Improved DTC relying on Hybrid Fuzzy-self tuning PI Regulator for the

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					                           ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009




      Improved DTC relying on Hybrid Fuzzy-self tuning PI Regulator for the
                  Permanent Magnet Synchronous Machine

                                             K. Nabti. K. Abed. H. Benalla
            Electrotechnic's laboratory of Constantine, faculty of engineering sciences Mentouri University,
                                       Campus Zerzara, Constantine, ALGERIA.
                                              E-mail : Idor2006@yahoo.fr

Abstract                                                          start-up. Several techniques developed to improve the
We propose in this paper a Self-adaptation PI for speed           DTC performance [3], [4], [5], [6], [7].In paper [8] the
regulation based on direct torque control (DTC) of                authors replace the conventional PI by the fuzzy logic
Permanent Magnet Synchronous Machine (PMSM).                      regulator when the output is the torque reference. In
Speed regulation with a conventional PI regulator                 paper [9] fuzzy logic is used to replace the switching
reduces the speed control precision, increases the torque         table of DTC which make possible to choose the very
fluctuation, and consequentially causes low performances          suitable voltage vector. The paper [6] realizes Fuzzy-PI
of the whole system. Using fuzzy logic method, by self-           speed regulation for induction machine; we utilize this
adaptation of conventional PI regulator parameters gives          idea for PMSM in this paper. The fuzzy control is
the appropriate Kp and Ki (proportional and integral              nonlinear and adoptive in nature, giving robust
coefficients respectively) which improve the system               performances in the face of parameter variations and load
performance. Simulation results show that the ripples of          disturbance effects. The regulator inputs are speed error
both torque and flux are reduced remarkably, small                and its change. Self-adaptation PI regulator, based on
overshooting and good dynamics of speed and torque.               conventional PI regulator; consist to adjust dynamically
                                                                  the conventional PI parameters kp and ki. Simulation
Keywords: Permanent Magnet Synchronous Machine,                   results show that the method improves the Direct Torque
Direct Torque Control, Fuzzy PI regulator.                        Control system performances. This paper consists of
                                                                  mathematical model of PMS machine, direct torque
1. Introduction                                                   control principle; fuzzy logic technique applied to DTC,
The PMSM control difficulty resides in the coupling of            simulation results with interpretation, and finally
control variables such as flux and electromagnetic torque.        conclusion.
Two principal strategies were developed almost at the
same time in two different research centers, Direct               2. Motor equations in the α, β reference
Torque Control strategy was first introduced by I.                   frame
Takahashi, in 1986 [1]. M. Depenbrock, develop a                  In the stationary α-β reference frame, the model can be
similar idea in 1988 under the name of Direct Self                expressed as [8]:
Control [2]. The DTC is one of the recent researched                             dψ α
control schemes based on the decoupled control of stator          uα = Rs .iα +
                                                                                  dt
flux and torque providing a quick and robust response                                                                     (1)
with a simple implementation in AC drives. DTC has the                           dψ β
                                                                  u β = Rs .iβ +
advantages of simplicity, good dynamic performance,                               dt
and insensitive to motor parameters except the stator              ⎡ψ α ⎤ ⎡cosθ r − sinθ r ⎤ ⎡ψ d ⎤
resistance. In DTC strategy, the speed sensor is not               ⎢ψ ⎥ = ⎢                  ⎥ .⎢ ⎥                       (2)
essential for the flux and torque estimation. Direct               ⎣ β ⎦ ⎣ sinθ r cosθ r ⎦ ⎣ψ q ⎦
Torque Control employs two hysteresis controllers to              ψ d = Ld .id + ψ m
regulate the stator flux and torque, which results an                                                                     (3)
                                                                     ψ q = Lq .iq
approximate decoupling between the flux and the torque
control. The key issue of DTC scheme is how to choose a           ⎡ψ α ⎤ ⎡ Ld .iα ⎤      ⎡cosθ r ⎤
                                                                  ⎢ψ ⎥ = ⎢ L .i ⎥ + ψ m .⎢        ⎥                       (4)
suitable stator voltage vector to keep the stator flux and        ⎣ β⎦ ⎣ q β⎦            ⎣ sinθ r ⎦
torque in their hysteresis band. The conventional DTC
                                                                  The mechanical equation given by:
disadvantages are the high torque ripples and the slow
transient response to the step changes in torque during




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                                       ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009



 dω r p
      = (Tem − TL − Bmω r )                              (5)
  dt     J
In addition, the electromagnetic torque expressed as
follow:
       3
       2
              (
Tem = p ψ α .iβ −ψ β .iα           )                     (6)
Where (uα, uβ), (iα, iβ) and (ψsα, ψsβ) are the stator
voltages, stator currents, and stator flux linkages in α, β
reference frame, Ld, Lq are the d,q axes inductance, Rs is
the stator resistance. ψm is the flux linkage of permanent
magnet, p is the number of pole pairs, Tem is the
electromagnetic torque, TL is the load torque, Bm is the
damping coefficient, ωr is the rotor speed and J is the
moment of inertia.
                                                                                        Figure1. Stator flux variation in stationary (α, β) frame
3. Direct torque control principles
3.1. Flux and torque estimation and control                                    In the DTC technique, the inverter switches obtained
In stationary reference frame, the machine stator voltage                      using the flux and torque errors, and the position of the
space vector is represented as follows:                                        stator flux within the six-region control of the flux. The
                  dψ s                                                         flux and torque errors evaluated as follows:
Vs = Rs ⋅ i s +                                                     (7)
                   dt                                                           Δψ = ψ sref − ψ s                                     (14)
                          ⎡             ⎛ 2π ⎞         ⎛ 4π ⎞ ⎤

Vs = usα + jusβ =
                         2⎢             ⎜ j⋅ ⎟         ⎜ j⋅ ⎟
                           VaN + VbN ⋅ e⎝ 3 ⎠ + VcN ⋅ e⎝ 3 ⎠ ⎥      (8)        ΔT = Tref − Tem                                                      (15)
                         3⎢                                   ⎥
                          ⎣                                   ⎦                         ⎛ψ β ⎞
                                                                               θ = tg −1 ⎜   ⎟                                                      (16)
                                                                                         ⎜   ⎟
Where: Rs, is, ψs stator resistance, current and flux                                   ⎝ψ α ⎠
respectively. VaN, VbN, VcN the three phase voltage                            Where θ is the angle between stator flux vector and α
inverter outputs given as follows:                                             axis, ψ sα , ψ sβ are the stator flux components in (α, β)
              Uc
VaN = Vsa =      (2 ⋅ C1 − C 2 − C3 )                                          reference frame.
               3
              U                                                     (9)        3.2. Switching table:
VbN   = Vsb = c (2 ⋅ C 2 − C1 − C 3 )                                          In order to determine the inverter switching pattern using
               3
              Uc                                                               flux and torque errors, two hysteresis controllers are
VcN   = Vsc =    (2 ⋅ C3 − C 2 − C1 )                                          employing. The inverter is switched based on these errors
               3
Uc is the inverter DC supply voltage, C1, C2, C3 are the                       and the position of the stator flux within the six-region
switching table outputs, and they are relevant to the                          control as can be seen from Table 1, in such a way that
switching strategy.                                                            the inverter output voltage vector minimizes the flux and
From (7) we can estimate the stator flux as follow:                            torque errors and determines the flux rotation direction.
ψ s = ψ s 0 + ∫ (Vs − Rs ⋅ i s )                                  (10)
So we can write:                                                                              n
ψ sα = ∫ (v sα − Rs i sα )dt                                                        Flux          Couple
                                                                                                                1      2       3      4      5      6
                                                                  (11)
ψ sβ = ∫ (v sβ − Rs i sβ )dt                                                                      KCem=1       V2      V3     V4     V5     V6      V1
                                                                                    Kψ=1          KCem=0       V7      V0     V7     V0     V7      V0
The module of the stator flux is:
ψ s = ψ s2α + ψ s2β                                               (12)                            KCem=-1      V6      V1     V2     V3     V4      V5
                                                                                                  KCem=1       V3      V4     V5     V6     V1      V2
ψ s is the stator flux vector, and ψ s 0 is its initial value.
                                                                                    Kψ=0          KCem=0       V0      V7     V0     V7     V0      V7
For simplicity, it is assumed the stator voltage drop Rs.is
is small and neglected, the stator flux variation can be                                          KCem=-1      V5      V6     V1     V2     V3      V4
expressed as: ∆ψs ≈ Vs.∆t.
                                                                                                    Table.1. DTC switching table.
We can estimate the electromagnetic torque using the
following relation:
                                                                               4. Control structure
        3
        2
              (
Tem = p ψ α .iβ −ψ β .iα           )                        (13)               Figure (2) illustrates the PMSM drive scheme considered
                                                                               in this investigation. The drive consists of a Fuzzy PI
We can be controlled the change of torque by keeping the
                                                                               speed controller, flux and torque controllers, space flux
amplitude of the stator flux linkage constant and by
                                                                               position, and PMSM. The rotor speed wr compared with
controlling the rotating speed of the stator flux as fast as
                                                                               the reference speed wref. The resulting error and its rate of
possible. We show in this section that both of the
                                                                               change are processed in the fuzzy PI speed controller for
amplitude and rotating speed of the stator flux controlled
                                                                               each sampling interval. The output of speed regulator
by selecting the proper stator voltage vectors as shown in
                                                                               considered as the reference torque Tref.
fig.1. The primary voltage vector Vs, is defined by the
equation (8)

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                              ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009


                                                                       Ri: If Eω is Ai, ΔEω is Bi then KP is Vi, KI is Wi.
                                                                       Where Ai, Bi, Vi and Wi denote the fuzzy subsets.


                                                                                Kp,                                  Eω
                                                                                Ki             NL          NM   NS   ZE       PS    PM   PL
                                                                                        N      L,          M,   S,   M,       S,    M,   L,
                                                                          ΔEω                  Z            S   M     L       M      S    Z
                                                                                        Z      L,          M,   L,    Z,      L,    M,   L,
                                                                                               Z            S   M     L       M      S   Z
                                                                                        P      L,          M,   L,    Z,      L,    M,   L,
                                                                                               Z            M   L     L       L      M    Z
                                                                                                 Tab1e. 2- Fuzzy Rules Base

                                                                       The inference method used in this paper is Mamdani’s
                                                                       procedure (inference) based on min-max decision. The
               Figure2. A direct torque control scheme                 firing strength (applied fuzzy operators) αi, for ith rules is
5. Fuzzy controller                                                    given by:
Speed error “Eω,” and its rate of change ΔEω are using                             (
                                                                       α i = min μ Ai (Eω ), μ Bi (ΔEω )        )               (17)
as inputs to the fuzzy controller. Proportional coefficient            By fuzzy reasoning, Mamdani’s minimum procedure
Kp and integral coefficient Ki are the outputs of the fuzzy            gives:
controller. The number of fuzzy segments is chosen to
have maximum control with a minimum number of rules.                                  (              )
                                                                       μVi (KP ) = min α i , μVi (KP )
                                                                        '
                                                                                                                                         (18)
                                                                       μW (KI ) = min (α i , μW (KI ))
Triangle and trapezoidal membership functions have                      '
been used. The fuzzy membership functions of input and                    i                            i

output variables are shown in (Fig. 3) [6].                            Where µA, µB, KP and KI are membership functions of
                                                                       sets A, B V and W of the variables Eω, ΔEω, Kp and KI,
                                                                       respectively.
                                                                       Thus, the membership functions µv and μw of the outputs
                                                                       KP and KI are given by:
                                                                                       21
                                                                                       '
                                                                                         (
                                                                       μV (KP ) = max μVi (KP )
                                                                                       i =1
                                                                                                        )
                                                                                                                                         (19)
                                                                              (KI ) = max(μ         (KI ))
                                                                                         21
                                                                                               '
                                                                       μWi                     Wi
                                                                                       i =1
                                                                        The Maximum criterion method is used for
                                                                       defuzzification. The final single-valued output is
                                                                       obtained by this method.

                                                                       6. Simulation results
                                                                       To verify the technique proposed, digital simulations
                                                                       based on MATLAB/SIMULINK have been implemented.
                                                                       The PMSM used for the simulations has the following
                                                                       parameters [10]:

    Figure3. The fuzzy membership functions of input and output
                           variables.
                                                                                              Uc[V]                                350
                                                                                              f[Hz]                                50
From the experience of simulation and experiment, the
range of coefficients kp and ki are [1, 5] and [0.005, 0.02],                           Rs[Ω]                                    0.3
respectively [6].The speed error universe of discourse is                              Ld[mH]                                   3.366
divided into seven fuzzy sets. {NL (negative large), NM                                Lq[mH]                                   3.366
(negative middle), NS (negative small), ZE (zero), PS                                 J [Kg/m2]                                10.8e-5
(positive small), PM (positive middle), PL (positive                                Bm[Nm/rad/s]                                  0
large)}. rate of change ΔEω includes 3 fuzzy subsets, it is                          ψm[V/rad/s]                               0.0776
not necessary to subdivide it, because it's changes quickly
                                                                                          p                                       5
in DTC. Output membership KP and KI, both contain                                                Table3. PMS motor parameters
four fuzzy subsets as shown in (fig. 3).
There are total of 21 rules as listed in table 2. Each                 Conventional PI regulator coefficient:
control rule can be described using the inputs variables               ki = 0.0553; kp =1.441.
speed error “Eω”, it rate of change ΔEω, and output                    For proposed DTC and conventional DTC the dynamic
variables (controller parameters ki and kp). The ith rule Ri           responses of speed, flux, and torque for the starting
can be expressed as:


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                                                                            ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009


process without load Tl=0, we applied an load torque equal to Tl=7Nm at 0.6s, at t=1.7s we remove the load torque.
We Inverse the speed at t=1s.



                                                        10                                                                                                            10
                      Electromagnetique torque (N.m)




                                                                                                                                       Electromanetic torque (N.m)
                                                         5                                                                                                             5




                                                         0                                                                                                             0




                                                         -5                                                                                                            -5




                                                        -10                                                                                                           -10


                                                              0   0.5   1            1.5     2       2.5                                                                    0   0.5   1           1.5   2        2.5
                                                                              t(s)                                                                                                         t(s)

                                                                                                                                                                                          (a2)
                                                                            (a1)

                                                                                                                                                                     100
                                                       100



                                                                                                                                                                      50
                                                        50
                                                                                                                             Speed (rad/s)
           speed (rad/s)




                                                                                                                                                                       0
                                                         0



                                                                                                                                                                      -50
                                                        -50



                                                                                                                                                                     -100
                                                       -100
                                                                                                                                                                            0   0.5   1           1.5   2        2.5
                                                              0   0.5   1            1.5     2       2.5                                                                                   t(s)
                                                                              t(s)

                                                                            (b1)                                                                                                          (b2)
                                    0.254                                                                                                         0.254

                                    0.253                                                                                                         0.253

                                    0.252                                                                                                         0.252

                                    0.251                                                                                                         0.251
                                                                                                                    stator flux (Wb)
   stator flux (Wb)




                                                       0.25                                                                                                      0.25

                                    0.249                                                                                                         0.249

                                    0.248                                                                                                         0.248

                                    0.247                                                                                                         0.247

                                    0.246                                                                                                         0.246

                                    0.245                                                                                                         0.245

                                    0.244                                                                                                         0.244
                                                              0   0.5   1            1.5     2       2.5                                                                    0   0.5   1           1.5   2        2.5
                                                                              t(s)                                                                                                         t(s)



                                                                            (c1)                                                                                                          (c2)

                                        Figure4. (a1) Torque response, (b1) speed response, (c1) flux                                                  Figure5. (a2) Torque response, (b2) speed response, (c2) flux
                                             response, for DTC with conventional PI regulator.                                                                 response, for DTC with fuzzy PI regulation.




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                                                                                                     ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009


We compare between speed response for DTC with conventional regulator and fuzzy PI speed regulator.

                                                                                                                               Fuzzy PI
                                                              100                                                                                                                                                       4
                                                                                                                               Conventional PI


                                                                                                                                                                                                                       3.5
                                                               50




                                                                                                                                                                                         Proportional coefficient kp
                                                                                                                                                                                                                        3
               Speed (rad/s)




                                                                0
                                                                                                                                                                                                                       2.5



                                                               -50                                                                                                                                                      2



                                                                                                                                                                                                                       1.5
                                                              -100


                                                                     0        0.5                1                  1.5            2             2.5                                                                    1
                                                                                                       t(s)                                                                                                                  0   0.5   1           1.5   2   2.5
                                                                                                                                                                                                                                            t(s)

                                                                                                                                                                                                                                           (a)
 Figure6. Speed responses for DTC conventional PI regulator and DTC
                          fuzzy PI regulator.
                                                                                                                                                                                                      0.019


                                                                                                                                                                                                      0.018


                                                                                                                                                                                                      0.017
                                           0.252
                                                                                                                                                               Integral coefficient ki



                                                                                                                                                                                                      0.016
                                           0.251
   Zoom stator flux (Wb)




                                                                                                                                                                                                      0.015
                                                              0.25

                                                                                                                                                                                                      0.014
                                           0.249

                                                                                                                                                                                                      0.013
                                           0.248

                                                                                                                                                                                                      0.012
                                                                                                                                                                                                                             0   0.5   1           1.5   2   2.5
                                           0.247                                                                                                                                                                                            t(s)


                                                                 1.4468 1.4469      1.447     1.4471 1.4472 1.4473 1.4474 1.4475 1.4476
                                                                                                                                                                                                                                           (b)
                                                                                                       t(s)
                                                                                                                                                             Figure9. Proportional and integral coefficient estimated using fuzzy PI
                                                                                                                                                                                           regulator.
 Figure7. Comparison between stator flux, dashed line stator flux using
    conventional PI regulator and solid line using fuzzy PI regulator.
                                                                                                                                                            The simulation results show that flux and torque
                                                                                                                                                            responses are very fast for two DTC methods. By
                                                                                                                                                            proposed DTC technique, the ripple of torque and flux in
                                                                                                                                                            steady state is reduced remarkably compared with
                                                               7.4
                                                                                                                                                            conventional DTC that reduce the acoustic noise and
                                                               7.3                                                                                          vibrations.
                           Zoom Electromagnetic torque (Nm)




                                                               7.2                                                                                          In fuzzy PI regulation good dynamic responses of torque
                                                                                                                                                            with neglected influence of load disturbances in speed
                                                               7.1
                                                                                                                                                            which restored its reference quickly.
                                                                7
                                                                                                                                                            Figures 7 (a) and (b) represent the estimated parameters
                                                               6.9                                                                                          kp and ki of the PI regulator, we observe that kp ∈ [1, 5]
                                                               6.8
                                                                                                                                                            and ki ∈ [0.005, 0.02], as shown in section 5.
                                                               6.7
                                                                                                                                                            7. Conclusion
                                                               6.6
                                                                                                                                                            In this paper, a fuzzy logic direct torque control scheme
                                                                         1.5712      1.5713      1.5713          1.5714   1.5714       1.5715               using fuzzy PI regulator technique is presented. Using
                                                                                                          t(s)
                                                                                                                                                            fuzzy logic technique, the kp and ki can be obtained
                                                                                                                                                            dynamically that gives a fast speed response. The
    Figure8. Comparison between electromagnetic torque, dashed line                                                                                         simulation results suggest that FLDTC can achieve
 stator flux using conventional PI regulator and solid line using fuzzy PI                                                                                  precise control of the stator flux and torque .Compared to
                                regulator.
                                                                                                                                                            conventional DTC, presented method the steady
                                                                                                                                                            performances of ripples of both torque and flux are
                                                                                                                                                            considerably improved.




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                          ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009



8. References                                                     9. Biographies
[1] I. Takahashi, and T. Noguchi. A new quick-response                                  NABTI .K (Master) was born in
    and high- efficiency control strategy of an induction                              11/03/1979               Constantine,
    machine. IEEE Transactions on Industry Applications.                               ALGERIA. Received an engineer
    22 (5), 820- 827, 1986.                                                            from the University of Constantine
[2] M. Depenbrock. Direct self-control (DSC) of                                        / Algeria in 2003; a master degree
    inverter-fed induction machine. IEEE Transactions on                               in electrical machines control.
    Power Electronics. 3(4), 420-429, 1988.                                            Prepare      doctoral    degree    in
[3] F. Jawad, M.B.B. Sharifian. Comparison of different                                electrical      engineering.     His
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    of induction motors. ELSEVIER, Electric Power                 and field oriented control and direct torque control for
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    2001.                                                         he worked at VSI (verrier Silice international) .
[4] Z. Longji, R. Wang. A novel direct torque control
    system based on space vector PWM. Power                                                ABED .K (Master) was born in
    Electronics and Motion Control Conference, IPEMC                                      06/02/1979            Constantine,
    2004. The 4th International. Vol.2, Page(s) 755 – 760,                                ALGERIA.
    14-16 Aug 2004.                                                                       Received an engineer from the
[5] X. Del Toro, S. Calls, M. G. Jayne, P. A. Witting, A.                                 University of Constantine /
    Arias, and J.L. Romeral, Direct torque control of an                                  Algeria in 2003; a master degree
    induction motor using a three-level inverter and fuzzy                                in electrical machines control.
    logic. Industrial Electronics, 2004 IEEE International                                Prepare doctoral degree in
    Symposium. On Vol. 2, Page(s):923 – 927, 4-7 May                                      electrical    engineering.    His
    2004.                                                         professional research in fuzzy logic and field oriented
[6] J. Yang, and J. Huang, Direct torque control system           control and direct torque control for AC machines drives.
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    Proceedings of the Fourth International Conference                                   BENALLA. H (Professor) was
    on Machine Learning and Cybernetics, Guangzhou.                                     born in Constantine, Algeria in
    568-573, 18-21 August 2005.                                                         1957. He received the MS, and
[7] M. Zelechowski, M. P. Kazmierkowski, and F.                                         Doctorate engineer degrees in
    Blaabjerg, Controller design for direct torque                                      power electronics, from the
    controlled space vector modulated (DTC-SVM)                                         National Polytechnic Institute of
    induction motor drives. Industrial Electronics ISIE                                 Toulouse, France, respectively, in
    2005, Proceedings of the IEEE International                                         1981, and 1984. In 1995, he
    Symposium. On Vol. 3, Page(s) 951 – 956, 20-23                                      received the PHD degrees in
    June 2005.                                                    Electrical Engineering from university of Jussieu-Paris
 [8] Y. Sayouti, A. Abbou, M. Akherraz, H. Mahmoudi.              VI; France. Since 1996, he is currently professor of
    Fuzzy speed control of induction motor with DTC-              Electrical Engineering in Department of Electrical
    based neural networks. Journal of Theoretical and             Engineering at Constantine University Algeria.
    Applied Information Technology in volume 04, Issue
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[9] R.Toufouti S.Meziane ,H. Benalla. Direct Torque
    Control for Induction Motor Using Fuzzy Logic.
    ACSE journal, volume (06), Issue (2), June, 2006.
[10] Xi Zhu, Z. Zi-Qiang., and H. David. Application of
    full-order and simplified EKFs to sensorless PM
    brushless AC machines. International journal of
    automation and computing 2, 179-186, 2005.




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