# A Decoupling Control Strategy of IPM Machine Accounting for.pdf

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A Decoupling Control Strategy o…

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**简介：**本文档为《A Decoupling Control Strategy of IPM Machine Accounting forpdf》，可适用于电子通讯领域，主题内容包含ADecouplingControlStrategyofIPMMachineAccountingforCompensationofCrosssatu符等。

A Decoupling Control Strategy of IPM Machine Accounting for
Compensation of Cross-saturation Based on SVPWM Technique
WANG Aimeng1, SHI Wenjuan2
School of Electrical and Electronic Engineering, North China Electric Power University,
Baoding, Hebei 071003, P. R. China
1. E-mail: aimeng668@yahoo.com 2. E-mail:ishiwenjuan@126.com
Abstract: In this paper, the evaluation of magnetic saturation effects in an interior permanent magnet synchronous motor (IPMSM)
over the entire operation range including constant torque region and in flux-weakening range is presented. The decoupling control
model for IPMPM with magnetic saturation compensation based on SVPWM method is established. Upon the comparison the model
with saturation compensation and ones without saturation compensation, the simulation results show that performance of the
decoupling control system with saturation compensation is more stable and more accurate than that of without compensation in
constant power region especially operating at a higher speed. And the decoupling control system with saturation compensation
improves effectively the system following-up performance, robustness and the control accuracy.
Keywords: Decoupling Control, Compensation of Magnetic Saturation, SVPWM, IPMSM
1 INTRODUCTION
Interior permanent magnet (IPM) machine is mostly used
in electric traction application because it can exhibit a high
torque density and has a wide constant power region [1-3].
Since the effective air gap in the IPM motor is small, and
the effects of magnetic saturation and cross-saturation are
dominant, which influence its control performances [4].
Mostly previous work reported in the literature has focused
on cross saturation model and saturation impacts on IPM
machine drives [5-8]. Paper [9] reports a method of fully
decoupling the problematic cross-coupling with estimated
parameters from on-line self-tuning to improve the
performance of the current regulator. In this paper, the
purpose is to present an improved current control method
for IPM machine accounting for magnetic saturation and
cross coupling based on decoupling control method by
using SVPWM technology. Since the inductances are
function of d- and q-axes currents that vary with operating
conditions due to magnetic saturation, the compensated
value of inductance is used in the control algorithm.
Several models of IPM machine drives are set up by using
different parameters including liner and non liner magnetic
cross-saturation inductance parameters in the machine in
flux-weakening control. Through the comparison of
different models verify the excellent performance of the
control system with decoupling control and compensation
of magnetic saturation.
2 THE MATHEMATIC MODEL AND CONTROL
STRATEGIES OF IPMSM
2.1TheMathematic Model of IPMSM
The machine model in the rotor reference frame is
represented by
( )
( ) ( )
d d d q q
q q q d d f
u R pL i L i
u R pL i L i
ω
ω ψ
= +
= + + +
(1)
3 ( )
2e n f q d q d q
T p i L L i iψ = + (2)
Where id, iq are the d- and q-axes components of armature
current , ud, uq are the d- and q-axes components of terminal
voltage, Ψf are the permanent magnet flux linkage, Ld, Lq are
the d- and q-axes stator inductances, pn is the number of pole
pairs and p=d/dt.
2.2 Control Strategies of IPMSM
In the constant torque region, the reluctance torque [the
second term in (2)] developed by saliency is exploited
through the maximum torque per ampere control strategy.
The relationship between Id and Iq for the maximum torque
per ampere control as followed:
2
2
2
2 2
2( ) 4( )
f f
d q
q d q d
q a d
i i
L L L L
i I i
ψ ψ = +
=
(3)
Due to current constraint, when Ia=Iam, the maximum torque
is produced. The maximum torque per ampere control
strategy is superior to the Id=0 control method, and converts
smoothly flux-weakening control.
In the constant power region, the current and voltage are
limited by the inverter capacity, and the current and the
voltage constraint are followed:
2 2
2 2
a d q am
a d q am
I I i I
V u u V
= +
= +
(4)
In the flux-weakening constant power region, for the current
vector is on the voltage limit ellipse in all operating region,
the current vector track can be derived from Va=Vam:
2
2
2
1 ( )f amd q q
d d
Vi L i
L L
ψ
ω
= + (5)
When Va=Vam, the current vector is controlled according for
(5) in the steady state.
Proceedings of the 29th Chinese Control Conference
July 29-31, 2010, Beijing, China
1672
3 THE EFFECT AND COMPENSATION OF
MAGNETIC SATURATION
For IPM machine, due to the larger effective air-gap length
on the d-axis, the variation of magnetizing reactance Ld
depending on Id current is minimal. Since saturation in the d-
axis results in a reduced d-axis inductance, the torque
capability of the saturated motor in the constant torque range
may be slightly increased due to the increase of the saliency
ratio Lq/Ld. But the field-weakening performance is reduced
due to a reduction of the d-axis inductance.
The effective air-gap length on the q-axis is small and
the magnetic saturation is dominant. The q-axis inductance
varies depending on the q-axis current and as a result, the
control performance is affected by magnetic saturation. The
variation of the measured q- and d-axes inductance values
versus the q- and d-axes current of IPM motor used for our
experimental results are shown in Fig.1. In the low speed
range, the obvious variation of Lq is caused by the larger Iq
current due to the big torque. In the high speed range, the
torque is small, i.e the Iq is relatively small, so the variation of
Lq is minimal. Therefore the effects of magnetic saturation
exist mainly in the low speed range. The q- and d-axes
inductance values are respectively 0.47Hm and 0.2Hm in
rated operation. The cross-coupling is presented mainly as the
effect of a q-axis current on the back-emf or magnet flux, the
back-emf reducing slightly with an increase of q-axis current
due to the magnetic saturation on the d-axis. The torque and
the terminal voltage reduce when the control system operate
with maximum torque per amp control, as shown in fig.2.
0 10 20 30 40 50 60 70 80
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
Iq(A)
Lq
(H
m
)
(a)
-80 -70 -60 -50 -40 -30 -20 -10 0
0.1
0.15
0.2
0.25
0.3
0.35
Id(A)
Ld
(H
m
)
(b)
Fig.1 Variation of q- and d-axes inductance versus q- and d-axes
current (a) q-axis inductance (b) d-axis inductance
In flux-weakening range, the demagnetizing current Id is
increase while Iq must be reduced, as a result Lq increase as
shown in figure 1[10]. If the Lq is assumed to be a constant
parameter, i.e the magnetic saturation is ignored, so the
control performance become worse and the control system
may be unstable. The figure.1 shows the relationship
between Lq and Iq, Ld and Id, this information can be used to
build a lookup table to compensate the effects of magnetic
saturation. The compensation of magnetic saturation extend
the speed range in flux-weakening region as shown in the
fig.3
0 10 20 30 40 50 60 70
0
5
10
15
20
25
Is(A)
Te
(N
.
m
)
with consideration of saturation
without consideration of saturation
(a)
0 10 20 30 40 50 60 70
107
108
109
110
111
112
113
114
115
Is(A)
Te
rm
in
a
lv
o
lta
ge
(V
)
with consideration of saturation
without consideration of saturation
(b)
Fig. 2 Comparison of torque and terminal voltage vs .Is current with
consideration and without ones at the condition of MTPA region. (a)
Torque(b) Terminal voltage
0 1000 2000 3000 4000 5000 6000 7000
0
5
10
15
20
25
30
35
40
45
we(rpm)
Te
(N
.
m
)
without compensation of saturation
with compensation of saturation
Fig.3 Torque versus speed with and without compensation of
saturation
4 THE DECOUPLING ALGORITHM WITH
COMPENSATION OFMAGNETIC SATURATION
In the IPMSM vector control system, Id,Iq and Ud,Uq exist
cross-coupling which is ignored to simplify the control
strategy. But in the high-performance control system, this
simplification will affect the integration of control
performance. The d-and q-axes currents cannot be controlled
independently by Ud and Uq, due to cross-coupling effects
between d- and q-axes back-emf. In low-speed region, the
influence of cross-coupling is small on the control system.
However, the effect increases as the speed increases,
especially in high-speed flux-weakening region, the current
responses is affected by cross-coupling effect. The terminal
voltage exceeds the limited value in this region, the same
time, the current controller is saturated and the actual current
cannot follow the commanded current. So the feedforward
decoupling method is used to compensate the terminal
1673
voltage. Decoupling model is established through theoretical
analysis.
( )
dec d e q q
qec q e f d d
u u L i
u u L i
ω
ω ψ
=
= + +
(6)
In some cases, the decoupling control does not work
perfectly when the motor current is increased. In order to find
the causes of these problems, various parameters due to
magnetic saturation are examined. The decoupling block with
compensation of magnetic saturation is added to the speed
control system. It eliminates interactions between d- and q-
axes current control. The decoupling block is shown in fig 4.
di
qi
qi
di
eω
+
+
eω qi
di
Fig.4 Decoupling control model with parameters compensation
5 CONTROL SYSTEM OF IPMMOTORWITHPROPOSED
STRATEGY AND SIMULATION RESULTS
Fig.5 describes the variable-speed IPMSM Drive system on
which the decoupling scheme is investigated. The parameters
of IPM motor are listed in the Table1.
,d q
,α βq
i
di
eT
decu
qecu
uα
uβ
dqi eθ
eθ
eω
di
Fig.5 Control block diagram of the proposed decoupling control for
IPMSM with compensation of magnetic saturation.
Tab. 1 A 7.5kW IPM motor parameters
Parameter Value
Number of pole pairs
Armature resistance
Magnet flux-linkage
D-axis inductance
Q-axis inductance
Maximum torque
Output power
Maximum speed
4
0.025Ω
0.062Wb
0.2mH
0.47mH
24Nm
7.5kW
6500rpm
The decoupling control is equal to the compensation of
terminal voltage and this effect is apparent, especially in
high-speed range. The effects of proposed voltage command
compensation in the flux-weakening range are shown in
figure.6. Due to the current regulator saturation, the d- and q-
axes currents controlled by conventional current regulator
cannot follow the current commands. The responses time of
current and the speed is reduced by the proposed voltage
command compensation. The motor start quickly to the
commanded speed by higher start torque, and the followed
performance is ideal, no overshoot. When added the 5 Nm
load at 0.15s, the speed reduce slightly and is recovered
immediately. Then the control system step up from 4000rmp
to 5000rpm at 0.2s and it with decoupling control reaches the
commanded speed faster than ones without decoupling
control. The d-and q-axes currents are unstable and recover
faster than without decoupling control. The q-axes inductance
varies depending on q-axis current, according to different
operation mode (start motor, no-load operation, loaded
operation, add speed with load), as shown in figure.7. The
start torque is improved and the motor reaches quickly the
commanded speed, i.e the dynamic performance is optimal.
6 CONCLUSIONS
The simulation results indicate that the decoupling control
method can effectively improve the system following-up
performance, robustness and control accuracy. The
decoupling control eliminates unstable transient responses
due to saturation of current controller caused by the terminal
voltage exceeding the limited voltage in high-speed flux-
weakening range. The compensation of magnetic saturation
extends the speed range in flux-weakening region. Therefore,
it should find a wide application in the design of high-
performance drive system for interior permanent magnet
motor taking account for magnetic saturation. The system
will be realized and the algorithm will be verified by DSP
control system in the future work, and the decoupling control
can eliminate cross-coupling effects, especially in high-speed
flux-weakening region.
0.05 0.1 0.15 0.2 0.25 0.3
-10
0
10
20
30
40
50
t(s)
Te
(N
.
m
)
w ithout decoupling compensation
w ith decoupling compensation
(a)
0 0.05 0.1 0.15 0.2 0.25 0.3
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
t(s)
w
e
(rp
m
)
with decoupling compensation
without decoupling compensation
(b)
1674
0 0.05 0.1 0.15 0.2 0.25 0.3
-20
0
20
40
60
80
100
120
t(s)
Iq
(A
)
without decoupling compensation
with decoupling compensation
(c)
0 0.05 0.1 0.15 0.2 0.25 0.3
-100
-50
0
t(s)
Id
(A
)
without decoupling compensation
with decoupling compensation
(d)
Fig.6 Step responses of speed and torque with and without
decoupling compensation in flux-weakening range
(w* 40005000rpm,Te05Nm) (a) Torque, (b) Speed, (c)
Q-axis current , (d) D-axis current
0 0.05 0.1 0.15 0.2 0.25
1
2
3
4
5
6
7
8
x 10-4
t(s)
Ld
,L
q(m
H)
Lq
Ld
Fig.7 Variation of Lq and Ld in different operation modes
ACKNOWLEDGEMENTS
The acknowledgement is for funding of study abroad
scientific research foundation of North China Electric Power
University.
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