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					                                                                     Performance Evaluation of Rotor Flux-oriented Control on FPGA


     Performance Evaluation of Rotor Flux-Oriented Control on
                 FPGA for Advanced AC Drives
                  St´ phane Simard∗ , Rachid Beguenane∗ , and Jean-Gabriel Mailloux∗
                                 Department of Applied Sciences, University of Quebec at Chicoutimi
                                  555, boul. de l’universit´ , Chicoutimi, Quebec, G7H 2B1, Canada
                                                      E-mail: rbeguena@uqac.ca
                                     [Received February 7, 2008; accepted September 29, 2008]

Hardware implementation of mechatronic systems be-                   the computation burden of DSPs [3–5], raising the allow-
come more and more feasible with the constant de-                    able switching frequencies into the 10–15 kHz range.
velopment of simulation software tools and more per-                    Until now application-specific integrated circuit
forming computer hardware. The work presented                        (ASIC) solutions had always been judged inappropriate
here explains the use of Matlab/Simulink and Xilinx                  for motion control due to a relatively low-volume market.
System Generator tools and FPGA hardware in de-                      As a step towards the integration in ASIC technology of
signing, simulating and evaluating control laws for                  multiple hybrid control systems cooperating within tight
mechatronic systems. Particularly, this paper reports                dynamics, we have developed an FPGA prototype of
improved results for FPGA implementation and hard-                   Rotor Flux-Oriented Control (RFOC) for three-phase AC
ware/software co-simulation of a rotor flux-oriented                  induction motors.
control loop for three-phase AC induction motors. On                    RFOC is widely recognized, among vector control
FPGA, the computation time achieved for the com-                     schemes, as one of the most accurate AC machine control
plete control loop proves to be short enough that many               methods, providing the smoothest motion at low speeds
enhancements proposed in theory become possible, in-                 and efficient operation at high speeds. It is a variant of the
cluding the use of neural networks, matrix calcula-                  well-known field-oriented control method introduced by
tions, on-line monitoring, advanced control of PWM                   Blaschke in 1972 [6]. It has been selected for the present
inverter-fed AC machines, and multiple hybrid con-                   prototype to serve as a pilot application given its qualities
trols, without affecting system performance or sacri-                as one of the most used control schemes for AC drives,
ficing precision.                                                     and for the fact that it could widely benefit from custom
                                                                     hardware implementation.
                                                                        A closely competing method is direct-torque control
Keywords: AC induction motor drives, rotor flux-                      (DTC), which is an advanced version of the classical
oriented control, field programmable gate arrays, xilinx              scalar control, also called direct-self control. In contrast
system generator, simulink.                                          to RFOC, DTC operates in a stationary reference frame,
                                                                     and directly controls both torque and stator flux by in-
                                                                     verter voltage space vector selection using a lookup ta-
1. Introduction                                                      ble. Performances similar to RFOC have been claimed
                                                                     for DTC, with the added benefits of being exempt from
   With today’s ultra-high densities of integration, auto-           an explicit current controller, a PWM generator, vector
mated analysis and synthesis tools, and rapid prototyp-              transformations and knowledge of machine parameters.
ing techniques, it becomes economically feasible to im-              In the fact, DTC compared to RFOC exhibits a slightly
plement a highly complex control for mechatronic sys-                better performance at high speeds, but, due to its hys-
tems, that include analog/digital interfaces and pulse-              teresis band-based control, suffers from pulsating flux and
width modulation (PWM) generators, on a single custom                torque at low speeds, causing undesirable mechanical vi-
chip. Even for full-scale versions of advanced hybrid                brations [8, 9]. Its hardware implementation is also much
control algorithms, switching frequencies in the range               less complex.
of 16 kHz and even more, can be achieved. Previous                      The present work is aiming to show the usefulness
technologies, based on microcontrollers and digital sig-             of using Xilinx System Generator (XSG), a high-level
nal processors (DSPs), led to a total cycle time in ex-              tool for designing high-performance DSP systems un-
cess of 100 μ s, with switching frequencies in the range             der Simulink environment, to rapidly prototype a com-
of 1–5 kHz [1, 2]. This produced vibrations and disturb-             plex control algorithm such as RFOC. The combined
ing noise in the audible band. The introduction on the               XSG/Simulink tool can easily make the direct translation
market of large field-programmable gate arrays (FPGAs)                into hardware of the control algorithm while simulating
in the late 1990s has enabled the realization of separate            and evaluating its performance. Previous works towards
pulse width modulation (PWM) coprocessors to alleviate               FPGA implementation of RFOC include [10] and [11].

Journal of Robotics and Mechatronics Vol.21 No.1, 2009                                                                        113
Simard, S., Beguenane, R., and Mailloux, J.G.

Unfortunately, besides estimating hardware resources and        torque load.
execution times for every system module, no results were
reported to illustrate the profiles of the controlled sig-       2.1. RFOC Algorithm
nals. This gap is filled in this paper by giving synthe-           The derived expressions for each block composing the
sis results which are then validated by response curves         induction motor RFOC scheme, as shown in Fig. 1, are
obtained by hardware/software co-simulation. This pa-           given as follow:
per discusses the hardware/software co-simulation fea-
tures of the XSG/Simulink environment for the design and           a. Speed PI controller
verification of modular high performance algorithms for
mechatronic systems.                                                   i∗ = k pv εv + kiv
                                                                        sq                      εv dt ;             ∗
                                                                                                              εv = ωr − ωr        . . (6)
   We begin with a detailed overview of RFOC in the next           b. Rotor flux PI controller
section. Section 3 discusses the principal hardware de-
sign issues. Section 4 describes the hardware/software                 i∗ = k p f ε f + ki f
                                                                        sd                       ε f dt ;     ε f = Ψ∗ − Ψr . . (7)
co-simulation environment and methodology that served
for the development, validation and hardware synthesis of          c. Rotor flux estimator
the prototype. Simulation and hardware synthesis results
are presented in Section 5, followed by the conclusion.                   Ψr =         Ψ2α + Ψ2β
                                                                                        r     r           . . . . . . . . . . (8)
                                                                                   Ψrα                    Ψrβ
2. Rotor Flux-Oriented Control                                         cos θ =         ,       sin θ =             . . . . . . . (9)
                                                                                   Ψr                     Ψr
   RFOC algorithm consists on partial linearization of the      with
physical model of the induction motor by breaking up the                                     Lr
                                                                                  Ψrα      =     (Ψsα − σ Ls isα ) ;
stator current is into its components in a suitable refer-                                   M                       . . . . (10)
ence frame (d, q). Such frame is synchronously revolving                                      Lr
                                                                                  Ψrβ      =      Ψsβ − σ Ls isβ
along with the rotor flux space vector in order to get a sep-                                  M
arate control of the torque and rotor flux. The overall strat-          Ψsα =          (usα − Rs isα ) ; Ψsβ =             usβ − Rs isβ (11)
egy consists then in regulating speed while maintaining
rotor flux constant (e.g. 1 Wb). This provides smooth mo-        and using Clarke transformation.
tion at low speeds and efficient operation at high speeds.
                                                                                         1        2
   The RFOC algorithm is directly derived from the                     isα = isa ;isβ = √ isa + √ isb . . . . . (12)
electromechanical model of a three-phase, Y-connected,                                    3        3
squirrel-cage induction motor. This is described by equa-                                  1         2
tions in the synchronously rotating reference frame (d, q)            usα = usa ; usβ = √ usa + √ usb . . . . (13)
                                                                                            3         3
as :
                                                                   To be noticed that sine and cosine, of Eq. (9), sum up
                            d                  M d
         usd = Rs isd + σ Ls isd −σ Ls ω isq +      Ψ (1)       to a division, and therefore do not have to be directly cal-
                            dt                 Lr dt r          culated.
                                                Dd                 d. Current PI controller
                           d                 M
        usq = Rs isq + σ Ls isq +σ Ls ω isd + ω Ψr . (2)               vsd = k pi εisd + kii       εisd dt;     εisd = i∗ − isd
                                                                                                                        sd          . (14)
                           dt                Lr
                                                                       vsq = k pi εisq + kii     εisq dt;       εisq = i∗ − isq . . (15)
      d       Rr
         Ψr =    (Misd − Ψr ) . . . . . . . . . (3)
      dt      Lr                                                   e. Decoupling
          ω = Pp ωr +       isq . . . . . . . . . (4)                  usd = σ Ls vsd + Dd ;          usq = σ Ls vsq + Dq         . . (16)
                      Ψr Lr
       d ωr   3 M              D     Tl                         with
            = Pp      Ψr isq − ωr −     . . . . . (5)                                          M d
         dt   2 JLr            J     J                                 Dd       = −σ Ls ω isq +      Ψr ,
where usd and usq are d and q components of stator volt-                                       Lr dt      . . . . . . . (17)
age us , isd and isq are d and q components of stator cur-             Dq       = +σ Ls ω isd + ω Ψr
rent is , Ψr and is the modulus of rotor flux modulus,
and θ is the angular position of rotor flux angular, ω is           f. Omega (ω ) estimator
synchronous angular speed of the (d, q) reference frame                                  MRr
(ω = dθ /dt), and Ls , Lr , M are stator, rotor and mutual             ω = Pp ωr +             isq     . . . . . . . . . . (18)
                                                                                         Ψr Lr
inductances, Rs , Rr are stator and rotor resistances, σ is
the leakage coefficient of the motor, and Pp is the num-            g. Park transformation
ber of pole pairs, ωr is the mechanical rotor speed, D is                 isd            cos θ        sin θ         isα
                                                                                  =                                            . . . (19)
damping coefficient, J is the inertial momentum, and Tl is                 isq            − sin θ      cos θ         isβ

114                                                              Journal of Robotics and Mechatronics Vol.21 No.1, 2009

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