Direct Torque Control of Permanent Magnet Synchronous Machines by yvu15812


									           Direct Torque Control of Permanent Magnet
                     Synchronous Machines
                                                                Thomas J. Vyncke
                                        Supervisors: Jan A.A. Melkebeek and Ren´ K. Boel

   Abstract—Following increased automation of industrial processes during          β                                                 β
the past decades, the use of high-performance servo drives has expanded                                                      V3             V2
tremendously. For these drives fast and accurate torque control is needed.                                                   ¯              ¯
With the advance of power electronics, torque controlled AC drives have
been developed. Their reliability often is reduced by the dependence on                        Ψs
a motion-state sensor, measuring speed or position, and (uncertain) motor                      ¯                     V4                  Vz0         V1
parameters to achieve torque control. Direct torque control (DTC) does                                               ¯                   ¯           ¯
not need this information and as permanent magnet synchronous machines                          δ                                        Vz1              α
(PMSMs) have a high torque/inertia ratio, the combination of PMSMs and                                Ψf
DTC results in highly dynamic drives. However, torque ripple and vari-                                ¯
able switching frequency remain as disadvantages. Research on DTC for                                          α
PMSMs attempts to reduce flux and torque ripples. The research presented                                                     V5               V6
                                                                                                                            ¯                ¯
in this paper is focused on altering the original switching table and sector
selection of the DTC algorithm for digitally controlled drives, without using             Fig. 1. Control of |Ψs | and δ with VSI voltage vectors.
a motion-state sensor.
   Keywords—torque control, permanent magnet synchronous motor                     The idea of combining the advantages of DTC and PMSMs
                                                                                into a highly dynamic drive appeared in the literature in the late
                                                                                1990’s, an overview of the research since then is given in [2].
                          I. I NTRODUCTION                                         In this paper the basic principles of DTC are discussed in sec-
                                                                                tion II. Possible performance improvements of DTC drives by
T     HE market of servo drives has been growing steadily due to
      the increasing automation of industrial processes. Direct
current (DC) motor drives used to dominate this market until
                                                                                changes in the sector and switching table selection are presented
                                                                                in section III.
quite recently, yet now permanent magnet synchronous motor
(PMSM) drives are rapidly taking over high-performance servo                           II. O PERATION P RINCIPLES OF DTC FOR PMSM S
applications, such as industrial robots. Advantages of PMSMs                      The electromagnetic torque T of a PMSM can be written as
over DC motors include low inertia, high efficiency, high power
density and high reliability. This makes PMSMSs excellent for                           3 Np |Ψs |
                                                                                 T =           ¯ (2 |Ψf | Lq sin δ − |Ψs | (Lq − Ld ) sin 2δ), (1)
use in high-performance servo drives, where a fast and accurate                         4 Ld Lq        ¯                 ¯
torque response is required. In addition, the breakthrough of                   in steady-state where Np is the number of pole pairs, Ld and Lq
PMSM drives has been accelerated by a significant reduction in                   are the direct and quadrature axis inductances respectively and
the cost of rare-earth permanent magnets.                                       δ denotes the load angle between the stator flux linkage vector
   However, PMSM drives are much more difficult to control                       Ψs and permanent magnet flux linkage vector Ψf , as shown in
than DC drives and accurate torque control has been made pos-                   ¯
                                                                                Fig.1. It is clear that, for a constant level of the¯stator flux link-
sible only by the advances in power electronics. In PMSMs the                   age, the torque T can be controlled with the load angle δ.
electromagnetic torque is usually controlled indirectly via the                    A three-phase two-level voltage source inverter (VSI) can
stator current components in a reference frame fixed to the rotor                generate eight voltage vectors as shown in Fig.1, six active vec-
flux field. To obtain this reference frame, the rotor flux position                tors (V1 − V6 ) and two zero vectors (Vz0 and Vz1 ). The stator
has to be determined and as such the rotor speed or position has                      ¯
                                                                                flux vector ¯ be calculated as
                                                                                             can                           ¯        ¯
to be measured with a motion-state sensor. The sensor, being a                                             t
tachogenerator, optical encoder or resolver, must be mounted on                                Ψs =      (Vs − Rs Is )dt + Ψs |t=0 ,             (2)
the shaft and as such reduces the reliability of the drive whilst                              ¯       0 ¯         ¯         ¯
increasing the cost.                                                            where Rs is the stator resistance, Vs and Is denote the stator
   Direct torque control (DTC) was proposed as an alternative                                                        ¯        ¯
                                                                                voltage and current space vector respectively. When the stator
control scheme for induction motors in [1]. It is an inherently                 resistance Rs is neglected, the variation of the stator flux linkage
motion-state sensorless scheme as the calculations are executed                 vector for a switch-on time Ts of the voltage vector Vi is
in a stationary reference frame. Moreover, DTC uses no current                                                                          ¯
controller and no motor parameters other than the stator resis-                                           ∆Ψs = Vi Ts .                          (3)
                                                                                                             ¯     ¯
tance, which yields a faster torque response and a lower param-                 Each voltage vector has a component radial and a component
eter dependence than field oriented control.                                     tangential to the stator flux linkage vector. The radial compo-
                                                                                nent changes the amplitude of the stator flux linkage while the
  T. Vyncke is with the Electrical Energy Laboratory (EELAB), Department of     tangential component changes the rotation speed of the stator
Electrical Energy, Systems and Automation (EESA), Ghent University (UGent),
St.-Pietersnieuwstraat 41, B-9000, Gent, Belgium. Tel: +32 (0)9 264 3442,       flux vector and consequently the load angle. As such the stator
Fax: +32 (0)9 264 3582, E-mail:                          flux linkage |Ψs | and the torque T can be controlled with a VSI.
                                                                                                                                control, but the combination of DTC EMC and shifted sectors
T∗                                      eT                                                                              motor
      -                                                                                                                         can give better results.
                                                 switching                                                                         Also in Table I, a switching table is given that achieves max-
          |Ψs |∗                                 table                                inverter
                   -                    eΨ
                                                                                                                                imum torque change in every sector, called DTC ∆Tmax . The
                                                                                                                                sectors are defined as [(k − 1) π , k π [. This switching table is not
                                                                                                                                                                 3    3
                                                                                                                                able to control the flux and thus only can be used for dynamic
          |Ψs |                                                                          ¯
           ¯                                     Ψs            flux and                                                          torque changes (e.g. torque boosts of short duration).
                                                 ¯                                       Vs
                                                               estimator                 ¯                                         Finally, it has to be noticed that implementation with digitally
                                                                                                                                controlled inverters allows flexible changing of switching tables,
                                             Fig. 2. DTC scheme                                                                 depending on the required behaviour of the drive.
                                                                                                                                Torque (Nm)                                    Torque (Nm)
The DTC scheme in its most simple form has hysteresis com-                                                                      3                                              3

parators for the stator flux linkage error and the torque error, as
shown in Fig.2. The quantisized error for the stator flux linkage                                                                2                                              2
eΨ and the quantisized torque error eT are defined as
           (                                                              (
               1 if T ∗ − T > hh                                               1 if |Ψs |∗ − |Ψs | > Hh                         1                                              1
  eT =                                                         eΨ =                  ¯        ¯
              −1 if T ∗ − T < hl                                              −1 if |Ψs |∗ − |Ψs | < Hl
                                                                                     ¯        ¯
   with |Ψs | and T ∗ as reference values and hh , hl , Hh and Hl                                                               0                                              0
as hysteresis boundaries. Furthermore, the (αβ) plane is divided                                                                              0.1
                                                                                                                                                          0.2         0.3
                                                                                                                                                                    time (s)
                                                                                                                                                                                                             0.2     0.3
                                                                                                                                                                                                                   time (s)

in six sectors [(k − 1) π − π , (k − 1) π + π [ , k = {1, 2, ..., 6}.
                        3    6           3   6
                                                                                                                                Torque (Nm)
                                                                                                                                                                                Speed (rad/s)
The errors eΨ and eT together with k, the sector containing the                                                                                                                120

stator flux vector, are the inputs for a switching table; the output
is one of the six active vectors1 as in Table I, classic DTC.                                                                   2                                               90

                                     TABLE I
                   S WITCHING TABLES FOR DIFFERENT TECHNIQUES                                                                                                                  30
     eT    eΨ                classic DTC                     DTC EMC                      DTC ∆Tmax
      1       1                  Vk+1                           Vk                          Vk+2                                0
                                                                                                                                              0.1         0.2         0.3
                                                                                                                                                                                                 0.1         0.2     0.3
            -1                   ¯
                                 Vk+2                          V¯                           ¯
                                                                                                                                                    (c)             time (s)                           (d)         time (s)
      -1      1                  ¯
                                 Vk−1                          ¯V                           ¯
                                                                  k                                                             Fig. 3. Torque: classic DTC (a), shifted sectors (b), DTC EMC (c). Speed (d).
            -1                   ¯
                                 Vk−2                          V¯                           ¯
                                 ¯ π π                         ¯π π                         ¯ π π                                                              TABLE II
       sector                  [(k − 1)
                                                          , (k − 1)
                                                                                  [         [(k − 1)
                                                                                                                                               M OTOR PARAMETERS USED IN THE SIMULATIONS
                                                                                                                                                    Np          2       Rs     19.4 Ω
                       III. D IFFERENT SWITCHING TABLES                                                                                          base speed 1500 rpm    Ψf    0.477 Wb
                                                                                                                                                    Lq      0.4755 H    Ld    0.3885 H
   Different switching tables are demonstrated by means of sim-
ulations, with the motor parameters of Table II. The inverter DC                                                                                                IV. C ONCLUSIONS
bus voltage is 340 V and the update frequency of the controller                                                                    With the increased demand for reliable, efficient and torque-
is 10 kHz. With digitally controlled inverters a fixed cycle time                                                                controlled drives, DTC for PMSMs offers good perspectives. In
is required for the calculations and as such the gate signals of                                                                this paper is shown by simulation that, by altering switching
the inverter switches can be changed only at fixed times (i.e. ev-                                                               tables and sector selection, performance improvements are pos-
ery 0.1 milliseconds in these simulations). Clearly, as result the                                                              sible. In future research improved switching tables and sector
instantaneous errors eT and eΨ can travel out of the hysteresis                                                                 divisions will be constructed within a theoretical framework.
bounds, producing undesired torque ripples as seen in Fig.3. In                                                                                      ACKNOWLEDGEMENT
Fig. 3(d) the motor speed is given.                                                                                               T. Vyncke received a Ph.D. grant from the Special Research Fund (BOF) of
   Furthermore, additional torque ripple occurs at high speed                                                                   Ghent University during his first year of research, and is currently a Research
with a classic DTC, but can be reduced by shifting the sectors in                                                               Assistant of the Research Foundation - Flanders (FWO).
the direction of the rotation. In Fig. 3(a) and Fig. 3(b) respec-
tively, the torque is compared for a classic DTC and for DTC                                                                                                      R EFERENCES
                       π                                                                                                        [1] I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency
with a sector shift of 12 , the high-speed ripple is reduced in (b).
                                                                                                                                    control strategy of an induction motor,” IEEE Trans. Ind. Applicat., vol. 22,
   Another possible switching table for induction motors is                                                                         no. 5, pp. 820–827, Sept./Oct. 1986.
given in [4] to reduce the common-mode emissions of the drive                                                                   [2] T. J. Vyncke, J. A. Melkebeek, and R. K. Boel, “Direct torque control
and as such improve the electromagnetic compatibility (EMC).                                                                        of permanent magnet synchronous motors – an overview,” in Conf. Proc.
                                                                                                                                    3rd IEEE Benelux Young Researchers Symposium in Electrical Power En-
This switching table, called DTC EMC, is given in Table I                                                                           gineering, no. 28, Ghent, Belgium, Apr. 27–28, 2006, p. 5.
and the simulation result of Fig.3(c) proves it is applicable for                                                               [3] M. F. Rahman and L. Zhong, “Voltage switching tables for DTC controlled
                                                                                                                                    interior permanent magnet motor,” in Conf. Proc. IEEE 25th Annual Con-
PMSMs as well. Still, a deterioration of the torque ripple can be                                                                   ference of the Industrial Electronics Society (IECON’99), vol. 3, San Jose,
noticed as DTC EMC emphasizes flux control rather than torque                                                                        CA, USA, Nov. 29-Dec. 3 1999, pp. 1445–1451.
                                                                                                                                [4] M. Cirrincione, M. Pucci, G. Vitale, and G. Cirrincione, “A new direct
  1 The original scheme [1] uses eight voltage vectors, however loss of flux and                                                     torque control strategy for the minimization of common-mode emissions,”
torque control at low speeds can be avoided by using only the active vectors [3].                                                   IEEE Trans. Ind. Applicat., vol. 42, no. 2, pp. 504–517, Mar./Apr. 2006.

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