Research on SVM-based direct torque control for PMSM of artillery speed servo system

Research on SVM-Based Direct Torque Control for PMSM of Artillery Speed
Servo System
CHEN Teng-fei, HAN Chong-wei, XIE Yi-na,ZHAO Yu-he
Northwest Institute of Mechanical and Electrical Engineering
E-mail: chentengfe[email protected]om
Abstract: The performance of direct torque control (DTC) based on space vector modulation (SVM) for permanent
magnet synchronous motor (PMSM) of artillery speed servo system is researched in this paper. The PMSM of artillery
speed servo system has small stator inductance and permanent magnet flux linkage, so high sampling interval is needed
to reduce torque ripples when using classical DTC scheme. A SVM-based DTC scheme is applied in artillery speed servo
system and the simulation is done. The simulation results indicate that the speed response of SVM-based DTC
(SVMDTC) is as fast as classical DTC and the motor’s torque ripples are small. By using the SVM-based DTC scheme a
better performance at low speed and a wider speed range is achieved.
Key Words: SVM-based DTC, PMSM, Artillery speed servo system
1 Introduction
Permanent magnet synchronous motors are widely applied
in modern artillery speed servo system due to their
advantages of small size, high power density and
maintenance-free. As calculations are executed in
stationary frame, DTC for PMSM uses no current
controller and only depends on stator resistance parameter,
which yields a faster torque response and less parameter
dependence than the vector control. With the features of
fast dynamic response and robustness, the DTC-based
PMSM servo system becomes a popular issue of high
performance AC motor servo system. [1][2]
The classical DTC (CDTC) scheme for PMSM proposed in
[3] uses two hysteresis comparators for stator flux linkage
and electromagnet torque respectively. The instantaneous
error values of stator flux linkage and electromagnet torque
combined with the section number containing the stator
flux vector are inputted into a switching table to choose a
proper voltage vector to control the motor. So low
sampling frequency often leads to large torque ripples. It is
the main drawback of the classical DTC scheme. [4] The
sampling frequency is limited by some physical factors
such as the microprocessor computing capability and the
efficiency of power devices in practical application. The
cost effectiveness is low when only the sampling
frequency of control system is increased. Predictive
control methods are used in [5] [6] to reduce the torque
ripples but the predictive control algorithm is complicate
and the effect at high speed is not obvious. The SVMDTC
schemes for interior and surface mounted PMSM are
proposed in [7] [8] .The torque ripples are tremendously
reduced and the system sampling frequency is not very
high. Both of the PMSM used in [7] [8] meet the
requirements described in [3] but their speed is not very
high. The DC bus voltage of the PMSM used in artillery
speed servo system is low and the motor’s stator
inductance is very small, which is different from the
PMSM in [7] [8].It is worth investigating the performance
of SVMDTC for this kind of PMSM.
In this paper, the structure and features of the artillery
speed servo system are introduced firstly. Then the model
of the SVMDTC for PMSM of artillery servo system is
built and analyzed. Finally, the simulation of the
SVMDTC for PMSM and comparative analysis with
CDTC is done.
2 Structure and Features of the Artillery Speed
Servo System
The structure of the artillery speed servo system is
illustrated in Fig.1 constituting of azimuth speed servo
system and elevation speed servo system, and its main
parts include such as AC drive box, PMSM and gearbox.
Artillery speed servo system receives speed commends
given by semi-automatic console or position controller,
completes azimuth or pitching adjustment. And there is a
rotary transformer installed on the motor shaft to provide
the mechanical angle information of the rotor.
Azimuth AC
Drive Box PMSM
Azimuth
Position
Controller
Azimuth Turret
Semi-automatic
Console
Rotary
Transformer
Gear Box
Elevation
AC Drive Box PMSM
Elevation
Position
Controller
Elevation Turret
Rotary
Transformer
Gear Box
Fig. 1: Structure of the Artillery Speed Servo System
Due to the limitations of vehicle’s power supply and the
gearbox’s transmission ratio, the low DC-bus voltage and
high-speed PMSM is used. The permanent magnet flux
linkage and stator inductance of the PMSM are very small,
while amplitude of phase current is very large. When using
the CDTC scheme, a very high sampling frequency should
be applied to achieve low torque ripples and stabilized low
speed performance. But high sampling frequency will lead
to low efficiency of power device and of which the
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switching frequency is unfixed as well. By using accurate
voltage vector modulation, the performance of SVMDTC
is better than that of CDTC especially in the situation of
lower sampling frequency. SVMDTC is more suitable for
artillery speed servo system.
The PMSM of azimuth speed servo system will be used to
investigate the performance of SVMDTC for PMSM of
artillery speed servo system.
3 The SVMDTC Scheme for PMSM
The azimuth motor is non-salient pole PMSM. The
machine equations of PMSM in stator static Įȕ frame are
expressed as follows:
The stator voltage is:
s
s
d
uRi dt
d
uRi dt
α
αα
β
ββ
ψ
ψ
=+
=+
 (1)
The stator flux linkage equation is:
cos
sin
s
fe
s
fe
Li
Li
αα
ββ
ψψ
θ
ψψ
θ
=+
=+
(2)
The electromagnet torque equation is:
3sin
2
3()
2
n
efs
s
n
s
p
TL
pii
L
α
ββ
α
ψψ
δ
ψψ
=
=−
(3)
Where
R
s
stator resistance
L
s
stator inductance
ȥ
f
permanent magnet flux linkage
ȥ
s
stator flux linkage
p
n
pole pairs
į load angle
ș
e
electric angle of permanent magnet flux linkage
u
Į
u
ȕ
Į-axis and ȕ-axis stator voltage
i
Į
i
ȕ
Į-axis and ȕ-axis stator current
ȥ
Į
ȥ
ȕ
Į-axis and ȕ-axis stator flux linkage
T
e
electromagnet torque
The ȥ
f
and L
s
of PMSM can be considered unchanged. So
the electromagnet torque T
e
is a function of stator flux
linkage ȥ
s
and load angle į.
In a very short sampling interval T
s
of the digital control
system, the equation (1) can be rewritten as:
_
_
_
_
cos( ) cos
sin( ) sin
sref s s s
ref s
s
sref s s s
ref s
s
uRi
T
uRi
T
αα
ββ
ψ
θδ
ψ
θ
ψθδψθ
+Δ −
=+
+Δ −
=+
(4)
Where ȥ
s_ref
is the reference amplitude of stator flux
linkage, ș
s
is electric angle of stator flux linkage vector, ǻį
is the increment of load angle, u
Į_ref
and u
ȕ_ref
are Į-axis and
ȕ-axis reference stator voltage for SVM unit.
Fig.2 demonstrates the SVMDTC scheme for PMSM. Two
PI regulators are used for speed controller and torque
controller respectively. Speed controller calculates the
reference torque T
s_ref
with the speed feedback errors and
torque controller calculates the increment of load angle ǻį
with the torque feedback errors. Then the ǻį together with
i
Į
, i
ȕ
ș
s
, ȥ
s
, ȥ
s_ref
are substituted into equation(4) to obtain
u
Į_ref
and u
ȕ_ref
.
Fig. 2: SVMDTC scheme for PMSM
The reference amplitude of stator flux linkage ȥ
s_ref
can be
calculated as the following equation to achieve Maximum
torque per ampere.
22
()
15
se_ref
s_ref f
nf
LT
.p
ψψ ψ =+ (5)
Due to the existence of dead-time and reverse voltage drop
of the power devises, the measurement offset of phase
current and dc-bus-voltage, it is difficult to obtain accurate
stator flux linkage using pure integrator. As a result of the
error information of stator flux linkage, the system will be
out of control. Since there is a rotary transformer installed
on the motor shaft, the accurate mechanical angle
information of the rotor can be obtained. Using p
n
multiply
the mechanical angle can easily obtain the ș
e
. Then the ȥ
Į
and ȥ
ȕ can
be calculated by equation (2). The amplitude and
the electric angle of stator flux linkage can be calculated as
follows:
22
s
α
β
ψψψ
=+
 (6)
atan( )
s
α
β
ψ
θ
ψ
=
 (7)
4 The Simulation and Analysis of SVMDTC
Scheme for PMSM
The MATLAB/SIMULINK models are established to
investigate the performance of CDTC and SVMDTC for
PMSM. The parameters of the PMSM are presented in
Table 1.
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Table 1: PMSM parameters
DC-bus voltage 56V
Stator resistance Rs 0.015ȍ
Stator inductance Ls 0.22mH
Number of pole pairs pn 4
Permanent flux linkage ȥf 0.013Wb
Inertia J 0.00077kgm2
Inertia of Load 0.0012kgm2
Load 4.2N·m
The sampling interval of speed controller and torque
controller in CDTC scheme is 300us and 75us, and the
sampling interval of speed controller and torque controller
in SVMDTC scheme is 450us and 150us.The speed, torque
and phase current of the PMSM will be compared at
reference speed of 20r·min-1and 2500r·min-1 respectively.
The steady states of PMSM with a torque load of 4.2N·m
and at a reference speed of 20r·min-1 are presented in Fig.4
and Fig.5, respectively. As presented in Fig.3 (a), the speed
error range of CDTC is ±20%. The speed error range of
SVMDTC is ±5% in Fig.4 (a).The torque ripples of CDTC
are about ±1.8N·m, and the higher harmonic of phase
current is large. The torque ripples of SVMDTC are about
±0.1N·m, and the phase current carve is smooth. By
comparison with Fig.3 and Fig.4, a better performance at
low speed is achieved by SVMDTC.
The dynamic states of PMSM with a torque load of 4.2N·m
and at a reference speed of 2500r·min-1 are presented in
Fig.5 and Fig.6, respectively. As presented in Fig.5 (a) and
Fig.6 (a), the time of the speed response of CTDC and
SVMDTC are almost the same. The torque ripples of
CDTC are about ±2.5N·m, however, the torque ripples of
SVMDTC are as the same as at low speed. In Fig.5 (c) and
Fig.6 (c), the spectrum of the phase current is presented for
comparative more clearly. There is a lot of higher
harmonic of phase current in CTDC except fundamental
harmonic, and in SVMDTC, there is almost no higher
harmonic between 500-2000Hz.
00.5 11.5 2
0
5
10
t/sec.
Te/N·m
(b) Electromagnetic Torque of CDTC
00.5 11.5 2
-100
0
100
t/sec.
i
A
/A
(c) phase current of CDTC
00.5 11.5 2
15
20
25
t/sec.
ω
m
/r·min
-1
• a• Speed response of CDTC
Fig.3 Static state of CDTC at speed of 20r·min-1 (a) speed
response (b) electromagnetic torque (a) phase current
00.5 11.5 2
0
5
10
t/sec.
Te/N·m
(b) Electromagnetic Torque of SVMDTC
00.5 11.5 2
-100
0
100
t/sec.
i
A
/A
(c) phase current of SVMDTC
00.5 11.5 2
15
20
25
t/sec.
ω
m
/r·min
-1
• a• Speed response of SVMDTC
Fig.4 Static state of SVMDTC at speed of 20r·min-1 (a) speed
response (b) electromagnetic torque (a) phase current
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00.1 0.2 0.3 0.4 0.5
0
5
10
15
t/sec.
Te/N·m
(b) Electromagnetic Torque of CDTC
0500 1000 1500 2000
0
10
20
(c) Spectrum of phase current of CDTC
Frequency (Hz)
|i
A
(f)|
00.1 0.2 0.3 0.4 0.5
0
1000
2000
3000
t/sec.
ω
m
/r·min
-1
• a• Speed response of CDTC
Fig.5 Dynamic response of CDTC at speed of 2500r·min-1
(a) speed response (b) electromagnetic torque (a) spectrum of
phase current
00.1 0.2 0.3 0.4 0.5
0
5
10
t/sec.
Te/N·m
(b) Electromagnetic Torque of SVMDTC
0500 1000 1500 2000
0
10
20
(c) Spectrum of phase current of SVMDTC
Frequency (Hz)
|i
A
(f)|
00.1 0.2 0.3 0.4 0.5
0
1000
2000
3000
t/sec.
ω
m
/r·min
-1
• a• Speed response of SVMDTC
Fig.6 Dynamic response of SVMDTC at speed of 2500r·min-1 (a)
speed response (b) electromagnetic torque (a) spectrum of phase
current
5 Conclusion
According to the practical features of artillery speed servo
system, a SVMDTC scheme for PMSM is designed.
Compared with CTDC scheme, SVMDTC scheme for
PMSM has a similar dynamic response and a better
performance at very low speed, and the torque ripples are
tremendously reduced as well. SVMDTC-based artillery
speed servo system has improved the control performance
of the torque and current of PMSM, and a wider speed
range is achieved.
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