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7/27/2019 The Comparison of Sensorless Estimation Techniques for PMSM Between Extended Kalman Filter and Flux-linkage …
A simple rectangular integration technique is used to
produce the following recursive difference equations:
)11()
~~(
~ˆ
)]()~([~ˆ
111111111
11111
⎪⎩
⎪⎨⎧
+′++=
++=
−−−−−−−−−
−−−−−
d ck k k k k k k k k k
ck k k k k k k
QT F P P F P P
T B x f x x υ
where Fk-1 is computed for x=11
~−− k k
x .
The second step is an innovation step, correcting the
predicted state estimate and its covariance matrix througha feedback correction scheme that makes use of the actual
measured quantities; it is realized by the following
equations .
1
)ˆ(ˆ
)12(ˆˆ~)ˆ(ˆ~
11
11
11
−
+′′=
⎪⎩
⎪⎨⎧
−=
−+=
−−
−−
−−
R H P H H P K
P H K P P
x H y K x x
k k k k k
k k k k k k k
k k k k k k k k
IV. EXPERIMENTAL SETUP
Figure 3 DSP-control PMSM experimental rig
Sensorless algorithms of EKF and RLKF are implemented
in the experimental set-up including : PMSM ACM2n320-
4/2-3, TMS320C31-50 DSP DSK , MOSFET inverter andDC shunt motor as a load generator. PMSM ACM2n320-
4/2-3 has the specification given in table 1:
TABLE I. PMSM SPECIFICATION
Rated power 1.4kW
Rated DC-link voltage 350V
Pole pair number 3
Phase resistance 1Ω
Phase inductance 5.5mH
Rated speed 4000rpm
The controller chosen is TMS320C31DSK which embeds
DSP TMS320C31-50 on board; The peripheral out-data/acquisition cards are respectively based on 12- bit
Analogue-to-Digital converter AD678 and Digital-to-
Analogue converter DA767, the system sub-rack frameobeys the Euro-card standard. The operation frequency of DSP is 50MHz. The position sensor is an optical encoder
which has a precision of 2048 pulse per turn.
V. EXPERIMENTAL R ESULT
A. Estimation Error Comparision:
The average error for rotor position by FLO is 8.09º/cycle
shown in figure 4. The error analysis shows that the angleerror via FLO is less than 10° in absolute position angle [-
180°, 10°] while the error via FLO falls into range [10°,
20°] in the absolute position angle [10°, 180°]. Inevitably,the maximum error in the sensorless controlled PMSM
always occurs at the start and end of the cycle when the
error can be up to ±360°. This type of edge error
occasionally occupies about 10° of a cycle for FLO.
position estimation via flux linkage observer (FLO)
-360.0
-310.0
-260.0
-210.0
-160.0
-110.0
-60.0
-10.0
40.0
90.0
140.0
190.0
0 0.005 0.01 0.015 0.02
time(s)
p o s i t i o n ( d e g r e e
real position es timated pos ition error
position estimated error in flux linkage observer (FLO)
-30.0
-20.0
-10.0
0.0
10.0
20.0
30.0
0.00 0.01 0.01 0.02 0.02
time(s)
p o s i t i o n ( d e g r e e )
Real position Estimated position error
Figure 4 Estimated position (top) and error (bottom) via FLO
Figure 5 illustrates the position estimation via EKF anderrors. P40 and Q40 represent the initial value of state
covariance P0(4) and noise covariance Q0(4), which
determines the convergence precision for EKF. Explicitly
the estimation error via EKF is distributed quite even in
amplitude other than that of FLO. The average error is
about 12.4°/ cycle. The error analysis denotes that mosterrors fall in the range [10°, 20°], a minority of errors
occur beyond the average value. The edge error shift
where maximum error occurs is about 13°.
Position estimation via EKF P40=2E-12,Q40=-12
-400.0
-300.0
-200.0
-100.0
0.0
100.0
200.0
0.000 0.005 0.010 0.015 0.020 0.025 0.030
time(s)
p o s i t i o n ( d e g r e e )
rea l pos it ion est ima ted pos it ion error
(a)
656
7/27/2019 The Comparison of Sensorless Estimation Techniques for PMSM Between Extended Kalman Filter and Flux-linkage …
capability of tracking instantaneous position transition
caused by operation in four-quadrant. However, FLOwould produce fugacious oscillation when speed
switching in 4-quadrant occurs in the angular positionwhich is not only the peak value (+π) in the clockwise
direction but also the same value (-π) in the anticlockwise
direction. When speed via FLO passes zero-speed, theinitial error caused via FLO is relatively larger than thatvia EKF. This also proves that EKF has a very strong self
start-up capability. The phase shift caused via FLO is still
obviously smaller than that via EKF regardless of the error
analysis mentioned above.
Speed Response in 4 QUADRA EKF Operation
-1500.00
-1000.00
-500.00
0.00
500.00
1000.00
1500.00
16 21 26 31
time(s)
S p e e d
( r p m )
spe ed c omma nd S pee d Respo nse via EK F
(b) Figure 10 shows that FLO and EKF both track real
position transition at the negative peak value – π where
PMSM passes zero-speed from clockwise to anticlockwisedirection. Fugacious oscillation happened in figure 9 (a)
also can be seen in figure 10 (a). EKF causes phase lag for
positive jump to π while FLO causes no phase lag.However, FLO takes a little longer time to get close to
real track while EKF has no lag to converge into real track
promptly.
Figure 8 Speed response in four-quadrant region by FLO(a) and EKF(b)
The modern servo industry requires actuators such as
PMSM to acquire the capability of speed zero crossing,which allow actuators to switch among 4 quadrants.
Actuators should go through zero velocity promptly
without any delay from the switch instructs from
microprocessor. Figure 8 compares the characteristics of
the velocity zero-crossing ability of FLO and EKF.Bidirectional speed command would lead PMSM to pass
zero from +1000rpm to -1000rpm or from -1000rpm to
+1000rpm.Figure 8 (b) shows that estimated speed via EKF smoothly
crosses zero-speed and quickly reaches state-steady
command without any overshooting, or severe ripples,
even minor offset while estimated speed via FLO passeszero with high ripple and finally enter the state-steady
situation with a large offset.
E. Estimated Position transition for cross zero-speed:
Estimated position transition for rising speed
cross-zero via FLO
-250.0
-200.0
-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
0.125 0.175 0.225 0.275 0.325 0.375
time(s)
P o s i t i o n ( d e g r e e )
Real Estimated
(a)
Estimated position transition for rising speed cross-zero
via EKF
-250.0
-200.0
-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
0.7 0.9 1.1 1.3 1.5
Time(s)
P o s i t i o n ( d e g r e e )
Real Estimated
(b)
Figure 9 Estimated position transition for rising speed cross-zero
Estimated position transition for falling
spee d cross-zero via FLO
-250.0
-200.0
-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
0 .03 0 .08 0.13 0 .18 0.23
Time(s)
P o s i t i o n ( d e g r e e )
R ea l P o sit io n E st ima te d P o sit io n via FLO
(a)
Estimated position transition for falling speed cross-
zero via EKF
-250.0
-200.0
-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
0.3 0.35 0.4 0.45 0.5 0.55 0.6
Time(s)
P o s i t i o n ( d e g r e e )
Real Estimated
(b)
Figure 10 Estimated Position Transition for the falling speed cross-zero
VI. CONCLUSION
Sensorless control based on FLO and EKF both can be
applied in AC servo drives, EKF needs to solve parameter
tuning so as to match the requirement in the four-quadrant. EKF has a faster speed response than FLO. FLO
implemented by cheap floating point processors is also an
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7/27/2019 The Comparison of Sensorless Estimation Techniques for PMSM Between Extended Kalman Filter and Flux-linkage …
alternative method for time –tight development tasks. In
four quadrant regions, position error from FLO obviously
is smaller than EKF. Generally, the estimated position precision via FLO is a little higher than that of EKF.
R EFERENCES
[1] T. Senjyu, ,” Vector control of permanent magnet synchronousmotors without position and speed sensors”, Power ElectronicsSpecialists Conference, 1995. PESC '95 Record., 26th Annual
[2] Longya Xu, “Implementation and experimental investigation of sensorless control schemes for PMSM in super-high variablespeed operation”, Industry Applications Conference, 1998. Thirty-Third IAS Annual Meeting. The 1998 IEEE Volume 1, 12-15 Oct.1998 Page(s):483 - 489 vol.1;
[3] D, Yousfi,” Position and speed estimation with improvedintegrator for synchronous motor”, Industrial Electronics Society,1999. IECON '99 Proceedings. The 25th Annual Conference of the