 

gravitational 𝑔 = 9.81 𝑚/𝑠2 , the mass of the 
object 𝑚 = 340 𝑔 , the coil’s resistance 𝑅 =
7.3 𝛺 , the magnetic force constant 13 ∙
10−5𝑁𝑚2 /𝐴2, and the inductance 𝐿 = 0.089 𝐻.  

The simulation results of chattering 
phenomenon are shown in Figure 2 and Figure 3. 

The simulation results of CSMC are shown in 

Figure 2 to Figure 7. The simulation results of 
GSMC are shown in Figure 8 to Figure 11. 

The chattering phenomenon is considering as 

a problem in sliding mode control. The 

simulation in Figure 2 shows the controller has 
high chattering phenomenon and Figure 3 shows 

the position of the object can follow the reference. 

Although the object can follow the reference, in 
actual plant, chattering phenomenon will make 

the system unstable due the limited ability of 

electronics component. The chattering 

phenomenon can be reduced by saturated 
function.  

Figure 4 is control versus time for the system 

without uncertainties. Figure 5 shows the object 
can follow the reference very well. The matches 

between mathematical model of the controller 

and dynamics of the magnetic levitation make the 
system stable. Figure 6 and Figure 7 are 

simulation results of the system with 

uncertainties and disturbance. The parameters in 

Figure 6 and Figure 7 are the mass of the object 

𝑚 = 340 𝑔 + 20 𝑔 , the coil’s resistance 𝑅 =
7.3 𝛺 + 1.7 𝛺 , and the inductance 𝐿 =
0.089 𝐻 + 0.032 𝐻 .The cosine disturbance is 
−5 ∗ cos 5 ∗ 𝑡  𝑉. 



 R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

 

21 

 

  
Figure 2. Control with signum function (CSMC) 

 
 

  
Figure 3. Output with signum function (CSMC) 

 
 

  
Figure 4. Control without parameter uncertainty and disturbance (CSMC) 

 

 

  
Figure 5. Output without parameter uncertainty and disturbance (CSMC) 

 



R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

22 

Figure 7 shows that the object can follow the 
reference but have larger steady state error than 

the system without parameter uncertainties and 

disturbances. 

Simulation results of GSMC are shown in 

Figure 8 to Figure 11. Figure 8 is control versus 

time for the system without uncertainties. The 
position object in Figure 9 shows that the object 

can follow the desired reference and have faster 

response than CSMC.  

The robustness of controller from disturbance 
and parameter uncertainties are shown in Figure 

10 and Figure 11. Figure 11 shows the object can 

follow the desire reference more closely than 
CSMC. The parameters in Figure 10 and Figure 

11 are mass of the object 𝑚 = 340 𝑔 + 20 𝑔, the 
coil’s resistance 𝑅 = 7.3 𝛺 + 1.7 𝛺 , and the 
inductance 𝐿 = 0.089 𝐻 + 0.032 𝐻. Besides that 
the cosine disturbance −5 ∗ cos 5 ∗ 𝑡  𝑉 is given 
in Figure 10 and Figure 11. 

 

V. EXPERIMENTAL RESULTS 
Matlab Simulink with block set embedded 

target for microchip device was used to construct 

program in the microcontroller. The experiment 

set up consists of iron ball, dsPIC33FJ128MC802 
microcontroller with 16 bit resolution, 

electromagnet coil, and infrared-photodiode 

sensor. The output and control was recorded by 
DAQ 6009 with 1,000 Hz sample rate. The set 

point position of the object is 1 𝑐𝑚. Parameters 
values were conditioned as follow. Nominal mass 

was 𝑚 = 340 𝑔 , and it was supposed that 
𝑅 = 7.3 𝛺 and 𝐿 = 0.089 𝐻. Mass deviation was 
𝑚 = 340 𝑔 + 20 𝑔.  Uncertainties of 𝑅  and 𝐿 
occur naturally when the temperature of the coil 

increases. External disturbance was undefined. 

They can make the system unstable if the 
controller is not really robust. 

Experimental results of CSMC are shown in 

Figure 12 to Figure 15. Figure 12 describes 
control versus time for the system without 

uncertainties. Figure 13 shows the object can 

follow the reference. The matches between 

mathematical model of the controller and 
dynamics of the magnetic levitation make the 

system stable. Figure 14 represents control versus 

time for the system with uncertainties. Figure 15 
shows the object cannot follow the reference 

1 𝑐𝑚 because the CSMC is not really overcome 
the parameter uncertainties. 

Experimental results of GSMC are shown in 

Figure 16 to Figure 19. Figure 16 is control 

versus time for the system without uncertainties. 

The position object in Figure 17 shows the object 
can follow the desired reference. Figure 18 is 

control versus time for the system with 

uncertainties. The position object in Figure 19 
shows the object can follow the set point 

although the parameter uncertainties occur. 

 
Figure 6. Control with parameteruncertainties and disturbance (CSMC) 

 

 
Figure 7. Output with parameter uncertainties and disturbance (CSMC) 

 



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23 

 

 
Figure 8. Control without parameter uncertainty and disturbance (GSMC) 

 
 

 
Figure 9. Output without parameter uncertainty and disturbance (GMSC) 

 

 

 
Figure 10. Control with parameter uncertainties and disturbance (GSMC) 

 
 

 
Figure 11. Output with parameter uncertainties and disturbance (GSMC) 

 



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24 

 

 

 
Figure 12. Control without parameter uncertainty (CSMC) 

 
 

 
Figure 13. Output without parameter uncertainty (CSMC) 

 
 

 
Figure 14. Control with parameter uncertainties (CSMC) 

 
 

 
Figure 15. Output with parameter uncertainties (CSMC) 

 



 R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

 

25 

 

 
Figure 16. Control without parameter uncertainty (GSMC) 

 
 

 
Figure 17. Output without parameter uncertainties (GSMC) 

 
 

 
Figure 18. Control with parameter uncertainties (GSMC) 

 
 

 
Figure 19. Output with parameter uncertainties (GSMC) 

 



R. Uswarman et al. / Mechatronics, Electrical Power, and Vehicular Technology 05 (2014) 17-26 

 

26 

VI. CONCLUSION 
This paper described the robustness of CSMC 

and GSMC from disturbances and parameter 

uncertainties. The CSMC is not necessarily 
robust at attaining phase. The mismatches 

between mathematical model of the controller 

and dynamics of the magnetic levitation make the 

system unstable. The GSMC shows good 
performance from disturbances and uncertainties. 

This technique can eliminate the mismatches 

between mathematical model of the controller 
and dynamics of the magnetic levitation. In the 

GSMC, the attaining motion phase was 

eliminated, so that the robustness of the 
controller can be improved. However, the value 

of the parameter uncertainties needs to be limited. 

Based on simulation and experimental results, the 

GSMC has better performance than CSMC. 
 

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