Considerations about direct torque control and encoder

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					       Considerations about direct torque control and encoder-less
                  operation of induction motor drives
                      Viorica Spoiala*, Helga Silaghi* and Dragos Cristian Spoiala*
                                          Department of Electrical Drives and Automatics ,
                      University of Oradea, Faculty of Electrical Engineering and Information Technology,
     Universitatii Street, no.1, Oradea, Romania, E-Mail:,,

Abstract – The paper presents the principle of direct               the stator flux linkagespace vector determine the stator
torque control and encoder-less operation of the                    voltage space vector u s that is applied to the motor
induction machines. Direct Torque Control - or DTC -
is the most advanced AC drive technology developed by               during each sampling interval ΔT.
any manufacturer in the world. Comparative to vector
control, direct torque control (DTC) techniques need
no axis transformation and the electromagnetic torque
and the stator flux are estimated and directly
controlled by applying the appropriate stator voltage
vector. Aditionally, it is possible to estimate the rotor
speed without the use of an encoder.
Keywords: direct torque control, speed control, space

                  I. INTRODUCTION

    There are many electromechanical systems where it
is very important to precisely control their torque, speed
or position. Direct Torque Control technique is a part of
the advanced electric drive systems absolutely                                  Figure 1. Block diagram of DTC
necesssary in different fields of activity: elevators in
highrise buildings, industrial robots in automated                      Estimating the electromagnetic torque and the stator
factories, pumps and compressors systems, wind electric             flux linkage vector requires measuring the stator
systems, hybrid-electric vehicles, etc.                             currents and the stator phase voltages. The latter
    This paper is structured as follows: first is presented         quantities are indirectly calculated by measuring the dc-
the block diagram of the DTC system, then the principle             bus voltage and knowing within the digital controller the
of encoder-less DTC operation, the calculation of the               status of the inverter switches.
main quantities (stator flux, rotor flux, electromagnetic
torque and rotor speed), the calculation of the stator
voltage space vector and finally are presented some                        II. THEORETICAL CONSIDERATIONS
results of simulation, conclusions and references.
                                                                    A.  PRINCIPLE          OF     ENCODER-LESS            DTC
A.   SYSTEM BLOCK DIAGRAM                                           OPERATION

    The block diagram of the system is presented in                     The various steps in the estimator block of Figure 1
Figure 1, which includes the speed and the torque loops,            can be detailed in the following relations, where all
wthout a speed encoder. The estimated speed Ωest is                 space vectors are implicitly expressed in electrical
substracted from the reference speed Ω* and the error               radians with respect to the stator a-axis as the reference
between the two acts on the PI-controller to generate the           axis:
                                                                         1. From the measured stator voltages and currents,
torque reference signal for the stator flux linkage Ψ *                                                            r
                                                          s         calculate the stator flux linkage space vector Ψs :
which is compared with the estimated stator flux linkage                            r         r
 ˆ                                                                       2. From Ψs and is calculate the rotor flux space
Ψs,est . The errors in the electromagnetic torque and the                    r
stator flux, combined with the angular position ∠θ s of             vector Ψr and hence the speed of the rotor flux linkage

vector, where ΔTΩ is a sampling time for speed                                Therefore, the rotor flux linkage space vector in Eq.
calculation:                                                             (6) can be written as:
                 r         r                                                         r     L     r         r     r
     3. From Ψs and is , calculate the estimated                                    Ψr = r (Ψs − σL s is ) = Ψr e jθr            (8)
electromagnetic torque M:                                                                  Lm
               r                                                              We observe that similar to Eq. (1) for the stator flux
     4. From Ψr and M est estimate the slip speed Ωslip
                                                                         linkage vector, the rotor flux linkage space vector can be
and the rotor speed Ωm:                                                  expressed as follows, knowing that the rotor voltage in a
     In the stator voltage selection block of Fig.1, an                  squirrel-cage rotor is zero:
appropriate stator voltage vector is calculated to be                                                     t
                                                                         r           r                              r
applied for the next sampling interval ΔT based on the                                                                                  A

errors in the torque and the stator flux, in order to keep
                                                                         ΨrA ( t ) = ΨrA ( t − ΔT ) +     ∫   (−R r irA ) ⋅ dτ = Ψr e jθr
                                                                                                                                 ˆ          (9)
                                                                                                        t − ΔT
them within a hysteretic band.
                                                                         where the space vectors and angles (in electrical radians)
                  r r                                                    are expressed with the respect to the rotor A-axis shown
B. CALCULATION OF Ψs , Ψr , M AND Ω m                                    in Fig.2. The expression (9) shows that the rotor flux
                                 r                                       changes very slowly with time only due to a small
1.Calculation of the Stator Flux Ψs                                      voltage drop across the rotor resistance.

    The stator voltage equation with the stator a-axis as
the reference is:
                       r         r d r
                       u s = R s is + Ψs                     (1)
    The stator flux linkage space vector at time t can be
calculated in terms of the flux linkage at the previous
sampling time as:                                                            Figure 2. The position of the stator and rotor flux
  r          r                t
                                        r                                                    linkage vectors
                              ∫                     ˆ
  Ψs ( t ) = Ψs ( t − ΔT ) + (u s − R s is ) ⋅ dτ = Ψs e jθs (2)
                          t − ΔT                                         3. Calculation of the Electromagnetic Torque M
where τ is the variable of integration, the applied stator
voltage remains constant during the sampling interval                        The expression of the electromagnetic torque
ΔT and the stator current value is that measured at the                  depends on the magnitude of the stator and the rotor
previous time step.                                                      fluxes and the angle between the two space vectors.
                                                                                             p Lm ˆ ˆ
                                 r                                                      M=         Ψs Ψr sin θ sr            (10)
2. Calculation of the Rotor Flux Ψr                                                          2 L2σ
                                                                         where Lσ is the machine leakage inductance and
      It is known that [1]:                                                                     θsr = θs - θr                   (11)
                              r        r                                      The angles in the expressions (10) and (11) are
                     Ψs = L s is + L m ir                   (3)          expressed in electrical radians with respect to the stator
                     r        r        r                                 a-axis, as shown in Fig.2.
and                  Ψr = L r ir + L m is                   (4)               Eq. (1) and Fig. 2 show that the torque can be
   Calculating ir from eq. (3), results:                                 controlled quickly by rapidly changing the position of
                          r                                              the stator flux linkage space vector ( θs ), by applying an
                         Ψs      L r
                    ir =      − s is                        (5)          appropriate voltage space vector during the sampling
                         Lm Lm                                           interval ΔT, while the rotor flux space vector position θr
and subtituting it into eq. (4):                                         changes relatively slowly. Expression (10) shows that
           r      L r        L L r       r                               the desired change in torque is obtained by the change in
           Ψr = r Ψs − s r is + L m is =                                 θsr.
                  Lm          Lm
                                                                              To estimate the torque, a better expression is
                ⎡                        ⎤                               presented below [1]:
                          r⎛         2 ⎞⎥                   (6)
                                                                                                  p      r    r
             L ⎢r                   L    ⎥                                                   M = Im(Ψsconj is )
          = r ⎢Ψs − L s is ⎜1 − m ⎟⎥                                                              2
             Lm              ⎜ Ls Lr ⎟
                ⎢            ⎝ 4243 ⎥
                             1         ⎠                                 where does not appear the rotor flux linkage.
                ⎣                ( =σ)   ⎥
where the leakage factor σ is defined as:                                4.Calculation of the Rotor Speed Ωm
                       σ = 1−                               (7)              The speed of the rotor flux (in electrical rad/s) is
                                   Ls Lr                                 calculated from the phase angle of the rotor flux space
                                                                         vector (Eq. 13) as follows:

                 d      θ ( t ) − θ r ( t − ΔTΩ )
          Ωr =      θr = r                              (13)
                 dt               ΔTΩ
where the sampling interval ΔTΩ may be smaller, for
example equal to 1 ms.
   The slip speed is given by the following expression:
                            1 ⎛ Lm      ⎞
              Ω slip = R r     ⎜ L i sq ⎟
                           Ψrd ⎝ r      ⎟           (14)
   The electromagnetic torque has the expression:
                       p     ⎛L      ⎞
                  M = Ψrd ⎜ m i sq ⎟
                             ⎜L      ⎟              (15)
                       2     ⎝ r     ⎠                                                          Figure 4
   Calculating isq from Eq. (15) and substituting it into
                                            ˆ                        The roles of various voltage vectors can be tabulated in
Eq. (14) and knowing that Ψ = 2 / 3Ψ [4], we
                                     rd             r                the following table, assuming that the stator flux linkage
obtain the slip speed:                                               space vector is along the central vector:
                             ⎜ R M ⎟
                   Ω slip =         r                 (16)           TABLE 1. Effect of Voltage Vector on the Stator Flux-Linkage
                             ⎝        Ψr2 ⎟
                                          ⎠                          Vector in Sector 1
    So, the rotor speed can be calculated from (13) and                   r
(16), as:                                                                 us                M                     ˆ
                  Ωm = Ωr - Ωslip                     (17)                r             increase
                                                                          u3                                   increase
where all speeds are in electrical radians per second.                    r
                                                                          u2            increase               decrease
C.CALCULATION            OF   THE     STATOR        VOLTAGE               r             decrease
                                                                          u4                                   decrease
                                                                          r             decrease
                                                                          u5                                   increase
    In DTC often the torque and the stator flux
amplitude are controlled with a hysteretic band around
                                                                         The voltage vectors would have the same effects as
the desired values [3]. Therefore, at a sampling time the
                                                                     tabulated above, provided the stator flux-linkage space
decision to change the voltage space vector is                                                                           r
implemented only if the torque and/or the stator flux                vector is anywhere in sector 1. The use of vectors u 1
amplitude are outside their range.
                                                                     and u 6 is avoided because their effect depends on
    Selection of the new voltage vector depends on the
                                                                     where the stator flux-linkage vector is in sector 1. A
signs of the torque and the flux errors and the sector in
                                                                     similar table can be generated for all other sectors.
which the stator flux linkage vector lies.                                                         r            r
                                                                          Use of zero vectors u 0 (000) and u 7 (111) results
    The plane of the stator voltage space vector is
divided into six sectors as shown in Figure 3. The                   in the stator flux linkage vector esentially unchanged in
central vectors for each sector, which lie in the middle of          amplitude and in the angular position θs.
a sector, are the basic inverter vectors as shown in Fig.3.               In the torque expression of Eq. (10) for small values
                                                                     of θsr in electrical radians:
                                                                                             sin θsr ≈ θs - θr              (18)
                                                                     With a zero voltage vector applied, assuming that the
                                                                     amplitudes of the stator and the rotor flux linkage
                                                                     vectors remain constant:
                                                                                             M ≈ k (θ s − θ r )             (19)
                                                                     where k is a constant.
                                                                          The position of the stator flux-linkage vector
                                                                     remains essentially constant, thus Δθ s ≅ 0 . Similarly,
                                                                     the position of the rotor flux-linkage vector, with respect
                                                                     to the rotor a-axis remains essentially constant, that is,
                                                                     Δθ A ≅ 0 . However, Δθ r = Δθ m + Δθ A (Fig.2).
                                                                        r                                         r
                                                                     Therefore the position of the rotor flux-linkage vector
                                                                     changes, slowly, and the change in torque in Eq. (19)
       Figure 3 Inverter basic vectors and sectors                   can be expressed as:
                                                                                          ΔM = −k (Δθ m )                  (20)
         The choice of the voltage space vector for
sector 1 is explained below based on Fig.4 and Eq. (10)                 Eq. (20) shows that applying a zero stator voltage
and (11).                                                            space vector causes change in torque in adirection
                                                                     opposite to that of Ωm. Therefore, with the rotor rating in

a positive direction for example, it may be preferable to
                                                                                                 Torque error vs.Time
apply a zero voltage vector to decrease torque in order to            10
keep it with hysteretic band.

             III. SIMULATION RESULTS                                   0

    The Simulink model is made based on the block                          0   0.1   0.2   0.3    0.4       0.5         0.6   0.7   0.8   0.9   1
diagram of DTC control of AC drives shown in Figure
1.                                                                                                  Figure 7
    The block diagram shows that DTC has two
                                                                                                    Torque vs. Time
fundamental sections: the Torque Control Loop and the
Speed Control Loop.                                                  15
     Some parameters of the induction motor are: stator
resistance Rs = 1,56 Ω, rotor resistance Rr = 1,23 Ω,
stator reactance Xls = 4,93 Ω, rotor reactance Xlr = 5,11
Ω, mutual reactance Xm = 141 Ω, number of pairs of
poles p = 4.                                                          5

     The simulations were made in Matlab/Simulink, the                     0   0.1   0.2   0.3    0.4       0.5         0.6   0.7   0.8   0.9   1
motor having the model presented in Figure 5 and DTC
estimator model is presented in Figure 6 (the hole model                                            Figure 8
is too large):                                                                                      Speed vs. Time







                                                                       0       0.1   0.2   0.3    0.4       0.5         0.6   0.7   0.8   0.9   1

                                                                                                    Figure 9
            Figure 5. Simulink motor model                          1.79
                                                                                                        Flux vs. Time






                                                                           0   0.1   0.2   0.3    0.4       0.5         0.6   0.7   0.8   0.9   1

                                                                                                   Figure 10
             Figure 6. DTC estimator model

    We assumed a steady state motor operation At time t
                                                                        Better product quality, which can be partly achieved
= 0.2 s , a load-torque disturbance causes it to reduce to
                                                                    with improved speed accuracy and faster torque control,
one-half of its initial value. The objective is to keep the
                                                                    is obtained with DTC.
load speed constant at its initial value. Some simulation
                                                                    • Less down time which means a drive that will not trip
results are presented in Figure 7, 8, 9 and 10.
                                                                    unnecessarily, a drive that is not complicated by
    Because torque and flux are motor parameters that
                                                                    expensive feedback devices and a drive which is not
are being directly controlled, there is no need for a
                                                                    greatly affected by interferences like harmonics and
modulator, as used in PWM drives, to control the
frequency and voltage. This, in effect, cuts out the
                                                                    • Fewer products can be realized; one drive capable of
middle man and dramatically speeds up the response of
                                                                    meeting all application needs whether AC, DC or servo.
the drive to changes in required torque. DTC also
                                                                    That is a truly “universal” drive.
provides precise torque control without the need for a
                                                                    • A comfortable working environment with a drive that
feedback device[2].
                                                                    produces much lower audible noise is available.

                  III. CONCLUSIONS                                          • Controlling variables are taken directly from
                                                                    the motor
    DTC techniques are very performant, having the                          • The fast processing speeds of the DSP and
following advantages:                                               Optimum Pulse Selector hardware
• Fast torque response: this significantly reduces the                      • No modulator is needed .
speed drop time during a load transient, bringing much
improved process control and a more consistent product
quality.                                                                                  REFERENCES
• Torque control at low frequencies: compared to PWM
flux vector drives, DTC brings the cost saving benefit              [1] Ned Mohan, Advanced electric drives. Analysis, Control
that no tachometer is needed.                                          and Modeling using Simulink, Mnpere Minneapolis USA,
• Torque linearity: this is important in precision                     2001.
applications.                                                       [2] Richard Crowder, Electric drives and electromechanical
                                                                       systems, Newnes Elesevier, 2006
• Dynamic speed accuracy: after a sudden load change,
                                                                    [3] Viorica Spoiala, Helga Silaghi, D.C. Spoiala, ″Aspects
the motor can recover to a stable state remarkably fast.               about direct torque control of induction machine″, in
DTC technology allows a drive to adjust itself to varying              Proceedings of the 9th International Conference on
application needs.                                                     Engineering of Modern Electric Systems, Oradea,
• DTC not need a tachometer or position encoder to tell                Romania, pp. 244 – 247, 2007.
it precisely where the motor shaft is at all times, because         [4] N.R.N. Idris, ″Improved direct torque control of induction
of:                                                                    machines ″, PhD Thesis, Universiti Teknologi Malaysia,
          • The accuracy of the motor model                            2000.
                                                                    [5] ***** ABB DTCguide, 2009