World Applied Sciences Journal 18 (12): 1855-1869, 2012ISSN 1818-4952© IDOSI Publications, 2012DOI: 10.5829/idosi.wasj.2012.18.12.208

Corresponding Author: Farzin Piltan, Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia 43400 Serdang, Selangor, Malaysia

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Review of Sliding Mode Control of Robotic Manipulator

Farzin Piltan and Nasri B. Sulaiman

Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia 43400 Serdang, Selangor, Malaysia

Abstract: Control of robotic systems is vital due to wide range of their applications because this system is multi-input multi-output, nonlinear and uncertainty. Consequently, it is difficult to design accurately mathematical models for multiple degrees of freedoms robot manipulator. Therefore, strong mathematical tools used in new control methodologies to design a controller with acceptable performance. As it is obvious stability is the minimum requirement in any control system, however the proof of stability is not trivial especially in the case of nonlinear systems. One of the best nonlinear robust to control of robot manipulator is sliding mode controller. A review of sliding mode controller for robot manipulator will be investigated in this paper.

Key words: Robotic system • nonlinear system • robust controller • sliding mode controller

INTRODUCTION

There are a lot of control methodologies that can be used for control of robot manipulators. These range of various controllers applied from linear to nonlinear, to lots of non-classical non-linear and adaptive non-classical non-linear. In this paper an attempted has been made to do a review of Sliding Mode Control (SMC) for robotics manipulator.

Non linear control methodologies are more general because they can be used in linear and non linear systems. These controllers can solve different problems such as, invariance to system uncertainties andresistance to the external disturbance. The mostcommon non linear methodologies that have beenproposed to solve the control problem consist of the following methodologies: feedback linearization control methodology, passivity-based control methodology,sliding mode control methodology, robust Lyapunov-based control methodology, adaptive controlmethodology and artificial intelligence-basedmethodology [1].

Sliding Mode Controller (SMC) is a powerfulnonlinear controller which has been analysed by many researchers especially in recent years. This theory was first proposed in the early 1950 by Emelyanov and several co-workers and has been extensively developed since then with the invention of high speed control devices [2, 3]. The main reason to select this controller in wide range area is have acceptable controlperformance and solve two most important challenging

topics in control which names, stability and robustness [1, 4, 5]. However, this controller used in wide range but, pure sliding mode controller has followingdisadvantages. Firstly, chattering problem; which can caused the high frequency oscillation of the controllers output. Secondly, sensitivity; this controller is very sensitive to the noise when the input signals very close to the zero. Last but not the least, nonlinear equivalent dynamic formulation; which this problem is veryimportant to have a good performance and it is difficult to calculation because it is depending on the nonlinear dynamic equation [6-9].

Chattering phenomenon can cause some problems such as saturation and heat for mechanical parts of robot manipulators or drivers. To reduce or eliminate the chattering, various papers have been reported by many researchers and classified in two most important methods, namely, boundary layer saturation method and estimated uncertainties method [1, 3, 10-20].

In recent years, artificial intelligence theory has been used in sliding mode control systems. Neuralnetwork, fuzzy logic and neuro-fuzzy are synergically combined with sliding mode controller and used in nonlinear, time variant and uncertainty plant (e.g., robot manipulator). The strategies for robotics are classifiedin two main groups: classical and non-classicalmethods, where the classical methods use themathematical models to control systems and non-classical methods use the artificial intelligence theory such as fuzzy logic, neural networks and/or neuro-fuzzy.

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After the invention of fuzzy logic theory in 1965 by Zadeh, this theory was used in wide rangeapplications. Fuzzy Logic Controller (FLC) is one of the most important applications in fuzzy logic theory. This controller can be used to control of nonlinear,uncertain systems and transfer expert knowledge to mathematical formulation. However pure FLC works in many areas but, it cannot guarantee the basicrequirement of stability and acceptable performance[12]. Some researchers applied fuzzy logicmethodology in sliding mode controllers (FSMC) to reduce the chattering and equivalent problems in pure sliding mode controller so called fuzzy sliding mode controller [21-25] and the other researchers applied sliding mode methodology in fuzzy logic controller(SMFC) to improve the stability of system that is most important challenge in pure FLC [26-29].

Fuzzy Sliding Mode Controller (FSMC) is a sliding mode controller which combined to Fuzzy LogicSystem (FLS) to reduce or eliminate the high frequency oscillation (chattering), to compensate the unknown system dynamics and also to adjustment of the linear sliding surface slope. H.Temeltas has proposed FSMC to achieving robust tracking of nonlinear systems. C. L. Hwang have proposed a fuzzy model based sliding mode control based on N fuzzy based linear state-space[24, 30]. A multi-input multi-output FSMC to reduce the chattering and constructed to approximate theunknown system has been presented for a robotmanipulator [22].

Sliding Mode Fuzzy Controller (SMFC) is a fuzzy logic controller based on sliding mode methodology to reduce the fuzzy rules and to refine the stability of close loop system. Research on SMFC is significantlygrowing as their applications, for instance, in control robot manipulator which, have been reported in [26-29]. H.K.Lee have presented self tuning SMFC toreduce the fuzzy rules, increase the stability and to automatically adjusted control parameters. Palm R has proposed SMFC to increase the robustness andtrajectory disturbance [11, 31].

Another method to intelligent control of robotmanipulator is Artificial Neural Networks (ANNS) or Neural Networks (NNs). It is a parametric nonlinearfunction and the parameters are the weights of the NNs. It can be used in two areas in robotics, namely, control robot manipulator and identification. Neural networks control is very effective tool to control robotmanipulator when robot manipulators have uncertainty in dynamic part. With this method, researcher candesign approximator for an unknown dynamical system only by knowing the input-output data ofsystems (i.e., training data) [9, 32].

Adaptive control used in systems whose dynamic parameters are varying and need to be training on line.

In general states adaptive control classified in two main groups: traditional adaptive method and fuzzy adaptive method, that traditional adaptive method need to have some information about dynamic plant and somedynamic parameters must be known but fuzzy adaptive method can training the variation of parameters by expert knowledge. Combined adaptive method toartificial sliding mode controllers can help tocontrollers to have better performance by online tuning the nonlinear and time variant parameters. F Y Hsu have presented adaptive fuzzy sliding mode control,which can update fuzzy rules to compensate nonlinear parameters and guarantee the stability robotmanipulator controller. Y.C. Hsueh have presented self tuning sliding mode controller which can resolve the chattering problem without to use of satura tion function [33, 34].

This paper is organized as follows. In section 2, main subject of sliding mode controller and formulation are presented. This section covered the followingdetails, classical sliding mode control, model of robotic manipulators, classical sliding for robotic manipulators, equivalent control and chatter free sliding control. A review of the fuzzy logic system is presented and introduces the description and analysis of fuzzy logic systems and adaptive fuzzy control in section 3. In section 4, review of adaptive fuzzy sliding modecontrol is presented. This section covered the following details, description of most important algorithms and comparison between these algorithms. In section 5,review of neural sliding mode controller are presented,this method is used to training and estimation to reduce the chattering and estimation the equivalent part. In section 6, the conclusion is presented.

INTRODUCTION TO CLASSICAL SLIDING MODE CONTROL

This section provides a review of classical slidingmode control and the problem of formulation based on [3, 35-37]. Consider a nonlinear single input dynamic system of the form:

(1)

where u is the vector of control input, x(n) is the nth derivation of x,

is the state vector, ƒ(x) is unknown and b(x) is of known sign. The control problem is truck to the desired state,

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and have an acceptable error which is given by:

(2)

Consider a time-varying sliding surface s(x,t) is given by:

(3)

where λ is the positive constant. Most of researcher used an integral term to further penalize tracking error as follows:

(4)

The main target in this methodology is keep s(x,t) at zero when tracking is outside of s(x,t). Therefore, one of the common strategies is to find input U outside of s(x,t)

(5)

where ζ is strictly positive constant, so, equation (5) forces tracking trajectories towards sliding condition as shown in Fig. 1. A simple solution to get the sliding condition when the dynamic parameters haveuncertainty is the switching control law:

(6)

where the is the positive constant. Since the control input U has to be discontinuous term, thecontrol switching could not to be perfect and this will have chattering. Chattering can caused the highfrequency oscillation of the controllers output and fast breakdown of mechanical elements in actuators.Chattering is one of the most important challenging in sliding mode controllers which, many papers have been presented to solve this problems [37]. Figure 2 shows the chattering as a result in control switching.

Several different methods have been proposed to reduce and eliminate the chattering, but two basiccommon method presented in this paper:

• The boundary layer method, which in this method the basic idea is replace the discontinuous

Fig. 1: Sliding surface (J.J. Slotine and H. Asada,41986)

Fig. 2: Chattering as a result of imperfect controlswitching (Slotine and Li, 1991)

method by saturation(linear) method with smallneighbourhood of the switching surface. Thisreplace caused to increase the error performance. Several papers have been presented about trade-offbetween performance and chattering [11-13].Therefore, to have a smote control law, thesaturation function Sat(S/∅) added to the control law:

(7)

The control input U is shown in Fig. 3.R. Palm has presented a fuzzy method to nonlinear

approximation instead of linear approximation inside the boundary layer to improve the chattering andperformance result. Figure 4 shows the nonlinearoperating line [11].

L.X. Wang has proposed a method, universalapproximation methods, to approximate any continuous function on a compact set to arbitrary accuracy based on stone-weierstrass theorem. Emami have proposed fuzzy logic approximation to improve the palm method in calculate nonlinear approximator inside the boundary layer [12, 13].

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Fig. 3: Control law in the boundary layer (Slotine and Li, 1991)

Fig. 4: Nonlinear operating line (Palm, R., 1992)

• Estimated uncertainty method, which this method used the uncertainty estimator for compensation of the uncertainties structures and unstructured of the plant. If estimator has an acceptable performance to compensate the uncertainties there is no need to use discontinuous control law to achieve sliding mode which, caused to reduce or eliminate thechattering. This method implement by someresearchers in different area [15, 16, 18, 38-41].

• Elmali and Moura have presented sliding modecontrol with perturbation estimation method(SMCPE) to reduce the classical sliding modelimitation [15, 38, 39]. This method was tested for the tracking control of the first two links of aSCARA type HITACHI robot. Figure 5 shows the block diagram of this method to reduce oreliminate the chattering. Figure 6 shows theexperimental block diagram representation of SMC and SMCPE.

Y. Li and Q. Xu have introduced adaptive SMCPE with PID sliding surface [41]. This method has better performance than the previous method (e.g., Elmami

et al., Moura et al.). Figure 7 shows the block diagram of the adaptive SMCPE PID robust controller.

Model of robotic manipulator: The dynamicequations of robot manipulators with rigid links can be written as:

M(q)q V(q,q)q G(q)•• • •

+ + = Γ (8)

where, V (q, ) : Centrifugal and Coriolis forces, G(q) : Gravity forces, G: Generalized forces, M(q) : Mass Matrix-Kinetic Energy Matrix, q: Generalized JointCoordinates. By writing the velocity dependent term

V(q,q)•

in different form, all the matrices becomefunctions of only the manipulator position; in this case the dynamic equation is called configuration spaceequation and has the following form: [42]If

2

V(q,q) B(q).[q.q] C(q)[q ]• • • •

= +2

M(q).q B(q)[q.q] C(q)[q] G(q)•• • • •

⇒ τ = + + + (9)

where,

n(n 1)B(q) n

2−

= × matrix of coriolis torques,

C(q) n n= × matrix of centrifugal torques,

n(n 1)[qq] 1

2

• • −= × vector of joint velocity products given

by :

1 2 1 3[q .q ,q .q , . . . . . . . ]•• • •

2

[q] n 1•

= × vector given by: 2 2

1 2[q ,q , . . . ]• •

.

The angular acceleration is found as to be:

2

1q M (q).{ [B(q).qq C(q).q g(q)]}•• • • •

−= τ− + + (10)

Classical sliding mode control for robotic manipulatorIt is well known that the equation of multi DOF

manipulator governed by the equation (9) and thetracking error is defined as:

(11)

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Fig. 5: The block diagram representation of the experimental set-up (Elmali and Olgac, 1992)

Fig. 6: Block diagram representation of: (A) SMC, (B) SMCPE (Elmali and Olgac, 1996)

Fig. 7: Block diagram of the adaptive SMCPE-PID robust controller (Yangmin and Qingsong, 2009)

where qd is desired output and qa is actual output. The sliding surface is defined as follows:

(12)

where λ is chosen as the bandwidth of the robot manipulator controller. The time derivative of S is:

(13)

The Lyapunov function V defines as:

(14)

Based on above discussion, the control law for a multi DOF robot manipulator can be written as:

(15)

where, the model-based component Ueq compensate for the nominal dynamics of systems. So Ueq can calculate as follows:

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(16)

and Udis can calculate as follows:

(17)

To reduce the chattering problem, the saturation function introduced in control law instead of signfunction as follows:

(18)

where ∅ is the width of the boundary layer, therefore the control output can be write as follows:

(19)

Figure 8-11 shows the tracking joint and tracking errors for two degrees of freedom robotmanipulator [43].

INTRODUCTION TO FUZZY CONTROL

After the introduced fuzzy set theory in 1965 by Zadeh (Zadeh) fuzzy systems have been widely used indifferent area, especially in nonlinear and complexcontrol methodology [44]. This method can transferexpert to mathematical knowledge. In control robotmanipulator it can used in different area (e.g., estimate the dynamic part, tuning the parameters and……) by used if-then rules. Fuzzy logic control (FLC) systems, do not use complex mathematically models of plant for analysis. This method is free of some of the problems associated with the model-based techniques that used in classical controllers. It mu st be noted that application of fuzzy logic is not limited only to systems difficult for modelling [45-48] but also this method can helpengineers to design controller significantly easier.

Design and analysis fuzzy logic system: A blockdiagram of fuzzy controller shows in Fig. 12. Howeverthe application area for fuzzy control is really wide, the basic form for all command types of controllers consists of: Input fuzzification (binary-to-fuzzy [B/F] conversion), Fuzzy rule base, Inference engineand Output deffuzzification (fuzzy-to-binary [F/B]conversion) [49].

The basic structure of a fuzzy controller is shown in Fig. 13.

This controller has two inputs ( e,e•

) and one output (t). Two inputs are used for accessing the current

Fig. 8: (a) Tracking and (b) errors of joint 1 in classical SMC (Xiaosong Lu, 2007)

Fig. 9: Control input; joint 1 (Xiaosong Lu, 2007)

Fig. 10: (a) Tracking and (b) errors of joint 1 in classical SMC by using saturation function (Xiaosong Lu, 2007)

conditions of the process. The inputs are error (e) which measure the difference between desired and actual

position and the rate of error (e

) which measure the difference between desired and actual velocity. Thecomplete fuzzy rule base for conventional fuzzycontroller is shown in Table 1.

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Fig. 11: Control input; joint 1 SMC with saturationfunction (Xiaosong Lu, 2007)

Fig. 12: Block diagram of pure fuzzy controller (S. Mohan and S. Bhanot, 2006)

Fig. 13: Structure of fuzzy logic controller (S. Mohan and S. Bhanot, 2006)

Fuzzy logic and its application to sliding modecontroller: Many combinations of fuzzy logicsystems with sliding mode method have been proposed by several researchers. As mentionpreviously, SMFC is fuzzy controller based on sliding mode method for easy implementation, stability and robustness. The SMFC initially proposed by Palm to design nonlinear approximation boundary layerinstead of linear approximation [11]. Emami haveproposed fuzzy logic approximate inside the boundary layer [13]. The main drawback of SMFC is the value of sliding surface λ must be pri-defined very carefully and the most important advantage of SMFC compare to pure SMC is design a nonlinearity boundary layer. Control rules for SMFC can be described as [11, 31, 50, 51]:

Table 1: Rule table for fuzzy controller (S. Mohan and S. Bhanot, 2006) for 2 DOF robot manipulator

e,e•

NB NM NS ZE PC PM PB

NB NB NB NB NM NS NS ZENM NB NM NM NM NS ZE PSNS NB NM NS NS ZE PS PMZE NB NM NS ZE PS PM PBPS NM NS ZE PS PS PM PBPM BS ZE PS PM PM PM PBPB ZE PS PS PM PB PB PB

Table 2: Rule table for SMFC (F.C, Sun et al., 1996)

jS•

∆uej

Sj N Z P

P Z N NZ P Z NN P P Z

IF S is<ling.var> THEN U is<ling.var> (20)

Table 2 shows the sliding mode fuzzy rule table [51]Although most of time the control performance for

FLC and SMFC is similar to each other, but SMFC has two most important advantages:The number of rule base is smallerIncrease the robustness and stabilityIn this method the control output can be calculated by

(21)

where is the nominal compensation term and τfuzzy(s) is the output of sliding mode fuzzy controller. Figure 14 shows the block diagram of SMFC.

The most important target in FSMC is designsliding mode control combined to fuzzy logic systems to solve important problems in classical sliding mode controller. Several papers have been proposed about this method and several researchers’ works in this area [52-57]. Figure 15 shows the fuzzy model base sliding mode controller which including a fuzzy equivalentcontrol that was employed to obtain the desired control behaviour and a fuzzy switching control was applied to reinforce system performance.

Adaptive fuzzy control: For any plants (e.g., robot manipulators) whose time variant, adaptive control canlearn the dynamic parameter to design an acceptable controller. All pure fuzzy controllers have commondifficulty, which they need to find several scale factors.

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Fig. 14: The structure of SMFC (H.K. Lee, 1994)

Fig. 15: Fuzzy model base sliding mode controller (C.L. Hwang and S.F. Chao, 2004)

Fig. 16: The structure of MIMO fuzzy login systems (B.K. Yoo abd W.C. Ham, 2000)

Therefore, adaptive method can adjust and tuneparameters. Research on adaptive fuzzy control issignificantly growing, for instance, the differentadaptive fuzzy controllers have been reported in [58-65].

ADAPTIVE FUZZY SLIDING MODE CONTROL

The addition of adaptive methodology to a fuzzy sliding mode controller caused to improve the tracking performance by online tuning the parameters. Theadaptive sliding mode controller is used to estimate the unknown dynamic parameters and external

disturbances. Several researchers works on adaptivesliding mode control and their applications in robotic manipulator in the following references [33, 66-79].Generally, adaptive fuzzy sliding mode control of robot manipulator classified in two main groups: multi-inputmulti-output (MIMO) and single-input single-output(SISO) fuzzy systems. MIMO and SISO fuzzy systemsare designed to compensate the uncertainties of the robot manipulator.

The general MIMO if-then rules are given by [68]:

then (22)

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Fig. 17: The structure of adaptive fuzzy compensate control of robot manipulator (B.K. Yoo and W.C. Ham 2000)

Fig. 18: Performance MIMO adaptive fuzzy slidingmode controller (B.K. Yoo and W.C. Ham2000) a) Error performance, b) Torqueperformance to show chattering

Fig. 19: The structure of a SISO fuzzy logic controller (B.K. Yoo and W.C. Ham 2000)

Fig. 20: Adaptive fuzzy sliding mode controller (Y, Guo and P.Y. Woo, 2003) a) Torque performance b) Error performance with load and disturbance

where, l = 1,2,3,…,m are fuzzy if-then rules, x and y are the inputs and outputs vectors of fuzzy systems. Figure 16 shows the structure of MIMO fuzzy logic system.Several papers have been used MIMO fuzzy systems in compensation [33, 66, 68-69, 76].

Yoo and Ham have proposed a MIMO fuzzysystem to help the compensate and estimate the torque coupling. In n-DOF robot manipulator with k membership function for each input variable, thenumber of fuzzy rules for each joint is equal to 3k2n that will be result in high computation load

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and also this controller has chattering. This methodcan only tune the consequence part of the fuzzy rules [66, 68]. Figure 17 shows the structure ofadaptive fuzzy compensator control of robotmanipulator.

The validity of the control performance inthis method are shown by computer simulationsof two DOF robot manipulator which is shown in Fig. 18.

Medhafer have proposed an indirect adaptive fuzzy sliding mode controller to control robot manipulator[76]. This MIMO algorithm, are applied to estimate the nonlinear dynamic parameters. If each input variable have K2 membership functions, the number of fuzzy rules for each joint is Compared with the previous algorithm the number of fuzzy rules are reduce by introduce the sliding surface as inputs of fuzzy systems. This method also cannot tuning for the premise part of the fuzzy rules but it can attenuated the chattering.The general SISO if-then rules are given by [68]:

then(23)

where, l = 1,2,3,…,M are fuzzy if-then rules and j = 1,2,3,…,m. Figure 18 shows the structure of SISO fuzzy logic system. Several papers have beenused SISO fuzzy systems in compensation [67, 73-75, 80-82].

Y. Guo and P. Y. Woo have proposed a SISOfuzzy system to help compensate and reduced thechattering [80]. First if each input variable have K2membership functions the number of fuzzy rules for each joint is K2 which is decreased vis -a-vis previous algorithm and the chattering is also alleviate. Figure 20 shows tracking performance in this method for two link robotic manipulator.

The previous methods used only for tuning the consequence part of fuzzy rules. C. M. Lin and C. F. Hsu can solve this problem with design the premise part [71]. These researchers can tune both consequence and premise parts of fuzzy rules. In this method the number of fuzzy rules equal to K2 and the computational load is low but it has chattering. Figure 20 shows the block diagram of adaptive fuzzy sliding mode control.

Shahnazi have proposed a SISO PI direct adaptive fuzzy sliding mode controller based on Lin and Hsu algorithm to reduce or eliminate chattering [73, 74].This method can tune premise and consequence part and the number of fuzzy rules are equal to K2. The bounds of PI controller and the parameters are online adjusted by low adaption computation. Figure 22 shows the tracking performance in adaptive fuzzy PI sliding mode controller.

NEURAL NETWORK AND ITS APPLICATION TO SLIDING MODE CONTROLLER

Many combinations of neural network and sliding mode method have been proposed by severalresearchers in some paper journals [83-88] and several paper conferences [89-93]. The sliding mode neuralnetwork initially has been proposed by R. Safaric et alto design estimator for nonlinear uncertain parameter [94]. Figure 23 shows the sliding mode neural network controller.

M. Lee and have proposed a robust neuralcontroller to improve the uncertain estimation [83]. C. K. Lin has presented sliding mode based on fuzzy neural network controller [85]. The applications ofneural network in adaptive sliding mode controller have been proposed by S. H. Huh and shows in Fig. 24 [86].

The application of neural-fuzzy network inadaptive sliding mode control to improve theperformance has been presented by C. S. Chen and shows in Fig. 25 [87].

Fig. 21: Block diagram of adaptive fuzzy sliding mode controller (C.M. Lin and C.F. Hsu, 2004)

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Fig. 22: Tracking performance in adaptive fuzzy PISMC (Shahnazi et al., 2006) a) Torque performance b) Error performance

Fig. 23: Sliding-mode neural network controller (R. Safaric et al., 1996)

Fig. 24: Schematic diagram of the variable structure model reference adaptive control (S.H. Huh et al., 2007)

Fig. 25: Neuro fuzzy adaptive sliding mode controller (C.S. Chen, 2008)

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The application of neural-fuzzy network inadaptive sliding mode control to improve theperformance has been presented by C. S. Chen and shows in Fig. 25 [87].

CONCLUSIONS

In this paper, review of sliding mode control is discussed for robotic manipulators. In this paper, first of all, main subject of classical sliding mode controller are presented. Classical sliding mode controllers have some disadvantages, therefore, in the next part fuzzy logic system presented to reduce or eliminate these problems. Because robot manipulator is nonlinear and uncertain system therefore most of researchers work on adaptive part to estimation the non linear and uncertain term of robot manipulator.

REFERENCES

1. Slotine, J.J.E. and W. Li., 1991. Applied nonlinear control. Prentice-Hall Inc.

2. Young, K.D., 1978. Controller design for amanipulator using theory of variable structures.IEEE Trans. On systems, Man and Cybernetics, SMC-8: 210-218.

3. Slotine, J.J.E., 1984. Sliding controller design for nonlinear systems. Int. J. Control, 40: 421-434.

4. Utkin, I.V., 1992. Sliding mode in controloptimization. New York: Springer-Verlag.

5. Iordanov, H.N. and B.W. Surgenor, 1997.Experimental evaluation of the robustness ofdiscrete sliding mode control versus linearquadratic control. IEEE Trans. On control System Technology, 5 (2): 254-260.

6. Harashima, F., H. Hashimoto and K. Maruyama, 1986. Practical robust control of robot arm using variable structure system. IEEE Conference, pp: 532-539.

7. Taha, E.Z. and S. Kawaji, 1993. Robust control of a constrained robot arm. InternationalConference on Intelligent Robots and Systems,IEEE, pp: 91-96.

8. Hamerlain, M., 1995. Robust control with reduced knowledge of unmodeled dynamics using sliding mode application to robot manipulators. IEEEconference, pp: 261-268.

9. Ertugrul, M. and O. Kaynak, 1998. Neuralcomputational the equivalent control in slidingmode for robot trajectory control applications.IEEE. International Conference on Robotic andAutomation, pp: 2042-2047.

10. Slotine, J.J.E. and S.S. Sastry, 1983. Trackingcontrol of nonlinear systems using sliding surfaces, with application to robot manipulators. Int. J.Control, 38 (2): 465-492.

11. Palm, R., 1992. Sliding mode fuzzy control. IEEEConference, pp: 519-526.

12. Wang, L.X., 1993. Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Systems, 1 (2): 146-154.

13. Emami, M.R., I.B. Turksen and A.A. Goldenberg, 1998. Development of a systematic methodology of fuzzy logic modelling. IEEE Trans. On Fuzzy Systems, 6 (3): 346-361.

14. Emami, M.R., I.B. Turksen and A.A. Goldenberg, 2000. Fuzzy-logic control of dynamic systems:From modelling to design. EngineeringApplication of Artificial Intelligence, pp: 47-69.

15. Elmali, H. and N. Olgac, 1992. Theory andimplementation of sliding mode control withperturbation estimation. International Conferenceon Robotic and Automation, pp: 2114-2119.

16. Young, K.D. and V.D. Sergey, 1992. Single mode control with chattering reduction. IEEE American Control Conference, pp: 1291-1292.

17. Kim, N., C.W. Lee and P.H. Chang, 1998. Sliding mode control with perturbation estimation:Application to Motion Control of ParallelManipulators, Control Engineering Practice, 6 (11): 1321-1330.

18. Curk, B. and K. Jezernik, 2001. Sliding modecontrol with perturbation estimation: Application on DD Robot Mechanism, Robotica, pp: 641-648.

19. Khalil, K.H., 2002. Nonlinear systems (3rd Edn.), Prentice Hall.

20. Yan, J., W. Chang, J. Lin and K. Shyu, 2005.Adaptive chattering free variable structurecontrol for a class of chaotic systems withunknown bounded uncertainties, Physics Letters A, pp: 274-281.

21. Barrero, F., A. Torralba, A. Gonzalez, E. Galven and L.G. Franquelo, 2002. Speed control ofinduction motors using a novel fuzzy sliding mode structure. IEEE Transactions on Fuzzy Systems, 10 (3): 375-383.

22. Hsu, Y.C. and H.A. Malki, 1998. Fuzzy variablestructure control for MIMO systems. IEEEConference on Fuzzy System Proceeding, pp: 280-285.

23. Lin, H.R. and W.J. Wang, 1998. Fuzzy controldesign for the pre-spesified tracking withsliding mode. In fuzzy systems proceeding. IEEEWorld Congress on Computational Intelligence,pp: 292-295.

24. Temeltas, H., 1998. A fuzzy adaption technique for sliding mode controllers. IEEE Conference onIndustrial Electronics, pp: 110-115.

World Appl. Sci. J., 18 (12): 1855-1869, 2012

1867

25. Wong, L.K., F.H.F. Leung and P.K.S. Tam, 2001. A fuzzy sliding controller for nonlinearsystems. IEEE Journals, Industrial Electronics,48 (1): 32-37.

26. Chen, J.Y and Y.H. Lin, 1995. A self-tuning fuzzy controller design. IEEE International Conference,pp: 1358-1362.

27. Lhee, C.G., J.S. Park, H.S. Ahn and D.H. Kim,1999. Sliding like fuzzy logic control with selftuning the dead zone parameters. IEEEInternational Fuzzy Systems ConferenceProceeding, pp: 544-549.

28. Lhee, C.G., J.S. Park, H.S. Ahn and D.H. Kim,2001. Sliding mode like fuzzy logic control with self tuning the dead zone parameters. IEEE Trans. On Fuzzy Systems, 9 (2): 343-348.

29. Zhang, X., H. Su and J. Chu, 2003. Adaptivesliding mode-like fuzzy logic control for high order nonlinear systems. IEEE Conference on Intelligent Control, pp: 788-792.

30. Hwang, C.L. and S.F. Chao, 2004. A fuzzy model based variable structure control for robot arms: Theory and Experiments, IEEE Conference, pp: 5252-5258.

31. Lee, H.K. and K. Fms, 1994. A Study on theDesign of Self-Tuning Sliding Mode FuzzyController. Domestic Conference, pp: 212-218.

32. Yu, W., A.S. Poznyak and E.N. Sanchez, 1999.Neural adaptive control of two link manipulatorwith sliding mode compensation. IEEE Conference on Robotics and Automation, pp: 3122-3127.

33. Hsu, F.Y. and L.C. Fu., 1995. Nonlinear control of robot manipulators using adaptive fuzzy slidingmode control. IEEE Conference on IntelligentRobots and Systems, pp: 156-161.

34. Yao-Chu Hsueh, Shun-Feng Su and Wen-JuneWang, 2008. Self tuning sliding mode controller design for class a of nonlinear control systems. International Conference on Systems Man and Cybernetics, pp: 2337-2342.

35. Ertugrul, M. and O. Kaynak, 1998. Neuralcomputationof the equivalent control in slidingmode for robot trajectory control applications.IEEE International Conference on Robotic andAutomation, pp: 2042-2047.

36. Decarlo, R.A., S.H. Zak and G.P. Matthews, 1988. Variable structure of nonlinear multivariablesystems: A tutorial, Proc. IEEE, 76 (3): 212-232.

37. Utkin, I.V., 1977. Variable structure systems with sliding modes. IEEE. Trans. Auto. Control, 22 (2): 2121-222.

38. Elmali, H. and N. Olgac, 1996. Implementation of sliding mode control with perturbation estimation. IEEE Trans. Control System Technology, 4 (1): 79-85.

39. Moura, J.T. and N. Olgac, 1994. A comparativestudy on simulations vs Experiments of SMCPE. IEEE Conference on Control, pp: 996-1000.

40. Dong, Y., S. Wu, D. Xu and K. Zhao, 2006. An integral variable structure controller with fuzzytuning design stewart platform. IEEE, Int. Conf.On Innovative Computing, Information andControl, pp: 445-449.

41. Li, Y. and Q. Xu, 2009. Adaptive sliding modecontrol with perturbation estimation and PIDsliding surface for motion tracking of a piezo-Driven micromanipulator. IEEE Trans. on Control Systems Technology, 99: 1-13.

42. Bejczy, A., T.J. Taran, X. Yun and S. Man, 1985. Nonlinear Feedback Control of PUMA 560 Robot Arm by Computer. IEEE Transaction IndianElectron, 3 (24): 1680-1687.

43. Lu, X., 2007. An investigation of adaptive fuzzy sliding mode control for robotic manipulators, M.S. Thesis, Carleton Univ., Ottawa, Ontario.

44. Lotfi, A. Zadeh, 1997. Toward a theory of fuzzy information granulation and its centrality in human easoning and fuzzy logic. 1997 Elsevier ScienceB.V Fuzzy Sets and Systems, 1 (14): 111-127.

45. Zhou, J. and P. Coiffet, 1992. Fuzzy Control of Robots. Proceedings IEEE InternationalConference on Fuzzy Systems, pp: 1357-1364.

46. Banerjee, S. and Peng Yung Woo, 1993. Fuzzy logic control of robot manipulator. Proceedings Second IEEE Conference on Control Applications,pp: 87-88.

47. Lotfi, A. Zadeh, 1994. Fuzzy logic,Nural network and Soft computing. Communications of the ACM, 3 (37): 77-84.

48. Akbarzadeh-T A.R., K. Kumbla, E. Tunstel and M. Jamshidi, 2000. Soft Computing for autonomous Robotic Systems. IEEE International Conferenceon Systems, Man and Cybernatics, pp: 5252-5258.

49. Sudeept Mohan and Surekha Bhanot, 2006.Comparative Study of Some Adaptive Fuzzyalgorithms for Manipulator Control. InternationalJournal of Computation and Intelligence, 3 (4): 303-311.

50. Frank Hoffmann, 2003. An Overview on SoftComputing in Behavior Based Robotics. 10th

International Fuzzy System Associations WorldCongress Istanbul, IFSA, pp: 544-551.

51. Sun, F.C., Z.Q. Sun and G. Feng, 1996. Design of adaptive fuzzy sliding mode controller for robot manipulators. IEEE Conferences on FuzzySystems, pp: 62-67.

52. Lin, S.C. and C.C. Kung, 1992. A linguistic fuzzy sliding mode controller. IEEE Conference, pp: 1904-1905.

World Appl. Sci. J., 18 (12): 1855-1869, 2012

1868

53. Kung, C.C. and S.C. Lin, 1992. A fuzzy slidingmode controller design. IEEE Conference onSystem Engineering, pp: 608-611.

54. Kung, C.C. and C.C. Liao, 1994. Fuzzy slidingmode controller design for tracking control ofnonlinear system. IEEE Conference on Control, pp: 180-184.

55. Perez, R. and R. Soto, 1994. The effect of fuzzy logic theory on a fuzzy sliding mode controller’s performance. IEEE Conference on Industrial Fuzzy Control and Intelligent Systems, pp: 139-140.

56. Song, F. and S.M. Smith, 2000. A comparison of sliding mode controller and fuzzy sliding modecontroller. IEEE Conferences on FuzzyInformation Processing Society, pp: 480-484.

57. Zhang, X. and Z. Man, 2000. A new fuzzy sliding mode control scheme. 3rd World Congress onIntelligent Control and Automation, pp: 1692-1696.

58. Lin, C.K. and S.D. Wang, 1997. Robust self tuning rotated fuzzy basis function controller forrobot arms. IEE Proc-control Theory Appl., 144 (4): 293-298.

59. Elshafei, A.L. and A. Elnaggar, 1997. Adaptiveversus adaptive fuzzy logic control. IEEE,International Symposium on Intelligent Control,pp: 49-54.

60. Kwan, E. and M. Liu, 1999. An adaptive fuzzy approach for robot manipulators tracking. IEEEConference on Computation Intelligent in Robotics and Automation, pp: 53-58.

61. Liu, M., 2000. Stability analysis of decentralized adaptive fuzzy logic control for robot arm tracking. IEEE Conference on Decision and Control, pp: 883-888.

62. Berstecher, R.G., R. Palm and H.D. Unbehaven,2001. An adaptive fuzzy sliding modecontroller. IEEE Trans. on Industrial Electronics,48 (1): 18-31.

63. Kim, V.T., 2002. Independent joint adaptive fuzzy control of robot manipulator. IEEE Conference on Automation Congress, pp: 645-652.

64. Wang, Y.F. and T.Y. Chai, 2004. Robust adaptive fuzzy observer design in robot arms. IEEEConference on Control, pp: 857-862.

65. Sharma, R. and M. Gopal, 2008. A Markov game-adaptive fuzzy controller for robot manipulators. IEEE Trans. On Fuzzy Systems, 16 (1): 171-186.

66. Yoo, B. and W. Ham, 1998. Adaptive fuzzy sliding mode control of nonlinear system. IEEE Trans. On Fuzzy Systems, 2 (6): 315-421.

67. Chain, C.C and C.C. Hu, 1999. Adaptive fuzzycontroller for nonlinear uncertain systems, pp: 1131-1136.

68. Yoo, B.K. and W.C. Ham, 2000. Adaptive controlof robot manipulator using fuzzy compensator.IEEE Trans. On Fuzzy Systems, 8 (2): 186-199.

69. Hwang, C.L., 2000. Takagi-sugeno-based robust and adaptive fuzzy sliding mode control systems. IEEE Conference, pp: 530-535.

70. Sadati, N. and A. Talasaz, 2004. Chattering free adaptive fuzzy sliding mode control. IEEEConference on Cybernatics and IntelligentSystems, pp: 29-34.

71. Lin, C.M. and C.F. Hsu, 2004. Adaptive fuzzysliding mode control for induction servomotorsystems. IEEE Trans. on Energy Conversion, 19 (2): 362-368.

72. Shahnazi, R. and M.R. Akbarzadeh-T, 2005. Direct adaptive fuzzy PI sliding mode control for a class of uncertain nonlinear systems. IEEE Conferences on Systems Man and Cybernetics, pp: 2548-2553.

73. Shahnazi, R., H. Shanechi and N. Pariz, 2006.Position control of induction and servomotors: A novel adaptive fuzzy PI sliding mode control. IEEE Conferences on Power Engineering, pp: 1-9.

74. Shahnazi, R., H. Shanechi and N. Pariz, 2008.Position control of induction and servomotors: A novel adaptive fuzzy PI sliding mode control. IEEE Journals on Energy Conversions, 23 (1): 138-147.

75. Liu, J.K. and F.C. Sun, 2006. Global sliding mode control with adaptive fuzzy chattering free method for nonlinear system. IMAC Multi Conference on Computational Engineering in SystemsApplications, pp: 541-546.

76. Medhaffar, H., N. Derbel and T. Damak, 2006. A decoupled fuzzy indirect adaptive sliding modecontroller with application to robot manipulator.Int. Journal on Modeling, Identification andControl, 1 (1): 23-29.

77. Chiang, C.C. and C.H. Wu, 2007. Observer-basedadaptive fuzzy sliding mode control of uncertain multi-input multi-output nonlinear systems. IEEEFuzzy Systems Conference, pp: 1-6.

78. Weng, C.C. and W.S. Yu, 2008. Adaptive fuzzy sliding mode control for linear time-varyinguncertain systems. IEEE Conference on FuzzySystems, pp: 1483-1490.

79. Yu, Z.X., 2009. Adaptive sliding mode-like fuzzy logic control for nonlinear systems. Journal ofCommunication and Computer, 6 (1): 53-60.

80. Guo, Y. and P.Y. Woo, 2003. An adaptive fuzzy sliding mode controller for robotic manipulators. IEEE. Trans. Man and Cybernetics, 33 (2): 149-159.

81. Guo, Y. and P.Y. Woo, 2003. Adaptive fuzzysliding mode control for robotic manipulators.IEEE Conference on Decision and Control, pp: 2174-2179.

World Appl. Sci. J., 18 (12): 1855-1869, 2012

1869

82. Ho, H.F., Y.K. Wong and A.B. Rad, 2004.Adaptive fuzzy sliding mode control design:Lyapunov approach. IEEE, 5th Asian ControlConference, pp: 1502-1507.

83. Lee, M. and H.S. Choi, 2000. A robust neuralcontroller for underwater robot manipulators. IEEE Trans. On Neural Networks, 11 (6): 1465-1470.

84. Visioli, A. and G. legnani, 2002. On the trajectory tracking control of industrial SCARA robotmanipulators. IEEE Trans. Industrial Electronics,49 (1): 224-232.

85. Lin, C.K., 2006. Nonsingular terminal slidingmode control of robot manipulators using fuzzy wavelet networks. IEEE Trans. on Fuzzy Systems, 14 (6): 849-859.

86. Huh, S.H. and Z. Bien, 2007. Robust sliding mode control of a robot manipulator based on variable structure-model reference adaptive controlapproach, IET Journals on Control Theory and Applications, 1 (5): 1355-1363.

87. Chen, C.S., 2008. Dynamic structure neural fuzzy networks for robust adaptive control of robotmanipulators. IEEE Transactions of IndustrialElectronics, 55 (9): 3402-3414.

88. Xu, D., D. Zhao, J. Yi and X. Tan, 2009.Trajectory tracking control of omnidirectionalwheeled mobile manipulators: Robust neuralnetwork based sliding mode approach. IEEE Trans.Systems Man and Cybernetics, 39 (3): 788-799.

89. Ak, A.G. and G. Ganserver, 2009. NN approaches on fuzzy sliding mode control design for robot trajectory tracking, pp: 1170-1175.

90. Xiaojiang, M. and C. Yangzhou, 2008. Neuralsliding mode control for multi-link robots. IEEE Conferences on Control and Decision, pp: 3513-3517.

91. Chaoui, C., W. Gueaieb and M.C.E. Yagoub, 2007. FPGA implementation of a hybrid neural fuzzycontroller for flexible joint manipulators withuncertain dynamics. IEEE Conference, pp: 70-75.

92. Ak, A.G. and G. Ganserver, 2006. Three link robot control with fuzzy sliding mode controller based on RBF neural network, pp: 2719-2724.

93. Sadati, N., R. Ghadami and M. Bagherpour, 2005. An adaptive neural network sliding modecontroller for robotic manipulators. IEEEConference on Industrial Technology, pp: 1246-1251.

94. Safaric, R., K. Jezernik, M. Rodic, A. Sabanovic and S. Urban, 1996. Sliding mode neural network robot controller. IEEE Conferences on Advanced Motion Control, pp: 395-400.