Download Vector Control Drive of Permanent Magnet Synchronous Motor Using Resolver Sensor

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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007
Vector Control Drive of Permanent Magnet
Synchronous Motor Using Resolver Sensor
Weera Kaewjinda1 and Mongkol Konghirun2 , Non-members
ABSTRACT
The rotor position is necessary to achieve the vector control drive system of Permanent Magnet Synchronous Motor (PMSM). In this paper, the resolver
sensor detecting the rotor position of PMSM is focused. The outstanding features of this sensor are
its robust structure and noise insensitivity. The
resolver algorithm is proposed and implemented in
the vector control drive system of PMSM. The proposed scheme has been verified by both simulation
and experiment using MATLAB/Simulink and the
TMS320F2812 based digital controller, respectively.
Keywords: PMSM, Resolver, Vector control drive
1. INTRODUCTION
Permanent magnet synchronous motor (PMSM)
used in servo-mechanical systems is generally called
“brushless servomotor or brushless AC servomotor”.
The power density of a PMSM is higher than one of
induction motor with the same ratings due to the no
stator power dedicated to the magnetic field production. Nowadays, PMSM is designed not only to be
more powerful but also with lower mass and lower
moment of inertia. Due to its high power density and
smaller size, PMSM has in recent years evolved as
the preferred solution for speed and position control
drives on machine tools and robots. In vector control
drive, the highly accurate position from position sensor is required to transform the abc variables to the
dq variable in the synchronously rotating reference
frame aligned with the rotor flux linkage vector. Resolver is the one of position sensors that can measure
the initial rotor position at standstill. This feature
is important to gain the maximum starting torque in
such drive system.
The resolver is also the most reliable and robust
sensor for severe environments such as high temperature. Its signals are not degraded through the long
cables. The concept of resolver is actually similar to
transformer operation. There are one rotating coil as
the primary winding and two stationary coils as the
Manuscript received on August 1, 2006 ; revised on October
25, 2006.
1,2 The authors are with department of Electrical Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, E-mail: [email protected] and
[email protected].
secondary windings. The primary coil is applied by
the high-frequency sinusoidal voltage in an order of
kHz. Two secondary coils are placed in the stator by
90 differences. Once the rotor is rotated, the induced
voltages would be produced in the secondary coils.
The amplitudes of these induced sinusoidal voltages
are modulated with the rotor position. The demodulation technique must be designed to extract the rotor
position. This demodulation process could be implemented on the R/D converter IC [1]. This chip is
designed to calculate the error between actual angle
and computed angle. This angle error is controlled
to zero, resulting in the computed angle converges to
the actual one. However, the resolver algorithm is
implemented by special IC chip which increases the
overall cost. In [2], the calculated rotor angle is obtained by the similar method. However, the calculation requires the resolver parameters, resulting in
the complicated equations of the rotor angle. The
phase lock loop demodulating method is presented in
[3]. This scheme employs the additional analog circuit that requires the parameter adjustments due to
the drift problems. In [4], the calculated position is
basically obtained by a closed loop operation. The
digital 16th-order FIR band-pass filters (to limit the
signal bandwidth) and downsamplers (to reduce the
sampling rate) are incorporated in their proposed algorithm. Obviously, the phase lag due to the filters
is noticed in the system. The angle is needed to be
compensated when implementing in the vector control drive of PMSM. Also, the computation time of
these filters is significantly long because of their high
order structure. This may not be practical when the
low-cost fixed-point digital controller is used.
In this paper, the computed rotor angle is computed by means of the feedback loop control. The error signal is introduced by the difference of the cross
product of modulated signals and measured excitation signal. Then, this error would be controlled by
PI controller. The computed rotor angle is guaranteed to be the actual one once the error becomes zero
without usage of filters. Thus, the delay effects due
to filters are eliminated. The proposed resolver algorithm is successfully implemented in the vector control drive of PMSM.
Vector Control Drive of Permanent Magnet Synchronous Motor Using Resolver Sensor
135
2. THEORY AND OPERATION
2. 1 Dynamic model of PMSM
The mathematical model of the non-salient PMSM
in the synchronously rotating reference frame aligned
with the rotor flux linkage can be expressed as follows.
Vd = rs id − ωr λq + pλd
(1)
Vq = rs iq − ωr λd + pλq
(2)
λd = Ls id + λm
(3)
λq = Ls iq
µ ¶µ ¶
3
P
Te =
(λd iq − λq id )
2
2
(4)
(5)
where Vd and Vq = the stator voltages in dq-axis;
id and iq = the stator currents in dq-axis;
λd and λq = the stator flux linkages in dq-axis;
λm = the permanent-magnet flux linkage;
Te = the electromagnetic torque;
ωr = the angular velocity of rotor;
rs = the stator resistance;
Ls = the stator self inductance;
P = the number of poles;
d
.
p = dt
Substituting equations (3) and (4) into the stator voltage equations (1) and (2), the stator current
dynamic equations in the state-space form can be derived as follows.
did
= −γid + ωr iq + βVd
dt
(6)
diq
= −γiq + ωr id + βωr λm + pVq
dt
(7)
1
Ls
rs
Ls .
where β =
and γ =
When the id current is controlled to be zero, the
stator flux linkages and torque equations (3) and (5)
become.
λd = λm
(8)
µ ¶µ ¶
3
P
(λm iq )
(9)
Te =
2
2
As a result, the electromagnetic torque is controlled
merely by the current iq , similarly to the DC motor
operation.
2. 2 The Resolver sensor
Resolver is a type of sensor that uses in servo system. The schematic of resolver is shown in Fig.1.
Three signals (i.e., excitation, sine and cosine signals) are obtained from the resolver. The sinusoidal
excitation signal (U0 ) is applied to the rotor winding. The resolver outputs (stator windings) consist
of two sinusoidal signals whose amplitudes are modulated according to the sine and cosine (U1 and U2 )
of the rotor position (φ).
Fig.1: Schematic and signals of resolver sensor
The relevant equations of rotor winding (U0 ) and
stator windings (U1 and U2 ) are summarized as follow.
U0 (t) = Û 0 · sin ωref t
(10)
U1 (φ, t) = Û 0 · k · sin φ · sin ωref t
(11)
U2 (φ, t) = Û 0 · k · cos φ sin ωref t
(12)
k = turn ratio of the resolver.
Û 0 = is the peak value
ωref = frequency (rad/sec) of the excitation signal
φ = rotor position (rad.)
Fig.2 shows the block diagram of the vector controlled drive system of PMSM using resolver sensor on
a Digital Signal Processor (DSP) based controller. In
this system, two line currents and three resolver signals are fed thru the on-chip ADCs of DSP. The controller implements the vector control algorithm and
space-vector PWM generation as well as the resolver
algorithms such as demodulation, speed calculation,
etc.
3. CALCULATIONS OF ROTOR SPEED
AND POSITION FROM THE RESOLVER
SIGNALS
Fig.
3 shows the block diagram of resolver algorithm, including the demodulation and
speed/position calculation. The algorithm attempts
to minimize the error between the actual rotor angle
φ the computed angle θ, using a feedback loop. The
error calculation is formulated basing on the following trigonometric identity.
err = (Û 0 · sin ωref t · cos θ)(Û 0 · k sin φ · sin ωref t)
−(Û 0 · sin ωref t · sin θ)(Û 0 · k cos φ · sin ωref t) (13)
err = Û 0 (t) · (Û 0 · k · sin ωref t)[sin φ cos θ − cos φ sin θ]
(14)
err = A · [sin(φ − θ)]
(15)
A = U0 (t) · (Û 0 · k · sin ωref t)
(16)
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007
Fig.2: Vector controlled drive system of PMSM using resolver sensor
This error is controlled to zero by PI controller.
The integrator is used to increase the resolution of
computed angle. Once this control loop is accomplished (i.e., err = 0), then the computed angle θ,
which is limited within 0 − 2π rad, is equal the actual
rotor angle φ.
Fig.4:
rithm
Matlab/Simulink models of resolver algo-
Fig.3: Block diagram of resolver algorithm
4. SIMULATION RESULTS
The overall system seen in Fig. 3 is created in
the Matlab/Simulink blocks as shown in Fig.4. The
excitation signal generator feeds the high frequency
excitation signal to the resolver. When the rotor is
rotated, the resolver would induce the two modulated
sinusoidal signals. To obtain the rotor position from
the resolver, these modulated signals have to be demodulated. The error signal shown in Eq. 14 is introduced and controlled by PI controller. The output
of PI would be the rotor speed, ωm . Finally, the mechanical angle, θm is obtained by the integration of
the rotor speed. The simulation results can be seen in
Figs. 5 and 6. Fig. 5 shows the modulated sine and
cosine signals from resolver sensor are demodulated
by the proposed algorithm. In Fig.6 the top trace is
the rotor speed, the middle trace is the error in Eq.
14. The mechanical angle is shown in the bottom
trace.
Fig.5: Simulation results: modulated sine and cosine signals and their demodulated signals at 600 rpm
Vector Control Drive of Permanent Magnet Synchronous Motor Using Resolver Sensor
137
Fig.6: Simulation results: rotor speed, error and
mechanical angle at 600 rpm
5. EXPERIMENTAL RESULTS
To validate the proposed method, the algorithm is
implemented on a 32-bit fixed point TMS320F2812
DSP. The speed controlled system shown in Fig. 2
is implemented to verify the proposed resolver algorithm. The ISR/PWM frequency is 10 kHz. The frequency of sinusoidal excitation signal is 1 kHz. During experiment, the PMSM is driven at a constant
speed of 600 rpm. The experimental results can be
seen in Fig. 7, the demodulated signals and computed
mechanical angle by using the proposed algorithm are
successfully obtained corresponding to the simulation
results. In Fig.8, the top trace shows the speed response for a gradual change of speed from −0.1 p.u. (600 rpm) to 0.1 p.u. (600 rpm). Obviously, the speed
response can be successfully tracked the speed command and the computed mechanical angle is shown
in the lowest trace. In the middle trace, the error in
Eq. 14 is controlled within the ±0.1 p.u. (±36◦ ) during transient. However, this error could be less if the
PI controller in resolver algorithm is further tuned
to obtain the optimal tracking of angle over a wide
range of operation.
Fig.7: Experimental results: modulated sine and cosine signals and their demodulated signals at 600 rpm
Fig.8: Experimental results: rotor speed, resolver
error and mechanical angle at 600 rpm
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6. CONCLUSIONS
In this paper, the proposed resolver algorithm has
been verified in the current controlled drive system
of PMSM. Both simulation and experimental results
are presented. According to these results, the resolver algorithm can force the angle error to zero.
Thus, the computed angle can eventually match with
the actual rotor angle. Then, the correct rotor speed
computation is guaranteed. In the future works, this
algorithm will be extensively tested in the speed controlled drive system of PMSM.
7. APPENDIX
The motor parameters and PI gains used in the
system are summarized below:
d-axis current loop: Kp = 0.5, Ki = 0.1
q-axis current loop: Kp = 0.5, Ki = 0.05
Speed loop: Kp =40, Ki = 0.2
Resolver algorithm : Kp = 0.00015,Ki = 0.0008
Table 1: Parameters of the PMSM motor
Stator resistance
2.2Ω
Stator inductance
0.0029 mH
Number of poles
4
Base voltage
179.629 V
Base current
10 A
Base flux linkage
1 volt.sec/rad
Base electric frequency 200 Hz
Base Speed
6000 rpm
References
[1]
[2]
[3]
[4]
B. Murray, Hare, and A. Hirao, “Resolver Position Sensing System With Integrated Fault
Detection for Automotive Applications”, IEEE
Proceedings in Sensors, Vol. 2, pp. 864-869, 2002.
Wan Jiuqing, Li Xingshan, and Guo Hong, “The
analysis and design of high-speed brushless resolver plus R/D converter shaft-angle measurement system”, IEEE Conference Electrical Machines and Systems, Volume 1, pp. 289 - 292,
2001.
D. Hanselman, “Resolver signal requirements
for high accuracy resolver-to-digital conversion”,
IEEE Conference Industrial Electronics Society,
Vol.2 , pp. 486 - 493,1989.
A.O.Di Tommaso, and R.Miceli, “A new high
accuracy software based resolver-to-digital converter”, IEEE Conference Industrial Electronics
Society, Vol.3, pp. 2435 - 2440, 2003.
Weera Kaewjinda received a bachelor’s degree in Electrical Engineering from King Mongkut’s University of
Technology Thonburi, Thailand. Nowadays he is pursuing a Master degree
in Department of Electrical Engineering, King Mongkut’s University of Technology Thonburi, Thailand. His ongoing research is the sensor drive system
of permanent magnet synchronous motors.
Mongkol Konghirun received a B.Eng.
Electrical from King Mongkut’s University of Technology Thonburi, Thailand
in 1995. And he received M.Sc. and
Ph.D. degrees in electrical engineering
from the Ohio State University, USA in
1999 and 2003, respectively. Presently,
he is working in Electrical Engineering
department at King Mongkut’s University of Technology Thonburi, Thailand.
His research interests include electrical
machine drives, and real-time control using digital signal processors.