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025 1 A DSP-based Discrete Space Vector Modulation Direct Torque Control of Sensorless Induction Machines F. Khoucha, K. Marouani, A. Kheloui, K. Aliouane UER Electrotechnique, EMP(Ex-ENITA) BP 17 Bordj-El-Bahri, Algiers, Algeria Fax n° : ++213 21 86 32 04 Correspondent co-author E-mail : khoudir-marouani@eudoramail.com Abstract—In this paper, we present a Direct Torque ϕ∗ ˆS + Control scheme of an induction motor operating without speed Look-up - VSI sensor. The estimation of the stator flux and the rotor speed is Table performed by an adaptive observer. In order to reduce the ˆ T∗ e + torque, flux, current and speed ripple a Discrete Space Vector - Sector N Modulation (DSVM-DTC) strategy is implemented using a ˆ ϕS Flux and Torque DSP-based hardware. To illustrate the performances of this ˆ estimator control scheme, experimental results are presented. Te Index Terms— Adaptive Observer, Direct Torque Control, IM Fig.1 Basic Direct Control Scheme Induction Motor, Space Vector Modulation. This paper presents a sensorless induction motor control scheme using an adaptive observer for the stator flux and I. INTRODUCTION the rotor speed estimation based on discrete space vector Alternating current motors are getting more and more modulation (DSVM-DTC) switching strategy. popular for applications in industrial environments. Particularly in speed control systems, ac induction motors are more widely used nowadays due to the characteristics of II. DIRECT TORQUE CONTROL higher efficiency, less inertia, smaller volume and lower Direct Torque Control (DTC) was proposed by cost. Moreover, in contrast to dc motors, induction motors M. Depenbrock and I. Takahashi. This method presents the can be used for a long time without maintenance because of advantage of a very simple control scheme of stator flux and their brushless structures. The capabilities to operate at torque by two hysteresis controllers, which give the input higher speeds, higher torques and larger power ratings voltage of the motor by selecting the appropriate voltage make the induction motors more attractive than dc motors vectors of the inverter through a look-up-table in order to for medium and high power motor drives. keep stator flux and torque within the limits of two In recent years, research interest in IM sensorless drives hysteresis bands as shown in Fig.1. The application of this has grown significantly due to some of their advantages, principle allows a decoupled control of flux and torque such as mechanical robustness, simple construction and without the need of coordinate transformations, PWM pulse maintenance [1]. Present efforts are devoted to improve the generators and current regulators. Different voltage vector sensorless operation, especially for low speed and to selection criteria can be employed to control the torque develop robust control strategies. according to whether the flux has to be reduced or The DTC is one of the actively researched control increased, leading to different switching tables. Very high scheme wich is based on the decoupled control of stator dynamic performance can be achieved by DTC, however, flux and torque providing a quick and robust response with the presence of hysteresis controllers leads to a variable a simple control construction in ac drives. However, the inverter switching frequency operation. In addition, the time conventional DTC strategy using only one switching table discretization, due to digital implementation, plus the at high and low speed present notable torque, flux, current limited number of available voltage vectors is source of and speed ripple. 025 2 large current and torque ripple, causing the deterioration of single voltage vector during the whole switching period the steady performance especially in low speed range. assures quick response. However, if the errors are small the In order to improve the steady performance, different application of a single voltage vector can cause great DTC strategies have been proposed to perform constant variation of flux or torque and it can be source of ripple. switching frequency operation and to decrease the torque With DSVM-DTC strategy, 19 voltage vectors can be ripple. In general, they require more complex control selected for each sector, according to the rotor speed, the schemes in comparison to the basic DTC ones. flux and the torque errors range as is represented in Fig. 2c and TABLE I. The switching period is divided into three equal time intervals and one voltage vector is applied at III. FLUX AND TORQUE CONTROL each time interval. With reference to current and torque ripple, it has been For example, the label "23Z" denotes the voltage vector verified that a large influence is exerted by the amplitude of which is synthesized by using the voltage space vectors V2, the flux and the torque hysteresis bands, and the voltage V3 and V0 or V7, each one applied for one third of the vector selection criteria. It can be noted also that a given cycle period. voltage vector has a different effect on the drive behaviour at high and low speed. Taking these considerations into β β account, a good compromise has been obtained using V3 V2 different switching tables at high and low speed. In general, 010 110 V3 V2 the determination of the switching tables is carried out on V1 the basis of physical considerations concerning the effects V4 011 111 000 100 α Sector 1 α determined by radial and tangential variations of the stator V7 V0 flux vector on torque and flux values. A substantial reduction of current and torque ripple could V6 be obtained using, at each cycle period, a preview technique 001 101 V5 V5 (a) V6 (b) in the calculation of the stator flux vector variation required to exactly compensate the flux and torque error. In order to (a) Voltage vectors obtained by two level VSI (b) Voltage vectors selection in basic DTC apply this principle, the control system should be able to generate, at each sampling period, any voltage vector. This β ideal behaviour can be approximated using a control system 333 332 223 222 able to generate a number of voltage vectors higher than 23Z that used in basic DTC scheme. These solutions are good 33Z 22Z for high power applications, but are not acceptable for medium or low power applications cause to the increased 3ZZ 2ZZ α Sector 1+ complexity of the power circuit. ZZZ Sector 1- 5ZZ 6ZZ 55Z 66Z IV. DSVM-DTC CONTROL STRATEGY 56Z The main idea the DSVM-DTC control strategy is to 555 556 665 666 force the torque and stator flux to approach their reference (c) Voltage vectors selection in DSVM-DTC by applying in one sampling period several voltage vectors strategy for sector 1 instead of only one voltage vector as in basic DTC. B′ T This control algorithm uses prefixed time intervals +2 within a cycle period and in this way a higher number of +1 voltage space vectors can be synthesized with respect to those used in basic DTC technique [4]. The increased 0 T∗ − T∗ ˆ -1 e e number of voltage vectors allows the definition of -2 BT B′ switching tables according to the rotor speed (Fig. 2e), the T flux and torque errors. The switching tables are derived (d) Five level torque hysteresis comparator from the analysis of the equations linking the applied voltage vector to the corresponding torque and flux Clockwise Counter Clockwise variations. To understand the principle of the DSVM-DTC control High Medium Low Medium High ω m ϕ s strategy, let us take, for example, the case when the stator -1 -1/2 -1/6 1/6 1/2 1 flux is located in sector 1, in basic DTC five voltage vectors 0 can be selected (Fig. 2b) and a single voltage vector is (e) Emf range subdivision in p.u. of the rate voltage applied during the whole switching period. When the flux Fig. 2 DSVM-DTC strategy scheme or torque error is big positive or negative the application of 025 3 TABLE I ω r : is the rotor mechanical speed. Voltage vectors selection in DSVM-DTC strategy for sector 1 and Counter Clockwise rotor speed A linear state observer for the rotor flux can then be Low emf range derived as follows by considering the mechanical speed as a Cϕ CT -2 -1 0 1 2 constant parameter since its variations are very slow in 0 555 5ZZ ZZZ 3ZZ 333 comparison to those of the electrical variables: 1 666 6ZZ ZZZ 2ZZ 222 Medium emf range x = Ax + Bu + K ( y − y ) & ˆ ˆ ˆ (2) Cϕ CT -2 -1 0 1 2 0 555 ZZZ 3ZZ 33Z 333 The symbol ^ denotes an estimated quantity. K is a gain 1 666 ZZZ 2ZZ 22Z 222 matrix, which is used to suitably locate the observer’s poles. Using Lyapounov stability theory, we can construct a High emf range sector 1+ mechanism to adapt the mechanical speed from the Cϕ CT -2 -1 0 1 2 asymptotic convergence’s condition of the state variables 0 555 3ZZ 33Z 333 333 estimation errors: 1 666 2ZZ 23Z 223 222 High emf range sector 1- ω = − K ∫ (e ϕ + e ϕ )dt − K ˆ s ˆ ˆ iω sα rα sβ rβ (e ϕ + e ϕ ) ˆ ˆ pω sα rα sβ rβ (3) Cϕ CT -2 -1 0 1 2 0 555 3ZZ 23Z 332 333 Where ˆ esα = i sα − i sα and ˆ esβ = i sβ − isβ . 1 666 2ZZ 22Z 222 222 K iω and K pω : are positive gains. V. ADAPTIVE FLUX AND SPEED OBSERVER In this section we present the global structure of the The voltage drop over the stator resistance at low rotor observer under study, which is based on the induction speed reduces the amplitude of the stator flux remarkably. motor model written in stator reference frame [5]. The In order to improve the estimation precision of both flux motor model is given by: and speed variables, we included an adaptation mechanism of the stator resistance [6], which is subject to drift due to ⎧ x = Ax + Bu & motor heating. In the same manner that for the speed ⎨ (1) variable, the stator resistance estimate is given by: ⎩ y = Cx Where x = isα [ isβ ϕ rα ϕ rβ ]t ˆ ( ˆ ˆ ) ( ˆ ˆ Rs = − K ir ∫ e sα iαs + e sβ i βs dt − K pr e sα iαs + e sβ i βs ) (4) u = [vsα vsβ ] y = [i sα i sβ ] t t Fig. 3 presents the global adaptive observer structure. isα vsα ⎡ 1 ⎛ 1− σ 1 ⎞ M M ⎤ ⎢− ⎜ + ⎟ ⎜T T⎟ 0 ωr ⎥ isβ Induction Motor vsβ ⎢ σ⎝ r s ⎠ σL LsTr σL Ls ⎥ r r ⎢ 1 ⎛ 1− σ 1 ⎞ M M ⎥ - + ⎢ 0 − ⎜⎜ T + T ⎟ − σL L ωr σL L T ⎥ ⎟ A= ⎢ σ⎝ r s⎠ r s r sr⎥ + ˆ isα ⎢ Lm 1 ⎥ Observer model 0 − −ωr - ⎢ Tr Tr ⎥ ⎢ ⎥ ˆ isβ ) ) ⎢ Lm 1 ⎥ ϕrβ ϕrα Adaptive 0 ωr − observer ⎢ ⎣ Tr Tr ⎥ ⎦ Adaptation Mechanism ˆ ˆ ωr , Rs ⎡ 1 ⎤ ⎢ σL 0 ⎥ ⎢ r ⎥ ⎡1 0 0 0 ⎤ Fig. 3 Global adaptive observer structure 1 ⎥ C = B=⎢ 0 ⎢0 ⎣ 1 0 0⎥⎦ ⎢ σL r ⎥ ⎢ 0 0 ⎥ ⎢ ⎥ ⎣ 0 0 ⎦ 025 4 VI. EXPERIMENTAL RESULTS A series of experimental results are depicted on figures 5, The configuration of the experimental system used to 6 and 7, which represent the performances of the flux and validate the proposed control algorithm is shown in Fig. 4, speed adaptive observer under several conditions in it is made up of a 1Kw/380/50Hz squirrel cage induction association with the DSVM-DTC strategy and the stator motor fed by a 2-level IGBT voltage source inverter and resistance tuning. They prove the effectiveness of the digital signal processor (DSP) control board. adaptive observer in general and especially in association The whole control algorithm (Adaptive speed and flux with the DSVM-DTC strategy, even without the stator observer, stator resistance tuning, DTC algorithm and PI resistance tuning. The whole control algorithm was speed regulator) is implemented in a single fixed-point implemented on a single DSP-controller board within a TMS320F240 DSP-based development board from Texas reasonable computing time, which gives result to a good Instruments within less than 100µs of time computing. The performance/ease of implementation ratio. digital control signals of the power components are Fig. 5 shows a small ripple in the stator current, the generated by the DSP-controller via PWM outputs. The estimated torque and the rotor speed responses without control frequency is about 10Khz. Voltage and current stator resistance tuning, when the speed command is variables are measured by Hall-effect sensors and sampled changed from 1500 rpm to -1500rpm. However, Fig. 6 at the same frequency. A mechanical speed tachometer is present notable torque and speed ripple at low speed mounted on the motor’s shaft only to allow comparison (100rpm). Fig.7, shows a good torque and speed responses between estimated and measured speed. The tachometer’s with stator resistance tuning at low speed (100rpm). signal is not used in the closed-loop speed control. VSI Stator curent IM Estimated torque Load torque Reference and estimated speed removed Hall effect sensors Estimated Speed Reference Speed Control unit Development Software Digital OUT (a) Current, Torque and Speed responses at --- PC TMS320F240 Sensors transient state without stator resistance tuning --- DSP Development Interface board Analog IN Reference and estimated torque Fig. 4 Experimental system scheme Reference and estimated Speed Stator curent Estimated torque Load torque removed (b) Torque and speed responses at steady state Zero speed without stator resistance tuning Fig.6 Current, Torque and Speed responses at rated Reference and estimated speed load (2Nm) without stator resistance tuning Fig.5 Current, Torque and Speed responses for speed reversal operation from 1500rpm to -1500rpm 025 5 APPENDIX Stator current Induction motor data 1Kw Rated power. Load torque removed 2830rpm Rated speed. 220v Rated voltage. 4.67Ω Stator resistance. 8Ω Rotor resistance. Reference and Estimated Speed 0.347 H Stator inductance. 0.374 H Rotor inductance. 0.366 H Mutual inductance. (a) Torque and speed responses at transient state 0.003 Kg.m2 Motor-Load inertia with stator resistance tuning 1 # of pole pairs. Reference and estimated torque REFERENCES [1] Gil-Su Lee, Dong-Hyun Lee, Tae-Woong Yoon, Kyo-Beum Lee, Joong-Ho Song, and Ich Choy “Speed and Flux Estimation for an Induction Motor”, in Proceedings of ICCAS2002, South-Korea. [2] S. Stasi, L. Salvatore, and F. Cupertino “Comparison Between Adaptive Flux Observer- and Extended Kalman Filter-Based Reference and Estimated Speed Algorithms for Field Oriented Control of Induction Motor Drives” in Proceedings of 1999 European Power Electronics Conference, Lausanne, Switzerland. [3] R. Beguenane and M. Ouhrouche “MRAC- IFO Induction Motor Control with Simultaneous Velocity and Rotor-Inverse Time constant Estimation”, IASTED International Conference PES’2003. 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Experimental performance Observer With Online Tuning of Stator and Rotor Resistances for analysis of an adaptive stator flux and speed observer with Induction Motors” IEEE Transactions on Industrial Electronics, Vol. stator resistance tuning, performed by a DSP controller. The 49, N° 3, June 2002. analysis focuses both on transient and static characteristics. [7] K. Ohyama. G. M. Asher and M. Summer “Comparison of Pratical They prove the effectiveness of the adaptive observer in Performance and Operating Limits of Sensorless Induction Motor general and especially in association with the DSVM-DTC Drive using a Closed Loop Flux Observer and a Full Order Flux Observer” in Proceedings of 1999 European Power Electronics strategy. With the experimental results it has been verified Conference, Lausanne, Switzerland” in Proceedings of 1999 that the DSVM-DTC strategy allows the torque, the rotor European Power Electronics Conference, Lausanne, Switzerland. speed and the current ripple to be reduced in comparison to the basic DTC strategy.