An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation
Introduction. Sliding mode observer (SMO), with its simplicity and efficiency, is one of the widely used sensorless control techniques in induction motor (IM) drive systems. However, this method’s performance is highly sensitive to changes in motor parameters, especially increases in stator resistan...
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National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
2026
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Electrical Engineering & Electromechanics| _version_ | 1869562799231860736 |
|---|---|
| author | Nguyen, Q. T. Tran, C. D. |
| author_facet | Nguyen, Q. T. Tran, C. D. |
| author_institution_txt_mv | [
{
"author": "Q. T. Nguyen",
"institution": "Ton Duc Thang University"
},
{
"author": "C. D. Tran",
"institution": "Ton Duc Thang University"
}
] |
| author_sort | Nguyen, Q. T. |
| baseUrl_str | http://eie.khpi.edu.ua/oai |
| collection | OJS |
| datestamp_date | 2026-07-01T21:42:56Z |
| description | Introduction. Sliding mode observer (SMO), with its simplicity and efficiency, is one of the widely used sensorless control techniques in induction motor (IM) drive systems. However, this method’s performance is highly sensitive to changes in motor parameters, especially increases in stator resistance (Rs) due to thermal effects. Problem. As Rs increases due to thermal effects during operation, the estimation of rotor flux and virtual current becomes inaccurate, degrading the SMO method’s performance in generating estimated speeds for the controller. Goal. To develop an improved speed sensorless control scheme for IM drives that maintains high accuracy of estimation under variations in Rs. Methodology. SMO is first employed to estimate rotor speed from measured stator currents and voltages. Then, a Rs estimation mechanism based on a combined SMO-model reference adaptive system (SMO-MRAS) structure is proposed, in which the voltage model serves as the reference model and the SMO-based flux estimation acts as the adaptive model. The estimated resistance is obtained through a PI adaptation law. Results. Under 20 % and 40 % Rs increments, the proposed scheme reduces Integral Absolute Error (IAE) from 0.7699 to 0.4661, Integral Squared Error (ISE) from 0.555 to 0.4688, and Integral Time Squared Error (ITSE) from 0.6286 to 0.4502. The maximum stator current deviation decreases from 0.578 A to 0.005457 A, while stable speed tracking at 20 rad/s is preserved under load disturbance. Scientific novelty. The study proposes a structurally integrated SMO-MRAS framework that decouples speed estimation from MRAS while embedding resistance adaptation within the observer loop. Practical value. The proposed method enhances robustness against thermal parameter variation and improves the reliability of sensorless IM drives in real operating conditions. References 36, table 1, figures 9. |
| doi_str_mv | 10.20998/2074-272X.2026.4.05 |
| first_indexed | 2026-07-02T01:00:24Z |
| format | Article |
| fulltext |
34 Electrical Engineering & Electromechanics, 2026, no. 4
© Q.T. Nguyen, C.D. Tran
UDC 621.313 https://doi.org/10.20998/2074-272X.2026.4.05
Q.T. Nguyen, C.D. Tran
An enhanced sliding mode observer method applied to sensorless induction motor drives
under stator resistance variation
Introduction. Sliding mode observer (SMO), with its simplicity and efficiency, is one of the widely used sensorless control techniques in
induction motor (IM) drive systems. However, this method’s performance is highly sensitive to changes in motor parameters, especially
increases in stator resistance (Rs) due to thermal effects. Problem. As Rs increases due to thermal effects during operation, the estimation
of rotor flux and virtual current becomes inaccurate, degrading the SMO method’s performance in generating estimated speeds for the
controller. Goal. To develop an improved speed sensorless control scheme for IM drives that maintains high accuracy of estimation
under variations in Rs. Methodology. SMO is first employed to estimate rotor speed from measured stator currents and voltages. Then, a
Rs estimation mechanism based on a combined SMO-model reference adaptive system (SMO-MRAS) structure is proposed, in which the
voltage model serves as the reference model and the SMO-based flux estimation acts as the adaptive model. The estimated resistance is
obtained through a PI adaptation law. Results. Under 20 % and 40 % Rs increments, the proposed scheme reduces Integral Absolute
Error (IAE) from 0.7699 to 0.4661, Integral Squared Error (ISE) from 0.555 to 0.4688, and Integral Time Squared Error (ITSE) from
0.6286 to 0.4502. The maximum stator current deviation decreases from 0.578 A to 0.005457 A, while stable speed tracking at 20 rad/s
is preserved under load disturbance. Scientific novelty. The study proposes a structurally integrated SMO-MRAS framework that
decouples speed estimation from MRAS while embedding resistance adaptation within the observer loop. Practical value. The proposed
method enhances robustness against thermal parameter variation and improves the reliability of sensorless IM drives in real operating
conditions. References 36, table 1, figures 9.
Key words: resistance variation, speed sensorless control, sliding mode observer, thermal effect, voltage model.
Вступ. Спостерігач ковзного режиму (SMO) завдяки своїй простоті та ефективності є одним із найбільш поширених методів
бездатчикового керування в системах електропривода на базі асинхронних двигунів (IM). Проте ефективність цього методу
значною мірою залежить від зміни параметрів двигуна, особливо від збільшення опору статора Rs, спричиненого тепловими
ефектами. Проблема. Зі збільшенням Rs у процесі роботи внаслідок нагрівання погіршується точність оцінювання
потокозчеплення ротора та віртуального струму, що негативно впливає на якість формування оціненої швидкості для системи
керування на основі SMO. Мета. Розроблення вдосконаленої системи бездатчикового керування швидкістю приводів для IM,
здатної забезпечувати високу точність оцінювання за умов зміни опору статора Rs. Методика. На першому етапі SMO
використовується для оцінювання швидкості ротора за виміряними струмами та напругами статора. Далі запропоновано
механізм оцінювання Rs на базі комбінованої структури адаптивної системи на основі моделі SMO (SMO-MRAS), у якій модель
напруги використовується як еталонна модель, а оцінювання потоку на основі SMO – як адаптивна модель. Оцінювання опору
здійснюється за допомогою PI-закону адаптації. Результати. При збільшенні Rs на 20 % і 40 % запропонована схема забезпечує
зменшення інтеграла абсолютної похибки (IAE) з 0,7699 до 0,4661, інтеграла квадрата похибки (ISE) з 0,555 до 0,4688 та
інтеграла квадрата похибки, зваженого за часом (ITSE), з 0,6286 до 0,4502. Максимальне відхилення струму статора
зменшується з 0,578 А до 0,005457 А, при цьому забезпечується стабільне відстеження швидкості на рівні 20 рад/с за наявності
збурення навантаження. Наукова новизна. Запропоновано структурно інтегровану схему SMO-MRAS, у якій процес оцінювання
швидкості відокремлений від MRAS, а механізм адаптації опору інтегрований безпосередньо в контур спостерігача. Практична
значимість. Запропонований метод підвищує робастність системи до теплових змін параметрів та покращує надійність
бездатчикових асинхронних електроприводів у реальних умовах експлуатації.. Бібл. 36, табл. 1, рис. 9.
Ключові слова: зміна опору, безсенсорне керування швидкістю, спостерігач ковзного режиму, тепловий ефект, модель напруги.
Introduction. High-performance induction motor
(IM) drives continue to play a key role in industrial,
transportation, and renewable-energy applications due to
their robustness, cost-effectiveness, and favorable power
density. Nevertheless, achieving accurate speed and torque
regulation remains challenging, particularly under load
disturbances and parameter variations. Among existing
strategies, field-oriented control (FOC) is widely employed
thanks to its ability to decouple torque and flux dynamics,
enabling fast transient response and high steady-state
accuracy [1–5]. However, the effectiveness of typical FOC
strongly depends on model accuracy; in particular,
variations in Rs due to thermal effects significantly degrade
flux and angle reconstruction, especially at low speeds [6].
Alongside FOC, direct torque control (DTC) has
attracted considerable attention because of its simple
structure and rapid torque response. Recent studies focus
on improving voltage vector selection and reducing torque
ripple and harmonics through advanced or intelligent
techniques [7–10]. Despite these efforts, DTC still faces
inherent trade-offs among torque ripple, switching
frequency, and robustness over a wide speed range. In
contrast, scalar control remains attractive in low-cost
applications owing to its simplicity and minimal sensing
requirements, although its dynamic performance and low-
speed behavior are inherently limited. To address these
drawbacks, adaptive and closed-loop scalar schemes have
been proposed to enhance starting torque and regulation
capability [11, 12]. Beyond nominal operation, the
reliability of IM drives increasingly relies on fault-tolerant
strategies; observer-based sensor fault diagnosis and
reconfiguration within FOC frameworks have
demonstrated the ability to maintain stable operation when
current or speed measurements become unreliable [13].
These considerations highlight two closely related
practical requirements in modern IM drive systems. On the
one hand, speed-sensorless control has become increasingly
important for reducing system cost and wiring complexity
while enhancing reliability and fault tolerance in
demanding operating environments. On the other hand,
variations in the Rs directly and detrimentally affect flux
estimation accuracy, which propagates through the control
loop and degrades overall performance. Consequently,
estimating and compensating for Rs are essential to ensure
reliable operation, particularly at low speeds and during
thermal transients. These challenges provide strong
motivation for a critical review of recent developments in
sensorless control and parameter estimation, intending to
identify unresolved issues and research opportunities.
Electrical Engineering & Electromechanics, 2026, no. 4 35
Review of recent publications and selection of
unsolved tasks. Recent studies on sensorless IM drives can
be broadly classified according to the adopted estimation
principle and robustness strategy. Neural network
approaches aim to reduce model dependency through data-
driven mappings. Dual-field-oriented sensorless schemes
have been proposed to alleviate parameter sensitivity [14],
while neural observers have been combined with robust
control techniques to address disturbances and voltage
saturation, primarily demonstrated on permanent magnet
synchronous motors (PMSMs) [15]. Artificial neural
network (ANN)-based sensorless estimation has also been
reported for brushless DC drives [16]. Despite their
potential, these methods often suffer from limited
generalization under thermal parameter variations.
Kalman filter (KF) estimators remain attractive due to
their stochastic framework and noise-handling capability.
Extended KF-assisted sensorless IM control has been
combined with advanced control structures, including
fractional-order controllers [17], and integrated into
sensorless predictive control schemes with experimental
validation [18]. Comparative studies and Unscented KF-
based solutions have also been reported for PMSM drives
[19, 20]. However, their practical application is constrained
by computational complexity, sensitivity to noise
covariance tuning, and degraded performance under model
mismatch, particularly at low speeds.
Within the model reference adaptive system
(MRAS) family, current-based MRAS has been
extensively investigated, with stability enhancement
techniques and sensitivity analyses addressing known
instability regions and parameter dependence [21, 22].
Alternative MRAS formulations include reactive-power
MRAS, sometimes augmented with neural components to
extend the operating range [23], and stator-flux-based
MRAS schemes, which further emphasize the importance
of flux estimation accuracy in sensorless control [24]. In
rotor-flux-based MRAS, rotor flux angle estimation
remains central to sensorless FOC applications [25, 26].
Finally, sliding mode observer (SMO) approaches
emphasize robustness to uncertainties. A fractional-order
super-twisting SMO with flux linkage compensation
targets the chattering and accuracy trade-off [27]; SMO
has also been tailored to speed-sensorless linear IM drives
[28], and combined neural/fractional sliding-mode
schemes have been explored for bearingless IM [29].
Furthermore, the proven robustness of sliding mode
principles in advanced sliding mode control frameworks
for electric motor drives motivates their use in observer
design under varying operating conditions [30].
Separately, online parameter estimation is addressed via
modified flux SMO with simultaneous Rs and Ls
estimation [31], ANN-based online estimation of rotor
resistances and Rs in sensorless IM drives [32], and
parameter estimation embedded into sensorless FOC for
multiphase open-end winding IM [33].
Unsolved tasks become evident across these
streams. Despite these extensive efforts, several open
problems remain. A large portion of sensorless control
studies focuses on speed or flux estimation while assuming
a fixed Rs or compensating it only indirectly. Conversely,
works dedicated to resistance estimation often lack a
unified sensorless architecture that coherently integrates
speed estimation and Rs adaptation within a IM FOC
framework. Moreover, MRAS-based techniques may suffer
from stability limitations and parameter sensitivity in low-
speed regions, whereas SMO-based schemes require
careful design to suppress chattering without sacrificing
estimation accuracy. These limitations indicate the need for
a sensorless control structure that simultaneously enhances
low-speed robustness, preserves estimator stability, and
explicitly accounts for Rs variations.
The goal of the paper is to develop an improved
speed-sensorless control scheme for IM drives that
maintains high accuracy of estimation under variations in
Rs. The proposed approach improves robustness in low-
speed operation and under thermal parameter drift while
preserving dynamic performance and system stability.
Dynamic model of the IM. The electrical dynamics
of the IM are described in the stationary (α, β) frame.
Starting from the stator and rotor current equations, the
derivatives of the stator current components can be
rearranged as (1)–(4):
rrs
r
m
rr
r
r
s
m
s
m
ss ii
L
L
Ai
L
R
i
L
R
L
u
A
t
i
d
d
;(1)
rrs
r
m
rr
r
r
s
m
s
m
ss ii
L
L
Ai
L
R
i
L
R
L
u
A
t
i
d
d
;(2)
srr
m
r
rr
m
r
s
s
s
s
sr ii
L
L
Bi
L
R
i
L
R
L
u
B
t
i
d
d ;(3)
srr
m
r
rr
m
r
s
s
s
s
sr ii
L
L
Bi
L
R
i
L
R
L
u
B
t
i
d
d
,(4)
where is, us are the stator current and voltage along the
stationary -axis; is, us are the stator current and voltage
along the stationary -axis; Rs, Rr are the stator and rotor
resistances; Ls, Lr, Lm are the stator, rotor and magnetizing
inductances; ωm is the mechanical speed; ωr=pωm is the
rotor electrical speed; p is the number of pole pairs.
In these expressions, the coefficients A and B are:
A = LmLr / (Ls Lr – Lm
2); B = Ls Lm / (Lm
2 – Ls Lr).
The relationship between the electromagnetic torque
and the load torque is:
Le
r TT
J
p
t
d
d
, (5)
where J is the inertia; Te, TL are the electromagnetic and
load torque, respectively.
Speed estimation based on SMO. SMO estimates
rotor speed from measured stator currents and voltages.
Using the IM model in the stationary reference frame, it
reconstructs stator current and rotor flux dynamics from
these signals, as defined in equations (6)–(9):
;
1
1
d
d
1211
,,,2,1
,
iis
s
SMO
estrestr
SMO
estr
r
ests
ests
esatdesatdu
L
T
cic
t
i
(6)
;
1
1
d
d
1211
,,,2,1
,
iis
s
SMO
estrestr
SMO
estr
r
ests
ests
esatdesatdu
L
T
cic
t
i
(7)
36 Electrical Engineering & Electromechanics, 2026, no. 4
;
1
d
d
2221,,
,,
,
ii
SMO
estrestr
SMO
estr
r
ests
r
m
SMO
estr
esatdesatd
T
i
T
L
t (8)
,
1
d
d
2221,,
,,
,
ii
SMO
estrestr
SMO
estr
r
ests
r
m
SMO
estr
esatdesatd
T
i
T
L
t (9)
where:
s
r
r
m
ests
L
R
L
L
R
c
2
,
1
;
rs
m
LL
L
c
2 ;
rs
m
LL
L2
1 ; Tr = Lr / Rr; = 1 / (LsLr – Lm
2);
ei = is,m – is,est; ei = is,m – is,est;
d11 = –(C – 1)(Rs,estLr + RrLs); d12 = (C – 1)r,est;
d21 = (C – 1)(RrLs – CRs,estLr) / Lm;
d22 = –(C – 1)r,est / (Lm); C > 1;
where is,m, is,m are the measured stator currents; is,est,
is,est are their estimated values; SMO
estr , , SMO
estr , are the
rotor flux components estimated from the SMO. By
properly selecting the observer gains, the sliding
conditions ei0 and ei0 are enforced in finite time,
ensuring robust convergence of the current estimates
despite parameter uncertainties.
In these equations, the discontinuous correction
terms are governed by a saturation function, defined as:
sat(x) = max[–1, min(1, x/)], (10)
where is the positive constant.
Once the sliding regime is established, the rotor
speed is extracted through a scalar deviation signal
constructed from the stator current estimation error and
the estimated rotor flux components:
SMO
estrestsms
SMO
estrestsms iiii ,,,,,, . (11)
This signal reflects the mismatch between the
estimated electromagnetic state and the actual motor
behavior and serves as a physically meaningful indicator
of speed adaptation.
The estimated rotor electrical speed is then obtained
via a PI adaptation mechanism:
T
ipestr ttKtK
0,,, d , (12)
where Kp,, Ki, are the proportional and integral gains of
the PI controller used in the speed estimation loop.
The proposed SMO relies only on measured stator
voltages and currents and provides robust speed
estimation, which naturally motivates the incorporation of
a Rs estimation scheme in the next section.
Rs estimation based on the SMO-MRAS
structure. A rotor-flux MRAS-based resistance
adaptation mechanism is proposed to compensate Rs
variations. The rotor flux from the voltage model is the
reference, and the observer-based flux is the adaptive
model; their difference is used to estimate the Rs. The
complete SMO-MRAS scheme for joint speed and Rs
estimation is shown in Fig. 1.
Fig. 1. Block diagram of the SMO scheme for speed estimation
and the SMO-MRAS scheme for Rs estimation
In practical IM drives, the Rs varies with temperature
due to thermal effects, and this variation becomes significant
during low-speed operation and thermal transients. It has been
reported that neglecting such resistance changes leads to
inaccurate flux estimation and degraded drive performance,
underscoring the need for stator estimation [34–36].
To address this issue, a Rs estimation scheme is
developed by integrating the proposed SMO-MRAS. In
the proposed structure, the voltage model is selected as
the reference model, since it explicitly reflects the
influence of Rs as:
t
i
iRu
t
s
msestss
VM
r
d
d
d
d
,,
; (13)
t
i
iRu
t
s
msestss
VM
r
d
d
d
d
,,
; (14)
where the coefficients = Lr / Lm and = (Ls Lr – Lm
2) / Lr;
VM
r , VM
r are the rotor flux components calculated
from the voltage model.
The adaptive model employs the rotor flux estimated
by the SMO, which exhibits reduced sensitivity to
parameter uncertainties. The mismatch between the
reference and adaptive flux estimates is used to form an
adaptation deviation, which is processed by a PI
mechanism to obtain the estimated Rs:
m
VM
r
SMO
rms
VM
r
SMO
rR ss
ii ,, ; (15)
T
RRiRRpests ttKtKR
ssss 0,,_ d ; (16)
where
sRpK , ,
sRiK , are the proportional and integral
gains of the PI controller used in the Rs estimation loop.
The completed control architecture of the proposed
speed-sensorless FOC drive integrating the SMO and
SMO-MRAS mechanisms is illustrated in Fig. 2.
As shown in Fig. 2, the SMO provides the estimated
rotor speed information required by the FOC scheme,
while the SMO-MRAS loop operates in parallel to adapt
the Rs. The two estimation mechanisms are structurally
decoupled but dynamically coupled via electrical
measurements, thereby enhancing robustness against
parameter variations.
Electrical Engineering & Electromechanics, 2026, no. 4 37
Fig. 2. Control structure of the proposed speed sensorless FOC
with SMO and SMO-MRAS mechanisms
To quantitatively evaluate the control performance,
the following indices are adopted (17) – (20):
integral absolute error (IAE) is:
T
estmref tttIAE
0 , d ; (17)
integral squared error (ISE) is:
T
estmref tttISE
0
2
, d ; (18)
integral time squared error (ITSE) is:
T
estmref ttttITSE
0
2
, d ; (19)
where ref is the reference speed; m,est is the mechanical
estimated speed.
Maximum stator current deviation:
titi estsms
Tt
I ,,
,0
max, max
; (20)
where 2
,
2
,, msmsms iii ; 2
,
2
,, estsestsests iii .
Simulation. The drive system is simulated using the
FOC method with the following IM parameters (Table 1).
Таble 1
Parameters of a IM [25]
Parameter Value
Power P, W 2200
Rated frequency f, Hz 50
Stator/rotor resistance Rs / Rr, 3.179/2.118
Stator/rotor inductance Ls / Lr, H 0.209/0.209
Magnetizing inductance Lm, H 0.192
Simulation case 1 – without SMO-MRAS Rs
estimation. Figures 3–5 illustrates the dynamic behavior of
the sensorless FOC drive based on the SMO when the Rs
variation is not compensated. During the acceleration phase
from 0 to 0.5 s, the motor speed accurately follows the
reference and remains stable at 20 rad/s under nominal
parameter conditions. However, when the actual Rs increases
by 20 % at t = 1 s (Fig. 3), the mismatch between the real
motor parameters and the fixed resistance value used in the
observer leads to a degradation in rotor flux estimation.
This parameter mismatch directly affects the SMO-
based speed estimation mechanism. As observed in Fig. 4,
the estimated rotor speed begins to exhibit noticeable
oscillations after t = 1 s, which subsequently propagate to
the actual motor speed through the FOC loop. The situation
becomes more severe when the Rs increases by an
additional 40 % at t = 2.5 s, resulting in amplified speed
oscillations and reduced stability margins, particularly
under the increasing load torque applied at t = 2 s.
t, s
Rs,
Fig. 3. Estimated Rs response compared with the real Rs
simulation case 1
, rad/s
t, s
Fig. 4. Response speed in simulation case 1
is, A
t, s
Fig. 5. Stator current magnitude deviation between measured
and estimated values in simulation case 1
The underlying cause of this behavior is clarified in
Fig. 5, which shows the deviation between the measured
stator current magnitude and its estimated counterpart. As
the Rs deviates from its nominal value, the current
estimation deviation increases significantly, indicating
that the SMO can no longer accurately reconstruct the
stator current dynamics. Since the SMO relies on these
estimated currents to generate the speed adaptation signal,
the growing current mismatch leads to erroneous speed
estimation and deteriorated closed-loop performance.
Simulation case 2 – with SMO-MRAS Rs
estimation. Figures 6–8 present the dynamic performance of
the proposed speed-sensorless FOC scheme when the SMO-
MRAS-based Rs estimation is enabled. Under nominal
conditions (0–1 s), the motor accelerates to the reference
speed of 20 rad/s and maintains steady-state operation
without noticeable oscillations, similar to Case 1. However,
the system response differs significantly once the Rs varies.
As shown in Fig. 7, when the actual Rs increases by 20 %
at t = 1 s and by 40 % at t = 2.5 s, the estimated resistance
Rs,est rapidly converges to the new real values with minimal
transient deviation. The adaptation mechanism operates
smoothly, without inducing oscillatory behavior, indicating
that the SMO-MRAS structure effectively tracks parameter
variations caused by thermal effects. The impact of accurate
38 Electrical Engineering & Electromechanics, 2026, no. 4
resistance estimation is clearly reflected in the current
reconstruction performance. Figure 8 shows that the
deviation between the measured and estimated stator current
magnitudes remains close to zero even after the resistance
changes. Unlike Case 1, the current estimation error does
not grow with increasing parameter mismatch, confirming
that the observer model remains dynamically consistent
with the actual motor behavior. Consequently, the speed
response in Fig. 6 remains stable and well-regulated
throughout the entire simulation.
, rad/s
t, s
Fig. 6. Response speed in simulation case 2
Rs,
t, s
Fig. 7. Estimated Rs response compared with the real Rs
simulation case 2
is, A
t, s
Fig. 8. Stator current magnitude deviation between measured
and estimated values in simulation case 2
Although a temporary speed dip occurs at t = 2 s due
to the increased applied load, both the real and estimated
speeds rapidly recover to the reference value without
sustained oscillations. Importantly, no instability or
amplified ripple is observed after the 20 % and 40 %
resistance increments, demonstrating that the SMO-based
speed estimation is no longer degraded by parameter drift.
Discussion. Figure 9 quantitatively confirms the
superiority of the proposed SMO-MRAS scheme.
In simulation Case 1 (without Rs estimation), the
performance indices are IAE=0.7699, ISE=0.555,
ITSE=0.6286, with a maximum current deviation of 0.578 A.
When the SMO-MRAS mechanism is activated (Case 2),
these values are reduced to IAE=0.4661, ISE=0.4688,
ITSE=0.4502, and a maximum current deviation of 5.457 mA.
Fig. 9. Performance index comparison of the proposed scheme
with and without SMO-MRAS resistance estimation
These results show that although the SMO provides
robust speed estimation, it is sensitive to parameter
mismatch. Integrating SMO-MRAS compensates for
stator resistance variation, preserving current estimation
accuracy and improving overall stability.
Moreover, under simultaneous load disturbance and
20–40 % Rs variations, the conventional scheme exhibits
larger current estimation errors and speed oscillations,
whereas the proposed approach maintains accurate current
reconstruction and stable speed tracking, confirming its
robustness under practical conditions.
Conclusions. This paper developed a robust speed-
sensorless control scheme for IM drives under Rs
variation. The proposed SMO-MRAS framework
maintains accurate current reconstruction and stable speed
estimation despite large parameter changes.
Simulations show that integrating Rs estimation
significantly improves performance and robustness over
conventional SMO-based methods, indicating strong potential
for sensorless IM drives under thermal and load disturbances.
In the future, it is necessary to conduct experimental
studies of effectiveness of improvement of robustness
against thermal parameter variation and improves the
reliability of sensorless IM drives in real operating
conditions based on proposed method.
Acknowledgment. This research is funded by Ton
Duc Thang University.
Conflict of interest. The authors declare that they
have no conflicts of interest.
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Received 25.01.2026
Accepted 26.04.2026
Published 02.07.2026
Q.T. Nguyen1, PhD Student,
C.D. Tran1, Doctor on Electrical Engineering,
1 Power System Optimization Research Group,
Faculty of Electrical and Electronics Engineering,
Ton Duc Thang University, Ho Chi Minh City, Vietnam,
e-mail: trandinhcuong@tdtu.edu.vn (Corresponding Author)
How to cite this article:
Nguyen Q.T., Tran C.D. An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance
variation. Electrical Engineering & Electromechanics, 2026, no. 4, pp. 34-39. doi: https://doi.org/10.20998/2074-272X.2026.4.05
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| id | eiekhpieduua-article-352946 |
| institution | Electrical Engineering & Electromechanics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-02T01:00:24Z |
| publishDate | 2026 |
| publisher | National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | eiekhpieduua/47/9ccbe861fe93e23c970f2fe9a4a26747.pdf |
| spelling | eiekhpieduua-article-3529462026-07-01T21:42:56Z An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation Nguyen, Q. T. Tran, C. D. resistance variation speed sensorless control sliding mode observer thermal effect voltage model зміна опору безсенсорне керування швидкістю спостерігач ковзного режиму тепловий ефект модель напруги Introduction. Sliding mode observer (SMO), with its simplicity and efficiency, is one of the widely used sensorless control techniques in induction motor (IM) drive systems. However, this method’s performance is highly sensitive to changes in motor parameters, especially increases in stator resistance (Rs) due to thermal effects. Problem. As Rs increases due to thermal effects during operation, the estimation of rotor flux and virtual current becomes inaccurate, degrading the SMO method’s performance in generating estimated speeds for the controller. Goal. To develop an improved speed sensorless control scheme for IM drives that maintains high accuracy of estimation under variations in Rs. Methodology. SMO is first employed to estimate rotor speed from measured stator currents and voltages. Then, a Rs estimation mechanism based on a combined SMO-model reference adaptive system (SMO-MRAS) structure is proposed, in which the voltage model serves as the reference model and the SMO-based flux estimation acts as the adaptive model. The estimated resistance is obtained through a PI adaptation law. Results. Under 20 % and 40 % Rs increments, the proposed scheme reduces Integral Absolute Error (IAE) from 0.7699 to 0.4661, Integral Squared Error (ISE) from 0.555 to 0.4688, and Integral Time Squared Error (ITSE) from 0.6286 to 0.4502. The maximum stator current deviation decreases from 0.578 A to 0.005457 A, while stable speed tracking at 20 rad/s is preserved under load disturbance. Scientific novelty. The study proposes a structurally integrated SMO-MRAS framework that decouples speed estimation from MRAS while embedding resistance adaptation within the observer loop. Practical value. The proposed method enhances robustness against thermal parameter variation and improves the reliability of sensorless IM drives in real operating conditions. References 36, table 1, figures 9. Вступ. Спостерігач ковзного режиму (SMO) завдяки своїй простоті та ефективності є одним із найбільш поширених методів бездатчикового керування в системах електропривода на базі асинхронних двигунів (IM). Проте ефективність цього методу значною мірою залежить від зміни параметрів двигуна, особливо від збільшення опору статора Rs, спричиненого тепловими ефектами. Проблема. Зі збільшенням Rs у процесі роботи внаслідок нагрівання погіршується точність оцінювання потокозчеплення ротора та віртуального струму, що негативно впливає на якість формування оціненої швидкості для системи керування на основі SMO. Мета. Розроблення вдосконаленої системи бездатчикового керування швидкістю приводів для IM, здатної забезпечувати високу точність оцінювання за умов зміни опору статора Rs. Методика. На першому етапі SMO використовується для оцінювання швидкості ротора за виміряними струмами та напругами статора. Далі запропоновано механізм оцінювання Rs на базі комбінованої структури адаптивної системи на основі моделі SMO (SMO-MRAS), у якій модель напруги використовується як еталонна модель, а оцінювання потоку на основі SMO – як адаптивна модель. Оцінювання опору здійснюється за допомогою PI-закону адаптації. Результати. При збільшенні Rs на 20 % і 40 % запропонована схема забезпечує зменшення інтеграла абсолютної похибки (IAE) з 0,7699 до 0,4661, інтеграла квадрата похибки (ISE) з 0,555 до 0,4688 та інтеграла квадрата похибки, зваженого за часом (ITSE), з 0,6286 до 0,4502. Максимальне відхилення струму статора зменшується з 0,578 А до 0,005457 А, при цьому забезпечується стабільне відстеження швидкості на рівні 20 рад/с за наявності збурення навантаження. Наукова новизна. Запропоновано структурно інтегровану схему SMO-MRAS, у якій процес оцінювання швидкості відокремлений від MRAS, а механізм адаптації опору інтегрований безпосередньо в контур спостерігача. Практична значимість. Запропонований метод підвищує робастність системи до теплових змін параметрів та покращує надійність бездатчикових асинхронних електроприводів у реальних умовах експлуатації. Бібл. 36, табл. 1, рис. 9. National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2026-07-02 Article Article application/pdf https://eie.khpi.edu.ua/article/view/352946 10.20998/2074-272X.2026.4.05 Electrical Engineering & Electromechanics; No. 4 (2026); 34-39 Электротехника и Электромеханика; № 4 (2026); 34-39 Електротехніка і Електромеханіка; № 4 (2026); 34-39 2309-3404 2074-272X en https://eie.khpi.edu.ua/article/view/352946/351597 Copyright (c) 2026 Q. T. Nguyen, C. D. Tran http://creativecommons.org/licenses/by-nc/4.0 |
| spellingShingle | resistance variation speed sensorless control sliding mode observer thermal effect voltage model Nguyen, Q. T. Tran, C. D. An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title | An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title_alt | An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title_full | An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title_fullStr | An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title_full_unstemmed | An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title_short | An enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| title_sort | enhanced sliding mode observer method applied to sensorless induction motor drives under stator resistance variation |
| topic | resistance variation speed sensorless control sliding mode observer thermal effect voltage model |
| topic_facet | resistance variation speed sensorless control sliding mode observer thermal effect voltage model зміна опору безсенсорне керування швидкістю спостерігач ковзного режиму тепловий ефект модель напруги |
| url | https://eie.khpi.edu.ua/article/view/352946 |
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