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arxiv: 2606.07906 · v1 · pith:ORAEXHN5new · submitted 2026-06-06 · 📡 eess.SY · cs.SY

Extremum Seeking Control Based Adaptive Compensation of Position Sensor Harmonics in PMSM Drives

Gayan V. Dissanayake , Sandun S. Kuruppu This is my paper

Pith reviewed 2026-06-27 19:47 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords PMSM drivesposition sensor harmonicsextremum seeking controladaptive compensationtorque rippleexperimental validation
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The pith

Extremum seeking control adaptively compensates position sensor harmonics in PMSM drives to reduce torque ripple.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that an extremum seeking control algorithm can online estimate and cancel harmonic distortions in rotor position measurements for permanent magnet synchronous motors. Accurate position sensing matters because sensor harmonics create torque ripple that harms efficiency and smoothness. The method perturbs compensation gains while observing a ripple-related cost and drives those gains toward values that minimize the cost. Experiments confirm the compensation works across changing speeds, torques, and harmonic amplitudes and performs at least as well as a precomputed look-up table approach.

Core claim

The paper claims that extremum seeking control supplies an adaptive compensation scheme for position sensor harmonics in PMSMs; the scheme is shown experimentally to lower torque ripple under varying torque, speed, and harmonic conditions while matching the performance of a look-up table method.

What carries the argument

Extremum seeking control loop that continuously perturbs harmonic compensation parameters and updates them to minimize a measured torque-ripple cost index.

Load-bearing premise

The assumption that the small perturbations used by extremum seeking control will converge to correct compensation values in real time without causing instability or adding their own ripple.

What would settle it

Run the motor at a speed where a dominant sensor harmonic frequency coincides with the perturbation frequency and check whether torque ripple stops decreasing or the system becomes unstable.

Figures

Figures reproduced from arXiv: 2606.07906 by Gayan V. Dissanayake, Sandun S. Kuruppu.

Figure 1
Figure 1. Figure 1: Block Diagram of a Field-Oriented Controller for a PMSM. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Errors Associated with the LUT-Based Harmonic Error Correction [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: presents simulation results of V r ds and the injected harmonic components, which validate the mathematical proof [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: presents the open-loop simulation results illustrating the unimodal behavior of V r qs under amplitude perturbation (A), thereby supporting the above conclusion on unimodal behavior of the function. Subplot 1 shows the variation of V r qs during the correction process with injected multiple harmonics. Subplot 2 illustrates the corresponding variation in the position signal throughout the correction process… view at source ↗
Figure 5
Figure 5. Figure 5: Generalized Block Diagram of the ESC [20]. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Block Diagram of the Self-Regulating Position Sensor Harmonic Compensation using ESC Algorithm for PMSM Drive. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Experimental Setup Used for Validation of the PSHE Based on ESC [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: I r ds, I r qs, torque, and position signal variations across four regions for the harmonic case 1 (I r ds = 0 A, Ir qs = 2 A, and speed = 200 rpm) [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Torque spectrum in Regions 1, 2, and 4 for the harmonic case [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: I r ds, I r qs, torque, and position signal variations across four regions for the harmonic case 2 (I r ds = 0 A, Ir qs = 2 A, and speed = 200 rpm) [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Torque spectrum in Regions 1, 2, and 4 for the harmonic case [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 16
Figure 16. Figure 16: shows the responses of I r ds, I r qs, torque, and position signal variations across four regions for I r ds = 0 A, I r qs = 2 A, and a motor speed of 400 rpm [PITH_FULL_IMAGE:figures/full_fig_p009_16.png] view at source ↗
Figure 15
Figure 15. Figure 15: shows the responses of I r ds, I r qs, torque, and position signal variations across four regions for I r ds = 0 A, I r qs = 1.5 A, and a motor speed of 300 rpm [PITH_FULL_IMAGE:figures/full_fig_p009_15.png] view at source ↗
Figure 18
Figure 18. Figure 18: Error distribution and the corresponding maximum error with respect [PITH_FULL_IMAGE:figures/full_fig_p010_18.png] view at source ↗
Figure 17
Figure 17. Figure 17: Response of the position correction and torque characteristics of the [PITH_FULL_IMAGE:figures/full_fig_p010_17.png] view at source ↗
read the original abstract

Permanent Magnet Synchronous Machines (PMSMs) have become one of the preferred forms of electromechanical energy converters, attributing to their high efficiency, torque density, and other unique advantages. However, given the need for proper rotor position measurement for commutation and field orientation, accurate rotor position sensing is of paramount importance. In sensing motor rotor position with a sensor, harmonic errors that arise in the sensing subsystem lead to undesirable torque ripple. Thus, this paper presents an adaptive, extremum seeking control based approach capable of mitigating position signal harmonics in PMSMs. The proposed approach is experimentally validated under varying torque, speed, and harmonic conditions. Its harmonic compensation performance is comparatively evaluated against the look-up table based method. Furthermore, the accuracy of the proposed approach is analyzed, highlighting its effectiveness.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an extremum-seeking-control (ESC) based adaptive compensator for harmonic errors in rotor-position sensors of PMSMs. The method injects sinusoidal dither signals at estimated harmonic frequencies into the position measurement and adapts the compensation coefficients online; the authors claim that the approach reduces torque ripple, is experimentally validated across varying torque/speed/harmonic conditions, and outperforms a conventional lookup-table baseline.

Significance. If the convergence and stability claims hold, the work would supply a genuinely online, model-light alternative to offline-calibrated lookup tables for sensor-harmonic compensation, which is practically relevant for high-performance PMSM drives where resolver or encoder harmonics are a persistent source of torque ripple.

major comments (2)
  1. [method and stability analysis sections] The central claim that the ESC compensator converges reliably in real time without destabilizing the drive or injecting unacceptable torque ripple rests on an unproven separation of time scales between the slow ESC adaptation and the fast electrical dynamics. No averaging analysis, Lyapunov function, or explicit bound on the interaction of the dither signals through the Park transform and current controllers is supplied; experimental traces alone cannot rule out limit cycles or drift under the reported torque/speed transients.
  2. [experimental results section] The abstract asserts experimental validation and quantitative comparison to the lookup-table method, yet no error metrics (e.g., THD, position-error RMS, torque-ripple amplitude), operating-point ranges, or hardware description appear. Without these data the support for the performance claims cannot be assessed.
minor comments (2)
  1. [preliminaries] Notation for the harmonic coefficients and the ESC cost function should be introduced once and used consistently; several symbols appear without prior definition.
  2. [figures] Figure captions for the experimental waveforms should state the exact operating conditions (speed, load torque, harmonic order) rather than generic labels.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: [method and stability analysis sections] The central claim that the ESC compensator converges reliably in real time without destabilizing the drive or injecting unacceptable torque ripple rests on an unproven separation of time scales between the slow ESC adaptation and the fast electrical dynamics. No averaging analysis, Lyapunov function, or explicit bound on the interaction of the dither signals through the Park transform and current controllers is supplied; experimental traces alone cannot rule out limit cycles or drift under the reported torque/speed transients.

    Authors: We acknowledge that the manuscript does not provide a formal averaging analysis or Lyapunov-based proof of the time-scale separation. The presentation relies on standard ESC assumptions and experimental demonstration of convergence. To address this, the revised manuscript will add a dedicated subsection with a brief averaging analysis and explicit bounds on dither-signal effects through the Park transform and current controllers. revision: yes

  2. Referee: [experimental results section] The abstract asserts experimental validation and quantitative comparison to the lookup-table method, yet no error metrics (e.g., THD, position-error RMS, torque-ripple amplitude), operating-point ranges, or hardware description appear. Without these data the support for the performance claims cannot be assessed.

    Authors: The full manuscript (Section IV) presents experimental results with figures comparing the proposed method to the lookup-table baseline under varying torque, speed, and harmonic conditions. However, we agree that quantitative metrics and hardware details should be stated more explicitly. The revised version will update the abstract with key metrics (THD, position-error RMS, torque-ripple amplitude), add a summary table of operating-point ranges and performance values, and include a hardware description subsection. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes an ESC-based adaptive compensator for PMSM position sensor harmonics, presents the method as an application of standard extremum-seeking principles, and validates performance experimentally against an independent lookup-table baseline under varying operating conditions. No derivation step reduces by construction to its own inputs (no self-definitional relations, no fitted parameters renamed as predictions, and no load-bearing self-citations that close the argument). The central claim rests on experimental comparison rather than on any tautological reduction, making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No information is available from the abstract to identify specific free parameters, axioms, or invented entities. The approach appears to rely on standard assumptions in control theory for extremum seeking methods.

pith-pipeline@v0.9.1-grok · 5669 in / 1085 out tokens · 26696 ms · 2026-06-27T19:47:18.491944+00:00 · methodology

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Reference graph

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