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Adaptive High-Frequency Injection-Based Sensorless Control for an Outer-Rotor PMaSynRM Cover

Adaptive High-Frequency Injection-Based Sensorless Control for an Outer-Rotor PMaSynRM

Open Access
|Dec 2025

Figures & Tables

Figure 1.

Equivalent electrical circuit representation of the OR-PMaSynRM in the dq reference frame: (a) d-axis model, (b) q-axis model. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.
Equivalent electrical circuit representation of the OR-PMaSynRM in the dq reference frame: (a) d-axis model, (b) q-axis model. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.

Figure 2.

Cross-sectional views of PMaSynRM with (a) outer rotor and (b) inner rotor configurations. PMaSynRM, permanent magnet-assisted synchronous reluctance motors
Cross-sectional views of PMaSynRM with (a) outer rotor and (b) inner rotor configurations. PMaSynRM, permanent magnet-assisted synchronous reluctance motors

Figure 3.

Electromagnetic characteristics of the OR-PMaSynRM: (a) Variation of the Ld and Lq inductances with respect to the rotor position and (b) magnetic flux linkage characteristics of the motor and the rotor position graph. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.
Electromagnetic characteristics of the OR-PMaSynRM: (a) Variation of the Ld and Lq inductances with respect to the rotor position and (b) magnetic flux linkage characteristics of the motor and the rotor position graph. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.

Figure 4.

Demodulation stages in HFI-based rotor position estimation. HFI, high-frequency signal injection; HPF, high-pass filter; LPF, low-pass filter.
Demodulation stages in HFI-based rotor position estimation. HFI, high-frequency signal injection; HPF, high-pass filter; LPF, low-pass filter.

Figure 5.

Implementation structures of the first-order digital filters: (a) HPF used in the demodulation stage, (b) LPF used in the signal extraction stage. HPF, high-pass filter; LPF, low-pass filter.
Implementation structures of the first-order digital filters: (a) HPF used in the demodulation stage, (b) LPF used in the signal extraction stage. HPF, high-pass filter; LPF, low-pass filter.

Figure 6.

Flowchart of the adaptive frequency injection algorithm.
Flowchart of the adaptive frequency injection algorithm.

Figure 7.

Flowchart of the adaptive injected signal amplitude control.
Flowchart of the adaptive injected signal amplitude control.

Figure 8.

(a) Total stator voltage vector exceeding the voltage limit and (b) limited stator voltage vector.
(a) Total stator voltage vector exceeding the voltage limit and (b) limited stator voltage vector.

Figure 9.

(a) Vector representation of the proposed limiting strategy based on error vector decomposition and (b) flowchart of the adaptive voltage limiting strategy. SVPWM, Space Vector Pulse Width Modulation.
(a) Vector representation of the proposed limiting strategy based on error vector decomposition and (b) flowchart of the adaptive voltage limiting strategy. SVPWM, Space Vector Pulse Width Modulation.

Figure 10.

(a) Adaptive HFI signal generation and voltage limiting block and (b) mathematical flow diagram. HFI, high-frequency signal injection.
(a) Adaptive HFI signal generation and voltage limiting block and (b) mathematical flow diagram. HFI, high-frequency signal injection.

Figure 11.

Comparison of the VHFI signal integrity before and after the voltage limiting.
Comparison of the VHFI signal integrity before and after the voltage limiting.

Figure 12.

Block diagram of the FOC-based adaptive HFI sensorless control system. FOC, field-oriented control; HFI, high-frequency signal injection; HPF, high-pass filter; LPF, low-pass filter.
Block diagram of the FOC-based adaptive HFI sensorless control system. FOC, field-oriented control; HFI, high-frequency signal injection; HPF, high-pass filter; LPF, low-pass filter.

Figure 13.

(a) The established OR-PmaSynRM sensorless drive system: (1) DC power source, (2) motor drive circuit, (3) isolated ST-Link, (4) monitor, (5) digital oscilloscope, (6) PC, (7) current probe, (8) OR-PmaSynRM, (9) current brake and (b) the OR-PmaSynRM drive test unit. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.
(a) The established OR-PmaSynRM sensorless drive system: (1) DC power source, (2) motor drive circuit, (3) isolated ST-Link, (4) monitor, (5) digital oscilloscope, (6) PC, (7) current probe, (8) OR-PmaSynRM, (9) current brake and (b) the OR-PmaSynRM drive test unit. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.

Figure 14.

(a) Effect of a constant injection frequency on rotor position estimation error during motor speed increase and (b) impact of the adaptive injection signal frequency on rotor position estimation error during motor speed variations.
(a) Effect of a constant injection frequency on rotor position estimation error during motor speed increase and (b) impact of the adaptive injection signal frequency on rotor position estimation error during motor speed variations.

Figure 15.

Flux weakening behaviour and rotor position estimation performance of the OR-PmaSynRM. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.
Flux weakening behaviour and rotor position estimation performance of the OR-PmaSynRM. OR-PMaSynRM, outer-rotor permanent magnet-assisted synchronous reluctance motor.

Figure 16.

(a) Rotor position error resulting from a constant-amplitude injection signal under varying load conditions and (b) impact of the adaptive injection signal frequency on rotor position estimation error during motor speed variations.
(a) Rotor position error resulting from a constant-amplitude injection signal under varying load conditions and (b) impact of the adaptive injection signal frequency on rotor position estimation error during motor speed variations.

Figure 17.

Motor phase current under high-frequency injection.
Motor phase current under high-frequency injection.

Figure 18.

Iα and Iβ currents under high-frequency signal injection.
Iα and Iβ currents under high-frequency signal injection.

Figure 19.

IαHPF and IβHPF signals obtained after the HPF stage. HPF, high-pass filter.
IαHPF and IβHPF signals obtained after the HPF stage. HPF, high-pass filter.

Figure 20.

Outputs of Iαmod and Iβmod after sine-wave modulation.
Outputs of Iαmod and Iβmod after sine-wave modulation.

Figure 21.

IαLPF and IβLPF current outputs obtained after low-pass filtering. LPF, low-pass filter.
IαLPF and IβLPF current outputs obtained after low-pass filtering. LPF, low-pass filter.

Figure 22.

Rotor position estimation results: (a) Estimated rotor position compared with the real position and (b) rotor position estimation and corresponding error profiles under varying speed conditions.
Rotor position estimation results: (a) Estimated rotor position compared with the real position and (b) rotor position estimation and corresponding error profiles under varying speed conditions.

Figure 23.

Impact of the proposed voltage limiting method on rotor position estimation.
Impact of the proposed voltage limiting method on rotor position estimation.

Experimental hardware specifications_

ParameterValue
MicrocontrollerSTM32F407VG (168 MHz, ARM Cortex-M4F [32-bit])
DC bus voltage (Vin)90 VDC
Current sensor typeGHS 20-SME
Current sensor output sensitivity40 mV/A (typical)
Current sensing resolution12-bit ADC
Position sensor (for validation only)MA702, 14-bit magnetic encoder
Cooling methodAluminium heatsink and fan

Experimental software specifications_

ParameterValue
Control methodFOC, HFI
HFI injection axisd-axis only
Filter type (demodulation)HPF and LPF (first-order digital)
Angle estimation methodPLL-based estimator with PI compensation
RMS angle error evaluationRMSE
PWM switching frequency15 kHz
Proportional and integral gain values for the d-axis current controller Kpidp,Kiidp \left( {Kp_{id}^p,Ki_{id}^p} \right) Kpidp=0.0005 Kp_{id}^p = 0.0005 , Kiidp=0.00075 Ki_{id}^p = 0.00075
Proportional and integral gain values for the q-axis current controller Kpiqp,Kiiqp \left( {Kp_{iq}^p,Ki_{iq}^p} \right) Kpiqp=0.000001 Kp_{iq}^p = 0.000001 , Kiiqp=0.0075 Ki_{iq}^p = 0.0075

Specifications of the OR-PmaSynRM_

ParameterValueUnit
Phase voltage90VRMS
Rated current5.741ARMS
Reactive power313VAR
Output power1500W
Input power1639VA
Efficiency91.51%
Rated speed750RPM
Frequency50Hz
Load torque19.1Nm

Boundaries of adaptive control parameters_

Control parameterAdaptation variableOperating rangeAdaptive range
Adaptive injection frequency fHFIA \left( {f_{HFI}^A} \right) Motor speed (RPM)0–750 RPM200–900 Hz
Adaptive injection amplitude MHFIA \left( {M_{HFI}^A} \right) Load ratio (%)30%–60%–90%8–20 V
Adaptive filter cut-off frequency fHFIA f_{HFI}^A 200–900 Hz
Reference voltage limit Voutlim \left( {{V_{out\left( {lim } \right)}}} \right) VdErr,VqErr {V_{d\left( {Err} \right)}},{V_{q\left( {Err} \right)}} 45–49 V

RMS position error under different operating conditions_

Test conditionMotor speed (RPM)Load torque (Nm)RMS error (°electrical)Standard deviation (°electrical)Max error (°electrical)
Low speed, light load150≈5.71.10±0.021.23
Medium speed, nominal load450≈11.51.12±0.021.28
High speed, high load750≈17.21.15±0.031.35

Comparison of rotor position estimation errors reported in various studies_

StudyMotor typeControl methodEstimation methodAverage RMS error (electrical degrees)
Method in Chen et al. (2024a)PMSMFOCAdaptive BPF + HFI≈1.2°
Method in Tap et al. (2023)PmaSynRMFOCAdaptive HFI + modified PLL≈1°–1.5°
Method in Lu et al. (2018)IPMSMFOCAdaptive frequency & amplitude HFI<3°
Method in Chen and Liu (2012)IPMSMFOCHFI≈±2°
Method in Tongxing et al. (2019)PMSMFOCFrequency self-optimized HFI + PLL≈±14.4°
Method in Kumar et al. (2019)IPMSMFOCHFI + Self-adaptive PLL + adaptive amplitude≈1.5°
My workOR-PmaSynRMFOCHFI + adaptive frequency + adaptive amplitude + proposed voltage limiting±1.15°
DOI: https://doi.org/10.2478/pead-2025-0031 | Journal eISSN: 2543-4292 | Journal ISSN: 2451-0262
Language: English
Page range: 487 - 507
Submitted on: Oct 20, 2025
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Accepted on: Dec 5, 2025
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Published on: Dec 31, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2025 Hande Nevin Kılıç, Yusuf Öner, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.