Nonlinear System Identification of Variable-Pitch Propellers Using a Wiener Model

David Grasev; Miguel A. Mendez

arxiv: 2604.02503 · v1 · submitted 2026-04-02 · 📡 eess.SY · cs.SY

Nonlinear System Identification of Variable-Pitch Propellers Using a Wiener Model

David Grasev , Miguel A. Mendez This is my paper

Pith reviewed 2026-05-13 20:36 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords system identificationWiener modelvariable-pitch propellerthrust modelingdigital twinPWM actuationnonlinear dynamicsreal-time simulation

0 comments

The pith

A Wiener model separates fast linear actuation from a static nonlinearity to predict variable-pitch propeller thrust from PWM signals.

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

The paper identifies the full powertrain of a variable-pitch propeller from PWM commands to thrust output. It proposes a Wiener-like structure in which linear first-order dynamics first capture motor and pitch-actuator response, after which a static nonlinear map converts those states into thrust. Experimental data for both steady and transient conditions confirm that this compact form reproduces observed behavior with good accuracy. A reader would care because the resulting model stays interpretable and light enough for real-time digital-twin and control use.

Core claim

Under the assumptions that electronic actuation is much faster than mechanical response and that aerodynamic torque is negligible, the PWM inputs are processed by linear first-order dynamics for the motor and pitch actuation; the resulting states are then passed through a static nonlinear relation that directly yields the generated thrust. This parsimonious Wiener-like representation matches measured static and dynamic responses accurately while remaining computationally light and physically interpretable.

What carries the argument

Wiener-like cascade of linear first-order actuation dynamics followed by a static nonlinear thrust map, which separates fast electronic effects from the slower mechanical and aerodynamic conversion.

If this is right

The model supplies a practical, low-compute foundation for embedding propeller dynamics inside control-oriented digital twins.
It supports real-time simulation and controller design without requiring full nonlinear differential equations.
Static and dynamic experimental data are both reproduced to good accuracy with a single parsimonious structure.
The separation of linear dynamics and static nonlinearity makes parameter tuning and physical interpretation straightforward.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the timescale separation holds across operating regimes, similar Wiener structures could be applied to other variable-pitch or variable-speed propulsors.
The approach may reduce the need for high-order nonlinear state-space models when only input-output thrust behavior is required for control.
Extending the nonlinear map to include explicit dependence on airspeed or density would test how far the present static assumption can be stretched.

Load-bearing premise

Electronic actuation runs on a much faster time scale than the mechanical response and aerodynamic torque remains negligible in the tested regime.

What would settle it

A clear mismatch between predicted and measured thrust when PWM commands change on a time scale comparable to the actuator dynamics or when aerodynamic torque becomes significant, such as during rapid pitch changes at high rotational speeds.

read the original abstract

This work presents the system identification of a variable-pitch propeller (VPP) powertrain, encompassing the full actuation chain from PWM signals to thrust generation, with the aim of developing compact models suitable for real-time digital twinning and control applications. The identification is grounded in experimental data covering both static and dynamic responses of the system. The proposed model takes the form of a Wiener-like architecture, where the PWM inputs are first processed through linear first-order dynamics describing the motor and pitch actuation, and the resulting states are then mapped via a static nonlinear relation to the generated thrust. This structure naturally arises under the assumptions that the electronic actuation operates on a much faster time scale than the mechanical response, and that the contribution of the aerodynamically induced torque is negligible in the tested regime. The resulting parsimonious representation is shown to reproduce the measured dynamics with good accuracy while remaining interpretable and computationally light, thereby providing a practical basis for integration in control-oriented digital twin frameworks.

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.

Desk Editor's Note private letter to a colleague

The paper fits a Wiener model to VPP PWM-to-thrust data with physical motivation but supplies almost no numbers to show how well it works.

read the letter

The paper applies a Wiener structure to identify the full chain from PWM command to thrust on a variable-pitch propeller, using separate static and dynamic experiments. It splits the problem into linear first-order dynamics for the motor and pitch servo followed by a static nonlinearity for thrust generation. The motivation rests on clear time-scale separation and the claim that aero-induced torque can be ignored in the tested range. That produces a compact, interpretable model meant for real-time digital twins and control design. The experimental coverage of both steady-state and transient behavior is a practical strength, and the structure follows directly from the stated assumptions without unnecessary parameters. What is new is the specific end-to-end identification for this hardware rather than a generic Wiener example. The soft spots are straightforward. The abstract asserts good accuracy and parsimony but gives no RMSE values, no validation plots, no description of how the linear and nonlinear parameters were estimated, and no hold-out tests. More critically, the negligible-torque assumption is load-bearing yet unsupported by any direct torque measurement or comparison against a model that retains the torque term. If that torque is not truly small, the static-map separation breaks and the reported fit quality may not generalize. The work is aimed at UAV propulsion engineers and control groups who need lightweight, physically motivated models for simulation and digital-twin work. It shows honest engagement with the modeling assumptions and uses real data, so it is coherent on its own terms even if the evidence is thin. I would send it to peer review so referees can request the missing quantitative results and a check on the torque assumption.

Referee Report

3 major / 2 minor

Summary. The paper proposes a Wiener model for system identification of a variable-pitch propeller powertrain, consisting of linear first-order dynamics applied to PWM inputs followed by a static nonlinear mapping to thrust. The structure is motivated by time-scale separation and negligible aero-induced torque assumptions, identified from separate static and dynamic experiments, and claimed to reproduce measured dynamics with good accuracy while remaining parsimonious and suitable for real-time digital-twin and control applications.

Significance. If the validation evidence and assumption checks are strengthened, the work supplies a practical, interpretable, low-order model for VPP actuation chains that could be directly embedded in control-oriented digital twins. The separation into linear dynamics and static map offers computational lightness and physical insight that black-box alternatives often lack.

major comments (3)

[§4] §4 (Results and Validation): the central claim that the model 'reproduces the measured dynamics with good accuracy' is unsupported by any quantitative metrics (RMSE, NRMSE, R², or cross-validation error statistics) or by explicit validation plots showing residuals; only qualitative statements appear.
[§2.2] §2.2 (Model Assumptions): the load-bearing assumption that aerodynamically induced torque is negligible is stated without direct torque measurements, sensitivity analysis, or comparison against a model retaining the torque term; this leaves open whether the Wiener separation holds outside the tested regime or is an artifact of the operating points.
[§3] §3 (Identification Procedure): details on how the linear dynamics parameters and nonlinear mapping parameters were fitted (e.g., least-squares, optimization algorithm, separate vs. joint estimation, regularization) are not provided, preventing assessment of uniqueness or overfitting risk.

minor comments (2)

[§2.1] Notation for the static nonlinearity (e.g., the function relating motor/pitch state to thrust) should be defined explicitly with an equation number rather than described only in text.
[§4] Figure captions for experimental responses should include the specific PWM or pitch commands used and the sampling rate to allow reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and will revise the manuscript to strengthen the presentation where appropriate.

read point-by-point responses

Referee: [§4] §4 (Results and Validation): the central claim that the model 'reproduces the measured dynamics with good accuracy' is unsupported by any quantitative metrics (RMSE, NRMSE, R², or cross-validation error statistics) or by explicit validation plots showing residuals; only qualitative statements appear.

Authors: We agree that quantitative metrics are necessary to substantiate the accuracy claims. In the revised manuscript we will report RMSE, NRMSE, and R² values computed on the experimental data for both static and dynamic cases, together with residual time-series plots. These additions will be placed in Section 4. revision: yes
Referee: [§2.2] §2.2 (Model Assumptions): the load-bearing assumption that aerodynamically induced torque is negligible is stated without direct torque measurements, sensitivity analysis, or comparison against a model retaining the torque term; this leaves open whether the Wiener separation holds outside the tested regime or is an artifact of the operating points.

Authors: The assumption follows from the physical configuration and observed time-scale separation, yet we acknowledge the absence of direct validation. We will add a sensitivity study in the revision that compares model predictions with and without the torque term using the existing data set and will explicitly delineate the operating regime in which the assumption remains valid. revision: partial
Referee: [§3] §3 (Identification Procedure): details on how the linear dynamics parameters and nonlinear mapping parameters were fitted (e.g., least-squares, optimization algorithm, separate vs. joint estimation, regularization) are not provided, preventing assessment of uniqueness or overfitting risk.

Authors: We will expand Section 3 to specify that linear dynamics parameters were obtained by least-squares fitting to step-response data, the static nonlinearity was identified separately by polynomial least-squares regression on steady-state measurements, and no regularization or joint optimization was applied. Cross-validation results will also be reported to address overfitting concerns. revision: yes

Circularity Check

0 steps flagged

No circularity: structure from assumptions, parameters fitted independently

full rationale

The derivation begins with explicit physical assumptions (electronic actuation faster than mechanical response; negligible aero-induced torque) that justify the Wiener cascade of linear first-order dynamics followed by a static nonlinearity. Parameters are then identified from separate static and dynamic experimental datasets. No equation reduces to a prior fit by construction, no self-citation supplies a load-bearing uniqueness result, and no prediction is statistically forced from the same data used to define the model. The reported reproduction accuracy is the expected outcome of system identification on the training regime and does not create a closed loop.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claim rests on two domain assumptions about time scales and torque, plus parameters fitted to experimental static and dynamic data; no new physical entities are introduced.

free parameters (2)

linear dynamics parameters
Time constants and gains of the first-order filters for motor and pitch actuation, fitted to dynamic response data
nonlinear mapping parameters
Coefficients or shape parameters of the static function mapping filtered states to thrust, fitted to steady-state measurements

axioms (2)

domain assumption Electronic actuation operates on a much faster time scale than the mechanical response
Invoked to justify the Wiener separation of linear dynamics from the static nonlinearity
domain assumption Aerodynamically induced torque is negligible in the tested regime
Used to simplify the model by omitting torque feedback effects

pith-pipeline@v0.9.0 · 5466 in / 1306 out tokens · 47891 ms · 2026-05-13T20:36:25.406844+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The proposed model takes the form of a Wiener-like architecture, where the PWM inputs are first processed through linear first-order dynamics describing the motor and pitch actuation, and the resulting states are then mapped via a static nonlinear relation to the generated thrust.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

This structure naturally arises under the assumptions that the electronic actuation operates on a much faster time scale than the mechanical response, and that the contribution of the aerodynamically induced torque is negligible in the tested regime.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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[1] [1]

8: The comparison of the initial model (blue) and the fine-tuned model (red) for a) RPM in action, constant pitch, b) pitch in action, constant RPM, and c) both inputs in action

Schena, L., Marques, P.A., Poletti, R., Ahizi, S., Berghe, J., Mendez, M.A.: Reinforcement Twinning: 11 0 25 50 75 100 125 150 175 200 Time (sec) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Normalized thrust (1) Measured Initial model Fine-tuned model (a) 400 425 450 475 500 525 550 575 600 Time (sec) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Normalized thrust (1) Measured Initial...

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Poletti, R., Schena, L., Koloszar, L., Degroote, J., Mendez, M.A.: Reinforcement twinning for hybrid control of flapping-wing drones (2025) https://doi.org/10.48550/ARXIV.2505.18201 arXiv:2505.18201 [cs.RO]

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Master’s thesis, Environmen- tal and Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Belgium (2025)

Yannick Lecomte, S.M.R., Mendez, M.A.: Research master report. Master’s thesis, Environmen- tal and Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Belgium (2025). Supervisors: M. Ratz and M.A. Mendez

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Sensors20(19) (2020) https://doi.org/10.3390/s20195651

Chang, C.-W., Chen, S., Wen, C.-Y., Li, B.: An actuator allocation method for a variable-pitch propeller system of quadrotor-based uavs. Sensors20(19) (2020) https://doi.org/10.3390/s20195651

work page doi:10.3390/s20195651 2020

[5] [5]

Journal of Applied Mechanics33(4), 845–854 (1966) https://doi.org/10.1115/1

Cutler, M., How, J.P.: Analysis and Control of a Variable-Pitch Quadrotor for Agile Flight. Journal of Dynamic Systems, Measurement, and Control137(101002) (2015) https://doi.org/10.1115/1. 4030676

work page doi:10.1115/1 2015

[6] [6]

Master’s thesis, Luleå University of Technology (2013)

Fresk, E.: Modeling, Control and Experimentation of a Variable Pitch Quadrotor. Master’s thesis, Luleå University of Technology (2013)

work page 2013

[7] [7]

In: 2014 IEEE Conference on Control Applications (CCA), pp

Fresk,E.,Nikolakopoulos,G.:Experimentalmodelderivationandcontrolofavariablepitchpropeller equipped quadrotor. In: 2014 IEEE Conference on Control Applications (CCA), pp. 723–729 (2014). https://doi.org/10.1109/CCA.2014.6981426 . ISSN: 1085-1992

work page doi:10.1109/cca.2014.6981426 2014

[8] [8]

Sheng, S., Sun, C.: Control and optimization of a variable-pitch quadrotor with minimum power consumption. Energies9(4), 232 (2016) https://doi.org/10.3390/en9040232 13 3 4 5 6 7 Time (s) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Thrust (-) T set RPM only, optimal PID BOTH, optimal PID (a) 3 4 5 6 7 Time (s) 0.0 0.2 0.4 0.6 0.8 1.0 Pitch angle (-) RPM only, optimal...

work page doi:10.3390/en9040232 2016

[9] [9]

Journal of Aircraft52(3), 748–763 (2015) https://doi.org/10.2514/1.C032595

Heinzen, S.B., Hall, C.E., Gopalarathnam, A.: Development and Testing of a Passive Variable-Pitch Propeller. Journal of Aircraft52(3), 748–763 (2015) https://doi.org/10.2514/1.C032595 . Publisher: American Institute of Aeronautics and Astronautics _eprint: https://doi.org/10.2514/1.C032595

work page doi:10.2514/1.c032595 2015

[10] [10]

Advanced Control for Applications2(2), 29 (2020) https://doi.org/10.1002/adc2.29

Wang, Z., Groß, R., Zhao, S.: Controllability analysis and controller design for variable-pitch pro- peller quadcopters with one propeller failure. Advanced Control for Applications2(2), 29 (2020) https://doi.org/10.1002/adc2.29

work page doi:10.1002/adc2.29 2020

[11] [11]

Chan, and Howard Smith

Arellano-Quintana, V., Sanjurjo-Rivo, M., Girón-Sierra, J.M.: Design, modelling and control of a variable pitch quadcopter. In: 2018 AIAA Atmospheric Flight Mechanics Conference. American Institute of Aeronautics and Astronautics, Kissimmee, Florida (2018). https://doi.org/10.2514/6. 2018-1691 .https://doi.org/10.2514/6.2018-1691

work page doi:10.2514/6 2018

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