Simulation and Experimental Studies of Speed Sensorless

International Journal of Control and Automation
Vol.7, No.1 (2014), pp.55-68
http://dx.doi.org/10.14257/ijca.2014.7.1.05
Simulation and Experimental Studies of Speed Sensorless Control of
Permanent Magnet Synchronous Motors for Mine Electric
Locomotive Drive
Yudong Li1, Yujun Zhang 2 and Tianyu Zhang 3
1
School of Electrical Engineering & Automation, Henan Polytechnic University
Jiaozuo, Henan, P. R. China
2 Corresponding Author
School of Electrical Engineering & Automation, Henan Polytechnic
University, Jiaozuo, Henan, P. R. China
3
School of Mechanical and Electrical Engineering, Henan Vocational College of
Industry and Information Technology
Jiaozuo Henan, P. R. China
1
[email protected], 2 [email protected], 3 [email protected]
Abstract
This paper presents a novel sensorless control method of permanent magnet synchronous
motors at standstill and low speed based on a low-frequency current signal injection. The
approach superimposes a persistent LF current signal into the estimated d-axis to get the
rotor position error angle-related signal by detecting the corresponding voltage response and
current response. Then the rotor position and motor speed are obtained. Theoretical analysis
and simulation results demonstrate that the approach can achieve sensorless control of
permanent magnet synchronous motors at zero and low speed, ensure good dynamic and
static performances, and achieve effective control when applied to servo system. Finally, a
test prototype system which used a digital signal processor and space vector pulse width
modulation technology has been developed. Experimental results show that the system has
better static, the effectiveness and dynamic performance of the adaptive test signals in a
sensorless controlled surface-mounted permanent magnet synchronous machines.
Keywords: Direct-current line electric locomotive, Variable frequency drive, Voltage
signal injection, Permanent magnet synchronous machine (PMSM)
1. Introduction
Where there is great love, there are always miracles. Love is like a butterfly [1]. It goes
where it pleases and it pleases where it goes [2, 3]. If I had a single flower for every time I
think about you, I could walk forever in my garden [4-6]. Within you I lose myself, without
you I find myself wanting to be lost again. At the touch of love everyone becomes a poet.
Mining electric locomotive is one of the electrical equipments of traction, most electric
locomotives driven by direct-current (DC) motor, and its speed controlled by series
connection resistances. The DC drives have complex structure, low efficiency, maintenance
of large, short life and other issue [1-3]. Today PMSM drives are gradually replacing classic
DC drives in a large number of industrial applications, taking full advantage of key features
ISSN: 2005-4297 IJCA
Copyright ⓒ 2014 SERSC
International Journal of Control and Automation
Vol.7, No.1 (2014)
of PM-motors, such as compactness, robustness, high efficiency, reliability and shape
adaptation to the working environment [2-6]. However, to achieve precisely control of
PMSM, rotor position and speed are needed. Thus mechanical position sensors are usually
installed, resulting in an increasing of the cost, size and maintenance difficulties. The
sensorless vector control of PMSM has been under keen research for decades [1-3].
Various sensorless control schemes have been presented by scholars. Generally, according
to the estimated effect at different speed ranges, sensorless control methods can be classified
into two main types [10-12]: one is to zero and low speed, and the other is applicable to
medium and high speed. The former is mostly based on high frequency model of motor.
Using the non-ideal characteristics of PMSM structure or inductor saturation effect, a highfrequency (HF) signal is superimposed on the stator voltage or stator current and rotor
position information can be received from the corresponding current component [7-12]. These
methods pose various advantages such as insusceptibility to electrical parameter variations,
good robustness and superiority of position estimation at zero and low speed. Typically, the
injected signal can be a rotating HF voltage vector, a rotating HF current vector or a pulsating
HF voltage vector. As a consequence, most of them are more suitable for interior permanent
magnet synchronous motors (IPMSM), which has inherent saliency. The pulsating HF voltage
injection is carried out by the application of a HF sinusoidal voltage signal along the
estimated synchronous reference frame, taking advantage of the saliency caused by inductor
saturation [11, 12].
In [8-10], LF current signal is injected to the stator current and the resulting response of
back-electromotive force (EMF) is used to estimate the rotor speed. This method doesn’t rely
on the rotor saliency but just the fundamental-wave model, so it’s very suitable for surfacemounted permanent magnet synchronous machines (SPMSM).
Consider special conditions of coal mine safety production. This paper presents a novel
sensorless control method based on the superimposition of a LF current vector along the
estimated PMSM model d-axis. The approach superimposes a persistent LF current signal
into the estimated d-axis to get the rotor position error angle-related signal by detecting the
corresponding voltage response and current response. Then the rotor position is obtained.
Theoretical analysis and simulation results demonstrate that the approach can achieve
sensorless control of PMSM at zero and low speed, ensure good dynamic and static
performances, and achieve effective control when applied to servo system. Finally, a test
prototype system which used a digital signal processor (DSP) and space vector pulse width
modulation (SVPWM) technology has been developed. The system device replaces the series
resistance, greatly reduces the size of the control system, and realizes the integration.
Currently, the system device has been applied to direct-current lines of the coal mine electric
locomotive.
2. Basic Principle of Sensorless Method Based on LF Injected Signals
For simplicity, several assumptions are made in the SPMSM mathematical model. The
magnetic field is spatially sinusoidal and eddy current and hysteresis losses are assumed to be
negligible. Then id = 0 rotor magnetic field oriented control strategy is adopted. The electrical
equations of the PMSM can be described in the d-q rotating reference frame as follows:
ud   Rs
u   
 q   Ld
56
 Lq  id   Ld
 
Rs  iq   0
0  id   0 
.
p

Lq  iq   f 
(1)
Copyright ⓒ 2014 SERSC
International Journal of Control and Automation
Vol.7, No.1 (2014)
where, Ld, Lq, ud, uq, id and iq are respectively d, q frame inductances, stator voltages and
currents; f is rotor flux; Rs is stator resistance; ω is electrical angular speed and p is
differential operator. The back-EMF
eq   f
(2)
.
can be identified. The electromagnetic torque Te is given by
Te 
3n p
2
 f iq .
(3)
Where n p is the number of pole pairs. The equation of motion of the system is
n
d
  p (Te  TL ) .
dt
J
(4)
where J is the total moment of inertia and TL is the load torque.
In sensorless control, the rotor position angle  is estimated based on knowledge of the
stator current and voltage. The d-axis of the controller's reference frame is fixed to the
estimated rotor position angle ˆ . Due to estimation errors, there may be a non-zero error
angle   ˆ   , between the d-axes of the rotor and controller reference frames, as shown in
Figure 1.

q
dˆ
qˆ
ˆ

o

d

Figure 1. The diagram of coordinate systems
The used control method is a variant of a method previously applied in sensorless control
of induction motors [16]. An AC test signal varying at a low angular frequency c on the daxis of the estimated frame, as follows,
ic (t )  IC sin ct  .
(5)
The injected current signal can produce harmonic component icd and icq in the d-axis and
q-axis given by
icd (t )  ic (t ) cos 
icq (t )  ic (t )sin 
.
(6)
The current component icq (t ) causes the electromagnetic torque to show a response
Tec (t ) 
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3n p
2
 f ic (t )sin  .
(7)
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Vol.7, No.1 (2014)
Combining (4), (5) and (7), assuming constant load torque, the response in speed will be
c (t )  sin 
3n p 2
2J
 f  ic (t )dt .
(8)
Finally, (2) shows a response
ecq (t )   sin 
3n p 2 f 2 I c
2 J c
sin(ct ) .
(9)
In the rotor reference frame. This response appears in the controller's reference frame as

ecd
 ecq (t )sin 
(10)
.

ecq
 ecq (t ) cos 
If the error angle is small enough, then cos   1 and sin    and the q-component of the
response in (10) is approximately
ecq  
3n p 2 f 2 I c
2 J c
sin(ct ) .
(11)
According to ecq ,  will equal zero when the amplitude Ecq is regulated to zero. The
value of Ecq can be obtained via signal process as (12):
Ecq  LPF (ecq  sin ct )  
3np 2 f 2 Ic
2 2 J c
.
(12)
Consequently, the error signal is approximately
F  
3n p 2 f 2 Ic
2 2 J c
.
(13)
The error signal is controlled to zero by a PI controller, with the output estimated speed
  k p F  ki  F dt .
(14)
In principle,  from (14) could be used as the estimate ˆ of the electrical angular speed
of the rotor. However, to improve the dynamic performance of the controller, an additional
steady-state speed value ˆ u is the part of ˆ , and by Equation (1) ˆ u is obtained as
ˆ u 
uqref  Rˆ s iqref
Lˆ i ref ˆ
.
(15)
S d
Where the reference values are used instead of the actual stator current and voltage
components, and the estimate of the permanent magnet flux is f .The final estimate ˆ , is
obtained as
ˆ  ˆu   .
58
(16)
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International Journal of Control and Automation
Vol.7, No.1 (2014)
The rotor angle estimate is finally integrated from ˆ ,
ˆ   ˆ dt
(17)
.
and used in the coordinate transformations between the stationary and controller's reference
frames. The speed and current controllers are ordinary PI controllers.
From (13), estimation error function conditioning systems can be constructed as shown in
Figure 2. The estimated speed and the estimated position can be obtained through a closed
loop regulator role.
Figure 2. The diagram of initial rotor position estimation
The convergence of the initial position can be analyzed from (13) and Figure2. If the
initial value of ˆ is zero. The convergence of the initial position can be drawn shown in
Table 1.
Table 1. The convergence of the initial position
initial position
(  /rad)
0
when ˆ =0
(ε/rad)
0
Convergence
value of ε (rad)
0
Convergence
value of ˆ (rad)
0
(0, π)
θ
0
θ
π
π
0
π
(π, 2π)
θ
2π
θ - 2π
need to be amended
2π
2π
2π
0
need to be amended
remarks
3. The System Simulation and Modeling
3.1. The System Modeling
In order to verify the correctness of the design system, the system simulation model has
been built in MATLAB, which is the current in the inner closed loop and the speed in the
outer closed loop. The control scheme proposed is shown in Figure 3. It is based on the vector
control principle and SVPWM technique. SVPWM module consists of switch time
calculation module and pulse width modulation module. The models of two parts have been
shown in Figure 4. The current component is regulated to the reference value given by the
speed controller, while the direct current component is set to zero. The outputs of the current
controllers, representing the voltage references, are then impressed to the motor using the
SVPWM technique, once the inverse transformation from the rotating to the fixed stator
reference is performed. An outer speed control loop completes the scheme. All of the
controllers used are standard PI regulators.
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International Journal of Control and Automation
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Figure 3. MATLAB model diagram of the system
3.2. Simulation Results
During simulation of LF signal injection sensorless speed control, switching frequency of
the inverter is 10 KHz. A 100 Hz LF current signal is injected, with the amplitude of 1A.
Simulation under a sudden change of speed command in 5s has been carried out, with the 1.0
rad, 2.1 rad, π rad, 4.7 rad, 5.5 rad, and 2π rad initial position and a transient speed command
from 0 rpm to 60 rpm.
Vb
-K-
1
1 Demux
ualpha,ubeta
0.5
Va
1875
1
2
t1
Vc
1
1
Ta
1
0.5
MPeriod
1
0.5
MfuncC1
0
<
CMPR1
2
-K4
NOT
2
-K-
2
Tb
Va
2
0.5
MfuncC2
-K-K-
Convert
Relay
<
Convert
CMPR2
1
t2
NOT
3
2
3
Tc
MfuncC3
Convert
0.5
<
Convert
PWM
Convert
CMPR3
NOT
Convert
M=1,f=20k
（a）Switching time calculation module
（b）Space vector pulse width module
Figure 4. Space vector PWM wave generation modulation
The initial position estimation procedure of the system runs in two phases. One is initial
rotor position estimation in 2 seconds, the other is special position judgment and initial
position correction during 2 ~ 3 seconds. The motor starts at 4.5 seconds, and the motor speed
is increasing from 0 rpm to 60 rpm.
The simulation waveforms are shown in Figure 5, Figure 6, Figure 7, Figure 8, Figure 9
and Figure 10. In these figures, (a) is ˆ and  waveforms and (b) is Position estimation error
 . Simulation results indicate the effectiveness of the position estimation during start-up,
constant speed and speed variation operation periods.
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International Journal of Control and Automation
Vol.7, No.1 (2014)
Figure 5. The estimated position and actual position waveforms simulated with
0 rpm speed command
Figure 6. The estimated position and actual position waveforms simulated with
0 rpm speed command
Figure 7. The estimated position and actual position waveforms simulated with
0 rpm speed command
Figure 8. The estimated position and actual position waveforms simulated with
0 rpm speed command
Copyright ⓒ 2014 SERSC
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International Journal of Control and Automation
Vol.7, No.1 (2014)
Figure 9. The estimated position and actual position waveforms simulated with
0 rpm speed command
Figure 10. The estimated position and actual position waveforms simulated
with 0 rpm speed command
From Figure 5, Figure 6 and Figure 7  directly converges to 0 and don’t need to be
corrected. The control system is in a steady state. But from Figure 8, Figure 9 and Figure 10
 don’t directly converge to 0 and need to be corrected. Simulation results are consistent
with the theoretical analysis. It is verified that the sensorless control method proposed is
correct.
4. The System Design
4.1 Hardware systems design
System hardware circuit is drawn as Figure 11. In order to reduce the electromagnetic
interference, the control system hardware includes the DSP controller, the power converter,
the regulate circuit, the keyboard display circuit and the auxiliary power supply circuit.
The DSP control circuit mainly consists of the DSP and the peripheral circuit, such as the
clock circuit, the simulation external storage circuit, the interface circuit, the power
management of circuit and the I/O circuit. The keyboard and display circuit mainly realizes
the system to set the parameter and the correlation parameter demonstration. Signal
conditioning circuit includes a phase current detection and conditioning circuit, the
photoelectric encoder signal isolation circuit, a hardware protection circuit and the D/A
output circuit and so on.
This control system's hardware platform uses TMS320F2812 DSP, which completes the
position estimate and the vector control. The TMS320F2812 DSP Controller is suitable for a
wide range of motor drives, which provides a single chip solution by integrating on-chip a
high computational power along with all of the peripherals necessary for electrical motor
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control. It can be directly interfaced to the power electronics board. The power electronics
board is Fuji's 2MBI600U2E-060 module, which can better meet the requirements of motor
control. The protection module offers galvanic isolated feedback signals for two motor
currents and the DC bus voltage. Motor speed provided by a tachometer can be measured
through an adjustable-gain circuit. Motor position given by an incremental encoder, signals
can also be read through the QEP.
Figure 11. Principle chart of hardware circuit
4.2 Software system design
DSP control software is mainly consists of an initialization main program and control
module flowcharts. The former is performed only once at the beginning, the latter is based on
a waiting loop interrupted by the PWM underflow event. The second module includes the
capturing interruption program and the A/D interruption program. System settings, capture
interrupt priority is higher than A/D interrupt. Figure 12 shows the initialization main
program flow chart, whose role is to initialize the system and variable, set and enable the
interrupt, then wait for interrupt. Initialization system mainly sets the initial values of the
system clock, the watch dog, the event manager, A/D interrupt, and carries on the
corresponding set. Variable initialization in the main control algorithm sets the initial value of
each variable.
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International Journal of Control and Automation
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Control routine
Initialize system
Initialize A/D
Initialize
EV
Initialize
variable
Initialize system
register
Open interrupt
Initial position
estimation
N
Interrupt occur
Y
Interrupt
program
End
Figure 12. Flowchart of the main diagram
Control routine
Save contexts
Current
sample
Orientation finish
N
Y
Calculate
speed
Ask for ?
Speed loop
Calculate three
phrase current
Current loop
End
Figure 13. Flowchart of the interrupt program
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After the system initialization and variable initializations, the software jumps to the
waiting loop. It is interrupted every time an interrupt occurs to start the control. The A/D
interrupt program flow chart is shown in Figure 13, its role is to complete all of the control
algorithm. Control system achieve different functions in different periods, this article set
selection function module in the A/D interrupt program.
4.3 The System Physical Prototype
Figure 14.Test prototype
θ θ (2rad/div) n n (60rpm/div)
Figure 15.Estimated position
nˆ
n
ˆ

t (500ms/div)
Figure 16.Estimated position
Test prototype is shown in Figure 14. The SPMSM is a 1KW experimental motor. The
waveforms are shown in Figure 15 and Figure 16. Figure 15 is estimated position waveforms
in zero speed when initial position of the SPMSM is1rad. Figure 16 is estimated position in
low speed of 60 rpm under 1rad of initial position. Analysis of test results shows that,
SVPWM modulation wave were right, three-phase sinusoidal output current waveform is
good, the low harmonic content, the speed of the motor can be fast tracked for a given value,
the adjust time is short.
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Experimental results show that the proposed algorithm estimates the rotor position
well in zero and low speed region. The system has better static, the effectiveness and
dynamic performance of the adaptive test signals in a sensorless controlled SPMSM.
5. Conclusion
This paper presented a sensorless vector control scheme for a SPMSM drive based on
the TI TMS320F2812 DSP Controller. It has been shown how the real-time processing
capabilities of this DSP controller can lead to a highly reliable and effective drive.
Driving reliability, cost effectiveness and efficiency of the system have been improved.
This paper also described the speed variation capability, TMS320F2812 and power
electronics hardware, and excellent dynamic behavior. The device has the function of
power lost maintain and speed tracking. When DC bus power sudden fails, the electric
locomotive speed reduced to a certain speed, the locomotive in the inertia runs, at this
point, realizes electric braking. When DC bus power back to normal, the inverter output
frequency which is the same to the motor speed, realizes speed tracking.
From results, the output waveforms meet the motor steady operation when input DC
bus voltage range from 160V to 340V. The device has test run for a year in Yima Coal
Industry Group, whose static and dynamic performance is good, to fully meet the
requirements of the mining electric locomotive speed. It is proved that the design of the
system is validity and feasibility.
Acknowledgements
The paper is supported by Key Open Lab of Control Engineering of Henan Province (Grant No. KG
2011-13), Education Department of Henan Natural Science Research Key Project of China (Grant
No.13A470342) and Science and Technology Research Project of China National Coal Association（
Grant No.MTKJ2012-369）.
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Authors
Yudong Li. He received his Bachelor's degree in Industrial
Automation (1999) from Henan Polytechnic University and his M.S.
degree in Control Theory and Control (2005) from HPU. Now He is
currently an assistant professor of School of Electrical Engineering
and Automation, HPU. His current research interests include
electrical control, speed-adjustment system and sensorless vector
control system.
Yujun Zhang. He received his M.S. degree in Control Theory and
Control (2010) from Henan Polytechnic University. Now he is
currently a lecturer of School of Electrical Engineering and Automation,
HPU. His current research interests include electrical control,
industrial process control and industrial computer process.
Tianyu Zhang. He received his Bachelor's degree in Industrial
Automation (1999) from Henan Polytechnic University and his M.S.
degress in Control Control (2008) from Taiyuan University of
Technology. Now he is currently a lecturer of School of Mechanical and
Electrical Engineering, Henan Vocational College of Industry and
Information Technology. His current research interests include electrical
industrial process control and industrial computer process.
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