Fuzzy Sliding-Mode Control Using Adaptive Tuning Technique

586 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007

Fuzzy Sliding-Mode Control UsingAdaptive Tuning Technique

Rong-Jong Wai, Senior Member, IEEE

Abstract—This study mainly deals with the key problem ofchattering phenomena on the conventional sliding-mode control(SMC) and investigates an adaptive fuzzy sliding-mode control(AFSMC) system for an indirect field-oriented induction motor(IM) drive to track periodic commands. First, an indirect field-ori-entation method for an IM drive is introduced briefly. Moreover,a fuzzy logic inference mechanism is utilized for implementinga fuzzy hitting control law to remove completely the chatteringphenomena on the conventional SMC. In addition, to confront theuncertainties existed in practical applications, an adaptive algo-rithm, which is derived in the sense of Lyapunov stability theorem,is utilized to adjust the fuzzy parameter for further assuring ro-bust and optimal control performance. The indirect field-orientedIM drive with the AFSMC scheme possesses the salient advantagesof simple control framework, free from chattering, stable trackingcontrol performance, and robust to uncertainties. Furthermore,numerical simulation and experimental results due to periodicsinusoidal commands are provided to verify the effectiveness ofthe proposed control strategy, and its advantages are indicatedin comparison with the conventional SMC system and the SMCsystem with a boundary layer.

Index Terms—Fuzzy inference mechanism, indirect field-orien-tation method, induction motor (IM) drive, Lyapunov stability,sliding-mode control (SMC).

I. INTRODUCTION

SLIDING-MODE CONTROL (SMC) is one of the effec-tive nonlinear robust control approaches since it provides

system dynamics with an invariance property to uncertaintiesonce the system dynamics are controlled in the sliding mode[1]–[5]. The first step of SMC design is to select a sliding surfacethat models the desired closed-loop performance in state vari-able space. In the second step, design a hitting control law suchthat the system state trajectories are forced toward the slidingsurface and stay on it. The system state trajectory in the periodof time before reaching the sliding surface is called the reachingphase. Once the system trajectory reaches the sliding surface, itstays on it and slides along it to the origin. The system trajectorysliding along the sliding surface to the origin is the sliding mode.Under certain conditions, the SMC is robust with respect tosystem perturbation and external disturbance [1], [2]. However,this control strategy produces some drawbacks associated withlarge control chattering that may wear coupled mechanismsand excite unstable system dynamics. Though introducing a

Manuscript received September 8, 2004; revised August 21, 2006. Abstractpublished on the Internet November 30, 2006. This work was supported inpart by the National Science Council of Taiwan, R.O.C., under Grant NSC95–2221-E-155–085.

The author is with the Department of Electrical Engineering, Yuan Ze Uni-versity, Chung Li 32026, Taiwan, R.O.C. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TIE.2006.888807

boundary layer may reduce the chatter amplitude [1], [2], thestability inside the boundary layer cannot be guaranteed andthe poor selection of boundary layer will result in degenerateor unstable tracking responses. On the other hand, an adaptivealgorithm for estimating the bound of lumped uncertainties pro-posed in [5] was designed to reduce the chattering phenomenaof the control effort. However, the accumulative implementa-tion of the adaptive algorithm always holds a positive value sothat the tracking error introduced by any uncertainty, such assensor error or accumulation of numerical error, will cause theestimated bound increase even to infinity with time. This resultsin the actuator eventually being saturated and the system may beunstable. The basic idea for removing the chattering is taking offthe sign function in the hitting control law of SMC.

In the past three decades, fuzzy systems have replaced con-ventional technologies in many applications, especially in con-trol systems. One major feature of fuzzy logic is its ability to ex-press the amount of ambiguity in human thinking. Thus, whenthe mathematical model of one process does not exist, or existsbut with uncertainties, fuzzy logic is an alternative way to dealwith the unknown process [6]. But, the huge amounts of fuzzyrules for a high-order system makes the analysis complex. Forexample, Liaw et al. [7] introduced a two-degree-of-freedomcontroller with fuzzy adaptation to reduce the effects of param-eter variations on the desired performance; however, the adoptedlinguistic rule base was too complex. Nowadays, much atten-tion has focused on the combination of fuzzy logic and SMC.The main advantages of the fuzzy control design based on SMCare that the fuzzy rules can be reduced, and the requirement ofuncertainty bound can be relaxed. Wong et al. [8], [9] com-bined a fuzzy controller with SMC and state feedback controlor proportional-integral control to remedy the chattering phe-nomenon and to achieve zero steady-state error. However, theparameters of membership functions cannot be adjusted to af-ford optimal control efforts under the occurrence of uncertain-ties. Ha [10], [11] adjusted the SMC action during the reachingphase using fuzzy logic for reducing chattering without sacri-ficing robust performance. Lin et al. [12] utilized an adaptivefuzzy SMC system for a permanent magnet synchronous motordrive. However, there still exists some chattering in the con-trol efforts because the sign function is included in the ultimatecontrol law [10]–[12]. On the other hand, incorporating SMCinto fuzzy neural network provides a possible solution to al-leviate the chattering phenomena. In [13] and [14], intelligentuncertainty observers were designed to estimate the bound oflumped uncertainty; however, these network structures and in-ference mechanism were too complex. The aim of this study isto overcome the mentioned problems and reserve favorable con-trol performance in the opening literature [6]–[14].

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WAI: FUZZY SLIDING-MODE CONTROL USING ADAPTIVE TUNING TECHNIQUE 587

As compared with a DC motor, an IM is robust, cheap, andeasily maintained. These characteristics make it desirable to em-ploy them in variable-speed or servo systems. However, in thescalar control techniques, the transient dipping of flux reducesthe torque sensitivity with slip and lengthens the response time.In order to overcome the foregoing limitation, the field-orientedcontrol technique has been widely used in industry for high-per-formance IM drives to achieve the favorable decoupling control[15]–[17]. However, the performance is sensitive to the varia-tions of motor parameters, especially, the rotor time-constantparameter that varies with the temperature and the saturation ofthe magnetizing inductance. Recently, much attention has beengiven to the possibility of identifying the changes in motor pa-rameters of an IM, while the drive is in normal operation. Someresearchers have proposed various IM drives with rotor-resis-tance or rotor time-constant identification to produce better con-trol performance [15]–[20]. With these control approaches, thedynamic behavior of the IM is rather similar to that of a sepa-rately excited DC motor. However, the control performance ofthe IM is still influenced by the uncertainties, such as mechan-ical parameter variation, external disturbance, unstructured un-certainty due to nonideal field orientation in transient state, andunmodeled dynamics, etc. In the control fields, the acquirementof the uncertainty information is an important research topic.From a practical point-of-view, however, it is usually very dif-ficult to get the complete information of uncertainties. There-fore, the motivation of this study is to design a suitable controlscheme to confront the uncertainties existed in practical appli-cations of an indirect field-oriented IM drive.

To accomplish the mentioned motivation, an AFSMC systemis designed for an indirect field-oriented IM drive to track peri-odic commands. In the conventional SMC system, the equiva-lent and hitting control efforts are afforded to ensure that theerror state trajectory reaches and stays on a sliding surface.However, the undesired chattering phenomenon may exist inpractice. In order to remedy this phenomenon, a fuzzy hittingcontrol law is embedded into the SMC system, and an adaptivealgorithm derived in the sense of the Lyapunov stability theoremis utilized to adjust the fuzzy parameter. This study is organizedas follows. Section II briefly describes an indirect field-orienta-tion method for an IM drive. In Section III, an AFSMC systemis designed for an indirect field-oriented IM drive to track peri-odic commands. The design procedures and qualitative analysisof the proposed AFSMC system are described in detail. Numer-ical simulation and experimental results are provided to validatethe effectiveness of the proposed control system in Section IV.Conclusions are drawn in Section V.

II. INDIRECT FIELD-ORIENTED INDUCTION MOTOR (IM) DRIVE

The dynamic model of a three-phase squirrel-cage Y-con-nected IM can be described in a synchronous rotating referenceframe as [15]–[17], as shown in (1) at the bottom of the page,where is the stator resistance per phase; is the rotor re-sistance per phase referred to stator; is the magnetizing in-ductance per phase; is the stator inductance per phase; isthe rotor inductance per phase referred to stator; is the syn-chronous angular velocity; is the rotor angular velocity;is the number of pole pairs; is the rotor time-con-stant; is the leakage coefficient;and are axis and axis stator currents; and areaxis and axis rotor fluxes; and are axis and axisstator voltages; and the superscript “ ” represents the values inthe synchronous rotating reference frame. Moreover, the elec-tromagnetic torque equation can be expressed in terms of statorcurrent and rotor flux linkage as

(2)

In an ideally decoupled IM, the rotor flux linkage axis isforced to align with the axis. It follows that:

(3)

Using (3), the desired rotor flux linkage in terms of can befound from the last row of (1) as

(4)

where is the Laplace operator. According to the third row of(1), the slip angular velocity can be estimatedusing shown in (4) and as follows:

(5)

In the steady-state, the desired rotor flux linkage shown in (4)can be represented as , in which is the fluxcurrent command. Moreover, the synchronous angular velocity

in the indirect field-oriented mechanism is generated byusing the measured rotor angular velocity and the fol-lowing estimated slip angular velocity:

(6)

(1)


where is the torque current command. With the implementa-tion of indirect field-oriented control [15]–[17], the electromag-netic torque can be simplified as

(7)

with the torque constant is defined as

(8)

According to the above derivation, the most important factorin the indirect field-oriented mechanism is the precision of theestimated slip angular velocity. Since the rotor time-constant

is sensitive to different operating conditions, a sliding-moderotor time-constant estimation in [20] is adopted in this study toguarantee a correct estimation of the slip angular velocity, andto preserve the decoupling control characteristic.

The IM used in this drive system is a three-phase Y-connectedfour-pole 800 W 60 Hz 130 V/5.6 A type. The detailed param-eters of the IM are

(9)

Moreover, the drive system is a ramp comparison current-con-trolled pulsewidth-modulation (PWM) voltage source inverter(VSI). The current-controlled VSI is implemented by insulatedgate bipolar transistor (IGBT) switching components with aswitching frequency of 15 kHz. For the speed and position con-trol systems, the braking machine is driven by a current sourcedrive to provide braking torque. An inertia varying mechanismis coupled to the rotor shaft of the IM. The mechanical equationof an IM drive system can be represented as [15]–[17]

(10)

where is the rotor position, is the moment of inertia,is the damping coefficient, and represents the external loaddisturbance. Substituting (7) into (10) as follows can representthe mechanical dynamic of the IM drive system:

(11)

where , , , andis the control effort. Dynamic modeling based on

measurements [21] is applied to find the drive model offline atthe nominal condition. The results are

(12)

The overbar symbol represents the system parameters in nom-inal conditions.

Fig. 1. Block diagram of the AFSMC system.

Consider the parameters in the nominal condition without ex-ternal load disturbance, rewriting (11) as follows can representthe nominal model of the IM drive system:

(13)

where and are the nominalvalues of and , respectively. Consider (13) with parametervariation, external load disturbance, and unpredicted uncertain-ties for the actual IM drive system

(14)

where and denote the uncertainties introduced bysystem parameters and ; represents the unstructureduncertainty due to nonideal field orientation in transient state,and the unmodeled dynamics in practical applications; iscalled the lumped uncertainty and is defined as

(15)

Here, the bound of the lumped uncertainty is assumed to begiven, that is

(16)

where is a given positive constant.

III. ADAPTIVE FUZZY SLIDING-MODE

CONTROL (AFSMC) SYSTEM

The derivation of the proposed AFSMC system for an indirectfield-oriented IM drive is discussed in this section. The controlaim is to design a suitable control law so that the rotor posi-tion can track desired position commands. The overall schemeof the AFSMC strategy is depicted in Fig. 1, in which a sim-plified indirect field-oriented IM drive is used to represent thereal controlled plant described in Section II. In the conventional


SMC design, a sliding surface is chosen in the state-spaceby the following scalar equation:

(17)

where is a positive constant, and anddenote the tracking position and speed

errors, in which and are the rotor position and speedcommands. Take the derivative of sliding surface with respect totime and use (14), then

(18)

The control effort being derived as the solution ofwithout considering lumped uncertainty is toachieve the desired performance under nominal model, and itis referred to as equivalent control effort [1], [2], representedby

(19)

However, if unpredictable perturbations from the parametervariations or external load disturbance occur, the equivalentcontrol effort cannot ensure the favorable control performance.Thus, auxiliary control effort should be designed to eliminatethe effect of the unpredictable perturbations. The auxiliarycontrol effort is referred to as hitting control effort representedby . In conventional SMC, is given as follows:

(20)

where is a hitting control gain concerned with the upperbound of uncertainties, and is a sign function. Totally, theSMC law can be represented as . Thedetailed proof of this SMC law is similar to [1] and [2] and isomitted here. However, the upper bound of uncertainties, whichis required in the conventional SMC system, is difficult to ob-tain precisely in advance for practical applications. If the boundis selected too large, the sign function of the hitting control lawwill result in serious chattering phenomena in the control efforts.The undesired chattering control efforts will wear the bearingmechanism and might excite unstable system dynamics. On theother hand, if the bound is selected too small, the stability con-ditions may not be satisfied. It will cause the controlled systemto be unstable. For this reason, a boundary layer is generally in-troduced into the SMC law to reduce the chatter amplitude, i.e.,replacing the term by in (20), thenthe hitting control law can be rewritten as

(21)

where is the width of the boundary layer. Unfortunately, thestability inside the boundary layer cannot be ensured and the in-adequate selection of the boundary layer may result in unstabletracking responses. Therefore, an AFSMC system, in which afuzzy logic inference mechanism is used to mimic the hittingcontrol law, is introduced in the following paragraph.

Fig. 2. Membership functions. (a) Input fuzzy sets for S. (b) Output fuzzy setsfor U .

Let the sliding surface be the input linguistic variable of thefuzzy logic, and the fuzzy hitting control law be the outputlinguistic variable, the associated fuzzy sets for and areexpressed as follows:

• for [in antecedent proposition]: P (positive), N (nega-tive), Z (zero);

• for [in consequent proposition]: PE (positive effort),NE (negative effort), ZE (zero Effort).

According to the spirit of the hitting control law shown in(20), the fuzzy linguistic rule base involved in the AFSMCsystem can be summarized as follows.

Rule 1: If is P, then is PE.Rule 2: If is Z, then is ZE.Rule 3: If is N, then is NE.

The membership functions of input and output fuzzy sets aredepicted in Fig. 2(a) and (b), respectively. In this study, the sin-gleton fuzzification with triangular membership functions andcenter-of-gravity defuzzification method are adopted, as theyare computationally simple, intuitively plausible, and most fre-quently used in the opening literatures. Then, a fuzzy hittingcontrol law can be estimated by fuzzy logic inference mecha-nism as follows:

(22)

where , , and arethe firing strengths of rules 1, 2, and 3, respectively; ,

and are the center of the membershipfunctions PE, ZE, and NE, respectively; is a fuzzy parameter tobe tuned by an adaptive algorithm introduced later; the relation

is valid according to the special case oftriangular membership functions. Moreover, the fuzzy hittingcontrol effort can be further analyzed as the followingfour conditions, and only one of four conditions will occur forany value of according to Fig. 2(a).

Condition 1: Only rule 1 is triggered.

(23)

Condition 2: Rules 1 and 2 are triggered simultaneously.

(24)


Condition 3: Rules 2 and 3 are triggered simultaneously.

(25)

Condition 4: Only rule 3 is triggered.

(26)

According to four possible conditions shown in (23)–(26), it cansee that . Totally, theAFSMC law can be represented as

(27)

Define a Lyapunov candidate function as

(28)

Take the derivative of the Lyapunov function with respect totime, and using (18) and (27), one can obtain

(29)

If the following inequality:

(30)

holds, then the sliding condition can besatisfied [1], [2]. According to (30), there exists an optimal value

as follows to achieve minimum control efforts and match thesliding condition:

(31)

where is a small positive constant. Owing to the unknownlumped uncertainties, the optimal value cannot be exactlyobtained in advance for practical applications. Thus, a simpleadaptive algorithm is utilized in this study to estimate the op-timal value of , and its estimated error is defined as

(32)

where is the estimated value of the optimal value of . Insummary, the modified AFSMC law can be rewritten via (27) as

(33)

Choose a Lyapunov candidate as

(34)

where is a positive constant. Take the derivative of ,with respect to time, and using (18) and (33), one can

obtain

(35)

If the adaptation law is designed as

(36)

then (35) can be represented via (31) as

(37)

According to the inequality , onecan obtain that . Since

, is negative semidefinite, that is,, which implies and are

bounded. Let function, and integrate function with respect to time

(38)

Because is bounded, and is non-increasing and bounded, the following result is obtained:

(39)

Also, is a positive function and is bounded forall time, so by Barbalat’s Lemma [1], [2], it can be shown that

according to (39). That is, as. Taking a summary, the proposed AFSMC system is

presented in (33), where the equivalent control law is givenin (19) and the fuzzy hitting control law is given in (22) withthe fuzzy parameter adjusted by (36). As a result, the AFSMCsystem is stable even when the uncertainties occur. Moreover,the tracking error will converge to zero according to


Fig. 3. DSP-based computer control system.

. The effectiveness of the proposed AFSMC system can beverified by the following numerical simulation and experimentalresults.

IV. NUMERICAL SIMULATION AND EXPERIMENTAL RESULTS

A block diagram of the DSP-based computer control systemfor an indirect field-oriented IM drive system using the cur-rent-controlled technique is depicted in Fig. 3. The current-con-trolled PWM VSI is implemented by an IPM switching compo-nent (PM50RSA060) manufactured by the Mitsubishi Companywith a switching frequency of 15 kHz. A servo control card is in-stalled in the control computer, which includes multichannels ofD/A and encoder interface circuits. Digital filter and frequencymultiplied by four circuits are built into the encoder interfacecircuit to increase the precision of position feedback. The pro-posed AFSMC system is realized in a Pentium CPU, moreover,the sliding-mode rotor time-constant estimation system is real-ized in a TMS320C31 DSP [22]. Three-phase voltages and cur-rents are sampled by the A/D converters connected to the DSP toprovide input signals for the estimation system. The control in-terval of the sliding-mode rotor time-constant estimation systemis set at 0.2 ms, and the control interval of the position controlloop is set at 1 ms.

The simulation and experimentation of the proposed controlsystems are carried out using the “Matlab” package and “TurboC” language, respectively, and the control parameters are givenas

(40)All the parameters in the proposed control systems are chosen toachieve the superior transient control performance in both simu-lation and experimentation considering the limitation of control

effort and the requirement of stability. Two simulation cases in-cluding parameter variations and time-varying external load dis-turbance in the shaft due to periodic sinusoidal commands areaddressed as follows:

(41)

(42)

In the simulation, first, the conventional SMC system in (19)and (20) is considered for comparison. The simulated results ofthe SMC system due to periodic sinusoidal commands at Cases1 and 2 are depicted in Fig. 4. The robust tracking performancesshown in Fig. 4(a) and (e) are obvious under the occurrence ofparameter variations and external load disturbance. However,the chattering control efforts shown in Fig. 4(b) and (f) are se-rious due to the inappropriate selection of a large control gain

. Note that the individual control efforts including equiva-lent and hitting control laws at Cases 1 and 2 are depicted inFig. 4(c), (d), (g), and (h). It is obvious that the chattering phe-nomena are caused mainly by the hitting control law, as shownin Fig. 4(d) and (h). Moreover, the conventional SMC systemwith a boundary layer, as shown in (21), is applied to controlthe rotor position of the IM drive. The simulated results of theSMC system with a boundary layer for periodic si-nusoidal commands at Cases 1 and 2 are depicted in Fig. 5. Thetracking responses are depicted in Fig. 5(a) and (e), and the as-sociated control efforts are depicted in Fig. 5(b)–(d) and (f)–(h).From the simulated results, there are no chattering phenomenain the control efforts, but degenerate tracking performances areresults owing to the parameter variations and external load dis-turbance. Though narrow width of boundary layer may solve theproblem of delay or degenerate tracking responses, it will resultin impractical chattering control efforts. Therefore, the width


Fig. 4. Simulated results of the SMC system. (a) Tracking response at Case 1.(b)–(d) Control efforts at Case 1. (e) Tracking response at Case 2. (f)–(h) Controlefforts at Case 2.

of the boundary layer is ordinarily chosen as a compromise be-tween the chattering phenomena and tracking performance. Inaddition, the simulated results of the proposed AFSMC systemdue to periodic sinusoidal commands at Cases 1 and 2 are givenin Fig. 6 for comparison. The tracking responses are depictedin Fig. 6(a) and (e), and the associated control efforts are de-picted in Fig. 6(b)–(d) and (f)–(h). From the simulation results,not only are there no chattering phenomena in the control ef-forts but also favorable tracking response can be obtained underthe occurrence of uncertainties. Compare Fig. 6 with Figs. 4and 5, the AFSMC system yields superior control performancethan the conventional SMC system and the SMC system with aboundary layer.

Some experimental results are provided to further demon-strate the effectiveness of the proposed control systems. Twotest conditions are given to verify the system robustness. Oneis the external disturbance condition, that is the nominal inertiawith braking-load disturbance oc-curring at 4 s, and the other is the perturbation condition, that is

Fig. 5. Simulated results of an SMC system with a boundary layer. (a) Trackingresponse at Case 1. (b)–(d) Control efforts at Case 1. (e) Tracking response atCase 2. (f)–(h) Control efforts at Case 2.

the increasing of the rotor inertia to approximately two times thenominal value with braking-load dis-turbance occurring at 4 s. The experimental results of the SMCsystem due to periodic sinusoidal commands at two test condi-tions are depicted in Fig. 7. From the experimental results, therobust tracking performances shown in Fig. 7(a) and (c) are ob-vious under the occurrence of parameter variations and externalload disturbance. However, the chattering phenomena shown inFig. 7(b) and (d) are serious due to the inappropriate selectionof a large control gain . The undesired chattering control ef-forts will wear the bearing mechanism and might excite unstablesystem dynamics. Moreover, the SMC system with a boundarylayer is implemented to control the rotor position ofthe IM drive for attempting to attenuate the control chattering.The tracking responses at two test conditions are depicted inFig. 8(a) and (c), and the associated control efforts are shownin Fig. 8(b) and (d). Though there are no chattering phenomenain the control efforts, degenerate-tracking performances shownin Fig. 8(a) and (c) are results due to the wide width of the


Fig. 6. Simulated results of the AFSMC system. (a) Tracking response atCase 1. (b)–(d) Control efforts at Case 1. (e) Tracking response at Case 2.(f)–(h) Control efforts at Case 2.

Fig. 7. Experimental results of the SMC system. (a) Tracking response at theexternal disturbance condition. (b) Control effort at the external disturbance con-dition. (c) Tracking response at the perturbation condition. (d) Control effort atthe perturbation condition.

Fig. 8. Experimental results of the SMC system with a boundary layer. (a)Tracking response at the external disturbance condition. (b) Control effort at theexternal disturbance condition. (c) Tracking response at the perturbation condi-tion. (d) Control effort at the perturbation condition.

Fig. 9. Experimental results of the AFSMC system. (a) Tracking response atthe external disturbance condition. (b) Control effort at the external disturbancecondition. (c) Tracking response at the perturbation condition. (d) Control effortat the perturbation condition.

boundary layer. Therefore, the width of the boundary layer isdifficult to determine due to the unknown uncertainties in prac-tical applications, and is ordinarily chosen as a compromisebetween the chattering phenomena and tracking performance.In addition, the tracking responses and control efforts with theAFSMC system due to periodic sinusoidal commands at two testconditions are depicted in Fig. 9. The tracking responses are de-picted in Fig. 9(a) and (c), and the associated control efforts areshown in Fig. 9(b) and (d). From the experimental results, robustcontrol performance can be obtained, and the chattering phe-nomena are removed in the control efforts according to the on-line adjustment of the hitting control law via fuzzy tuning tech-nique. Compare Fig. 9 with Figs. 7 and 8, the AFSMC systemtranscends the conventional SMC system and the SMC systemwith a boundary layer to control the rotor position of the indirectfield-oriented IM drive.


V. CONCLUSION

This study has successfully demonstrated the application ofthe proposed AFSMC system to an indirect field-oriented IMdrive for tracking periodic commands. Compared with the con-ventional SMC system and the SMC system with a boundarylayer, the AFSMC system results in robust control performancewithout chattering control efforts. In general, the mechanicalequation of an electrical servo drive (e.g., direct-current motordrive, IM drive, or permanent magnet synchronous motor drive)can be represented as (10). With suitable impressed current orfield orientation control [15]–[17], the electromagnetic torquecan also be simplified as (11). Thus, the proposed AFSMCsystem can be utilized widely for the position control of anyelectrical servo drives.

The major contributions of this study are: 1) the successfuldevelopment of a fuzzy SMC system, in which a fuzzy hittingcontrol law is embedded into the conventional SMC system toremove the control chattering; 2) the successful developmentof an AFSMC system, in which an adaptive algorithm is uti-lized to adjust the fuzzy parameter to confront the system un-certainties online; 3) the successful application of the proposedAFSMC system to control an indirect field-oriented IM driveconsidering the possible occurrence of uncertainties; and 4) thecontrol methodologies designed in this study can be easily ex-tended to other electric drives.

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Rong-Jong Wai (M’99–A’00–SM’05) was born inTainan, Taiwan, R.O.C., in 1974. He received the B.S.degree in electrical engineering and the Ph.D. degreein electronic engineering from Chung Yuan ChristianUniversity, Chung Li, Taiwan, R.O.C., in 1996 and1999, respectively.

Since 1999, he has been with the Department ofElectrical Engineering, Yuan Ze University, ChungLi, where he is currently a Professor. He is also theDirector of the Electric Control and System Engi-neering Laboratory, Yuan Ze University, and the En-

ergy Conversion and Power Conditioning Laboratory at the Fuel Cell Center.He is a chapter-author of Intelligent Adaptive Control: Industrial Applicationsin the Applied Computational Intelligence Set (Boca Raton, FL: CRC, 1998)and the coauthor of Drive and Intelligent Control of Ultrasonic Motor (Tai-chung, Taiwan, R.O.C.: Tsang-Hai, 1999), Electric Control (Tai-chung, Taiwan,R.O.C.: Tsang-Hai, 2002), and Fuel Cell: New Generation Energy (Tai-Chung,Taiwan, R.O.C.: Tsang-Hai, 2004). He has authored numerous published journalpapers in the area of control system applications. His research interests includepower electronics, motor servo drives, mechatronics, energy technology, andcontrol theory applications.

Dr. Wai received the Excellent Research Award in 2000, and the Wu Ta-YouMedal and Young Researcher Award in 2003 from the National Science Council,R.O.C. In addition, he was the recipient of the Outstanding Research Award in2003 from the Yuan Ze University, R.O.C.; the Excellent Young Electrical Engi-neering Award in 2004 from the Chinese Electrical Engineering Society, R.O.C.;the Outstanding Professor Award in 2004 from the Far Eastern Y. Z. Hsu-Sci-ence and Technology Memorial Foundation, R.O.C.; the International Profes-sional of the Year Award in 2005 from the International Biographical Centre,U.K., and the Young Automatic Control Engineering Award in 2005 from theChinese Automatic Control Society, R.O.C. He was listed in Who’s Who in Sci-ence and Engineering (Marquis Who’s Who) in 2004–2007, Who’s Who (Mar-quis Who’s Who) in 2004–2007, and Leading Scientists of the World (Interna-tional Biographical Center) in 2005, Who’s Who in Asia (Marquis Who’s Who)in 2006–2007, and Who’s Who of Emerging Leaders (Marquis Who’s Who) in2006–2007.

Documents

Fuzzy Sliding-Mode Control Using Adaptive Tuning Technique