A globally converging observer of mechanical variables for senso...
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A
Globally Converging Observer
of
Mechanical Variables for Sensorless PMSM
B.
Nahid Mobarakeh, F. Meibody-Tabar, F.M. Sargos
Groupe de Recherche en Electronique et en Electrotechnique de Nancy,
CNRS
UPRESA 7037
Institut National Polytechniquc dc Lorraine,
2,
Ave. de la foret de Hayc.
545
I6
Vandocvrc-Lbs-Nancy, Francc.
Tel: +33 3 83
59
59
59
-
Fax: t33
3
83
59
56
53
bnahidmo@yahoo.com
Abstruct-
This paper analyzes h'latsui's paper which
presented two
PMSM
mechanical sensorless control methods
111.
Our studies show that the convergence of the estimated
variables depends on their initial values and is not guaranteed.
We propose a simple solution to start up the motor from any
rotor initial position by modifying Matsui's methods.
A
new
nonlinear model
of
PMSM
for mechanical sensorless application
is
also
presented. Simulation and experimental results illustrate
the validity of the model and the applicability of this approach.
1.
INTRODUCTIOh
Permanent Magnet Synchronous Machines (PMSM) are
successfully uscd in different domains becausc of their high
cfficicncy and good controllability. In vcctor control of
a
PMSM the rotor position must be known instantaneously.
This can be achieved by using
a
position sensor. The cost of
mechanical sensors, the difficulty to place them, and the lack
of reliability of the motor encourage rcscarchcrs to avoid thcir
use.
So,
the
scnsorless control of PMSM has been studicd for
about ten years
[
1-71. There are different solutions to evaluate
the mechanical vanables of the motor. Three different
categories can be distinguished
1
-
techniques based on the machine's physical properties,
2-
model-based techniques,
3- known techniqucs of the control theory
as
Extcndcd
Kalnian Filtcr (EKF) or state obscrvcrs.
The rotor position observation based on the back-emf
calculation (second category) is stable enough over
10%
of
the rated speed 131. In this paper, we analyze two model-based
techniques using nonlinear analyzing tools. Thcsc techniqucs,
proposed by N. Matsui
111,
arc casy to implement with a
DSP.
The experimental results show that they are really efEcient.
But at standstill, without using any specific starting
procedure, the niotor cannot start up from any arbitrary initial
rotor position. Some reliable starting procedures may be used
to start up the motor
[6]:
They exploit the physical properties
of
the machinc (first catcgory). But they are not suitable for
high specd applications. In addition, if Matsui's observcrs losc
the rotor position for any reason, they are not always capable
of
converging again. and the motor stops down. Thus,
a
globally converging solution of the model-based techniques is
preferable for both starting up and robust working.
In this papcr, wc propose a new modcl of PMSM for
sensorless control purposes. Sensorless control of the
PMSM
conies down to a state regulation problem using this
approach. Matsui's observers are analyzed using this model;
we prove tliat their domain of convergence is not global and is
limited to an initial position error between
-n/2
and
+n/2
if
a rapid correction is required
in
start
up.
This analysis gives
the idea
of
a modification of these methods which guarantees
the global convergence of the rotor position, for any initial
error. Simulation and experimental results show the validity
and thc efficiency of this approach.
The proposed model is presented in the next section.
Matsui's first method is presented and analyzed in the third
section, as well as our simple solution to it. The second
method of Matsui will be presented and analyzed, and its
convergence problem
is
solved by a simple modification, in
the fourth section. In the fifth section, the simulation and
experimental results illustrate the validity of
our
approach.
11. PMSM MODEL
Consider
a
non-salient-pole PMSM with a sinusoidal
back-emf waveform. For our purpose, we use
a
particular
Park
6
-
y
reference frame
(Fig.
11-
I)
in
which
the
electrical
equations can be expresscd
as
follows:
Llis
=
-Rig
-k
pLiyR,
-
e6
+
v6
dt
I
(11-1)
(I
.
L-i,
dt
=
-Ki,
-
pLigQ,
-
e-f
+
1'
Y
where
v6,
I>.{,
is
and
i,
are the
6-y
componeiits of stator
voltage and current vectors. and
R,
L,
p
and
KS
are the
paramctcrs of the modcl.
Q,
=
&/p
is the mcchanical angular
spccd of
6
-y
frame.
rg
and
e.{
arc thc stator back-cmf
components on
6
-
y
frame defined by:
qj
=
e.sin
cp
e.
=c.cos(P
i
(11-2)
where
cp
=
19-
8,
and
e
=
K,Q
with
SL
=
6/p
as the rotor
mechanical angular speed.
Fig.
11-
1.
6
-
y
and
d-q
reference frames.
0-7803-5692-6/00/!$10.00
(c)
2000
IEEE
885
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