Control of a 2-DOF omnidirectional mobile inverted pendulum

Journal of Mechanical Science and Technology 26 (9) (2012) 2921~2928 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-0710-2

Control of a 2-DOF omnidirectional mobile inverted pendulum† Tuan Dinh Viet, Phuc Thinh Doan, Hoang Giang, Hak Kyeong Kim and Sang Bong Kim* Department of Mechanical and Automotive Engineering, College of Engineering, Pukyong National University, Busan, 608-739, Korea (Manuscript Received October 20, 2011; Revised February 20, 2012; Accepted May 24, 2012) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract In this paper, stabilization of a 2-degrees-of-freedom (2-DOF) omnidirectional mobile inverted pendulum (OM-IP) is studied. The OM-IP consists of the rod that rotates around a rotary point of a universal joint which is connected at the center of the omnidirectional mobile platform (OMP). For ease of analysis, the OM-IP is decoupled into two subsystems: a 2-DOF inverted pendulum (IP) and an OMP. The IP is a rod that rotates around a universal joint with 2-DOF. The OMP is a body consisting of disk and three omnidirectional wheels that moves on plane and keeps the rod in balance. Dynamic modeling of the 2-DOF OM-IP is presented. From the dynamic equation, an adaptive backstepping control method is proposed to keep the rod in balance. Update law is presented as differential equation of an unknown parameter when the distance from the center of gravity of the rod to the rotary point on the OMP is unknown. Stability of the adaptive controller is proven by using Lyapunov function. Simulation and experimental results show the effectiveness of the proposed controller. Keywords: Omnidirectional mobile inverted pendulum (OM-IP); 2-DOF inverted pendulum (2-DOF IP); Omnidirectional mobile platform (OMP); Adaptive backstepping controller (ABC) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction The inverted pendulum is a classical problem. However, it is a perfect benchmark for the design of a wide range of nonlinear control theories. Most inverted pendulums considered in previous paper are: single, double or triple inverted pendulum on a cart [1, 4, 5, 7], a rotational single-arm [8] or two-link pendulum and an inverted pendulum on an x-y robot [2, 11]. In this paper, a new idea to develop a 2-DOF inverted pendulum using an OMP is introduced. The OMP employs three omni-wheels in a triangular configuration. Therefore, it has the ability to move in all directions on the floor and keep the rod, 2-DOF IP, balance consistently. The inverted pendulum has been widely studied by many researchers around the world. The reason for studying the pendulum relies on the fact that many important engineering systems can be approximately modeled as the pendulum. In previous studies, there are a large number of systems proposed for inverted pendulum. The most popular and simplest method used to control the inverted pendulum is PID controller. H. Zhang et al. developed a robust PID with disturbance, noise and unknown parameter [9, 10]. P. Ali et al. stabilized the inverted pendulum on the cart by using feedback linearization method converted to fuzzy controller based on Taylor series *

Corresponding author. Tel.: +82 51 629 6158, Fax.: +82 51 621 1411 E-mail address: [email protected] † Recommended by Associate Editor Yang Shi © KSME & Springer 2012

[1]. H. Wang et al. controlled 2-DOF inverted pendulum using a contact-less feedback low cost CCD camera [2]. H. Wang transformed the 2-DOF pendulum problem to a 1-DOF one. They realized two control loops controlled by a linearization and stabilization method based on an observer. Stabilization control of double inverted pendulum system was proposed by Q. Li et al. [4]. To control the IP, some kinds of controller can be used such as fuzzy controller [1], neural network controller [11], sliding mode controller and adaptive controller [4-7]. However, stabilization problem of 2-DOF inverted pendulum based on OMP still remains difficult task because of the slipping of omni-wheels and the limitation of the maximum acceleration of OMP driving by DC motors. This paper proposes a new idea about stabilization of a 2DOF IP using an OMP. It is the first time that an idea to develop a 2-DOF IP using an OMP is introduced. A control method using adaptive backstepping control technique is proposed when the distance from the center of gravity of the rod to a rotary point of a universal joint on the OMP is unknown. The stability and the convergence properties of OM-IP are guaranteed by Lyapunov function. First, the OM-IP is separated into two subsystems, the OMP and the 2-DOF inverted pendulum. The IP is a rod that rotates around a universal joint structure with 2-DOF. The OMP consists of platform and three omnidirectional wheels that are moving on x − y plane and keeping the rod in balance. Then, dynamic modeling of the OMP and the 2-DOF IP are presented. In order to reduce

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T. D. Viet et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2921~2928 z

R COG

α

Ry

z

m

O Hx

Fx

l y

M

θ

l yz

α

β

x

lxz k x x&

Mg

x

x

lxz

x

V O

cxα&

Hx

x

Fig. 2. Projection of the 2-DOF inverted pendulum on x − z plane.

O

l yz =

Fig. 1. 2-DOF OM-IP.

the control of the 2-DOF inverted pendulum into the controls of two subsystems of 1-DOF inverted pendulum, the motions of 2-DOF inverted pendulum and the OMP are also separated into two independent motions, motion in x − z plane and motion in y − z plane. Simulation and experimental results show the effectiveness of the proposed controller.

2. System modeling and analysis This section presents dynamic modeling of the OM-IP system. For a convenient modeling process, the modeling of the system is decomposed into two parts: OMP modeling and 2DOF inverted pendulum modeling. 2.1 2-DOF inverted pendulum modeling Fig. 1 shows the rod of the 2-DOF inverted pendulum rotating around the rotary point of the universal joint, O. As shown in Fig. 1, the 2-DOF inverted pendulum can be decoupled into 1-DOF of x − z plane and y − z plane. R is the center of gravity of the rod, l , is the distance from R to the rotary point, O ; R x and R y are the projection of R on x − z and y − z planes and lxz and l yz are the distances from R x and R y to the rotary point O , respectively; θ is the angle between the rod and z axis; α and β are the projection angles of the rod on x − z and y − z planes from z axis, respectively. The 2-DOF inverted pendulum is modeled under the following assumptions: (1) The angle between the rod and z axis is small; α,β ≪1 . (2) Mass is concentrated on the center of gravity (COG). (3) The friction forces and inertial moment of the rod about COG are zero. According to geometry in Fig. 1, the followings are obtained: tan 2 θ = tan 2 α + tan 2 β cosθ 1 lxz = l= l cos α cos 2 α 2 β 1+ sin cos 2 β

O

mg

α

Fx

Rx

(1) (2)

cosθ l= cos β

1 cos 2 β 1+ sin 2 α cos 2 α

l.

(3)

Fig. 2 shows the projection of the 2-DOF inverted pendulum on x − z plane. With the assumption (1) of α , β ≪ 1 , the following is obtained: lxz ≈ l yz ≈ l .

(4)

Referring to Fig. 2, by applying Newton’s 2nd law at the center of gravity of the pendulum along the horizontal and vertical components by using Eq. (4), the followings are obtained: d2 d2 l cos α ) ≈ m 2 ( l cos α ) 2 ( xz dt dt d2 d2 H x = m 2 ( x + lxz sin α ) ≈ m 2 ( x + l sin α ) dt dt

V − mg = m

(5) (6)

where m is the mass of the rod; g is the gravitational acceleration; and x is the horizontal displacement of the OMP. Taking moments about the COG yields the torque equation as: Iαɺɺ + cxαɺ = Vlxz sin α − H xlxz cos α ≈ Vl sin α − H xl cos α

Hx = m

d2 d2 x + lxz sin α ) ≈ m 2 ( x + l sin α ) 2 ( dt dt

(7) (8)

where cx is the pendulum viscous friction coefficient in x axis; I is the moment of inertia of the rod about the COG; V and H x are the vertical and horizontal reaction forces on the rod. Applying Newton’s 2nd law for the OMP yields: Fx − H x = Mxɺɺ + k x xɺ

(9)

where M is the mass of the OMP; k x is the viscous friction coefficient of OMP in x axis; and Fx is the horizontal control force on the OMP in x direction. Combining Eqs. (4)-(9), the modeling equations of the 1DOF inverted pendulum in x − z plane are given as follows:

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T. D. Viet et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2921~2928 y

y 1

F1

1

L

2π

Hx

O

L

3

F2

π

3

Hy

π

2

3

3

Fx

F2 x

Hy

3

2

π

3

F3x

2

sin α ) = Fx − k x xɺ

( I + l m )αɺɺ − lm( g sin α − xɺɺcos α ) = −c αɺ . 2

x

Fig. 4. OMP moving in the direction of x axis.

(10) (11)

With the assumption (3), the Eqs. (10) and (11) become: 2

sin α ) = Fx

lαɺɺ − g sin α + xɺɺ cos α = 0 .

(12) (13)

Similarly, the modeling equations of the 1-DOF inverted pendulum in y − z plane are given as follows:

( M + m ) ɺɺy + lm ( βɺɺ cos β − βɺ l βɺɺ − g sin β + ɺɺy cos β = 0

π

3

3

Fig. 3. Schematic of the OMP on x − y plane.

( M + m ) xɺɺ + lm (αɺɺ cos α − αɺ

O

x

F3

( M + m ) xɺɺ + lm (αɺɺ cos α − αɺ

2π

Hx

x

F1x

2

)

sin β = Fy

(14)

of the direction of x axis and the direction of y axis. The motion of OMP in the direction of x axis means that the OMP moves only in direction of x axis without rotating and the total of external forces generated on three wheels only has the component on x axis, and the component on y axis is zero. From this statement, the following is obtained:   F1 L + F2 L + F3 L = 0  π π  − F1 + F2 cos + F3 cos = Fx 3 3   π π  F2 sin − F3 sin = 0 . 3 3 

(16)

(15) (i = 1, 2,3) is denoted as the force applied to the i th wheel of the OMP to move in direction of x axis. F1x , F2 x and F3x are the solutions of Eq. (16). Fi x

where x, α and Fx of Eqs. (12) and (13) are replaced by y , β and Fy , respectively. y is the vertical displacement of the OMP; β is the projection angle of the rod on y − z plane and Fy is the vertical control force on the OMP in y direction. 2.2 OMP modeling Fig. 3 shows the configuration of OMP. The OMP consists of three omnidirectional wheels equally spaced at 1200 from one another. The three wheels have the same radius denoted by r and are driven by DC motors. L is the distance from wheel’s center to the center of OMP’s geometry, O . The OMP uses omni-wheels, so it can move in any direction of x − y plane. Therefore, it can keep the balance of the rod. Fig. 3 shows the schematic of the OMP on x − y plane. The forces applied to the OMP consists of the forces generated by DC motors on the omni-wheels, Fi (i = 1, 2,3) , the reaction forces on x axis and y axis by the rod, H x and H y . y axis is assumed to be a line connected from the center of OMP’s geometry, O , to the center of wheel 1. In Fig. 3, the direction of Fi (i = 1, 2,3) is assumed is positive direction. In this section, to separate the motion of OM-IP into two independent motions, motion in x − z plane and motion in y − z plane, the motion of OMP is also separated into motions

From Eq. (16), the followings are obtained: 2   F1x = − 3 Fx  1   F2 x = Fx 3   1  F3 x = Fx . 3 

(17)

Fig. 4 shows the OMP moving in the direction of x axis. F1x is negative because its direction is opposite with F1 in Fig. 3. Similarly, to make the OMP move in the direction of y axis, the following equations have to be satisfied.   F1 L + F2 L + F3 L = 0  π π   F2 sin − F3 sin = Fy 3 3   π π − F1 + F2 cos + F3 cos = 0 3 3 

(18)

(i = 1,2,3) is denoted as the force applied to the i th wheel of the OMP to move in direction of y axis. F1 y , F2 y Fi y

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g sin α − lαɺɺ + lm (αɺɺ cos α − αɺ 2 sin α ) cos α F cos α − ( M + m ) g sin α mαɺ 2 sin α cos α ⇔ αɺɺ = x + 2 −l ( M + m sin α ) − ( M + m sin 2 α ) Fx = ( M + m )

⇔ αɺɺ =

u +ϕ l

(24)

where Fig. 5. OMP moving in the direction of y axis.

and F3 y are the solutions of Eq. (18). From Eq. (18), the following equations are obtained:   F =0;  1y  1 Fy ;  F2 y = 3   1 Fy .  F3 y = − 3 

(19)

u Fx cos α − ( M + m ) g sin α = l −l ( M + m sin 2 α )

ϕ=

(26)

xɺ1 = x2

Fig. 5 shows the OMP moving in the direction of y axis. Because the motion in the direction of x axis is independent on the motion in the direction of y axis, the total force on each wheel is given as follows:

1 Fy 3 1 Fy . 3

( M + m ) xɺɺ + lm (αɺɺ cos α − αɺ 2 sin α ) = Fx

(21)

lαɺɺ − g sin α + xɺɺ cos α = 0 .

(22)

A feedback control law is chosen as following: u Fx cos α − ( M + m ) g sin α = l −l ( M + m sin 2 α )

u ( M + m sin 2 α ) cos α

.

(29)

In this section, the backstepping algorithm is used to design a controller to keep the rod in balance. The angle of the rod converges to its desired value from a wide set of initial conditions. The controller has not only to guarantee the stability and the regulation of the tracking error, but also to converge the estimated value of the unknown parameters towards its true constant values. Step 1) A tracking error variable is defined as: xe = x1 − xr

(23)

(30)

where xr is the reference angle of α . In applying the backstepping technique, a backstepping error eb is defined as: eb = x2 − δ

From Eq. (22), the following is obtained:

Substituting Eq. (23) into Eq. (21) yields:

(28)

(20)

Because the dynamic equations in x − z plane and y − z plane are similar, the controllers applied for them are designed in the same way. In this section, we only write the controller for x − z plane. From Eqs. (12) and (13), the dynamic equation of the inverted pendulum in x − z plane is as follows:

g sin α − lαɺɺ . cos α

(27)

u +ϕ . l

⇔ Fx = ( M + m ) g tan α −

3. Controller design

xɺɺ =

mαɺ 2 sin α cos α − ( M + m sin 2 α )

where u is part of the control law to be designed. By defining x1 = α , x2 = αɺ , Eq. (23) is rewritten in state space form as:

xɺ 2 =

 2  F1 = F1x + F1 y = − Fx 3   1  F2 = F2 x + F2 y = Fx + 3   1  F3 = F3 x + F3 y = Fx − 3 

(25)

(31)

where x2 is considered as a virtual control input and a stability function δ for x2 is defined as:

δ = − K1 xe + xɺ r

(32)

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where K1 > 0 is a design parameter. From Eqs. (27) and (30)-(32), differentiating xe with respect to time yields: xɺe = eb − K1 xe .

(33)

The first Lyapunov function candidate associated with the tracking error is chosen as: V1 =

1 2 xe . 2

(34)

From Eq. (33), the time derivative of the first Lyapunov function candidate is obtained as: Fig. 6. Block diagram of the proposed controller.

1 Vɺ 1 = xɺe2 = xe xɺe = xe (eb − K1 xe ) = − K1 xe2 + xeeb . 2

(35)

Eq. (35) cannot guarantee Vɺ 1 ≤ 0 when xe ≠ 0 and eb ≠ 0 . Thus, the second Lyapunov function candidate must be considered.

V3 = V2 +

Step 2) From Eqs. (31) and (32), differentiating eb with respect to time becomes: eɺb = xɺ 2 − δɺ = xɺ 2 + K1 xɺe − xɺɺr .

Eqs. (28), (33) and (36) can be rewritten in the space as: xɺe = eb − K1 xe eɺb = − K12 xe + K1eb − xɺɺr +

(36)

( x ,e ) e

b

(37) u +ϕ . l

(38)

Depending on whether l is known or not, two cases are considered. Case 1) If l is known, the second Lyapunov function candidate is chosen as: V2 = V1 +

1 2 eb . 2

u = −l ( K1 + K 2 ) eb + (1 − K12 ) xe − xɺɺr + ϕ  .  

(42)

⌢

⌢

where lɶ = l − l is the estimating error of l ; l is the estimation value for l ; λ > 0 is an adaptation gain. To design the control law such that xe → 0 and eb → 0 as t → ∞ , the following control law is proposed as: ⌢ u = −l ( K1 + K 2 ) eb + (1 − K12 ) xe − xɺɺr + ϕ  .  

(43)

The time derivative of the second Lyapunov function candidate negative as follows: ɺ lɶɶl Vɺ 3 = Vɺ 2 + = − K1 xe2 − K 2eb2 λl ( K1 + K 2 ) eb   lɶ  1 ⌢ɺ  . + − l + eb  l λ  + (1 − K12 ) xe − xɺɺr + ϕ     

(44)

So update law for l is chosen for Vɺ 3 to be negative as follows: ⌢ɺ l = λ eb ( K1 + K 2 ) eb + (1 − K12 ) xe − xɺɺr + ϕ  .  

(45)

(40)

It would render the time derivative of the second Lyapunov function candidate negative as follows:

The block diagram for the proposed control algorithm of the OM-IP is shown in Fig. 6.

4. Prototype of the experimental OM-IP

Vɺ 2 = Vɺ 1 + eb eɺb

u  = − K x + xeeb + eb  − K12 xe + K1eb − xɺɺr + ϕ +  l  2 2 = − K1 xe − K 2eb ≤ 0 .

1 ɶ2 l 2λ l

⌢

(39)

A control law is chosen as:

2 1 e

Case 2) If l is unknown, the second Lyapunov function candidate is chosen as:

(41)

A prototype of the experimental OM-IP is shown in Fig. 7. The OM-IP is considered as two subsystems of a 2-DOF IP and an OMP. The 2-DOF IP rotates around a universal joint. The potentiometer sensor is connected at the universal joint

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Fig. 7. 2-DOF OM-IP in experiment. z

R COG

Ry Rx l y

θ

l yz

α

β

x

Fig. 9. Control architecture of hardware system of the OM-IP.

lxz

O

Fig. 8. Structure of the potentiometer sensor.

for measuring its angle. The mobile platform has three omnidirectional wheels that are driven by 3 DC motors. A potentiometer sensor is used to measure the angles of the rod as shown in Fig. 8. The sensor has two potentiometers corresponding to its position in x and y directions, respectively. A control system is developed based on microcontrollers PIC18F452’s which are operated with the clock frequency 40MHz. A hardware configuration of the proposed control system using seven PIC18F452 is shown in Fig. 9. The projection angle α of the rod on x − z planes from z axis can be measured by a potentiometer sensor as shown in Fig. 10. V0 = (Vmin + Vmax ) / 2   α = ∠(OV 0 ,OV x ) =

π /3 × (Vx − V0 )[rad ] (Vmax − Vmin )

(46)

where Vmin and Vmax are the minimum and maximum voltage which are returned from the potentiometer sensor, respectively. V0 is average voltage of Vmin and Vmax . The Vx is the real voltage value on x − z planes which is returned by the sensor in the real time. Similarly, the projection angle β of the rod on y − z planes from z axis can be measured as follows: V0 = (Vmin + Vmax ) / 2   β = ∠(OV0 ,OV y ) =

π /3 × (Vy − V0 )[rad ] (Vmax − Vmin )

(47)

Fig. 10. Configuration of measuring the α angle.

where Vx and α of Eq. (47) are replaced by Vy and β , respectively.

5. Simulation and experimental result To verify the effectiveness of the proposed controllers, simulations and experiments have been done for the OM-IP. In the simulation, the numerical parameter values and the initial values are given in Tables 1 and 2. The tracking error eb in x − z and y − z planes in the full time of 20 seconds in simulation are shown in Fig. 11. They go to zero from 4 seconds. Figs. 12 and 13 show the projection angles in x − z plane and y − z , respectively. The continuous line is simulation result and the dot line is experimental result. The angle errors converge to zero after 4 seconds. The experiment result is bounded around simulation with ±0.025 rad . Fig. 14 shows the control forces applied three omni-wheels in simulation and Fig. 15 shows the control forces applied to three wheels in experiment. In simulation result, the control forces become zero after the angle errors go to zero. In experimental results, the control forces are bounded around zero with ±0.04 N ⋅ m . Fig. 16 shows the estimated

T. D. Viet et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2921~2928

2927

Table 1. Numerical parameter values. Parameters

Values

Units

M

0.5

[kg]

m

0.1

[kg]

l

0.3

[m]

L

0.2

[m]

g

9.81

[m/s2]

λ

2

K1

5

K2

5

Fig. 14. Forces of wheels in simulation.

Table 2. Initial values for simulation. Parameters

Values

Units

α0

0.2

[rad]

β0

0.1

[rad]

α ref

0

[rad]

β ref

0

[rad]

x0

0

[m]

y0

0

[m]

Fig. 11. Tracking error eb in x − z and y − z planes in simulation.

Fig. 15. Forces of wheels in experiment.

Fig. 16. Estimated distance from COG to rotating point.

estimation distance in experiment where lx is about 0.68 m and l y is about 0.3 m .

6. Conclusions

Fig. 12. Projection angle of the rod on x − z plane.

Fig. 13. Projection angle of the rod on y − z plane.

distances from the COG to the rotary point. The real distance denoted by continuous line is 0.3 m . The dot lines is estimation distance in simulation where lx converges to 0.57 m and l y converges to 0.18 m . The dashed lines denote for

In this paper, a new idea to develop a 2-DOF inverted pendulum based on OMP is presented and stabilization of a 2DOF OM-IP is studied. Based on the dynamic equation, an adaptive backstepping controller and update law for unknown parameter are proposed to keep the rod in balance. The stability and the convergence properties of OM-IP are guaranteed by the closed-loop Lyapunov functions. Simulation and experimental results show that the adaptive backstepping controller can keep the rod in balance when the distance from the center of gravity of the rod to the rotary point on the OMP is unknown. The results show that with a ideal inverted pendulum, the proposed controller is capable of making the errors converge to zero. These results demonstrate the effectiveness of the adaptive backstepping controller and update law.

References [1] P. Ali and V. Ali, Design and implementation of Sugeno controller for inverted pendulum on a cart system, Proc. of

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the 8th IEEE Int. Sym. on Intelligent System and Informatics, Serbia (2010) 641-646. [2] H. Wang, A. Chamroo, C. Vasseur and V. Koncar, Stabilization of a 2-DOF inverted pendulum by a low cost visual feedback, Proc. of 2008 American Control Conference, Seattle, Washington, USA (2008) 3851-3856. [3] T. Kalmar-Nagy, R. D’Andrea and P. Ganguly, Nearoptimal dynamic trajectory generation and control of an omnidirectional vehicle, Robotics and Autonomous System, 46 (1) (2004) 47-64. [4] Q. Li, W. Tao, S. Na, C. Zhang and L. Yao, Stabilization control of double inverted pendulum system, The 3rd Int. Conf. Inn. Comp. Inf. and Cont. ICICIC’ 2008. [5] A. Ebrahim and G. V. Murphy, Adaptive backstepping controller design of an inverted pendulum, IEEE (2005) 172-174. [6] M. Krstic, I. Kanellakopoulos and P. Kokotovic, Nonlinear and adaptive control desgn, John Wiley & Sons Inc., New York, USA, 1995. [7] O. T. Altinoz, Adaptive integral backstepping motion control for inverted pendulum, International Journal of Computer and Information Science and Engineering, 1 (4) (2007) 192-195. [8] Md. Akhtaruzzaman and A. A. Shafie, Modeling and control of a rotary inverted pendulum using various methods, Camparative Assessment and Result Analysis, Proceedings of the 2010 IEEE Int. Conf. on Mechatronics and Automation, Aug. 2010. [9] H. Zhang, Y. Shi and A. S. Mehr, Robust static output feedback control and remote PID design for networked motor systems, IEEE Transaction on Industrial Electronics, 58 (12) (2011) 5396-5405. [10] H. Zhang, Y. Shi and A. S. Mehr, Robust H_infity control for multivariable networked control system with disturbance/noise attenuation, Int. J. Robust. Nonlinear Control, Doi: 10.1002/rnc.1688 (2011) 183-204. [11] S. Jung, H. T. Cho and T. C. Hsia, Neural network control for position tracking of a two-axis inverted pendulum system: Experimental studies, IEEE Trans. On Neural Networks, 18 (4) (2007).

Tuan Dinh Viet was born in Vietnam on July 14, 1972. He received the B.S. degree in the Faculty of Computer Science, Hochiminh City Open University, Vietnam in 1997. He received the B.S. degree in the Faculty of Information Technology, College of Engineering, University of Danang, Vietnam in 2008. He is currently a Ph.D. student in the Dept. of Mechanical Engineering, Pukyong National University, Busan, Korea. His fields of interests are computer science, robust control and mobile robot control.

Phuc Thinh Doan was born in Vietnam on January 31, 1985. He received the B.S. degrees in Dept. of Mechanical Engineering, Hochiminh City University of Technology, Vietnam in 4/2007. He then received the M.S. degree in the Dept. of Mechanical Engineering, Pukyong National University, Busan, Korea in 2/2011. He is currently a Ph.D. student in the Dept. of Mechanical Engineering, Pukyong National University, Busan, Korea. His fields of interests are robotic, power electric, motion control and mobile robot control. Giang Hoang was born in Vietnam on April 24, 1984. He received the B.S. degree in Dept. of Computer Science, Hochiminh City University of Technology, Vietnam in 2009. He then received the M.S degree in the Dept. of Mechanical Engineering, Pukyong National University, Busan, Korea in 2/2012. He is currently a Ph.D student in the Dept. of Mechanical Engineering, Pukyong National University, Busan, Korea. His fields of interests are computer science, robotic and mobile robot control. Hak Kyeong Kim was born in Korea on November 11, 1958. He received the B.S. and M.S. degrees in Dept. of Mechanical Engineering from Pusan National University, Korea in 1983 and 1985. He received Ph.D degree at the Dept. of Mechatronics Engineering, Pukyong National University, Busan, Korea in February, 2002. His fields of interest are robust control, biomechanical control, mobile robot control, and image processing control. Sang Bong Kim was born in Korea on August 6, 1955. He received the B.S. and M.S. degrees from National Fisheries University of Pusan, Korea in 1978 and 1980. He received PhD. degree in Tokyo Institute of Technology, Japan in 1988. After then, he is a Professor of the Dept. of Mechanical Engineering, Pukyong National University, Busan, Korea. His research has been on robust control, biomechanical control, and mobile robot control.