Nonlinear Control of Engine Speed Regulation Using Grey Wolf Optimizer for Enhanced System Stability and Performance

Serdar Ekinci; Davut Izci; Mostafa Jabari; Alfian Ma'arif

doi:10.18196/jrc.v6i3.26818

Authors

Serdar Ekinci Istanbul Gedik University
Davut Izci Bursa Uludag University
Mostafa Jabari Sahand University of Technology
Alfian Ma'arif Universitas Ahmad Dahlan

DOI:

https://doi.org/10.18196/jrc.v6i3.26818

Keywords:

Engine Speed Control, Grey Wolf Optimizer, PIDF Controller Design, Stability Enhancement, Optimization

Abstract

Accurate control of internal combustion engine speed, especially under variable load conditions, has always been a significant challenge in the automotive industry. Classical PID controllers often fail to effectively compensate for nonlinearities and environmental disturbances in spark ignition (SI) engines. To address this issue, we propose a method based on tuning PIDF controller parameters using the grey wolf optimizer (GWO) to enhance system stability and performance. This approach aims to reduce steady-state error, settling time, and overshoot. A mathematical model of the engine speed control system is developed, and the GWO algorithm is applied to optimize the PIDF gains. The performance of the GWO-based controller is then compared to other metaheuristic methods such as particle swarm optimization (PSO), differential evolution (DE), and cuckoo search (CS) algorithms through simulation. Simulation results demonstrate that the proposed GWO-based approach outperforms the alternatives by achieving better error reduction, improved stability, enhanced disturbance rejection, and faster response times.

References

M. Jabari, D. Izci, S. Ekinci, M. Bajaj, and I. Zaitsev, "Performance analysis of DC-DC Buck converter with innovative multi-stage PIDn (1+ PD) controller using GEO algorithm," Scientific Reports, vol. 14, no. 1, p. 25612, 2024.

M. Jabari and A. Rad, "Optimization of speed control and reduction of torque ripple in switched reluctance motors using metaheuristic algorithms based PID and FOPID controllers at the edge," Tsinghua Science and Technology, vol. 30, no. 4, pp. 1526-1538, 2025.

S. Ekinci, D. Izci, R. Ghandour, M. Salman, and C. Turkeri, "Aquila Optimizer-Based Filtered PID Controller Design for A Spark Ignition Engine Speed Control," in 2024 8th International Symposium on Innovative Approaches in Smart Technologies (ISAS), pp. 1-5, 2024.

S. A. Alzakari, D. Izci, S. Ekinci, A. A. Alhussan, and F. A. Hashim, "A new control scheme for temperature adjustment of electric furnaces using a novel modified electric eel foraging optimizer," AIMS Math, vol. 9, no. 5, pp. 13410-13438, 2024.

S. Ekinci, Ö. Can, M. Ş. Ayas, D. Izci, M. Salman, and M. Rashdan, "Automatic generation control of a hybrid PV-reheat thermal power system using RIME algorithm," IEEE Access, vol. 12, pp. 26919-26930, 2024.

D. Izci, S. Ekinci, and A. G. Hussien, "An elite approach to re-design Aquila optimizer for efficient AFR system control," Plos one, vol. 18, no. 9, p. e0291788, 2023.

M. Jabari, S. Ekinci, D. Izci, M. Bajaj, and I. Zaitsev, "Efficient DC motor speed control using a novel multi-stage FOPD (1+ PI) controller optimized by the Pelican optimization algorithm," Scientific Reports, vol. 14, no. 1, p. 22442, 2024.

M. Jabari, M. A. Nasab, M. Zand, L. Tightiz, and S. Padmanaban, "Efficient parameter extraction in PV solar modules with the diligent crow search algorithm," Discover Energy, vol. 4, no. 1, p. 35, 2024.

J. Kennedy and R. Eberhart, "Particle swarm optimization," in Proceedings of ICNN'95-international conference on neural networks, vol. 4, pp. 1942-1948, 1995.

R. Storn and K. Price, "Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces," Journal of global optimization, vol. 11, pp. 341-359, 1997.

X.-S. Yang and S. Deb, "Cuckoo search: recent advances and applications," Neural Computing and applications, vol. 24, pp. 169-174, 2014.

S. Mirjalili, S. M. Mirjalili, and A. Lewis, "Grey wolf optimizer," Advances in engineering software, vol. 69, pp. 46-61, 2014.

P. Sharma, S. Raju, and R. Salgotra, "An evolutionary multi-algorithm based framework for the parametric estimation of proton exchange membrane fuel cell," Knowledge-Based Systems, vol. 283, p. 111134, 2024.

L. Abualigah et al., "Adaptive Gbest-Guided Atom Search Optimization for Designing Stable Digital IIR Filters," Circuits, Systems, and Signal Processing, pp. 1-23, 2025.

M. Jabari et al., "Parameter identification of PV solar cells and modules using bio dynamics grasshopper optimization algorithm," IET Generation, Transmission & Distribution, vol. 18, no. 21, pp. 3314-3338, 2024.

A. Sahoo, S. Samantaray, and D. K. Ghose, "Multilayer perceptron and support vector machine trained with grey wolf optimiser for predicting floods in Barak river, India," Journal of Earth System Science, vol. 131, no. 2, p. 85, 2022.

S. Yadav, P. Kumar, and A. Kumar, "Grey wolf optimization based optimal isolated microgrid with battery and pumped hydro as double storage to limit excess energy," Journal of Energy Storage, vol. 74, p. 109440, 2023.

B. Nayak, A. Mohapatra, and K. B. Mohanty, "Parameter estimation of single diode PV module based on GWO algorithm," Renewable Energy Focus, vol. 30, pp. 1-12, 2019.

S. Mohanty, B. Subudhi, and P. K. Ray, "A new MPPT design using grey wolf optimization technique for photovoltaic system under partial shading conditions," IEEE Transactions on Sustainable Energy, vol. 7, no. 1, pp. 181-188, 2015.

D. Guha, P. K. Roy, and S. Banerjee, "Load frequency control of interconnected power system using grey wolf optimization," Swarm and Evolutionary computation, vol. 27, pp. 97-115, 2016.

M. Rahmani, H. Komijani, and M. H. Rahman, "New sliding mode control of 2-DOF robot manipulator based on extended grey wolf optimizer," International Journal of Control, Automation and Systems, vol. 18, pp. 1572-1580, 2020.

S. Chatterjee, V. Shaw, and R. Das, "Multi-stage intrusion detection system aided by grey wolf optimization algorithm," Cluster Computing, vol. 27, no. 3, pp. 3819-3836, 2024.

Q. Al-Tashi, H. Md Rais, S. J. Abdulkadir, S. Mirjalili, and H. Alhussian, "A review of grey wolf optimizer-based feature selection methods for classification," Evolutionary machine learning techniques: algorithms and applications, pp. 273-286, 2020.

D. K. Geleta, M. S. Manshahia, P. Vasant, and A. Banik, "Grey wolf optimizer for optimal sizing of hybrid wind and solar renewable energy system," Computational intelligence, vol. 38, no. 3, pp. 1133-1162, 2022.

J. Czarnigowski, "A neural network model-based observer for idle speed control of ignition in SI engine," Engineering Applications of Artificial Intelligence, vol. 23, no. 1, pp. 1-7, 2010.

Y. Yildiz, A. M. Annaswamy, D. Yanakiev, and I. Kolmanovsky, "Spark-ignition-engine idle speed control: An adaptive control approach," IEEE Transactions on Control Systems Technology, vol. 19, no. 5, pp. 990-1002, 2010.

J. Duarte, J. Garcia, J. Jimenez, M. E. Sanjuan, A. Bula, and J. Gonzalez, "Auto-ignition control in spark-ignition engines using internal model control structure," Journal of Energy Resources Technology, vol. 139, no. 2, p. 022201, 2017.

Q. Zhu, R. Prucka, M. Prucka, and H. Dourra, "A nonlinear model predictive control strategy with a disturbance observer for spark ignition engines with external EGR," SAE International Journal of Commercial Vehicles, vol. 10, no. 2017-01-0608, pp. 360-372, 2017.

W. Wang, E. Chirwa, E. Zhou, K. Holmes, and C. Nwagboso, "Fuzzy ignition timing control for a spark ignition engine," Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 214, no. 3, pp. 297-306, 2000.

R. K. Sahu and D. K. Srivastava. Model Based Calibration of a Multi Cylinder Spark Ignition Engine for Idle Speed Control Using PID Control Strategy. SAE Technical Paper, 2023.