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A Simple Direct-Torque Neuro-Fuzzy Control of PWM-Inverter-Fed Induction Motor Drive Pawel Z. Grabowski, Associate Member, IEEE, Marian P. Kazmierkowski, Fellow, IEEE, Bimal K. Bose, Life Fellow, IEEE, and Frede Blaabjerg, Senior Member, IEEE

Abstract—In this paper, the concept and implementation of a new simple direct-torque neuro-fuzzy control (DTNFC) scheme for pulsewidth-modulation-inverter-fed induction motor drive are presented. An adaptive neuro-fuzzy inference system is applied to achieve high-performance decoupled flux and torque control. The theoretical principle and tuning procedure of this method are discussed. A 3-kW induction motor experimental system with digital signal processor TMS 320C31– based controller has been built to verify this approach. The simulation and laboratory experimental results, which illustrate the performance of the proposed scheme, are presented. Also, nomograms for controller design are given. It has been shown that the simple DTNFC is characterized by very fast torque and flux response, very-low-speed operation, and simple tuning capability. Index Terms—Direct torque control, induction motor control, neuro-fuzzy control, voltage-source pulsewidth modulation inverters.




DVANCED speed control of a pulsewidth-modulation (PWM)-inverter-fed drive, based on direct torque control (DTC), is receiving wide attention in the recent literature [1]–[4], [9]–[10], [14]–[16]. Fig. 1 shows two system configurations for the DTC-controlled induction motor drive. Both systems use stator flux vector and torque estimators on a and the PWM-inverter-fed drive. The stator flux amplitude are the command signals which are electromagnetic torque and values respectively, compared with the estimated and torque error , as giving instantaneous flux error shown in the figure. and In the conventional scheme [Fig. 1(a)] [14], the signals are delivered to two hysteresis comparators. The correand the stator flux sponding digitized output variables create a digital word, which selects the position sector appropriate voltage vector from the switching table. Thus, the to control the power selection table generates pulses switches in the inverter. Among the well-known disadvantages of the DTC scheme are the following [1], [3], [9], [10], [16]: Manuscript received July 19, 1999; revised May 20, 2000. Abstract published on the Internet April 21, 2000. P. Z. Grabowski was with the Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw 00-662, Poland. He is now with Schneider Electric Poland Ltd., 03-878 Warsaw, Poland. M. P. Kazmierkowski is with the Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw 00-662, Poland. B. K. Bose is with the Department of Electrical Engineering, University of Tennessee, Knoxville, TN 37996-2100 USA. F. Blaabjerg is with the Institute of Energy Technology, Aalborg University, Aalborg East 9220, Denmark. Publisher Item Identifier S 0278-0046(00)06819-2.

(b) Fig. 1. Comparison between two schemes of DTC of transistor PWM-inverter-fed induction motor drive. (a) Conventional scheme with hysteresis controllers and switching selection table [14]. (b) Proposed scheme with neuro-fuzzy (NF) controller and voltage modulator.

• • • • •

variable switching frequency; violence of polarity consistency rules; current and torque distortion caused by sector changes; start and low-speed operation problems; high sampling frequency needed for digital implementation of hysteresis comparators. All the above difficulties can be eliminated when, instead of the selection table, a voltage modulator is applied. In the reference [7], a voltage space vector is calculated from the torque and flux errors in a deadbeat fashion. However, such approach is computationally intensive and motor parameter sensitive. In this paper, a new controller based on an adaptive NF inference system (ANFIS) [11]–[13] for voltage space-vector generation is proposed. This controller combines fuzzy logic and artificial neural networks for decoupled flux and torque control.

0278–0046/00$10.00 © 2000 IEEE



Fig. 4. Triangular membership function sets.

Fig. 2. Two-input NF controller structure.


vector. The NF controller determinates the stator voltage comfor the voltage mand vector in polar coordinates to conmodulator, which finally generates the pulses trol the inverter. II. DIRECT-TORQUE NEURO-FUZZY CONTROLLER (DTNFC) SCHEME (a)

(b) Fig. 3.

DTNFC. (a) Block scheme. (b) NFC.

In the proposed scheme, shown in Fig. 1(b), the error sigand are delivered to the NF controller, which also nals uses information on the position ( ) of the actual stator flux

Combining both fuzzy logic and artificial neural networks allows achieving all of the advantages of both systems. Human expert knowledge can be used to build the initial structure of the regulator. Online or offline learning processes can improve underdone parts of the structure. The ANFIS structure [11], [13] is one of the proposed methods to combine fuzzy logic and artificial neural networks. An NF inference system is the same as a conventional fuzzy structure shown in Fig. 2. It contains rule base and database (knowledge base), fuzzyfication and defuzzyfication unit as well as a decision-making unit. The structure proposed in [11]–[13] (Fig. 2) contain five network layers: Layer 1: Every node in this layer contains membership functions. Usually, triangular or bell-shaped functions are chosen. Layer 2: This layer chooses the minimum value of two input weights. Layer 3: Every node of these layers calculates the weight which is normalized. Layer 4: This layer includes linear functions which are functions of the input signals. Layer 5: This layer sums all the incoming signals. The ANFIS structure has been tuned automatically by a least-square estimation (for output membership functions) and




Fig. 5. Reference voltage calculation (only three out of four v vectors are shown).


(b) Fig. 7.

(a) Torque and (b) flux error tuning surfaces.

Sampled flux error and torque error , multiplied by reand , are delivered to the three memberspective weights ship functions in both inputs. To simplify the digital signal processor (DSP) calculations, the functions are triangular shaped as shown in Fig. 4. This is the first layer of the NF structure. The second layer calculates the minimum of the input signals shown in Fig. 3(b). The output values are normalized in the third layer, to satisfy the following relation: (1)

Fig. 6. Stator flux vector estimator. Top: voltage model working with Cartesian coordinates; middle: voltage model working with polar coordinates; bottom: improved integration algorithm with limiter in flux amplitude feedback.

a backpropagation (for output and input membership functions) algorithms. Because of its flexibility, the ANFIS system can be used for a wide range of control tasks [11]–[13], [16]. The block scheme of the proposed self-tuned direct torque neuro-fuzzy controller (DTNFC) for a voltage-source PWM-inverter-fed induction motor is presented in Fig. 3(a). The internal structure of the NFC is shown in Fig. 3(b).

is the second where is the third layer th output signal, and layer output weight. The is the weight of th component of reference voltage vector amplitude, so that (2) is the amplitude of the th component of the referwhere ence voltage vector. is active , then the regulator When the weight value from Table I. The increchooses the increment angle is not needed when , because the multiplication ment







Fig. 8. Offline experimental tuning of input weight w weights during system tuning.

and w , where (a), (b) flux and torque error behavior, respectively, and (c), (d) flux and torque input


Fig. 10.

Laboratory control unit for test of the DTNFC.

There are four nonzero output signals from the first layer (two for each input) during the steady-state operation. It results in ) in every samfour generated voltage vectors components ( are added to each other and the result, pling time. Vectors voltage vector, is delivered to the space vector modulator. An calculation is presented in example of the reference voltage Fig. 5 (For simplicity, instead of four, there are only three nonzero vectors used for illustration). The space-vector moduand according to the lator calculates switching states well-known algorithm [7], [10], [16]. (b)


Fig. 9. Dependence of the (a) flux and (b) torque error on the switching (sampling) frequency in the properly tuned system.

is equal to zero. The angle of the reference voltage vector is calculated from the following equation: (3) where reference voltage angle; actual angle of the stator flux vector; increment angle (from Table I).

The most basic method for the stator flux vector estimation is based on the voltage model shown in Fig. 6(a). The voltage model does not require speed signal (as for example in the current model [9], [10], [16]). This makes the scheme directly applicable for speed sensorless control. However, deriving the stator flux from terminal voltages and currents is difficult because of open-loop integration [Fig. 6(a)] is subject to sensing errors and drift at low stator frequency. Therefore, to avoid an open integration, voltage flux model working in polar coordinates has been used. As shown in Fig. 6(b), thanks to a transformation from stator fixed to synchronous





(c) Fig. 11.

Experimental results for the steady state-operation for the tuned DTNFC system. (a) Stator current. (b) Line-to-line voltage. (c) Stator flux trajectory.

rotated coordinates – / – , the voltage model operates like a phase-locked loop (PLL) which guarantees better stability. A further improvement is achieved by using a new integration algorithm [8] with limiter in flux amplitude feedback [Fig. 6(c)]. IV. SELF-TUNING PROCEDURE There are many methods of tuning of fuzzy systems and neural networks. The ANFIS structure [11]–[13] used for inverted pendulum stabilization is very similar to the presented DTNFC controller. The controller has been tuned automatically by a least-quare estimation algorithm (for output membership function) and backpropagation algorithm (for output and input membership function). The DTNFC can be tuned in the same way. However, we propose another simple and effective off line tuning method. The proposed DTNFC system contains three membership functions for each input. The tuning of the membership functions width corresponds to scaling of the flux and torque errors. and weights. The scaling factors are The DTNFC is nonlinear high-order system. Therefore, it is very helpful to use simulation for controller design. Fig. 7 presents computed flux and torque error as function of the input weights. The surfaces have also been verified experimentally. It can be seen that there is clearly defined minimum without any other local minimum points. This is because, for small weights the controller chooses high value of the reference voltage amplitude, which results in high flux and torque errors (ripples). From the other hand, if the weights are too big, the steady state errors increase. This tendency allows to use a simple gradient and method to find the optimal working point (optimal values), which guarantees minimal flux and torque errors. However, the torque and flux are not fully decoupled. It can be work out the equations from the mathematical induction motor model [6], [10] as follows: (4a)

(4b) where reference voltage amplitude; reference voltage phase; synchronous angular speed,; stator resistance. It can be seen from (4a) and (4b) that, for nonzero syninfluences chronous angular speed, the changes of the flux the output torque, while the torque change does not influence the flux. That is why flux error minimum should be found first, before searching the torque error minimum. The offline tuning process of the system is presented in Fig. 8. Note that the tuning surfaces in Fig. 7 have a general validity. The numerical results may little differ according to motor parameters and supply voltage. Also the final flux and torque errors depend on the chosen inverter switching frequency (Fig. 9). The DTNFC scheme guarantees very fast flux and torque responses. It is thanks to the lack of integration. Unfortunately, this property causes constant torque error in steady state operation. One of the solutions is adding an integration block. However, as consequence, the torque response will be slow. In the can be used to DTNFC, instead of integration, the weight reach zero torque error at the steady state. This weight decides about the amplitude of the reference voltage vector. Therefore, instead of calculating by the controller, the value of the output is calculated from weight (5) and are experimentally chosen factors to comwhere pensate for the steady-state torque error (see the Appendix). V. EXPERIMENTAL RESULTS To verify the proposed DTNFC concept, a simulation program and the laboratory setup with a four-pole 3-kW induction motor drive with dSPACE DS1102 laboratory control board









Fig. 12. Experimental oscillograms for (a) motor magnetization at zero speed, (b) the torque transients to the step changes, (c) the stator flux transients to the step changes, (d) slow speed reversal for no loaded motor, (e) four-quadrant operation, and (f) small step changes of speed command, -stator flux amplitude, -reference stator flux amplitude, i -stator current, m -output torque, m -reference torque, ! -reference rotor speed, ! -rotor speed.


was constructed. The system is based on Texas Instrument TMS320C31 and TMS320P14 DSPs. The first (main) processor implements the DTNFC control algorithm, whereas the second provides the vector modulation. The board is equipped with four analog-to-digital converters (two 16-bit and two 12-bit), four digital-to-analog converters, and the input for an encoder. A PC Pentium 100 is used for software development and results visualization. Optic fibers are used as interface between the PWM voltage-source inverter and the DSP board. The software is written in high-level language C. The steady-state operation of the tuned system is presented in Fig. 11(a)–(c). The sampling time has been set to 500 s, what gave flux and torque errors in the range of 1% and 3.5%, respectively. The result has been obtained for half of the nominal


speed. The stator current is not distorted by the sector changes, as in the conventional DTC [6], [14], and the stator flux trajectory is circular. The motor magnetization process is presented in Fig. 12(a). It is visible that the magnetization process takes about ten sampling times (about 5 ms). The reference stator voltage chosen by the controller is parallel to the stator flux vector. It results in short torque distortion what is visible in the oscillogram. The torque transients to the step changes are presented in Fig. 12(b). It can be seen that, for the constant stator flux amplitude, the flux and torque are fully decoupled and the flux amplitude is not distorted during torque steps. The stator current response is also presented in the figure. The response time is


about 3 ms, which gives a similar dynamic as in the conventional DTC method [5], [6], [14]. The DTNFC system property is characterized by high stator flux dynamic, which is higher than in the conventional DTC. This is because the resultant reference voltage vector can be selected in parallel to the flux vector, what ensures the fastest flux response. Such a property makes the DTNFC controller useful for energy efficient systems, where flux changes are required. The flux response for small step change is presented in Fig. 12(c). It can be seen in Fig. 12(d) that the controller can operate successfully at low speed. The slow speed reversal shows that the induction motor is not demagnetized in the low speed region and the torque is controlled correctly. The speed transient for fast speed ramp reversal is presented in Fig. 12(e). When a speed sensor is used the system is stable in whole speed range (including zero speed at full load). However, instabilities can only occur for sensorless operation in zero speed region. The lower speed control range depends on the used flux and speed estimators’ quality. In the laboratory setup, the speed sensorless stable operation has been observed over 1%–2% of nominal speed. Small-signal behavior of the speed control loop is presented in Fig. 12(f). The speed response time is about 10 ms. The more detailed study of DTNFC and comparison to classical variants of DTC has been presented in [6]. The classical DTC [14] has not been realized practically, because it was not possible to sample correctly the hysteresis controller. In such a way, it can be noticed that one of the advantages of the DTNFC is that the sampling time for this method can be lower and the whole controller can be realized in single-processor systems. VI. CONCLUSIONS The application of an NF approach for direct torque control of a PWM-inverter-fed induction motor has been investigated through DSP-based experimental implementation. The design and tuning procedure have been described. Also, the improved stator flux estimation algorithm, which guarantees eccentric estimated flux has been proposed. The presented DTNFC scheme has the following features and advantages: • only one controller; • simple tuning procedure; • constant switching frequency and unipolar motor voltage thanks to applied space-vector modulator; • torque and current harmonics mainly dependent on sampling time; • no current and torque distortion caused by sector changes (there are no sectors borders); • fast torque and flux response; • no problems during low-speed operation; • lower sampling time; • possible online tuning. APPENDIX Motor Parameters: (stator resistance)—0.0384;


(rotor resistance)—0.0577; (stator reactance)—4.1621; (rotor reactance)—4.1621; (main reactance)—4.007; (dc-link voltage)—1.5; (speed scaling factor)—1.33; (torque scaling factor)—0.13; (flux scaling factor)—0.65. REFERENCES [1] G. Buja, “A new control strategy of the induction motor drives: The direct flux and torque control,” IEEE Ind. Electron. Soc. Newslett., vol. 45, pp. 14–16, Dec. 1998. [2] D. Casadei, G. Grandi, G. Serra, and A. Tani, “Effects of flux and torque hysteresis band amplitude in direct torque control of induction machines,” in Proc. IEEE IECON’94, 1994, p. 299. [3] A. Damiano and P. Vas et al., “Comparison of speed-sensorless DTC induction motor drives,” in Proc. PCIM, Nuremberg, Germany, 1997, pp. 1–11. [4] M. Depenbrock, “Direct self control of inverter-fed induction machines,” IEEE Trans. Power Electron., vol. 3, pp. 420–429, Oct. 1988. [5] P. Z. Grabowski, “Direct torque neuro-fuzzy control of induction motor drive,” in Proc. IEEE IECON’97, 1997, pp. 557–562. , “Direct flux and torque neuro-fuzzy control of inverter-fed in[6] duction motor drives,” Ph.D. thesis, Inst. Contr. Ind. Electron., Warsaw Univ. Technol., Warsaw, Poland, 1999. [7] T. G. Hableter, F. Profumo, M. Pastorelli, and L. M. Tolbert, “Direct torque control of induction machines using space vector modulation,” IEEE Trans. Ind. Applicat., vol. 28, pp. 1045–1053, Sept./Oct. 1992. [8] J. Hu and B. Wu, “New integration algorithms for estimating motor flux over a wide speed range,” IEEE Trans. Power Electron., vol. 13, pp. 969–977, Sept. 1998. [9] M. P. Kazmierkowski and A. Kasprowicz, “Improved direct torque and flux vector control of PWM inverter-fed induction motor drives,” IEEE Trans. Ind. Electron., vol. 45, pp. 344–350, Aug. 1995. [10] M. P. Kazmierkowski and H. Tunia, Automatic Control of Converter-Fed Drives. Amsterdam, The Netherlands: Elsevier, 1994. [11] J.-S. R. Jang, “ANFIS: Adaptive-network-based fuzzy inference system,” IEEE Trans. Syst., Man, Cybern., vol. 23, pp. 665–684, May/June 1993. [12] , “Self-learning fuzzy controllers based on temporal back propagation,” IEEE Trans. Neural Networks, vol. 3, pp. 714–723, Sept. 1992. [13] J.-S. R. Jang and C.-T. Sun, “Neuro-fuzzy modeling and control,” Proc. IEEE, vol. 83, pp. 378–406, Mar. 1995. [14] I. Takahashi and T. Noguchi, “A new quick-response and high efficiency control strategy of an induction machine,” IEEE Trans. Ind. Applicat., vol. IA-22, pp. 820–827, Sept./Oct. 1986. [15] P. Tiitinen, P. Pohjalainen, and J. Lalu, “The next generation motor control method direct torque control, DTC,” in Proc. PEDES Conf., New Delhi, India, 1996, pp. 37–43. [16] P. Vas, Sensorless Vector And Direct Torque Control. Oxford, U.K.: Oxford Univ. Press, 1998.

Pawel Z. Grabowski (S’95–A’99) was born in Warsaw, Poland, in 1970. He received the M.Sc.E.E. degree from Warsaw University of Technology, Warsaw, Poland, and the Ph.D. degree from the Institute of Control and Industrial Electronics, Warsaw University of Technology, in 1994 and 2000, respectively. Since August 1999, he has been with Schneider Electric Poland Ltd., Warsaw, Poland. His research areas are control systems, DSP-based controllers, intelligent control methods in power electronics, ac drives, and simulation. Dr. Grabowski is a Student Member of the IEEE Industrial Electronics Society. He received the 1994 SEP Award for his M.Sc.E.E. thesis and FIAT Award in 2000 for his Ph.D. dissertation.



Marian P. Kazmierkowski (M’89–SM’91–F’98) received the M.Sc., Ph.D., and Dr.Sc. degrees in electrical engineering from the Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland, in 1968, 1972 and 1981, respectively. From 1967 to 1969, he was with the Industrial Research Institute of Electrotechnics (IEl), Warsaw, Poland, and from 1969 to 1980, he was with the Institute of Control and Industrial Electronics, Warsaw University of Technology, as an Assistant Professor. From 1980 to 1983, he was with RWTH Aachen, Aachen, West Germany, as an Alexander von Humboldt Fellow. During 1986–1987, he was a Visiting Professor at NTH Trondheim, Trondheim, Norway. Since 1987, he has been a Professor and Director of the Institute of Control and Industrial Electronics, Warsaw University of Technology. He was a Visiting Professor at the University of Minnesota, Minneapolis, in 1990, at Aalborg University, Aalborg East, Denmark, in 1990 and 1995, and at the University of Padova, Padova, Italy, in 1993. He is also currently a Coordinating Professor in the International Danfoss Professor Program 1997–2000, Aalborg University. Since 1996, he serves as an elected member of the State Committee for Scientific Research in Poland. He is engaged in research and theoretical work on electrical drive control and industrial electronics. He is the author or coauthor of more than 140 technical papers and reports, as well as 11 books and textbooks. His latest book, with Dr. H. Tunia, is Automatic Control of Converter-Fed Drives (Amsterdam, The Netherlands: Elsevier, 1994). Dr. Kazmierkowski was the Chairman of the 1996 IEEE International Symposium on Industrial Electronics held in Warsaw, Poland. He is an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and Vice President, Publications, IEEE Industrial Electronics Society.

Bimal K. Bose (S’59–M’60–SM’78–F’89–LF’96) received the B.E. degree from Calcutta University (Bengal Engineering College), Calcutta, India, the M.S. degree from the University of Wisconsin, Madison, and the Ph.D. degree from Calcutta University in 1956, 1960, and 1966, respectively. He currently holds the Condra Chair of Excellence in Power Electronics at the University of Tennessee, Knoxville, where he is responsible for organizing the power electronics teaching and research program for the last 13 years. He is also the Distinguished Scientist of the EPRI-Power Electronics Applications Center, Knoxville, and Honorary Professor of Shanghai University, China University of Mining and Technology, and Xian Mining Institute (also Honorary Director of its Electrical Engineering Institute), China, and Senior Adviser of the Beijing Power Electronics Research and Development Center, Beijing, China. Early in his career, for 11 years, he served as a faculty member at Calcutta University (Bengal Engineering College). In 1971, he joined Rensselaer Polytechnic Institute, Troy, NY, as Associate Professor of electrical engineering and conducted its teaching and research program. In 1976, he joined General Electric Corporate Research and Development, Schenectady, NY, as a Research Engineer and served there for 11 years. He has served as a Consultant to more than ten industries. His research interests extend across the whole spectrum of power electronics, and specifically include power converters, ac drives, microcomputer control, EV drives, and expert system, fuzzy logic, and neural network applications in power electronics and drives. He has authored more than 150 published papers and is the holder of 20 U.S. patents. He is the author and editor of a number of books, including Power Electronics and AC Drives (Englewood Cliffs, NJ: Prentice-Hall, 1986), Adjustable Speed AC Drive Systems (New York: IEEE Press, 1981), Microcomputer Control of Power Electronics and Drives (New York: IEEE Press, 1987), Modern Power Electronics (New York: IEEE Press, 1992), and Power Electronics and Variable Frequency Drives (New York: IEEE Press, 1997). The book Power Electronics and AC Drives has been translated into Japanese, Chinese, and Korean, and is widely used as a graduate-level text book. He has travelled widely and has given keynote addresses, tutorials, and invited lectures to promote power electronics internationally. He has served in a numerous national and international professional organizations. In 1995, he initiated Power Electronics for Universal Brotherhood (PEUB), an international organization to promote humanitarian activities of the power electronics community.

Dr. Bose has served the IEEE in various capacities that include Chairman of the IEEE Industrial Electronics Society (IES) Power Electronics Council, Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, IEEE IECON Power Electronics Chairman, Chairman of IEEE Industry Applications Society (IAS) Industrial Power Converter Committee, IAS member in the Neural Network Council, and various other professional committees. He has been a member of the Editorial Board of the PROCEEDINGS OF THE IEEE since 1995. He was a Distinguished Lecturer of the IAS and IES. He received the IAS Outstanding Achievement Award in 1993, IES Eugene Mittelmann Award in 1994, IEEE Region 3 Outstanding Engineer Award in 1994, IEEE Lamme Gold Medal in 1996, and IEEE Continuing Education Award for in 1997. He was the Guest Editor of the PROCEEDINGS OF THE IEEE Special Issue on Power Electronics and Motion Control (August 1994). He received the GE Publication Award, Silver Patent Medal, and a number of IEEE Prize Paper Awards. For his research contributions, he was awarded the Premchand Roychand Scholarship and Mouat Gold Medal by Calcutta University in 1968 and 1970, respectively. He is listed in Marquis Who’s Who in America.

Frede Blaabjerg (S’86–M’88–SM’97) was born in Erslev, Denmark, in 1963. He received the Msc.EE. from Aalborg University, Aalborg East, Denmark, and the Ph.D. degree from the Institute of Energy Technology, Aalborg University, in 1987 and 1995, respectively. He was employed with ABB-Scandia, Randers, Denmark, from 1987 to 1988. He became an Assistant Professor in 1992 at Aalborg University, where, in 1996, he became and Associate Professor and, in 1998, he became a Full Professor in power electronics and drives. His research areas are power electronics, static power converters, ac drives, switched reluctance drives, modeling, characterization of power semiconductor devices, and simulation. He is involved in more than ten research projects with industry. Among them is the Danfoss Professor Programme in Power Electronics and Drives. Dr. Blaabjerg is a member of the European Power Electronics and Drives Association and the IEEE Industry Applications Society (IAS) Industrial Drives Committee. He is also a member of the Industry Power Converter Committee and the Power Electronics Devices and Components Committee of the IAS. He is the Paper Review Chairman of the Industrial Power Converter Committee of the IAS. He serves as a member of the Danish Technical Research Council in Denmark and a member of the board of the Danish Space Research Institute. In 1995, he received the Angelos Award for his contribution to modulation technique and control of electric drives and an Annual Teacher Prize from Aalborg University. In 1998, he received the Outstanding Young Power Electronics Engineer Award from the IEEE Power Electronics Society and an IEEE TRANSACTIONS ON POWER ELECTRONICS Prize Paper Award for best paper published in 1997. He also received two Prize Paper Awards at the IAS Annual Meeting in 1998.