The document proposes an online method for estimating the stator resistance and permanent magnet flux in sensorless permanent magnet synchronous motor drives. An adaptive observer augmented with high-frequency signal injection is used. Excess information in the observer is used to adapt the motor parameters. At low speeds, stator resistance is estimated from a speed correction term. At medium and high speeds, permanent magnet flux is estimated from d-axis current estimation error. Steady-state and small-signal analyses investigate parameter estimation sensitivity. Adaptation laws are designed for parameter convergence shown via simulation and experiment. Stator resistance adaptation works down to zero speed in sensorless control.

1. PEDS 2007
Adaptation of Motor Parameters in Sensorless PMSM Drives
Antti Piippo, Marko Hinkkanen, and Jorma Luomi
Power Electronics Laboratory
Helsinki University of Technology
P.O. Box 3000, FI-02015 TKK, Finland
Abstract-The paper proposes an on-line method for the error. On the other hand, the back-emf is small at low speeds,
estimation of the stator resistance and the permanent magnet and the stator resistance estimate plays an important role in
flux in sensorless permanent magnet synchronous motor drives. the estimation.
An adaptive observer augmented with a high-frequency signal
injection technique is used for sensorless control. The observer Several methods have been proposed to improve the per-
contains excess information that is not used for the speed and formance of a PMSM drive by estimating the electrical
position estimation. This information is used for the adaptationparameters. In [7], an MRAS scheme is used for the on-
of the motor parameters. At low speeds, the stator resistance isline estimation of the stator resistance and the PM flux with
estimated, whereas at medium and high speeds, the permanent position measurement. Reactive power feedback is used for
magnet flux is estimated. Steady-state analysis and small-signal
estimating the PM flux in [9]. The stator current estimation
analysis are carried out to investigate the parameter estimation,
and adaptation mechanisms are defined for the parameters. The error and a neural network can be used for estimating both the
convergence of the parameter estimates is shown by simulations PM flux and the stator resistance [10]. The stator inductances
and laboratory experiments. The stator resistance adaptation and the PM flux are estimated using the steady-state voltage
works down to zero speed in sensorless control. equations and the flux harmonics, respectively in [11]. A DC-
current signal is injected to detect the resistive voltage drop
I. INTRODUCTION
for the resistance estimation in [12], and the PM flux linkage
Permanent magnet synchronous machines (PMSMs) are is estimated by taking it as an additional state of an extended
used in many high-performance applications. For vector con- Kalman filter in [13].
trol of PMSMs, information on the rotor position is required. Some parameter estimation schemes have also been devel-
In sensorless control, the methods for estimating the rotor oped for sensorless control methods. In [7], an MRAS scheme
speed and position can be classified into two categories: is applied for the stator resistance estimation. A parameter
fundamental-excitation methods [1], [2] and signal injection estimator is added to two position estimation methods for
methods [3], [4]. The methods can also be combined by estimating the stator resistance and the PM flux in [14]. In
changing the estimation method as the rotor speed varies [5], [15], these parameters are estimated using both the steady-
[6]. state motor equations and the response to an alternating
The fundamental-excitation methods used for sensorless current signal. In [14], [15], the convergence of the estimated
control are based on models of the PMSM. Hence, the parameters to their actual values is not shown. [16] proposes a
electrical parameters are needed for the speed and position method where the resistance and the inductances of a salient
estimation [7]. The errors in the stator resistance estimate PMSM are extracted from an extended EMF model. Three
result in an incorrect back-emf estimate and, consequently, electrical parameters are estimated simultaneously, but the
impaired position estimation accuracy. The operation can also behavior of the stator resistance estimate is not convincing.
become unstable at low speeds in a loaded condition. The This paper proposes a method for the online estimation of
detuned estimate of the permanent magnet (PM) flux results the stator resistance and the PM flux in sensorless control.
in incorrectly estimated electromagnetic torque [8], and also The method is based on a speed-adaptive observer that is
impairs the position estimation accuracy. Errors in the d- augmented with a high-frequency (HF) signal injection tech-
and q-axis inductances of a salient PMSM also affect the nique at low speeds [17]. The excess information available
estimation and the torque production, and can degrade the in the observer is used for the adaptation of the parameters.
current control performance. At medium and high speeds, the PM flux is estimated from
The stator resistance and the PM flux depend on the motor the d-axis current estimation error. At low speeds, the stator
temperature, and thus change rather slowly. On the other hand, resistance is estimated from a speed correction term produced
magnetic saturation decreases the inductances, which thus by the signal injection method. The sensitivity of the d-axis
depend on the load condition. The inductances can be modeled current estimation error and the speed correction term to the
as functions of the stator flux or the stator current, but an parameter errors are investigated by means of steady-state and
estimation scheme is required for the stator resistance and the small-signal analyses, and adaptation laws are designed for the
PM flux. The rotor back-emf is proportional to the PM flux and estimation of the parameters. The stability and the convergence
the resistive voltage drop to the stator resistance. At medium of the parameter estimators are investigated by means of sim-
and high speeds, the effect of the PM flux estimation error is ulations and laboratory experiments. The resistance adaptation
more significant than that of the stator resistance estimation is shown to work down to zero speed in sensorless control.
1-4244-0645-5/07/$20.00©2007 IEEE 175

2. i/
F£ where estimated quantities are marked by ^ and Us,ref is the
stator voltage reference. The estimate of the stator current and
Us,ref Ad- + / m the estimation error of the stator current are
==>justable
L-'(,Os -,pm)
--A1t
model js is = (5)
AL
is~ ~ 1 is = il
*1
-
is (6)
respectively, where iV is the measured stator current expressed
Fig. 1. Block diagram of the adaptive observer. in the estimated rotor reference frame. The feedback gain
matrix A is proportional to the rotor speed up to the nominal
speed [17].
II. PMSM MODEL The speed adaptation is based on an error term
The PMSM is modeled in the d-q reference frame fixed to
the rotor. The d axis is oriented along the PM flux, whose Fe = Clis (7)
angle in the stator reference frame is 0m in electrical radians.
The stator voltage equation is where Ci = [O Lq], i.e., the current error in the estimated q
direction is used for adaptation. The estimate of the electrical
Us Rsis + s WmJ+5
+ (1) angular speed of the rotor is obtained using a PI speed
where us [ud Uq ]T is the stator voltage, is [id iq ]T the adaptation mechanism
stator current, sb= [bd /q ]T the stator flux, Rs the stator
resistance, Wm =m the electrical angular speed of the rotor, Wm =-kpF -kiJ Fedt (8)
and
The stator flux is
J K0 -1
I where kp and ki are nonnegative gains. The gain selection is
described in [17]. The estimate Om for the rotor position is
evaluated by integrating Win
sb= Lis+ bpm (2) B. High-Frequency Signal Injection
where 14pm = [/pm O]T is the PM flux and The adaptive observer described above is augmented with a
HF signal injection method to stabilize the speed and position
L
L Lq
Ld fq] estimation at low speeds [17]. By using the HF signal injection
method with an alternating voltage u, as a carrier excitation
is the inductance matrix, Ld and Lq being the direct- and signal [18], an error signal E 2K Om proportional to the
quadrature-axis inductances, respectively. The electromagnetic position estimation error 0m = m 0-m is obtained, KS
torque is given by being the signal injection gain. The error signal is used for
correcting the estimated position by influencing the direction
Te = 3p2TJTis (3) of the stator flux estimate of the adjustable model. For the
combined observer, the adjustable model (4) is modified to
where p is the number of pole pairs.
III. SPEED AND POSITION ESTIMATION Qs = Us,ref -Rss- (m - )JQs + Als (9)
A. Adaptive Observer where
An adaptive observer [17] is used for the estimation of the
stator current, rotor speed, and rotor position. The speed and
SE: = apE + -aj
+ dt (10)
position estimation is based on the estimation error between is the speed correction term, -yp and tYj being the gains of the
two different models; the actual motor can be considered as a
PI mechanism driving the error signal E to zero. In accordance
reference model and the observer including the rotor speed with [6], these gains are selected as
estimate Wm as an adjustable model. The error term used
in a speed adaptation mechanism is based on the estimation 2Ki 2
(1 1)
error of the stator current. The estimated rotor speed, obtained /yP 2K ' 6KE
using the adaptation mechanism, is fed back to the adjustable
model. where ai is the approximate bandwidth of the PI mechanism.
The adaptive observer is formulated in the estimated rotor At low speeds, the combined observer relies both on the
reference frame. The block diagram of the adaptive observer signal injection method and on the adaptive observer. The
is shown in Fig. 1. The adjustable model is based on (1) and influence of the HF signal injection is decreased linearly as the
(2), and defined by speed increases by decreasing both the HF excitation voltage
and the bandwidth ai. At speeds higher than a threshold speed
,bs = Us,ref -Rsis- mJQs + Ais (4) WoA, the estimation is based only on the adaptive observer.
176

3. TABLE I
IV. PARAMETER ADAPTATION MOTOR DATA
The current estimation error is of the adaptive observer Nominal voltage UN 370 V
contains information that can be used for the parameter Nominal current IN 4.3 A
adaptation. In [7], [10], the components of is are used for Nominal frequency fN 75 Hz
Nominal torque TN 14.0 Nm
the adaptation of two parameters in a PMSM drive equipped Stator resistance RS 3.59 Q
with a motion sensor. Solving the parameters from the steady- Direct-axis inductance Ld 36.0 mH
state voltage equations as in [11] would require filtering to Quadrature-axis inductance Lq 51.0 mH
PM flux <bpm 0.545 Vs
prevent incorrect operation in transients. It is to be noted that Total moment of inertia 0.015 kgm2
the PMSM dynamics offer only two degrees of freedom. Since
the component iq is used for the speed estimation in this paper,
one parameter can thus be adjusted using id because it is controlled to a considerably smaller value than
In low-speed operation, the HF signal injection method the q component. In the component form, the result is
provides additional information through the speed correction R
term w . Instead of solving the parameters directly from the Rs -Lqiq10'I 0°
L gmELd opm j ej L- q - Om opm
response to the injected signal [12], wo is used here for the (16)
parameter adaptation. Hence, if wo differs from zero in steady For investigating the sensitivity of id and wo to the pa-
state or if the current estimation error id is nonzero, the motor rameter errors, the variables id and wo are solved from (16).
parameter estimates are inaccurate and the variables wo and 'd Assuming Rs<pm »> WmoLdLqiq the result is
can be driven to zero by adjusting the parameter estimates.
R,Wmiq
L 2L q
[.td Rl k
;qqiq
Rs M
l
(17)
A. Steady-State Analysis Stator Resistance Adaptation L ej fpm L Som -
L opm
At low speeds, the stator resistance estimate plays an im- It can be seen that both variables on the left-hand side depend
portant role in the speed and position estimation, particularly both on Rs and <pm. The correction term w, is selected for
in loaded conditions. To extract the sensitivity of the d-axis parameter adaptation because iq has more effect on id than on
current estimation error id and the speed correction term w, w . When using relative parameter errors, the speed correction
to the parameter errors, the combined observer is investigated term is
in steady state. The position estimation error is assumed zero 1 ( Rs + 4bpm
because the HF signal injection method is in use. W =
Ypm
Rsi
jR
mpm
s
opmbm (18)
In steady state, the equations of the PMSM and the adaptive
observer can be written as The dependence between the stator resistance error and wo
is proportional to the resistive voltage drop, whereas the
Us = Rsis + WmJ(Lis + /pm) (12) dependence between the PM flux error and wo is proportional
to the back-emf.
Us = Rsis + (Win - o)J(Lis + 'pm)- Ais (13) The effect of the parameter errors on w, was calculated
respectively. The estimated quantities are expressed in terms numerically, using the parameters given in Table I. The effect
of their actual values and estimation errors, i.e. x = x. of the stator resistance error Rs /R, =-0.1 is illustrated in
The stator voltage is eliminated by combining (12) and (13), Fig. 2(a), and the effect of the PM flux error <pm/<)pm -0.1
yielding in Fig. 2(b). The results obtained from the approximate equa-
tion (18) are shown. In addition, the figures show the results
Rsis + WmJ(Lis + ,pm) (14) obtained using (15) and the results of steady-state simulations.
= (Rs - Rs) (is--I's)
The speed values used for the calculation and simulation in
Fig. 2(a) are -0.067 p.u., 0 p.u., and 0.067 p.u, and the torque
+ (Wmi-n )J[L(is-i-) +(spm 14pm)] -Ais values used in Fig. 2(b) are -TN, 0, and TN. According to
When it is assumed that the estimation errors and the speed Fig. 2, the assumptions used in (18) result in only a small error.
correction term wo are small, their products can be omitted At low speeds and large values of load torque, the resistive
and the equation reduces to voltage drop dominates, and the stator resistance is thus a
reasonable selection for the adaptation.
(RsI + WmJL + A)is (15) For the stator resistance adaptation, the closed-oop system
shown in Fig. 3 is investigated. The gain
-Ris- WmJ/npm - J(Lis + v/pm)
FR -tq/pm= (19)
The q component of the current estimation error is zero
in steady state because it is driven to zero by the adaptation corresponds to (17) with bpm 0= . The stator resistance is
mechanism (8). The observer gain A is proportional to the rotor estimated by integration from w , the transfer function of the
speed and is also omitted since low speeds are investigated. adaptation mechanism thus being
In addition, the d component of the stator current is ignored GR(S) -kR/S (20)
177

4. 50
tpm~~~~~~~~<p
qJpm+~ F, (s) 0 -G
V'pm
s
- 0
2-50 Fig. 4. Closed-oop system of the PM flux adaptation.
-1 0 1
Te /TN
(a) The estimates are replaced with the actual quantities and their
50 errors, i.e. x = x, and the estimation errors are assumed
TC small so that their products can be omitted. In addition, (23b)
is substituted for the current error in (23a), the result being
- 0 Q = (-RsL- -WmJ- AL-1) s
72 -50 A
-0.05 0 0.05
Wm (p.u.) + (R5L-' + AL-1) /pm Rsis (24a)
(b) B
Fig. 2. Effects of parameter estimation errors on speed correction term wE: (a) i, = LC 0s L1 14pm
D (24b)
effect of resistance error R/R =R - 0.1 as a function of torque for various C D
rotor speed values and (b) effect of PM flux error <-pm/<-pm =-0.1 as a
function of rotor speed for various electromagnetic torque values. Solid lines
The stator resistance error can be detected from is only
show the calculated values from (15) without additional assumptions, dashed
when the motor is loaded, and when the stator current is varies,
line shows calculated values from (18), and the circles are simulated values.
the gain from Rs to is changes. Because the stator resistance
is estimated at low speeds using the HF signal injection, only
Rs
the PM flux is selected for the adaptation at medium and
RS+ _ R,
FR GR(S) high speeds. It is also to be noted that only two quantities,
the current error components 'd and tq, can be used for the
adaptation and only two quantities can thus be estimated. Since
Fig. 3. Closed-oop system of the stator resistance adaptation. the rotor speed is estimated using the q component of the
current estimation error, the d component is selected for the
PM flux adaptation.
where kR is the stator resistance adaptation gain. The closed- For investigating the behavior of the PM flux adaptation, the
loop system has a bandwidth closed-oop system of Fig. 4 is studied. The transfer function
aR = iqkR/4pm
from the scalar-valued flux error pnpm to the current error id
(21) is obtained from
which can be affected by properly selecting the gain kR.
F. (s)= [1 0]{C(sI-A) 1B+D}[1 O]T (25)
B. Small-Signal Analysis PM Flux Adaptation
Integration is used for the adaptation of <pm, and the transfer
At medium and high speeds, the speed correction term w, function corresponding to the adaptation is
is not available since the HF signal injection is not used. The
parameter adaptation can be based on 'd, which is obtained G1,p(s) =-kp-Ld/S (26)
from the adaptive observer. Small-signal analysis is used for where
obtaining the sensitivity of td to the parameter errors. kp is the adaptation gain. The closed-oop transfer
function , ,
For the analysis, the rotor speed is assumed constant, and the
observer is written assuming zero orientation error, yielding Ff G(s)
G, IX- + (s) (s)
(s) 1 + (s)G (27)
Fp, Gp
,bs = u5 Rsis-WmJQs + Ais (22a) from Opm to <pm can be evaluated in any operating point.
is = L l (,Os- Opm) (22b) The closed-oop transfer function (27) was analyzed nu-
merically in different operating points. The parameter values
where only the stator resistance and the PM flux errors are given in Table I were used for the calculations. Fig. 5 shows
taken into account. The stator flux error Qs and the stator poles and Fig. 6 unit step responses obtained with a constant
current error is are solved by subtracting the estimates in (22) adaptation gain k= O.2WB, where WB is the base angular
from the actual variables solved from (1) and (2). The result speed. The speed varies from 0 to 1 p.u. in Fig. 5. The
is stator current and the rotational direction have no effect on the
results. Due to symmetry, only the upper half-plane is shown
I
,Os =Rsis + Rsis-S,J+bs Ais
I -
(23a)
in the pole plot. The step responses in Fig. 6 were obtained
is = L- (,Os -,pm) (23b) at speeds Wm = 0.25 p.u., 0.5 p.u., 0.75 p.u., and 1.0 p.u.
178

5. 1.5 1I
1
--: I -
Wm (p.U.)
0.2 0.5 -1
H1. -v) WA 0 Wm L
WO'm
0. 5-
Fig. 7. Functions f (wm,) (solid) and g(wm ) (dashed) as functions of
0 10.5 0 estimated rotor speed.
-8.2 0 0 .
-1 -0.5 0
Re{s} (p.u.)
Fig. 5. Pole plot of the closed-oop system of PM flux adaptation. The
vicinity of the origin is also shown as a magnification.
0 /0
0 0.025 0.05 0.075 0.1
t (s)
Fig. 6. Step response of the closed-oop system of PM flux adaptation for
various rotor speeds.
Fig. 8. Block diagram of the control system.
According to the results, the small constant gain gives a
relatively slow response. However, the actual PM flux changes load, IB is the base value of the current, and f(Jm) is a
slowly since it depends on the temperature. Although there speed-dependent function shown in Fig. 7.
are complex poles, the dominant pole is real-valued and it is The gain kp, for the PM flux adaptation is varied according
almost constant as the speed increases above 0.5 p.u. Hence, to
the response time to a changing PM flux does not vary kV, = ko g9(Wm) (30)
significantly at higher speeds, which can also be seen from where kpo is a positive constant and g(Wm ) is a speed-
the step responses in Fig. 6. dependent function shown in Fig. 7. At speeds higher than
C. Gain Scheduling w1,p, the gain kp is thus kept constant.
The adaptation of the stator resistance is in use only at low V. SIMULATION RESULTS
speeds in which the HF signal injection method is used. The The proposed method was investigated by means of simu-
PM flux adaptation is not used simultaneously with the statorlations and laboratory experiments. Fig. 8 shows the block
resistance adaptation, and is enabled when the rotor speed isdiagram of the control system comprising cascaded speed
higher than WA. The adaptation gains kR and kp are changed and current control loops. P14ype speed control with active
with the varying rotor speed and stator current. damping is used. The data of the six-pole interior-magnet
In order to have a nonnegative bandwidth (21) for the stator
PMSM (2.2 kW, 1500 rpm) are given in Table I. The base
resistance adaptation, the gain kR and the current iq must values for voltage, current, and angular speed are defined as
have the same sign. A constant bandwidth aR is infeasible, UB = 2/3UN, IB = W2N, and WB = 27fN, respectively.
since iq = 0 would imply infinite adaptation gain. A signum The electromagnetic torque is limited to 22 Nm, which is
function in the gain kR could cause chattering near zero tq. 1.57 times the nominal torque TN. The high-frequency carrier
Therefore, the gain kR is changed proportionally to iq, i.e. excitation signal has a frequency of 833 Hz and an amplitude
of 40 V. The threshold speeds WA = 0.13 p.u. and wX = 0.2
kR =
OqROJTn)Pm I2 (28) p.u., the resistance adaptation bandwidth aRo = 0.01 p.U.,
B and the constant kpo = 0.2WB. The current and speed control
which results in the adaptation bandwidth bandwidths are 5.33 p.u. and 0.067 p.u., respectively, and the
*2 bandwidth ai = 0.067 p.u.
aR = aROf(Wrn)]y (29) The MATLAB/Simulink environment was used for the sim-
B ulations. Fig. 9 shows results obtained at zero speed reference.
The parameter aRO is a constant corresponding to the adap- Except the stator resistance, the parameter values used in the
tation bandwidth at zero speed and at approximately nominal controller were equal to those of the motor model. In the
179

6. 0.1 0.6
7 -0.1 7 -0.2
1.5 2F
0
0O 0L
-0.5 -0.5
0
20 0
20
2 -20 2 -20
0.1 1.2
0.05 = 0.6
C O
vD~
0
0 1 2 3 0 0.5 1 1.5
t (s) t (s)
Fig. 9. Simulation results showing stator resistance adaptation. First subplot (a)
shows electrical angular speed of the rotor (solid), its estimate (dashed), and its 0.6
reference (dotted). Second subplot shows the load torque reference (dotted),
the electromagnetic torque (solid), and its estimate (dashed). Third subplot
shows the estimation error of the rotor position. Last sublot shows the stator S 0
resistance (dashed) and its estimate (solid). 72 -0.2
2
beginning of the simulation, the stator resistance estimate is 0O
15 % smaller than the actual stator resistance. A nominal load -0.5
torque step is applied at t = 1 s, and the stator resistance 20
0
estimate starts converging to the actual resistance immediately.
At t = 2 s, a 15 % step increase occurs in the stator resistance, t -20
and its estimate again follows the actual stator resistance.
The stator resistance estimate converges close to the actual 1.2
resistance in less than 1 s. 0.6
Results showing the behavior of the estimated PM flux are 0
depicted in Fig. 10. The estimated flux is 15 % bigger than 0 0.5 1 1.5
its actual value in the beginning of the simulations, and other t (s)
parameter estimates are equal to the actual values in the motor (b)
model. The speed reference is changed from zero to 0.5 p.u. Fig. I 0. Simulation results showing PM flux adaptation: (a) without
at t = 0.5 s, and a nominal load torque step is applied at parameter adaptation (b) with parameter adaptation. Explanations of the curves
t = 1 s. In Fig. 10(a), the parameter adaptation is not in are as in Fig. 9 except that the last subplot shows the PM flux (dashed) and
its estimate (solid).
use, whereas in Fig. 10(b), the adaptation is used. Fig. 10(a)
shows that the erroneous PM flux results in an error in the
rotor position estimate both at no load and when a load is compensation for dead times and power device voltage drops
applied. In addition, the electromagnetic torque is smaller than is applied.
the estimated torque. According to Fig. 10(b), the adaptation Results obtained in low-speed operation are depicted in
practically removes the PM flux error in less than 0.2 s after Figs. 12 and 13, showing the behavior of the stator resistance
the motor is started, and the errors in the rotor position and adaptation. Additional 1-Q resistors were added between the
the torque are avoided. frequency converter and the PMSM as shown in Fig. 11.
The resistance was changed stepwise by opening or closing
VI. EXPERIMENTAL RESULTS a manually-operated three-phase switch connected in parallel
The experimental setup is illustrated in Fig. 11. The PMSM with the resistors. The experiment in Fig. 12 corresponds to
is fed by a frequency converter that is controlled by a dSPACE the simulation in Fig. 9. The error in the stator resistance is
DS1 103 PPC/DSP board. Mechanical load is provided by decreased after the load torque step at t = 1 s. The estimated
a PMSM servo drive. An incremental encoder is used for stator resistance follows well the actual resistance after the
monitoring the actual rotor speed and position. The nominal stepwise increase at t = 2 s.
DC4ink voltage is 540 V, and the switching frequency and In the experiment of Fig. 13, the drive was operating at
the sampling frequency are both 5 kHz. The dc-ink voltage very low speed (W -0.05 p.u.) in the regenerating mode.
of the converter is measured, and a simple current feedforward The load torque was at the positive nominal value. The stator
180

7. 0.1
S 0
7 -0.1
1.5
E-- 0
-0.5
20
Computer with DS1103 0
Fig. 11. Experimental setup. Mechanical load is provided by a servo drive.
2 -20
0.1
0.1
0
S 0.0
-0.5
1 1 2 3 4
l 5r
F Ar t (s)
Fig. 13. Experimental results showing stator resistance adaptation. Explana-
0-
-0.5
°t tions of the curves are as in Fig. 12.
20 0.6
0
-20
a 0
t 7 -0.2
0.1 2F
0.05 = 0
0L
&0, 1
t (s)
2 3
-0.5
0
20
Fig. 12. Experimental results showing stator resistance adaptation. First
subplot shows the electrical angular speed of the rotor (solid), its estimate 2 -20
(dashed), and its reference (dotted). Second subplot shows the load torque
reference (dashed) and the electromagnetic torque estimate (solid). Third 1.2
subplot shows the estimation error of the rotor position. Last sublot shows
the stator resistance (dashed) and its estimate (solid). 0.6
0
0 0.5 1 1.5
t (s)
resistance estimate was forced to an incorrect value at t 0.6 Fig. 14. Experimental results showing PM flux adaptation. Explanations of
s. When the resistance adaptation is activated again at t 1 s, the curves are as in Fig. 12 except that the last subplot shows the PM flux
the estimated resistance returns close to the actual resistance in (dashed) and its estimate (solid).
about 1 second. After the stepwise decrease in the resistance
at t 2.5 s, the estimated resistance settles close to the new
-
value. It is to be noted that in the experiments in Figs. 12 15(b), respectively. The PM flux estimate was forced to an
and 13, the inverter unidealities contribute to the resistance erroneous value at t 0.5 s, and the adaptation was enabled
-
seen by the controller. Therefore, the estimated resistance is again at t r-1 s. The erroneous PM flux estimate causes an
not precisely the stator resistance shown in the figures. error in the electromagnetic torque estimate, and the position
Figs. 14 and 15 show results in the medium-speed operation, estimation error also impairs the performance of the drive.
where the PM flux adaptation is in use. The experiment in After t s, the estimated PM flux quickly converges close
-
1
Fig. 14 corresponds to the simulation in Fig. 10. The results to its actual value, leading to a reduced position estimation
are comparable to that of the simulation, and the initial 15 error and improved torque estimation accuracy.
% PM flux error is rapidly removed after the acceleration
at t = 0.5 s. The PM flux estimate also stays close to
VII. CONCLUSIONS
the actual flux when the load torque step is applied. Fig. This paper proposed a method for the estimation of the
15 shows results in constant-speed operation, the rotor speed stator resistance and the PM flux in a sensorless PMSM drive.
being 0.5 p.u. In Fig. 15(a), the load torque was at the positive The adaptive observer augmented with an HF signal injection
nominal value, while in Fig. 15(b) the load torque was at technique at low speeds was used for the adaptation of the
the negative nominal value. The drive operated thus in the parameters in addition to the speed and position estimation.
motoring and in the regenerating modes in Figs. 15(a) and The system was investigated by means of steady-state and
181

8. 0.6 ACKNOWLEDGEMENT
I
0.5 -
The authors gratefully acknowledge the financial support
7 0.4 given by ABB Oy, Walter Ahlstrom foundation, and KAUTE
1.5 foundation.
OL
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