Speed Observer System For Advanced Sensor Less Control Of Im

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003

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Speed Observer System for Advanced Sensorless Control of Induction Motor Haithem Abu-Rub, Member, IEEE, Jaroslaw Guzinski, Zbigniew Krzeminski, and Hamid A. Toliyat, Senior Member, IEEE

Abstract—This paper presents a sensorless control system for induction motors, which is realized on a fixed-point digital signal processor (DSP) and field programmable gate arrays (FPGAs). An observer system has been developed for estimation of speed and the other state variables. The proposed observer system is verified for different conditions of motor operation. Experimental results for the control system fed by voltage source inverter controlled using predictive current controller are presented. Index Terms—DSP, FPGA, induction motor, sensorless control, speed observer.

NOMENCLATURE , , , , , , , ,

, ,

,

,

, , , , , (subscript) —

Stator voltage, current, and flux, rotor flux. Stator resistance, rotor resistance, stator inductance, rotor inductance, magnetizing inductance. Rotor speed, rotor flux linkages speed, stator current angular frequency. Variables of multiscalar motor model. Stationary and rotating reference frames. Observer gains. Rotor flux speed PI controller parameters. Motor coefficients. Variable calculated from steady state. Variables estimated using the observer. Vector quantities. I. INTRODUCTION

A

speed sensor is an inconvenient device and has many drawbacks. The most important one is reducing the ruggedness and the simplicity of ac motors. It is also a cost factor, since the provision of a special motor-shaft extension to mount the encoder leads to more expensive machines. The

Manuscript received June 18, 2001; revised April 17, 2002. This work was supported by Fulbright Organization. H. Abu-Rub is with the Department of Electrical Engineering, Birzeit University, Palestine (e-mail: [email protected]). H. A. Toliyat is with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77843-3128 USA (e-mail: Toliyat@ ee.tamu.edu). J. Guzinski and Z. Krzeminski are with the Faculty of Electrical & Control Engineering, Technical University of Gdansk, Gdnask, 80-952, Poland (e-mail: [email protected]). Digital Object Identifier 10.1109/TEC.2003.811735

use of delicate optical encoders lowers the system reliability, especially in a hostile environment. Because of these problems, it is an important requirement to eliminate the speed sensor from the control systems. Thus, from the beginning of the 1980s, there were serious research works throughout the world to control induction machines without the need for speed sensors [1]–[7]. It is important to calculate all state variables from stator terminal. Different methods are used for flux and speed estimation. The calculation methods of state variables may be classified as models and observers. Models in comparison with observers are less complicated. In the case of induction motor, there are stator voltage model, rotor current model, and mixed models. Using these models, it is possible to identify the stator and rotor flux linkages. The accuracy of these variables depends on the motor operating point, exactness of the parameters used, and the sensitivity of the model to drift in these parameters. The voltage model is not precise at low frequencies; however, it is not sensitive to rotor resistance variations. On the other hand, the current model is sensitive to rotor resistance variations and is not accurate in calculating the rotor speed, especially at high speed. However, it is more precise, compared to the voltage model, at low frequencies. The mixed model integrates the advantages of both models. Because of these inaccuracies in calculating the flux linkages, in many solutions an observer by introducing an additional feedback loop is used. In [8], the principle operation of speed observer applied to field oriented induction motor is presented. A modified method for a drive with nonlinear control is used. Currently, in motor drive systems, fixed-point digital signal processors (DSPs) are widely used. Many research centers design their own systems using DSPs, which make it possible to realize research projects and to directly use the solution for industry application. The proposed control system is realized on a widely used fixed point DSP. FPGA systems are very significant since they have intelligent and convenient computer-aided design (CAD) systems, which replace the design of microprocessor control systems with higher order computer programming. The use of FPGA system makes it possible to realize parts of the control system using hardware, which unloads the main processor from parts of the realized tasks. In this paper, experimental results are presented for the control system implemented on the TMS320C50 and partly on a FPGA system (FLEX6000 family). A voltage source inverter with predictive current controller feeds the induction motor. The input commands for the PWM algorithm are the amplitude and the angular frequency of stator current. Variables are presented in per unit system.

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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003

II. VOLTAGE MODEL OF INDUCTION MOTOR The fundamental equation, which is used to introduce the relationship for speed observer system, is the stator circuit equation given by

Based on the estimated quantities of flux components, it is possible to identify the angular speed of rotor flux linkage vector using PI controller with zero command signal

(1) (12) is the stator voltage vector, stator flux vector, and where is the stator resistance. From (1), the - and - voltage components presented in the – reference frame with the rotor flux linkages oriented in the -axis are given by (2) (3)

(13) is the estimated angular speed of the rotor flux where and are the estimated currents using linkage vector. and defined in the stationary the measured currents reference frame and using the transformation from – system to – reference frame using the estimated angle

The estimated – components of stator flux linkages are as follows: (4) (5) Equations (4) and (5) present the voltage model of induction motor in – reference frame. This flux simulator operates in open loop—without any feedback from the rotor flux error. The flux is identified correctly when the motor parameters are exactly known. In a real system, motor parameters change with operating point and temperature. As a result, the estimated rotor flux and the actual flux are different, and this difference depends on the following: properties of the selected motor model; degree of accuracy of parameter identification; degree of accuracy of current and voltage measurements and motor operating point. The use of feedback minimizes the effect of the above factors on the identification of the rotor flux linkages. III. SPEED OBSERVER SYSTEM The rotor flux observer is based on the voltage model given by [8] (6) (7) (8) (9) It is possible to describe the system with only two equations when (8) and (9) are substituted into (6) and (7). In (6) and (7), a command flux quantity in feedback path is used instead of the actual quantity. Correction part in (6) and (7) appears gain, which needs to be tuned in the simulation. The with commanded components of rotor flux linkages are as follows:

(14) Rotor speed estimation is good only at steady state, but during the transients there is an error, which increases with a decreasing speed response [8], [9]. This is relative to the delays provided by integrating the -axis component of the rotor flux vector. A decrease in this error may be achieved by providing a proper initial value for the integrator. In this case, a proper initial value might be the angular speed of rotor flux vector at steady state. From the steady state relationships, it is possible to calculate the rotor speed as follows [9], [10]: (15) , , , , and are the angular frequency and stator current vector, respectively. The instantaneous reactive power is defined by where

(16) The observer system was applied in the fully decoupled model of induction machine using the nonlinear feedback, which includes the next state variables [11]: (17) (18) (19) , , , are rotor flux linkages and stator curwhere rent components, respectively. is the angle between stator current and rotor flux vectors. The state variables of the motor , and , and . These varimodel are the rotor speed ables, which are named multiscalar variables in [10] could be calculated directly from the observer system or using the steady state relationships (with subscript). Using the steady state relationships of induction motor, it is possible to modify the described estimator (12) in the following form:

(10) (11)

(20)

ABU-RUB et al.: SPEED OBSERVER SYSTEM FOR ADVANCED SENSORLESS CONTROL OF INDUCTION MOTOR

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Fig. 1. Block diagram of a modified rotor angular speed observer.

Fig. 2. Proposed induction motor control system.

where is the time constant of the first order delay filter. The first part of (20) is the equation of PI controller (12) and the second part is the filtered value of the rotor flux vector. The block diagram of a modified speed observer is presented in Fig. 1. As will be shown in the simulation results for the speed observer system from Fig. 1, the error at steady state is about 2%. This error is less than the case of using an observer without taking into account angular speed of flux linkages calculated from the steady state condition. IV. SIMULATION OF THE OBSERVER IN CLOSED-LOOP SYSTEM The overall closed-loop control system including the speed observer has been simulated using C language programming. The estimated speed has been applied to the speed controller for the nonlinear control system shown in Fig. 2. In Fig. 3, the actual and calculated rotor speed waveforms using steady state (15) are shown. It is seen that at steady state, the results are similar and a 15% error appears only during the transient. Figs. 4 and 5 show satisfactory results using the speed observer (20) for a wide range of different speeds. It is seen that the estimation

Fig. 3. Waveforms of actual speed ! and calculated speed ! state relationship (26).

using steady

error does not exceed 4%. The presented observer works also properly at low speeds. At around 1% of the rated speed, the error is only about 3%. At steady state, a speed estimation error in spite of tuned motor parameters appears. This is due to the observer principle of operation where rotor flux speed at the output of PI controller continuously traces real value. Error can only be reduced by the tuning of PI controller.

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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003

Fig. 4. Actual ! and estimated speed observer system.

!^

waveforms using the proposed

Fig. 6. Starting of the speed observer system.

1

^

Fig. 5. Waveforms of speed error ! , estimated speed ! , and actual speed ! using the proposed observer system.

The rotor speed observer operates well at the steady state and during the transients. Providing steady state relationship of the angular speed to the observer decreases the rotor speed estimation error. The observer could be used for identification of rotor flux magnitude and position. The performance of the observer is acceptable when the rotor magnetic field is kept constant. V. EXPERIMENTAL RESULTS For experimental investigation of the proposed induction motor control system, the physical set-up consists of the following elements: machine unit, squirrel cage induction motor-dc generator; voltage source inverter; input/output board with A/D converter and FPGA system; DSP board, TMS320C50 and PC computer as a host for commanding parameters and viewing the waveforms. In the set-up, a 1.5-kW squirrel cage induction motor is used. The induction motor was fed by a 2.5-kW voltage inverter, which was designed specifically for this experiment. The inverter was designed using intelligent modules with IGBT transistors. The driving system had been designed using fast opto-couplers, which guarantee galvanic separation between the inverter and control system. For motor currents

measurement, two Hall effect transducers are used, and for voltage measurement a linear opto-coupler on the dc bus is used. A dc/dc converter delivers all of the desired voltages needed by the inverter system. In this manner, suitable galvanic separation of outputs is guaranteed. The central element of the drive is a control system. It consists of a TC50A board with DSP TMS320C50. The TC50 board is dedicated to work as an individual controller. It can be connected to an IBM PC via a parallel interface LPT. Cross talk of the board with PC is used for running the systems, which are controlled by a signal processor. It is possible to simultaneously control and monitor the control process. In the experimental system, a TB6000-type I/O board is used. The board is the intermediate element between the signal processor board and the voltage inverter system. On the I/O board, there are a series of four A/D converters and programmable system, which realizes most functions of the digital systems located on the board. In the control system described before, an FPGA system from the FLEX6000 family is used. The use of FPGA system makes it possible to realize parts of the control system using hardware, which unloads the processor from parts of the assigned tasks. FPGA in the experimental set-up realizes the following functions: Timing of switching-on of each transistor for one switching period; providing a dead-time; control of breaking transistor; service of A/D converters; shut-down of inverter in the case of emergency signals and data exchange between DSP board and drive system. For experimental verification, a speed observer is operated in the open loop system (the calculated variables are not used in the closed loop system) and in the closed loop system with load angle controller [9]–[12]. The results obtained are shown in Figs. 6–9. Waveforms in Fig. 6 represent observed values at the instant of observer starting when the motor was running with constant speed. An observer starts with zero initial conditions and after 200 ms reaches a real angular speed. The identification process of the -component of rotor flux takes longer time.

ABU-RUB et al.: SPEED OBSERVER SYSTEM FOR ADVANCED SENSORLESS CONTROL OF INDUCTION MOTOR

Fig. 7.

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Observed speed as a function of measured speed.

Fig. 9. System response on step change of reference value of rotor speed in a sensorless closed loop system with load angle controller presented in Fig. 2.

totally located in the internal memory, the required time for the overall control system is about 120 s. The execution time for the speed observer is only 24 s. VI. CONCLUSION

Fig. 8. System response on step change of rotor speed in an open loop system.

-component of the rotor flux is nearly zero, except at starting instant of the observer. At this time, there appears to be significant deviation from the commanded value. In Fig. 7, the rotor angular speed waveform is presented as a function of measured speed. The obtained results are linear. In Fig. 8, the system response after step change of rotor speed is presented. It is shown that the speed calculation error at steady state does not exceed 2%. The error is bigger during transients and the maximum value of it is about 6%. During a rotor speed changing there appear some oscillations in the estimated rotor flux waveform. Error at the steady state is caused by inaccuracy of the motor parameters, which were calculated from motor rated data. Fig. 9 shows the results which were obtained for the true sensorless system. Estimated speed was used in the speed control system presented in Fig. 2. For the TMS320C50 signal processor with an instruction cycle equal to 50 ns and the program

In this paper, a speed observer system for sensorless control of induction motor is developed. The rotor speed has been calculated using the steady state relationships applied to the observer system. The simulation and experimental results illustrated that the system operates correctly for different running conditions. An observer system has been adopted for the nonlinear control scheme of induction motor. Presented observer is less complicated than the other observers known in the literature and has a good accuracy. The proposed control system was implemented on a nonexpensive fixed point DSP. An FPGA system was used to make it possible to unload the processor from parts of the realized tasks. REFERENCES [1] R. Joetten and G. Maeder, “Control methods for good dynamic performance induction motor drives based on current and voltage as measured quantities,” IEEE Trans. Ind. Applicat., vol. IA-19, pp. 356–363, May/June 1983. [2] F. Hillenbrand, “A method for determining the speed and rotor flux of the asynchronous machine by measuring the terminal quantities only,” in Proc. Int. Federation Automat. Contr., Lausanne, Switzerland, 1983, pp. 55–62. [3] C. Schauder, “Adaptive speed identification for vector control of induction motors without rotational transdusers,” in Proc. Ind. Applicat. Soc., vol. 3, Florence, Italy, 1989, pp. 493–499. [4] M. Boussak, A. G. Capolino, and T. V. Phuoc, “Speed measurement in vector-controlled induction machine by adaptive method,” Proc. Europe. Power Electron. Drives, pp. 653–658, 1991.

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[5] U. Baader, M. Depenbrock, and G. Gierse, “Direct self control (DSC) of inverter-fed induction machine—A basis for speed control without speed measurement,” IEEE Trans. Ind. Applicat., vol. 28, pp. 581–588, May/June 1992. [6] H. Tajima and Y. Hori, “Speed sensorless field orientation control of the induction machine,” IEEE Trans. Ind. Applicat., vol. 29, pp. 175–180, Jan./Feb. 1993. [7] T. Du and A. M. Brdys, “Shaft speed, load torque and rotor flux estimation of induction motor drive using an extended luenberger observer,” in Proc. Sixth Int. Conf. Elect. Mach. Drives, Oxford, U.K., 1993, pp. 179–184. [8] M. Tsuji, S. Chen, T. Ohta, K. Izumi, and E. Yamada, “A speed sensorless vector-controlled method for induction motor using q -axis flux,” in Proc. Int. Power Electron. Motion Contr. Conf., Hangzhou, China, 1997, pp. 353–358. [9] Z. Krzeminski and J. Guzinski, “DSP based sensorless control system of the induction motor,” in Proc. Power Electron. Intell. Motion, Nuremberg, Germany, 1998, pp. 137–146. [10] H. Abu-Rub and J. Guzinski, “Rotor angular speed, rotor resistance and state variables estimation in a nonlinear system control of induction motor,” in Proc. Fourth Int. Symp. Methods Models Automation and Robotics, Miedzyzdroje, Poland, 1997, pp. 613–618. [11] Z. Krzeminski, “Nonlinear control of induction motor,” in Proc. IFAC 10th World Congr. Automat. Contr., Monachium, Germany, 1987, pp. 349–354. [12] H. Abu-Rub, Z. Krzeminski, and J. Guzinski, “Nonlinear control of induction motor—Idea and application,” in Proc. Europe. Power Electron.—Power Electron. Motion Contr. Conf., vol. 6, Slovak Republic, 2000, pp. 213–218.

Haithem Abu-Rub (M’99) received the M.Sc. degree in electrical engineering from Polish Marine Academy, Gdynia, Poland, in 1990. He received the Ph.D. degree from the Electrical Engineering Department at the Technical University of Gdansk, Gdansk, Poland, in 1995. Currently, he is the Chairman of the Electrical Engineering Department of Birzeit University, Birzeit, Palestine, where he is also an Assistant Professor since 1997. Dr. Abu-Rub was a Fulbright visiting professor at the Texas A&M University, College Station, in 2001. His main research interests are the electrical drive control, power electronics, and electrical machines.

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003

Jaroslaw Guzinski received the M.Sc. and Ph.D. degrees from the Electrical Engineering Department at the Technical University of Gdansk, Gdansk, Poland, in 1994 and 2000, respectively. Currently, he is an Assistant Professor with the Technical University of Gdansk. He joined the Electrical Engineering Department at the Technical University of Gdansk in 1994. His current interest is nonlinear sensorless control of induction motors using signal processors.

Zbigniew Krzeminski received the Ph.D. degree from the Technical University of Lódz, Lódz, Poland, in 1983, and the D.Sc. degree from Silesian Technical University in 1991. Currently, he is a Professor with the Technical University of Gdansk, Gdansk, Poland, where he has been since 1993. In 1975, he joined the Department of Electrical Engineering at the University of Czestochowa, Czestochow, Poland. His main areas of research are modeling and simulation of electric machines, control of high performance electric drives and microcomputers-based control systems.

Hamid A. Toliyat (S’87–M’91–SM’96) received the Ph.D. degree in electrical engineering from the University of Wisconsin-Madison, in 1991. Currently, he is Professor in the Department of Electrical Engineering at Texas A&M University, College Station. Dr. Toliyat is an Editor of IEEE TRANS. ENERGY CONVERSION, an Associate Editor of IEEE TRANS.POWER ELECTRONICS, and a member of the Editorial Board of Electric Power Components and Systems Journal. His main research interests and experience include multiphase variable speed drives, fault diagnosis of electric machinery, analysis and design of electrical machines, and sensorless variable speed drives. He has published over 185 technical papers in these fields. He is actively involved in presenting short courses and consulting in his area of expertise to various industries. He has received the Texas A&M Select Young Investigator Award in 1999, Eugene Webb Faculty Fellow Award in 2000, NASA Space Act Award in 1999, and the Schlumberger Foundation Technical Award in 2000 and 2001. He is also Vice-Chairman of IEEE-IAS Electric Machines Committee, and is a member of Sigma Xi. He is the recipient of the 1996 IEEE Power Eng. Society Prize Paper Award for his paper on the Analysis of Concentrated Winding Induction Machines for Adjustable Speed Drive Applications—Experimental Results.