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An Improved SOGI-Higher-Order Sliding Mode Observer-Based Induction Motor Speed Estimation

Kobena Badu Enyam

Kobena Badu Enyam

Kwame Nkrumah University of Science and Technology, Department of Electrical/Electronic EngineeringKumasi, Ghana
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Enyam, Kobena Badu
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Francis Boafo Effah

Francis Boafo Effah

Kwame Nkrumah University of Science and Technology, Department of Electrical/Electronic EngineeringKumasi, Ghana
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Effah, Francis Boafo
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Desmond Hammond

Desmond Hammond

Ecole Centrale de Nantes, Department of Electrical EngineeringNantes, France
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Hammond, Desmond
  
Dec 21, 2024
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Article Category: Research paper
Published Online: Dec 21, 2024
Page range: 19 - 40
Received: Sep 08, 2024
Accepted: Nov 22, 2024
DOI: https://doi.org/10.2478/pead-2025-0002
Keywords
© 2025 Kobena Badu Enyam et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Block diagram of induction machine sensorless control scheme of the DRFO method. DRFO, direct rotor flux orientation.
Block diagram of induction machine sensorless control scheme of the DRFO method. DRFO, direct rotor flux orientation.

Figure 2.

Varying load torque.
Varying load torque.

Figure 3.

Block diagram of Induction machine sensorless control scheme with proposed SOGI-HOSM. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.
Block diagram of Induction machine sensorless control scheme with proposed SOGI-HOSM. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.

Figure 4.

Rotor fluxes in d–q reference frame.
Rotor fluxes in d–q reference frame.

Figure 5.

Electromagnetic torque (on the left) and the commanded stator current on the q-axis (on the right).
Electromagnetic torque (on the left) and the commanded stator current on the q-axis (on the right).

Figure 6.

MATLAB/Simulink implementation of the filtering of v^α {\hat V_\alpha } and v^β {\hat V_\beta } by the SOGI topology. SOGI, second-order generalised integrator.
MATLAB/Simulink implementation of the filtering of v^α {\hat V_\alpha } and v^β {\hat V_\beta } by the SOGI topology. SOGI, second-order generalised integrator.

Figure 7.

Performance of the proposed SOGI-HOSM at varying speed commands. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.
Performance of the proposed SOGI-HOSM at varying speed commands. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.

Figure 8.

Zoomed-in version of the performance of the proposed SOGI-HOSM during frequency ramps (on the left) and at low speeds (on the right). SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.
Zoomed-in version of the performance of the proposed SOGI-HOSM during frequency ramps (on the left) and at low speeds (on the right). SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.

Figure 9.

Current control command showing very little chattering using the proposed the SOGI-HOSM. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.
Current control command showing very little chattering using the proposed the SOGI-HOSM. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.

Figure 10.

Performance of the conventional STA at varying speeds. STA, super-twisting algorithm.
Performance of the conventional STA at varying speeds. STA, super-twisting algorithm.

Figure 11.

A zoomed-in version of the performance of the conventional STA during frequency ramps (on the left) and at low speeds (on the right). STA, super-twisting algorithm.
A zoomed-in version of the performance of the conventional STA during frequency ramps (on the left) and at low speeds (on the right). STA, super-twisting algorithm.

Figure 12.

Current control command showing very large chattering using the conventional STA. STA, super-twisting algorithm.
Current control command showing very large chattering using the conventional STA. STA, super-twisting algorithm.

Figure 13.

Performance of the conventional SOGI-FLL at varying speeds. SOGI-FLL, second-order generalised integrator-frequency locked loop.
Performance of the conventional SOGI-FLL at varying speeds. SOGI-FLL, second-order generalised integrator-frequency locked loop.

Figure 14.

A zoomed-in version of the performance of the conventional SOGI-FLL at during frequency ramps (on the left) and at low speeds (on the right). SOGI-FLL, second-order generalised integrator-frequency locked loop.
A zoomed-in version of the performance of the conventional SOGI-FLL at during frequency ramps (on the left) and at low speeds (on the right). SOGI-FLL, second-order generalised integrator-frequency locked loop.

Figure 15.

Gain varying according to the noise level from the Butterworth filter.
Gain varying according to the noise level from the Butterworth filter.

Figure 16.

Phase currents of induction machine showing abnormal high sensor noise addition.
Phase currents of induction machine showing abnormal high sensor noise addition.

Figure 17.

Performance of the proposed SOGI-HOSM under parameter variation, additional sensor noise and under varying load torque. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.
Performance of the proposed SOGI-HOSM under parameter variation, additional sensor noise and under varying load torque. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.

Figure 18.

A zoomed-in version of the performance of the proposed SOGI-HOSM under parameter variation, additional sensor noise and under varying load torque. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.
A zoomed-in version of the performance of the proposed SOGI-HOSM under parameter variation, additional sensor noise and under varying load torque. SOGI-HOSM, second-order generalised integrator-higher-order sliding mode.

Figure 19.

Performance of the STA method under parameter variation, additional sensor noise and under varying load torque. STA, super twisting algorithm.
Performance of the STA method under parameter variation, additional sensor noise and under varying load torque. STA, super twisting algorithm.

Figure 20.

A zoomed-in version of the performance of the conventional STA under parameter variation, additional sensor noise and under varying load torque. STA, super twisting algorithm.
A zoomed-in version of the performance of the conventional STA under parameter variation, additional sensor noise and under varying load torque. STA, super twisting algorithm.

Figure 21.

Performance of the SOGI-FLL method under parameter variation, additional sensor noise and under varying load torque. SOGI-FLL, second-order generalised integrator-frequency locked loop.
Performance of the SOGI-FLL method under parameter variation, additional sensor noise and under varying load torque. SOGI-FLL, second-order generalised integrator-frequency locked loop.

Figure 22.

A zoomed-in version of the performance of the SOGI-FLL method under parameter variation, additional sensor noise and under varying load torque. SOGI-FLL, second-order generalised integrator-frequency locked loop.
A zoomed-in version of the performance of the SOGI-FLL method under parameter variation, additional sensor noise and under varying load torque. SOGI-FLL, second-order generalised integrator-frequency locked loop.

Parameter variation and noise level_

Parameter Variation (%)
ΔRs Stator resistance variation +18
ΔLs Stator inductance variation +10
ΔZn Additional noise in current Sensor ±5

Parameters of Induction motor model used_

Motor parameters Values
Rs 2.3
Ls 0.261 H
Lr 0.261 H
P 4
B 0.0286 kg · m−2
J 0.02 kg · m−2
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