Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation

Isaac Itekulana Mwesigwa; Benjamin William Ndimila; Bakari Momba Ramadhan

doi:doi:10.11648/j.ajae.20251102.13

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Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation

Isaac Itekulana Mwesigwa^*

, Benjamin William Ndimila, Bakari Momba Ramadhan

Published in American Journal of Aerospace Engineering (Volume 11, Issue 2)

Received: 1 October 2025 Accepted: 13 October 2025 Published: 7 November 2025

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Abstract

Electro-hydraulic servo valves (EHSVs) are extensively used in aerospace actuation systems due to their capability to provide precise and rapid control of hydraulic flow. However, accurate mathematical modeling is essential to capture their complex nonlinear dynamics for purposes of simulation, analysis, and control system design. This paper presents a comprehensive mathematical model of a two-stage nozzle flapper EHSV applied to aircraft landing gear operations. The servo valve is divided into five key subsystems: the servo amplifier, voltage-current converter, torque motor, nozzle flapper mechanism, and spool valve integrated with a feedback sensor. Transfer functions are derived for each subsystem and subsequently combined to form an overall system model. The model’s accuracy is validated through simulations conducted in MATLAB/Simulink, enabling detailed performance analysis under various input conditions. Simulation results are used to evaluate system stability, transient response, and overall accuracy. The findings reveal a rapid settling time of 0.85 s, negligible overshoot, and a fine spool displacement of 1.43 × 10^-4 m (0.143 mm), demonstrating the model’s capability to achieve stable and precise hydraulic control. These findings highlight the significant potential of the proposed mathematical model to enhance the dynamic performance of aircraft landing gear systems by providing more accurate, stable, and responsive control of hydraulic actuation.

Published in	American Journal of Aerospace Engineering (Volume 11, Issue 2)
DOI	10.11648/j.ajae.20251102.13
Page(s)	36-45
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Electro-hydraulic Servo Valve, Landing Gear System, Nozzle Flapper, Spool Displacement

References

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APA Style

Mwesigwa, I. I., Ndimila, B. W., Ramadhan, B. M. (2025). Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation. American Journal of Aerospace Engineering, 11(2), 36-45. https://doi.org/10.11648/j.ajae.20251102.13

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ACS Style

Mwesigwa, I. I.; Ndimila, B. W.; Ramadhan, B. M. Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation. Am. J. Aerosp. Eng. 2025, 11(2), 36-45. doi: 10.11648/j.ajae.20251102.13

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AMA Style

Mwesigwa II, Ndimila BW, Ramadhan BM. Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation. Am J Aerosp Eng. 2025;11(2):36-45. doi: 10.11648/j.ajae.20251102.13

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@article{10.11648/j.ajae.20251102.13,
  author = {Isaac Itekulana Mwesigwa and Benjamin William Ndimila and Bakari Momba Ramadhan},
  title = {Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation
},
  journal = {American Journal of Aerospace Engineering},
  volume = {11},
  number = {2},
  pages = {36-45},
  doi = {10.11648/j.ajae.20251102.13},
  url = {https://doi.org/10.11648/j.ajae.20251102.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajae.20251102.13},
  abstract = {Electro-hydraulic servo valves (EHSVs) are extensively used in aerospace actuation systems due to their capability to provide precise and rapid control of hydraulic flow. However, accurate mathematical modeling is essential to capture their complex nonlinear dynamics for purposes of simulation, analysis, and control system design. This paper presents a comprehensive mathematical model of a two-stage nozzle flapper EHSV applied to aircraft landing gear operations. The servo valve is divided into five key subsystems: the servo amplifier, voltage-current converter, torque motor, nozzle flapper mechanism, and spool valve integrated with a feedback sensor. Transfer functions are derived for each subsystem and subsequently combined to form an overall system model. The model’s accuracy is validated through simulations conducted in MATLAB/Simulink, enabling detailed performance analysis under various input conditions. Simulation results are used to evaluate system stability, transient response, and overall accuracy. The findings reveal a rapid settling time of 0.85 s, negligible overshoot, and a fine spool displacement of 1.43 × 10-4 m (0.143 mm), demonstrating the model’s capability to achieve stable and precise hydraulic control. These findings highlight the significant potential of the proposed mathematical model to enhance the dynamic performance of aircraft landing gear systems by providing more accurate, stable, and responsive control of hydraulic actuation.
},
 year = {2025}
}

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TY  - JOUR
T1  - Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation

AU  - Isaac Itekulana Mwesigwa
AU  - Benjamin William Ndimila
AU  - Bakari Momba Ramadhan
Y1  - 2025/11/07
PY  - 2025
N1  - https://doi.org/10.11648/j.ajae.20251102.13
DO  - 10.11648/j.ajae.20251102.13
T2  - American Journal of Aerospace Engineering
JF  - American Journal of Aerospace Engineering
JO  - American Journal of Aerospace Engineering
SP  - 36
EP  - 45
PB  - Science Publishing Group
SN  - 2376-4821
UR  - https://doi.org/10.11648/j.ajae.20251102.13
AB  - Electro-hydraulic servo valves (EHSVs) are extensively used in aerospace actuation systems due to their capability to provide precise and rapid control of hydraulic flow. However, accurate mathematical modeling is essential to capture their complex nonlinear dynamics for purposes of simulation, analysis, and control system design. This paper presents a comprehensive mathematical model of a two-stage nozzle flapper EHSV applied to aircraft landing gear operations. The servo valve is divided into five key subsystems: the servo amplifier, voltage-current converter, torque motor, nozzle flapper mechanism, and spool valve integrated with a feedback sensor. Transfer functions are derived for each subsystem and subsequently combined to form an overall system model. The model’s accuracy is validated through simulations conducted in MATLAB/Simulink, enabling detailed performance analysis under various input conditions. Simulation results are used to evaluate system stability, transient response, and overall accuracy. The findings reveal a rapid settling time of 0.85 s, negligible overshoot, and a fine spool displacement of 1.43 × 10-4 m (0.143 mm), demonstrating the model’s capability to achieve stable and precise hydraulic control. These findings highlight the significant potential of the proposed mathematical model to enhance the dynamic performance of aircraft landing gear systems by providing more accurate, stable, and responsive control of hydraulic actuation.

VL  - 11
IS  - 2
ER  -

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Author Information

Isaac Itekulana Mwesigwa

Department of Automotive and Mechanical Engineering, National Institute of Transport, Dar es Salaam, Tanzania

Contact Email

http://orcid.org/0009-0004-5626-9735
Benjamin William Ndimila

Department of Automotive and Mechanical Engineering, National Institute of Transport, Dar es Salaam, Tanzania

Contact Email
Bakari Momba Ramadhan

Department of Research and Design, Tanzania Engineering and Manufacturing Design Organization, Arusha, Tanzania

Contact Email

http://orcid.org/0009-0006-2905-1436

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APA Style

Mwesigwa, I. I., Ndimila, B. W., Ramadhan, B. M. (2025). Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation. American Journal of Aerospace Engineering, 11(2), 36-45. https://doi.org/10.11648/j.ajae.20251102.13

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ACS Style

Mwesigwa, I. I.; Ndimila, B. W.; Ramadhan, B. M. Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation. Am. J. Aerosp. Eng. 2025, 11(2), 36-45. doi: 10.11648/j.ajae.20251102.13

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AMA Style

Mwesigwa II, Ndimila BW, Ramadhan BM. Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation. Am J Aerosp Eng. 2025;11(2):36-45. doi: 10.11648/j.ajae.20251102.13

Copy | Download

@article{10.11648/j.ajae.20251102.13,
  author = {Isaac Itekulana Mwesigwa and Benjamin William Ndimila and Bakari Momba Ramadhan},
  title = {Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation
},
  journal = {American Journal of Aerospace Engineering},
  volume = {11},
  number = {2},
  pages = {36-45},
  doi = {10.11648/j.ajae.20251102.13},
  url = {https://doi.org/10.11648/j.ajae.20251102.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajae.20251102.13},
  abstract = {Electro-hydraulic servo valves (EHSVs) are extensively used in aerospace actuation systems due to their capability to provide precise and rapid control of hydraulic flow. However, accurate mathematical modeling is essential to capture their complex nonlinear dynamics for purposes of simulation, analysis, and control system design. This paper presents a comprehensive mathematical model of a two-stage nozzle flapper EHSV applied to aircraft landing gear operations. The servo valve is divided into five key subsystems: the servo amplifier, voltage-current converter, torque motor, nozzle flapper mechanism, and spool valve integrated with a feedback sensor. Transfer functions are derived for each subsystem and subsequently combined to form an overall system model. The model’s accuracy is validated through simulations conducted in MATLAB/Simulink, enabling detailed performance analysis under various input conditions. Simulation results are used to evaluate system stability, transient response, and overall accuracy. The findings reveal a rapid settling time of 0.85 s, negligible overshoot, and a fine spool displacement of 1.43 × 10-4 m (0.143 mm), demonstrating the model’s capability to achieve stable and precise hydraulic control. These findings highlight the significant potential of the proposed mathematical model to enhance the dynamic performance of aircraft landing gear systems by providing more accurate, stable, and responsive control of hydraulic actuation.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modelling and Simulation of a Two-Stage Nozzle Flapper Electro-Hydraulic Servo Valve for Aircraft Landing Gear Operation

AU  - Isaac Itekulana Mwesigwa
AU  - Benjamin William Ndimila
AU  - Bakari Momba Ramadhan
Y1  - 2025/11/07
PY  - 2025
N1  - https://doi.org/10.11648/j.ajae.20251102.13
DO  - 10.11648/j.ajae.20251102.13
T2  - American Journal of Aerospace Engineering
JF  - American Journal of Aerospace Engineering
JO  - American Journal of Aerospace Engineering
SP  - 36
EP  - 45
PB  - Science Publishing Group
SN  - 2376-4821
UR  - https://doi.org/10.11648/j.ajae.20251102.13
AB  - Electro-hydraulic servo valves (EHSVs) are extensively used in aerospace actuation systems due to their capability to provide precise and rapid control of hydraulic flow. However, accurate mathematical modeling is essential to capture their complex nonlinear dynamics for purposes of simulation, analysis, and control system design. This paper presents a comprehensive mathematical model of a two-stage nozzle flapper EHSV applied to aircraft landing gear operations. The servo valve is divided into five key subsystems: the servo amplifier, voltage-current converter, torque motor, nozzle flapper mechanism, and spool valve integrated with a feedback sensor. Transfer functions are derived for each subsystem and subsequently combined to form an overall system model. The model’s accuracy is validated through simulations conducted in MATLAB/Simulink, enabling detailed performance analysis under various input conditions. Simulation results are used to evaluate system stability, transient response, and overall accuracy. The findings reveal a rapid settling time of 0.85 s, negligible overshoot, and a fine spool displacement of 1.43 × 10-4 m (0.143 mm), demonstrating the model’s capability to achieve stable and precise hydraulic control. These findings highlight the significant potential of the proposed mathematical model to enhance the dynamic performance of aircraft landing gear systems by providing more accurate, stable, and responsive control of hydraulic actuation.

VL  - 11
IS  - 2
ER  -

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