Abstract
Effective control of motorized wheelchairs needs methods with capabilities for stability, rapid response, accuracy, and robustness against nonlinearities and disturbances common in electromechanical systems. In this article, an optimized PID controller based on an Arithmetic Optimization Algorithm (AOA), known as AOA-PID, strategy is introduced. A full wheelchair model and an optimization model are used, offering a chance for a reduction in computation cost with retention of basic system dynamics. Experimental research on the role of PID factors will be conducted, followed by performance analysis on two axes: firstly, comparative research with multiple references on PID optimization methods, including Sine Cosine Algorithms (SCA), Kepler Optimization Algorithms (KOA), Salp Swarm Algorithms (SSA), Puma Optimizer Algorithms (POA), and Particle Swarm Optimization Algorithms (PSO); and secondly, comparative research on traditional and modern methods. The research result illustrates that AOA-PID exhibits quicker response and controlled overshoots with zero error and an extremely low IAE value, indicating simultaneous enhancement on stability, accuracy, and robustness. Additionally, Model-in-the-Loop (MIL), Software-in-the-Loop (SIL), and Processor-in-the-Loop (PIL) testing confirms the controller’s capability to maintain high performance within an embedded system with low CPU consumption that meets real-time processing. As a result, AOA-PID strategy proves an efficient and highly capable strategy on assistive mobility control with significant improvements on safety, stability, and accuracy.
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References
Meng, X., Yu, H., Zhang, J. & Yang, Q. Adaptive EPCH strategy for nonlinear systems with parameters uncertainty and disturbances. Nonlinear Dyn. 111 (8), 7511–7524 (2023).
Chestnov, V. N. & Shatov, D. V. Robust Controller Design for Multivariable Systems under Nonstationary Parametric Variations and Bounded External Disturbances. Autom. Remote Control. 85 (6), 489–501 (2024).
Thangavel, S. et al. A comprehensive review on electric vehicle: battery management system, charging station, traction motors. IEEE access. 11, 20994–21019 (2023).
Joseph, S. B., Dada, E. G., Abidemi, A., Oyewola, D. O. & Khammas, B. M. Metaheuristic algorithms for PID controller parameters tuning: Review, approaches and open problems. Heliyon, 8(5). (2022).
Borase, R. P., Maghade, D. K., Sondkar, S. Y. & Pawar, S. N. A review of PID control, tuning methods and applications. Int. J. Dynamics Control. 9 (2), 818–827 (2021).
Ansari, J., Homayounzade, M. & Abbasi, A. R. Load frequency control in power systems by a robust backstepping sliding mode controller design. Energy Rep. 10, 1287–1298 (2023).
Chen, Y., Hu, C., Bai, J. & Zou, H. Improved dynamic matrix control using co-optimization of dynamic control and economic performance enhancement (The Canadian Journal of Chemical Engineering, 2026).
Shezan, S. A. et al. Optimization and control of solar-wind islanded hybrid microgrid by using heuristic and deterministic optimization algorithms and fuzzy logic controller. Energy Rep. 10, 3272–3288 (2023).
Zhao, X., Zhou, X. & Li, G. Automatic database knob tuning: A survey. IEEE Trans. Knowl. Data Eng. 35 (12), 12470–12490 (2023).
Li, J., Luo, X., Yuan, Y. & Gao, S. A nonlinear PID-incorporated adaptive stochastic gradient descent algorithm for latent factor analysis. IEEE Trans. Autom. Sci. Eng. 21 (3), 3742–3756 (2023).
Abualigah, L. et al. Arithmetic optimization algorithm: a review and analysis. Metaheuristic Optim. algorithms, 73–87. (2024).
Goyal, D., Khanna, P. & Singh, S. Parameter estimation based IIR system identification using improved arithmetic optimization algorithm. Evol. Syst. 16 (3), 100 (2025).
Dhal, K. G., Sasmal, B., Das, A., Ray, S. & Rai, R. A comprehensive survey on arithmetic optimization algorithm. Arch. Comput. Methods Eng. 30 (5), 3379–3404 (2023).
Gabis, A. B., Meraihi, Y., Mirjalili, S. & Ramdane-Cherif, A. A comprehensive survey of sine cosine algorithm: variants and applications. Artif. Intell. Rev. 54 (7), 5469–5540 (2021).
Abdel-Basset, M., Mohamed, R., Azeem, S. A. A., Jameel, M. & Abouhawwash, M. Kepler optimization algorithm: A new metaheuristic algorithm inspired by Kepler’s laws of planetary motion. Knowl. Based Syst. 268, 110454 (2023).
Abed-Alguni, B. H., Paul, D. & Hammad, R. Improved Salp swarm algorithm for solving single-objective continuous optimization problems. Appl. Intell. 52 (15), 17217–17236 (2022).
Abdollahzadeh, B. et al. Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning. Cluster Comput. 27 (4), 5235–5283 (2024).
Shami, T. M. et al. Particle swarm optimization: A comprehensive survey. Ieee Access. 10, 10031–10061 (2022).
Lu, C. et al. A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler–Nichols approach. ISA Trans. 150, 322–337 (2024).
Divakar, K., Kumar, M. P., Dhanamjayulu, C. & Gokulakrishnan, G. A technical review on IMC-PID design for integrating process with dead time. IEEE Access (2024).
Utami, A. R., Yuniar, R. J., Giyantara, A. & Saputra, A. D. Cohen-Coon PID tuning method for self-balancing robot. In 2022 International Symposium on Electronics and Smart Devices (ISESD) (pp. 1–5). IEEE. (2022), November.
Clausen, C. S. B., Jørgensen, B. N. & Ma, Z. G. A scoping review of In-the-loop paradigms in the energy sector focusing on software-in-the-loop. Energy Inf. 7 (1), 12 (2024).
Zhang, Q. & Pei, W. DSP Processer-in-the-Loop Tests Based on Automatic Code Generation. Inventions 7 (1), 12 (2022).
Bernardo, R., Sousa, J. M., Botto, M. A. & Gonçalves, P. J. A novel control architecture based on behavior trees for an omni-directional mobile robot. Robotics 12 (6), 170 (2023).
Tao, Y. et al. Analysis of motion characteristics and stability of mobile robot based on a transformable wheel mechanism. Appl. Sci. 12 (23), 12348 (2022).
Ebel, H., Rosenfelder, M. & Eberhard, P. Cooperative object transportation with differential-drive mobile robots: Control and experimentation. Robot. Auton. Syst. 173, 104612 (2024).
Wen, C. K. et al. Design and verification innovative approach of dual-motor power coupling drive systems for electric tractors. Energy 247, 123538 (2022).
Lee, W., Kim, T., Kim, J. & Seo, T. Differential-Driven Wheeled Mobile Robot Mechanism with High Step-Climbing Ability. IEEE Robotics and Automation Letters. (2025).
Ma’arif, A. & Setiawan, N. R. Control of DC motor using integral state feedback and comparison with PID: simulation and arduino implementation. J. Rob. Control (JRC). 2 (5), 456–461 (2021).
Huang, X., Zhu, X. & Gu, G. Kinematic modeling and characterization of soft parallel robots. IEEE Trans. Robot. 38 (6), 3792–3806 (2022).
Ku, B. & Banerjee, A. Modeling and Control of a Bioinspired, Distributed Electromechanical Actuator System Emulating a Biological Spine. IEEE/ASME Trans. Mechatron. 30 (2), 1273–1285 (2024).
Liu, J., Li, X., Pang, R. & Xia, M. Dynamic modeling and vibration analysis of a flexible gear transmission system. Mech. Syst. Signal Process. 197, 110367 (2023).
Hong, Y., Fu, C. & Merci, B. Optimization and determination of the parameters for a PID based ventilation system for smoke control in tunnel fires: Comparative study between a genetic algorithm and an analytical trial-and-error method. Tunn. Undergr. Space Technol. 136, 105088 (2023).
Mohamed, M. A. E., Jagatheesan, K. & Anand, B. Modern PID/FOPID controllers for frequency regulation of interconnected power system by considering different cost functions. Sci. Rep. 13 (1), 14084 (2023).
Karthikeyan, S. et al. A systematic analysis on raspberry pi prototyping: Uses, challenges, benefits, and drawbacks. IEEE Internet Things J. 10 (16), 14397–14417 (2023).
Charadi, S. et al. A. Experimental validation of a hybrid AC/DC microgrid energy management system using Processor-in-the-Loop testing for green energy applications. Franklin Open, 100453. (2025).
Mohanraj, D., Gopalakrishnan, J., Chokkalingam, B. & Mihet-Popa, L. Critical aspects of electric motor drive controllers and mitigation of torque ripple. IEEe Access. 10, 73635–73674 (2022).
Li, Y. & Tong, S. Adaptive backstepping control for uncertain nonlinear strict-feedback systems with full state triggering. Automatica 163, 111574 (2024).
Ali, M. S., Wang, L., Alquhayz, H., Rehman, O. U. & Chen, G. Performance improvement of three-phase boost power factor correction rectifier through combined parameters optimization of proportional-integral and repetitive controller. IEEE Access. 9, 58893–58909 (2021).
Rzepka, K., Szary, P., Cabaj, K. & Mazurczyk, W. Performance evaluation of Raspberry Pi 4 and STM32 Nucleo boards for security-related operations in IoT environments. Comput. Netw. 242, 110252 (2024).
Acknowledgements
The authors would like to express their sincere gratitude to the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) for its valuable support and funding of this work under grant number IMSIU-DDRSP2603.
Funding
This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-DDRSP2603).
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Inssaf Harrade and Mohamed Kmich: Conceptualization, Formal analysis, Data curation, Software, Visualization, Writing – original draft. Zakaria Chalh, Mhamed Sayyouri and Hicham Karmouni: Validation, Methodology, Supervision, Writing – review & editing. Hassan M. Hussein Farh and Abdullrahman A. Al-Shamma’a: Writing – review & editing, Funding acquisition, Resources, Investigation.
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Harrade, I., Kmich, M., Karmouni, H. et al. Arithmetic optimization algorithm based PID control for reduced order motorized wheelchairs with real time MIL SIL PIL validation. Sci Rep (2026). https://doi.org/10.1038/s41598-026-47689-y
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DOI: https://doi.org/10.1038/s41598-026-47689-y
