Fuzzy-Logic-Based Vector Control Scheme for ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007

Fuzzy-Logic-Based Vector Control Scheme for Permanent-Magnet Synchronous Motors in Elevator Drive Applications Jae-Sung Yu, Student Member, IEEE, Sang-Hoon Kim, Member, IEEE, Byoung-Kuk Lee, Senior Member, IEEE, Chung-Yuen Won, Senior Member, IEEE, and Jin Hur, Senior Member, IEEE

Abstract—In elevator drive systems, the gains of a conventional proportional–integral (PI) speed controller cannot usually be set large enough because of its mechanical resonance. Consequently, the speed control performance deteriorates. In our work described in this paper, a fuzzy logic controller (FLC) was adopted for use in elevator drive systems in order to improve the speed control performance. The proposed FLC was compared with a conventional PI controller with respect to speed dynamic responses and load torque. Simulation and experimental results demonstrated that the proposed FLC was superior over the conventional PI. This FLC can be a good solution for high-performance elevator drive systems. Index Terms—Elevator drive system, fuzzy logic controller (FLC), proportional–integral (PI).

I. I NTRODUCTION

T

HE ADVENT of modern high-rise buildings has created the need for high-speed lift systems in order to provide quick access within these buildings [1]. The induction motor has been used for conventional elevator drives. However, induction motors suffer from limitations in terms of compactness and torque. This is because the power factor and efficiency decrease as the number of poles is increased. For these reasons, the permanent-magnet synchronous motor (PMSM) with a vector control algorithm is preferred in gearless elevators because it is smaller and more compact than the induction motor [2]. In the situation with elevators in tall buildings, the important factor is to translate an elevator ride into a more comfortable ride for the passengers. The comfortable ride is facilitated by following the speed profile of the drive motors. However, although the speed profile of drive motors is made in order to help facilitate a comfortable ride for passengers, if the performance of the speed controller involves degradation, then the comfortable ride for passengers can also be degraded. Manuscript received June 30, 2006; revised February 9, 2007. J.-S. Yu, B.-K. Lee, and C.-Y. Won are with the Energy Mechatronics Laboratory, School of Information and Communication Engineering, Sungkyunkwan University, Suwon 440-746, Korea (e-mail: bkleeskku@ skku.edu). S.-H. Kim is with the Department of Electrical and Electronics Engineering, Kangwon National University, Chuncheon 200-701, Korea (e-mail: [email protected]). J. Hur is with the Intelligent Mechatronics Research Center, Korea Electronics Technology Institute, Puchon 442-010, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2007.894692

In vector-controlled PMSM drive systems, the proportional– integral (PI) controller is widely used for speed control due to its simple implementation. However, the gains of the PI controller have to be adequately tuned so that, in normal drive systems, the controller can be used to establish high bandwidth for good speed characteristics. However, in the case of elevator drive systems, the bandwidth of the speed controller is usually limited to be below 1.0 Hz in order to prevent the system from entering into an excitation resonance frequency. For this reason, the speed controller has a low gain and the speed characteristics. The riding quality of the elevator can deteriorate [3]. Moreover, the design of a PI control system is normally based on the mathematical model of a plant. However, even if the plant model is well-known, building an accurate mathematical model is a very difficult job because of the parameter variation problems. Several methods, including adding an accelerated velocity feedback loop to the speed controller, have been proposed to solve these problems [3], [4], [10], [15]. However, all the proposed methods have drawbacks such as the requirements of having parameter information and the complexity of controller design. Compared with other speed controllers, a fuzzy logic controller (FLC) is basically a nonlinear and an adaptive controller. The fuzzy controller for speed control has time-varying gains according to system responses invoked by its several control rules. Therefore, the fuzzy speed controller can overcome the defects of a conventional PI controller. Moreover, the FLC system, in essence, is based on the experience and intuition of a human plant operator. Therefore, for a linear or a nonlinear plant with severe parameter variations, a robust control system can be designed and implemented [5]. In this paper, we propose a vector control scheme based on fuzzy logic control and PMSMs for elevator applications. In order to construct the fuzzy controller, offering a comfortable ride to passengers, control rules and membership functions have to be designed following the inherent character of systems. Control rules are designed following the inherent character of systems as described in Section II-B, and because membership functions have the inherent values per system as described in Section II-C. Membership functions are effectively designed following the inherent character of systems. The complete vector control scheme for the elevator drive system incorporating the FLC has been implemented in real time using the TMS320VC33-120 DSP.

0278-0046/$25.00 © 2007 IEEE

YU et al.: FUZZY-LOGIC-BASED VECTOR CONTROL SCHEME FOR PMSMs IN ELEVATOR DRIVE APPLICATIONS

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the FLC, processing the speed error and the rate of change of the speed error. Fig. 2 shows the control block diagram of the vector-controlled PMSM drive system using the FLC for speed control. B. Design of the FLC for the PMSM in Elevator Drive Applications Fig. 3 shows the block diagram of the FLC for the PMSM. The design of the fuzzy controller in elevator drive applications is as constructed as follows.

Fig. 1.

1) Determine the input and output variables. 2) Design control rules and membership functions following the inherent character of the systems. 3) Specify possible inference with control rules and membership functions. 4) Translate the fuzzy set into a crisp set after defuzzing the fuzzy set.

Space vector diagram of the PMSM.

II. C ONTROL A LGORITHM OF THE PMSM A. Mathematical Model of the PMSM Fig. 1 shows the general equivalent space vector diagram for the PMSM. Equation (1) expresses the voltage equations of the PMSM machine in the rotor reference frame as follows: r r vds Rs + pLds ids 0 −ωr Lqs = + (1) r ωr λf vqs ωr Lds Rs + pLqs irqs where p differential operator; r r , vqs d-, q-axes stator voltages in the rotor frame; vds d-, q-axes currents in the rotor frame; irds , irqs rotor flux linkage; λf Lds , Lqs d-, q-axes stator inductances; synchronous angular velocity. ωr Because the d- and q-axes stator inductances of the surfacemounted (SM) PMSM are equal, we can define Lds = Ls and Lqs = Ls . Equation (2) expresses the torque equations of the PMSM machine in the rotor reference frame [7], [12]–[14] as follows: 3P r λf iqs + (Lds − Lqs )irds irqs Te = 22

(2)

where Te is the electromagnetic developed torque, and P is the number of poles. In this paper, because of using SMPMSM, the d- and q-axis stator inductances (Lds , Lqs ) are equal. Therefore, the rewritten torque equation is Te =

3P λf irqs . 22

This equation reveals that the d-axis current in the rotor frame is no longer needed. Hence, we arrange in the current controller that the reference current of the d-axis is zero. Since the PMSM uses the excitation field induced by the permanent magnet on the rotor, λf is a constant value. Therefore, the torque of the PMSM can be directly controlled by adjusting the torque-producing current irqs . In our research described in this paper, irqs is generated by appropriate control rules in

If we would like to apply the designed fuzzy controller to elevator drive applications, first, we design the input, output gain, and membership functions to be able to provide a comfortable ride for passengers. Here, to achieve a comfortable ride for the passengers requires that the control rules and membership functions be designed to be able to follow the speed profile of the elevator systems without speed errors. The FLC is divided into four modules, namely: 1) the fuzzifier; 2) the knowledge base; 3) the fuzzy inference engine; and 4) the defuzzifier. 1) Input and Output Variables: To compose the FLC for the PMSM, first, the input and output variables of the FLC have to be determined. In this paper, the speed error and the rate of change of the speed error are considered as input crisp variables and are defined as follows [8]: ∆ωr (n) = ωr∗ (n) − ωr (n) ∆e(n) = ∆ωr (n) − ∆ωr (n − 1).

(3) (4)

The output of the FLC is the torque-producing current and is defined as irqs (n) = irqs (n − 1) + η · ∆irqs (n)

(5)

where ∆irqs (n) is the change in the torque-producing current inferred by the FLC at the nth sampling time, and η is the gain factor of the FLC. 2) Membership Functions: In the FLC, the input and output variables are expressed by linguistic variables. These variables are represented by a membership function. These linguistic variables are defined as fuzzy subsets. In our work, seven fuzzy subsets were chosen for the input and output variables: 1) negative big (NB); 2) negative medium (NM); 3) negative small (NS); 4) zero (ZE); 5) positive small (PS); 6) positive medium (PM); and 7) positive big (PB). A triangular-type membership function was adopted. Fig. 4 shows the membership

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Fig. 2. Control block diagram of PMSM using FLC.

Fig. 3. Block diagram of the FLC. Fig. 5.

Operation of triangular-type membership function. TABLE II FUZZY-RULE-BASED MATRIX

Fig. 4. Membership functions of the triangular type. TABLE I MATHEMATICAL CHARACTERIZATION OF TRIANGULAR MEMBERSHIP FUNCTIONS

functions that were adopted and whose mathematical expressions are shown in Table I [9]. Fig. 5 shows the operation of the triangular-type membership function where cL , cR is the “saturation point” and wL , wR is the slope of the nonunity and nonzero part of µL , µR , respectively. c is the center of the triangle, and w is the base width.


Fig. 6.

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Inference mechanism of the FLC. (a) G1 = 30. (b) G2 = 20. (c) G3 = 20. TABLE III MOTOR PARAMETERS

Fig. 7. Membership functions for the PMSM. (a) Input membership function: acceleration profile for the elevator drive. (b) Input membership function: speed reference for the elevator drive. (c) Output singleton membership function.

3) Derivation of the Control Rules: The control rules are derived from the experience or knowledge of experts. The fuzzy rules are defined as follows: Ri : IF ∆ωr (n) is Ai and ∆e(n) is Bi , THEN ∆irqs (n) is Ci

where Ai and Bi is the fuzzy subset, and Ci is a fuzzy singleton. Control rules contributing to a comfortable ride for passengers are described as follows. 1) When the speed of the PMSM is far from the reference value, the change in the torque-producing current must be large so as to bring the speed to the reference value. 2) When the speed of the PMSM approaches the reference value, a small change of the torque-producing current is required. 3) When the speed of the PMSM is near the reference value and is approaching the reference value rapidly, the torque-producing current must be kept constant in order to prevent it from overshooting the mark. 4) When the speed of the PMSM reaches the reference value and the speed is still changing, the torque-producing current is required to be changed slightly in order to prevent the output from moving away. 5) When the speed of the PMSM reaches the reference value and the speed is in a steady state, the torque-producing current remains unchanged.

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Fig. 8. Reference waveforms for the elevator drive. (a) Speed tracking response using a PI controller with a 1-Hz bandwidth under no load. (b) Speed tracking response using a fuzzy controller under no load.

6) When the speed of the PMSM is above the reference value, the sign of the change of the torque-producing current must be negative. According to the above criteria, we derived the rule table shown in Table II. The input linguistic variables are converted to output singleton variables through the fuzzy inference engine and the rule base. The inference mechanism is shown in Fig. 6. The inference result of each rule consists of two parts: a weighting factor and the degree of the torque-producing current Ci . For example, if ∆ωr (n) is 35 rad/s and ∆e(n) is 12 rad/s2 , then ∆ωr (n) belongs to PS, PM, and ∆e(n) belongs to ZE, PS. Therefore, the following four rules are possible. 1) IF ∆ωr (n) is PS and ∆e(n) is ZE, THEN ∆irqs (n) is 20 A. 2) IF ∆ωr (n) is PS and ∆e(n) is PS, THEN ∆irqs (n) is 40 A.

3) IF ∆ωr (n) is PM and ∆e(n) is ZE, THEN ∆irqs (n) is 40 A. 4) IF ∆ωr (n) is PM and ∆e(n) is PS, THEN ∆irqs (n) is 60 A. The weighting factor is obtained by means of the min operation, which is given by ωi = min {µe (∆ωr ), µce (∆e)} .

(6)

Finally, the inference results are obtained by means of the following equation: zi = ωi Ci .

(7)

4) Defuzziﬁcation: The inferred results should be converted to the crisp set. In our work described in this paper, the center


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Fig. 9. Speed tracking responses under no load. (a) Speed tracking response using a PI controller with a 1-Hz bandwidth under a 50% rated load. (b) Speed tracking response using a fuzzy controller under a 50% rated load.

of gravity defuzzification method is used. The output function is given as [11] 4

∆irqs (n)

=

ωi Ci

i=1 4

.

(8)

ωi

i=1

According to (8), we have ∆irqs =

20 × 0.4 + 40 × 0.6 + 40 × 0.166 + 60 × 0.166 0.4 + 0.6 + 0.166 + 0.166

= 36.486 A. The change in the torque-producing current at this sampling ∗ ∗ time is irqs (n) = irqs (n − 1) + η · ∆irqs (n).

C. Effects of G1 , G2 , G3 , and η G1 and G2 are the scaling factors of the input, and G3 is the scaling factor of the output. The membership functions are changed by the scaling factors [9]. Here are some examples. 1) If G1 = 1, then there is no effect on the membership function. 2) If G2 < 1, then the membership functions are uniformly “contracted” by a factor of G1 , and this changes the meaning of the linguistic so that, for example, “PB” is now characterized by a membership function that represents smaller number. 3) If G1 > 1, then the membership functions are uniformly “spread out,” and this changes the meaning of the linguistic. For example, “PB” is now characterized by the membership function that represents larger numbers.

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Fig. 10. Speed tracking responses under a half-rated-load condition. (a) Speed tracking response using a PI controller with a 1-Hz bandwidth under an inertia variation. (b) Speed tracking response using a fuzzy controller under the moment of inertia variation.

η is chosen to obtain the rated current for the rated condition. η is the maximum change of the torque-producing current. If η is set large, the rise time is decreased, and ringing is encouraged. However, if η is set small, the rise time is increased, and ringing is discouraged. In this paper, G1 = 30, G2 = 20, G3 = 20, and η = 0.9. Fig. 7 shows the membership functions scaled by the scaling factors.

III. S IMULATION AND E XPERIMENTAL R ESULTS A. Simulation Results Simulation and experiments were executed to compare the performance of the FLC with the PI controller. Table III shows the parameters of the PMSM used in both simulation and experiments. The whole controller was constructed according to the block diagram shown in Fig. 1. The PMSM dynamics were calculated every 2 µs. A current control was carried out every 100 µs, and a speed control

loop was activated every 1.0 ms. In both simulations and experiments, the FLC gain was set to be G1 = 30, G2 = 20, G3 = 20, and η = 0.9. For comparison, the bandwidth of the PI speed controller was set at 1.0 Hz, which was selected for the limiting condition to prevent system resonances. A simulation was executed to obtain the speed response characteristics for the no-load condition, load condition, and variation condition of the system inertia J. For the load condition, half of the rated torque was applied to the motor, assuming, in this case, that passengers consisted of about five persons (equivalent to 296 kg, assuming that the mass of a person is 60 kg). The variation of the moment of inertia J was varied by 5.92 kg · m2 . Fig. 8 shows the acceleration profile and the speed reference. A trapezoidal velocity reference based on the acceleration profile of real elevator systems was applied. The simulation results of Figs. 9 and 10 show speed responses for the no-load and half-rated-load conditions, respectively. The speed controller using the PI control demonstrated a


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Fig. 11. Speed tracking responses under the moment of inertia variation. (a) MG set with inertia load equipment. (b) System hardware configuration.

damped response with a high overshoot during transient due to off-tuned gain constants and a small bandwidth. However, the speed controller using the FLC correctly followed its reference for both load conditions. In the PI controller, if the bandwidth of the PI controller was high, then the gains of the PI controller became large; therefore, performance was improved. However, because of the elevator system resonances, the bandwidth of the speed controller cannot generally increase over 1.0 Hz. Fig. 11 shows the acceleration and deceleration with a 296-kg load (equivalent to five persons). The moment of inertia with respect to this mass was calculated as JADD (5.92 kg · m2 ) and is shown in Table IV by J=

1 2 mr 2

where m is the mass, and r is the radius.

(9)

TABLE IV MOMENT OF INERTIA OF THE SYSTEM

In the case of the above conditions, the gains of the PI controller have to be varied along with the moment of inertia variation; however, because the speed controller using the PI controller is a linear controller, the gain of PI controller cannot be varied. In addition to these problems, the PI controller must also add a positive acceleration feedback loop. However, the FLC is basically a nonlinear and adaptive controller. It is

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Fig. 12. MG set and system hardware configuration. (a) Speed tracking response using a PI controller with a 1-Hz bandwidth under no load. (b) Speed tracking response using a fuzzy controller under no load.

generally used to provide robust performance for the control of a linear or nonlinear plant with variable parameters. It does not need an additional controller such as a positive acceleration feedback loop. B. Experimental Results The simulated results were confirmed by experimental results. Experiments were performed on a motor–generator set with a 13.3-kW PMSM and a 16.8-kW dc generator. Fig. 12 shows the MG set and system hardware configuration used for the experiments. The PMSM (WSG-06.3), which was made by Witture, Germany, was used for the experiments, along with an absolute encoder made by Heidenhain. The encoder was a serial synchronous interface (SSI) type with a resolution of 13 bits (8192 pulses). A dc generator was used to apply the load torque to the PMSM, which was driven in the torque mode, at an arbitrary time or at the start of the PMSM. In order to measure torque, (2) was used as a torque estimator. The digital/analog channels were used to capture the necessary output signals in a digital storage oscilloscope. The complete PMSM drive was implemented through software using a

program developed in the high-level ANSI “C” programming language. The pulsewidth modulation frequency was 5.0 kHz, and the dead time was 3.0 µs. A current control was carried out every 100.0 µs. The speed control loop was activated every 1.0 ms. The complete algorithms for vector control were implemented using a TMS320VC33-150 floating-point DSP. The experimental results shown in Figs. 13–15 are comparable with the simulation results shown in Figs. 9–11. The speed command was identical to that in Fig. 8. Experimental results shown in Figs. 13(a) and 14(a) demonstrated that the speed controller using the PI controller did not adequately follow its reference in the no-load and the half-rated-load conditions. However, the speeds in the proposed speed controller using the FLC tracked the speed reference very well, as shown in Figs. 13(b) and 14(b). These experimental results were the same as the simulation results. Fig. 15 shows the experimental results in case of inertia variation. The moment of inertia of the system is shown in Table IV. Originally, the moment of inertia was JPM + Jdc (7.4 kg · m2 ). To obtain the speed response for the moment of inertia variation, the whole moment of inertia of system was


Fig. 13. Speed tracking responses under no load. (a) Speed tracking response using a PI controller with a 1-Hz bandwidth under a 50% rated load. (b) Speed tracking response using a fuzzy controller under a 50% rated load.

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Fig. 15. Speed tracking responses under the moment of inertia variation.

The experimental result for the PI speed controller illustrated in Fig. 15(a) showed significant speed error in the overall range because of the off-tuned gain constants, whereas as shown in Fig. 15(b), the FLC speed controller exhibited high performance in tracking the speed reference. In order to have high performance, the PI controller needed to have the additional means of adding a positive acceleration feedback loop. However, because the gains of the fuzzy controller did not require the basic parameters of system and the FLC essentially embedded the experience and intuition of a human plant operator, it did not require an additional controller. IV. C ONCLUSION The PI controller is widely used as the speed controller in many variable-speed drive applications. However, in the case where the bandwidth of the speed controller is limited, because of system characteristics such as the system resonance in elevators, the performance of the speed control deteriorates. Therefore, in our work described in this paper, we proposed a high-performance vector-controlled PMSM elevator drive system, which used the FLC for speed control. The performance of the FLC was verified through simulation and experiment. It has proven to be superior to the conventional PI controller in terms of speed responses. Fig. 14. Speed tracking responses under a half-rated-load condition. (a) Speed tracking response using a PI controller with a 1-Hz bandwidth under an inertia variation. (b) Speed tracking response using a fuzzy controller under the moment of inertia variation.

increased JTOTAL (13.32 kg · m2 ). Therefore, it resulted in a variation of 5.92 kg · m2 . In this case, the increased mass was 296 kg (equivalent to five persons).

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Jae-Sung Yu (S’04) was born in Korea in 1975. He received the M.S. degree in energy system engineering from Sungkyunkwan University, Suwon, Korea, in 2004. He is currently working toward the Ph.D. degree in the Department of Mechatronics Engineering of the same university. His research interests include high-performance electric machine drives and power electronics.

Sang-Hoon Kim (S’92–M’95) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1987, 1989, and 1994, respectively. From 1994 to 1996, he was with Daewoo Heavy Industries Ltd., Inchon, Korea, where he was involved in the development of propulsion systems for rolling stock. Since 1997, he has been with the Department of Electrical and Electronics Engineering, Kangwon National University, Chuncheon, Korea. His research interests include high-performance electric machine drives and power electronics.

Byoung-Kuk Lee (S’95–M’01–SM’04) received the B.S. and the M.S. degrees from Hanyang University, Seoul, Korea, in 1994 and 1996, respectively, and the Ph.D. degree from Texas A&M University, College Station, in 2001, all in electrical engineering. During 2002, he was a Postdoctoral Research Associate at the Power Electronics and Motor Drives Laboratory and Advanced Vehicle Systems Research Program, Texas A&M University. From 2003 to 2005, he was a Senior Researcher with the Power Electronics Group, Korea Electrotechnology Research Institute, Changwon, Korea, where he worked on fuel cell generation systems. Since 2006, he has been with the School of Information and Communication Engineering, Sungkyunkwan University, Suwon, Korea, as an Assistant Professor. His research interests include sensorless drives for highspeed PM motor drives, power conditioning systems for fuel cells, modeling and simulation, and power electronics. Prof. Lee has been serving as a Reviewer for the IEEE TRANSACTIONS ON I NDUSTRY A PPLICATIONS , IEEE T RANSACTIONS ON P OWER E LEC TRONICS , IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS , and IEEE TRANSACTIONS ON ENERGY CONVERSION, IEE Electronics Letters, and Proceedings of Electric Power Applications since 2000. He is a member of the IEEE Industry Applications Society Industrial Drive Committee and Industrial Power Converter Committee. He is the General Secretary of the International Conference on Electric Machines and Systems (ICEMS) 2007.

Chung-Yuen Won (S’85–M’88–SM’05) was born in Korea in 1955. He received the B.S degree in electrical engineering from Sungkyunkwan University, Suwon, Korea, in 1978, and the M.S. and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1980 and 1988, respectively. From 1990 to 1991, he was with the Department of Electrical Engineering, University of Tennessee, Knoxville, as a Visiting Professor. Since 1988, he has been with the faculty of Sungkyunkwan University, where he is currently a Professor in the School of Information and Communication Engineering. His research interests include dc–dc converters for fuel cells, electromagnetics modeling and prediction for motor drives, and control systems for rail power delivery applications.

Jin Hur (S’92–A’98–M’99–SM’03) received the Ph.D. degree in electrical engineering from Hanyang University, Seoul, Korea, in 1999, for research on the design and analysis of electric machines. From 1999 to 2000, he was with the Department of Electrical Engineering, Texas A&M University, College Station, as a Postdoctoral Research Associate. From 2000 to 2001, he was a Research Professor of electrical engineering for BK21 projects at Hanyang University. Since 2002, he has been a Managerial Researcher in the Intelligent Mechatronics Research Center, Korea Electronics Technology Institute (KETI), Puchon, Korea, where he is currently working on the development of special electric machines and systems. He is the author of over 100 publications on electric machine design, analysis, and control, and power electronics. He has ten granted and pending Korean patents, one patent pending in the U.S., and one patent pending in Japan. His current research work is in high-performance electrical machines, modeling, drives, new concept actuators for special purposes, and numerical analysis of electromagnetic fields. Dr. Hur has been serving as a Reviewer for the IEEE TRANSACTIONS ON E NERGY C ONVERSION , IEEE T RANSACTIONS ON V EHICULAR T ECH NOLOGY , IEEE T RANSACTIONS ON P OWER S YSTEMS , and Power Engineering Society Letters and was a Technical Program Committee Member of the International Conference on Electric Machines and Systems (ICEMS) 2004 and ICEMS 2005. He is an Associate Editor of the Korean Institute of Electrical Engineers Electric Machinery and Energy Conversion Systems Society and the General Secretary of ICEMS 2007.