A DSP-based Discrete Space Vector Modulation Direct by ltq12245


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              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
                                                                        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
                                                                        e    +
torque, flux, current and speed ripple a Discrete Space Vector               -                      Sector N
Modulation (DSVM-DTC) strategy is implemented using a                                       ˆ
                                                                                                    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.
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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
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
   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.
   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∗
                                                                  -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
   To understand the principle of the DSVM-DTC control                  High          Medium            Low            Medium             High       ω
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
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                                     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     ˆ
                                                                                           iω sα rα sβ rβ
                                                                                                                   (e ϕ + e ϕ )
                                                                                                                      ˆ     ˆ
                                                                                                                 pω sα rα sβ rβ
      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.
  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
     ⎢      Lm                         1           ⎥                                                             Observer model
                           0        −       −ωr                                                 -
     ⎢      Tr                        Tr           ⎥
     ⎢                                             ⎥                                                    ˆ
                                                                                                        isβ         )         )
     ⎢                    Lm                   1 ⎥                                                                  ϕrβ ϕrα              Adaptive
             0                       ωr     −                                                                                            observer
     ⎣                    Tr                  Tr ⎥ ⎦                                                                Adaptation
                                                                                                                                       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 ⎦
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               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
                                                              Hall effect

                                                                                         Estimated Speed          Reference Speed
  Software                               Digital OUT
                                                                                          (a) Current, Torque and Speed responses at
     PC            TMS320F240                            Sensors
                                                                                        transient state without stator resistance tuning

    ---           DSP Development                       Interface
                                            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
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                     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.
           (b) Torque and speed responses at steady state
                    with stator resistance tuning                [4]    D. Casadei, G. Serra and A. Tani “Implementation of Direct Torque
                                                                        Control Algorithm for Induction Motors Based on Discrete Space
         Fig.7 Current, Torque and Speed responses with
                                                                        Vector Modulation” IEEE Transactions on Power Electronics, Vol.
            stator resistance tuning at low speed (100rpm)
                                                                        15, N°4 ,July 2000.
                          and rated load (2Nm)
                                                                 [5]    J. Maes and J. Melkebeek “Adaptive Flux Observer for Sensorless
                                                                        Induction Motor Drives with Enhanced Dynamic Performance” in
                                                                        Proceedings of 1999 European Power Electronics Conference,
                      VII. CONCLUSION                                   Lausanne, Switzerland.
   This paper presents an induction motor drive technique        [6]    Seok Ho Jeon,, Kwang Kyo Oh, and Jin           Young Choi “Flux
using the DSVM-DTC strategy. 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.

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