Skip to main content
SpringerLink
Log in

A novel balanced Aquila optimizer using random learning and Nelder–Mead simplex search mechanisms for air–fuel ratio system control

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

An air–fuel ratio system has a crucial role in helping protect the environment from the harmful emissions of the lean combustion spark-ignition engines and regulating fuel consumption. Due to such importance, an efficient control mechanism poses an utmost necessity for this system. However, the air–fuel ratio system has a time-delayed structure with nonlinear nature making its control difficult. This paper considers the last challenge and proposes a novel method to effectively control the air–fuel ratio system. In this regard, a feedforward proportional–integral controller based on a novel balanced Aquila optimizer (bAO) is proposed with this work to achieve adequate control of the respective system. The proposed bAO algorithm is constructed via the integration of the random learning mechanism and the Nelder–Mead simplex search method for better exploration and exploitation tasks. A novel objective function is also proposed for the first time in the literature for such a system in order to achieve the optimal parameters of the employed controller via the proposed bAO algorithm. Different recent and good performing metaheuristic algorithms are employed to comparatively assess the performance of the proposed method in terms of statistical, transient, input signal tracking, and robustness analyses. The related evaluations demonstrate that the proposed method has more excellent air–fuel ratio system control ability as performance improvement of more than 64% is reached for overshoot, whereas around 9 and 7% are achieved for rise time and settling time, respectively. Similar figures are achieved for robustness and input signal tracking. To further demonstrate the capability of the proposed bAO algorithm, well-known performance indices are also employed in this study as objective functions which also shows a performance improvement of up to 12% for the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Simpson NP, Mach KJ, Constable A et al (2021) A framework for complex climate change risk assessment. One Earth 4:489–501. https://doi.org/10.1016/j.oneear.2021.03.005

    Article  Google Scholar 

  2. Jacyna M, Żochowska R, Sobota A, Wasiak M (2021) Scenario analyses of exhaust emissions reduction through the introduction of electric vehicles into the City. Energies 14:2030. https://doi.org/10.3390/en14072030

    Article  Google Scholar 

  3. Buonomano A, Barone G, Forzano C (2022) Advanced energy technologies, methods, and policies to support the sustainable development of energy, water and environment systems. Energy Rep 8:4844–4853. https://doi.org/10.1016/j.egyr.2022.03.171

    Article  Google Scholar 

  4. Na J, Chen AS, Huang Y et al (2021) Air-fuel ratio control of spark ignition engines with unknown system dynamics estimator: theory and experiments. IEEE Trans Control Syst Technol 29:786–793. https://doi.org/10.1109/TCST.2019.2951125

    Article  Google Scholar 

  5. Zhao B, Song K, Xie H (2022) Air-fuel ratio control for gasoline engines based on physical model assisted extended state predictive observer. In: 2022 41st Chinese control conference (CCC). IEEE, pp 5505–5510

  6. Meng L, Wang X, Zeng C, Luo J (2019) Adaptive air-fuel ratio regulation for port-injected spark-ignited engines based on a generalized predictive control method. Energies 12:173. https://doi.org/10.3390/en12010173

    Article  Google Scholar 

  7. Manzie C, Palaniswami M, Ralph D et al (2002) Model predictive control of a fuel injection system with a radial basis function network observer. J Dyn Syst Meas Control 124:648–658. https://doi.org/10.1115/1.1515328

    Article  Google Scholar 

  8. Salavati S, Grigoriadis K, Franchek M (2021) An explicit robust stability condition for uncertain time-varying first-order plus dead-time systems. ISA Trans. https://doi.org/10.1016/j.isatra.2021.07.046

    Article  Google Scholar 

  9. Li Z, Li J, Zhou Q et al (2019) Intelligent air/fuel ratio control strategy with a PI-like fuzzy knowledge–based controller for gasoline direct injection engines. Proc Inst Mech Eng Part D J Automob Eng 233:2161–2173. https://doi.org/10.1177/0954407018779180

    Article  Google Scholar 

  10. Mamun A, Zhu Q, Hoffman M, Onori S (2021) Physics-based linear model predictive control strategy for three-way catalyst air/fuel ratio control. Proc Inst Mech Eng Part D J Automob Eng 235:3339–3357. https://doi.org/10.1177/09544070211021207

    Article  Google Scholar 

  11. Xiong W, Ye J, Gong Q et al (2022) Multi-input model predictive speed control of lean-burn natural gas engine in range-extended electric vehicles. Energy 239:122165

    Article  Google Scholar 

  12. Jiao X, Zhang J, Shen T, Kako J (2015) Adaptive air-fuel ratio control scheme and its experimental validations for port-injected spark ignition engines. Int J Adapt Control Signal Process 29:41–63. https://doi.org/10.1002/acs.2456

    Article  MATH  Google Scholar 

  13. Yang J, Shen T, Jiao X (2014) Stochastic adaptive air-fuel ratio control of spark ignition engines. IEEJ Trans Electr Electron Eng 9:442–447. https://doi.org/10.1002/tee.21991

    Article  Google Scholar 

  14. Iqbal MS, Amin AA (2022) Genetic algorithm based active fault-tolerant control system for air fuel ratio control of internal combustion engines. Meas Control 55:703–716. https://doi.org/10.1177/00202940221115233

    Article  Google Scholar 

  15. Amin AA, Mahmood-Ul-Hasan K (2019) Advanced fault tolerant air-fuel ratio control of internal combustion gas engine for sensor and actuator faults. IEEE Access 7:17634–17643. https://doi.org/10.1109/ACCESS.2019.2894796

    Article  Google Scholar 

  16. Alsuwian T, Iqbal MS, Amin AA et al (2022) A comparative study of design of active fault-tolerant control system for air-fuel ratio control of internal combustion engine using particle swarm optimization, genetic algorithm, and nonlinear regression-based observer model. Appl Sci 12:7841. https://doi.org/10.3390/app12157841

    Article  Google Scholar 

  17. Ebrahimi B, Tafreshi R, Masudi H et al (2012) A parameter-varying filtered PID strategy for air–fuel ratio control of spark ignition engines. Control Eng Pract 20:805–815. https://doi.org/10.1016/j.conengprac.2012.04.001

    Article  Google Scholar 

  18. Shahbaz MH, Amin AA (2021) Design of active fault tolerant control system for air fuel ratio control of internal combustion engines using artificial neural networks. IEEE Access 9:46022–46032. https://doi.org/10.1109/ACCESS.2021.3068164

    Article  Google Scholar 

  19. Wu H-M, Tafreshi R (2018) Air–fuel ratio control of lean-burn SI engines using the LPV-based fuzzy technique. IET Control Theory Appl 12:1414–1420. https://doi.org/10.1049/iet-cta.2017.0063

    Article  MathSciNet  Google Scholar 

  20. Alsuwian T, Riaz U, Amin AA et al (2022) Hybrid fault-tolerant control for air-fuel ratio control system of internal combustion engine using fuzzy logic and super-twisting sliding mode control techniques. Energies 15:7010. https://doi.org/10.3390/en15197010

    Article  Google Scholar 

  21. Ebrahimi B, Tafreshi R, Mohammadpour J et al (2014) Second-order sliding mode strategy for air-fuel ratio control of lean-burn si engines. IEEE Trans Control Syst Technol 22:1374–1384. https://doi.org/10.1109/TCST.2013.2281437

    Article  Google Scholar 

  22. Salehi Z, Azadi S, Mousavinia A (2021). Sliding mode air-to-fuel ratio control of spark ignition engines in comprehensive powertrain system. In: 2021 7th international conference on control, instrumentation and automation (ICCIA). IEEE, pp 1–5

  23. Alsuwian T, Tayyeb M, Amin AA et al (2022) Design of a hybrid fault-tolerant control system for air-fuel ratio control of internal combustion engines using genetic algorithm and higher-order sliding mode control. Energies 15:5666. https://doi.org/10.3390/en15155666

    Article  Google Scholar 

  24. Abualigah L, Yousri D, Abd Elaziz M et al (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250

    Article  Google Scholar 

  25. Yan B, Zhao Z, Zhou Y et al (2017) A particle swarm optimization algorithm with random learning mechanism and levy flight for optimization of atomic clusters. Comput Phys Commun 219:79–86. https://doi.org/10.1016/j.cpc.2017.05.009

    Article  Google Scholar 

  26. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313. https://doi.org/10.1093/comjnl/7.4.308

    Article  MathSciNet  MATH  Google Scholar 

  27. Houssein EH, Saad MR, Hashim FA et al (2020) Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 94:103731

    Article  Google Scholar 

  28. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Base Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  29. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, USA

    Book  Google Scholar 

  30. Tafreshi R, Ebrahimi B, Mohammadpour J et al (2013) Linear dynamic parameter-varying sliding manifold for air–fuel ratio control in lean-burn engines. IET Control Theory Appl 7:1319–1329. https://doi.org/10.1049/iet-cta.2012.0823

    Article  MathSciNet  Google Scholar 

  31. Wu H-M, Tafreshi R (2019) Observer-based internal model air–fuel ratio control of lean-burn SI engines. IFAC J Syst Control 9:100065. https://doi.org/10.1016/j.ifacsc.2019.100065

    Article  MathSciNet  Google Scholar 

  32. Wu H-M, Tafreshi R (2018) Fuzzy sliding-mode strategy for air-fuel ratio control of lean-burn spark ignition engines. Asian J Control 20:149–158. https://doi.org/10.1002/asjc.1544

    Article  MathSciNet  MATH  Google Scholar 

  33. Ekinci S, Izci D, Eker E, Abualigah L (2022) An effective control design approach based on novel enhanced aquila optimizer for automatic voltage regulator. Artif Intell Rev. https://doi.org/10.1007/s10462-022-10216-2

    Article  Google Scholar 

  34. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J Optim 9:112–147. https://doi.org/10.1137/S1052623496303470

    Article  MathSciNet  MATH  Google Scholar 

  35. Yıldız AR, Yıldız BS, Sait SM et al (2019) A new hybrid Harris hawks-Nelder-Mead optimization algorithm for solving design and manufacturing problems. Mater Test 61:735–743. https://doi.org/10.3139/120.111378

    Article  Google Scholar 

  36. Izci D, Ekinci S, Orenc S, Demiroren A (2020) Improved artificial electric field algorithm using nelder-mead simplex method for optimization problems. In: 2020 4th international symposium on multidisciplinary studies and innovative technologies (ISMSIT). IEEE, pp 1–5

  37. Panagant N, Yıldız M, Pholdee N et al (2021) A novel hybrid marine predators-Nelder-Mead optimization algorithm for the optimal design of engineering problems. Mater Test 63:453–457. https://doi.org/10.1515/mt-2020-0077

    Article  Google Scholar 

  38. Liu Y, Heidari AA, Ye X et al (2021) Boosting slime mould algorithm for parameter identification of photovoltaic models. Energy 234:121164. https://doi.org/10.1016/j.energy.2021.121164

    Article  Google Scholar 

  39. Izci D, Hekimoğlu B, Ekinci S (2022) A new artificial ecosystem-based optimization integrated with nelder-mead method for PID controller design of buck converter. Alex Eng J 61:2030–2044. https://doi.org/10.1016/j.aej.2021.07.037

    Article  Google Scholar 

  40. Weng X, Heidari AA, Liang G et al (2021) An evolutionary Nelder-Mead slime mould algorithm with random learning for efficient design of photovoltaic models. Energy Rep 7:8784–8804. https://doi.org/10.1016/j.egyr.2021.11.019

    Article  Google Scholar 

  41. Montoya-Ríos AP, García-Mañas F, Guzmán JL, Rodríguez F (2020) Simple tuning rules for feedforward compensators applied to greenhouse daytime temperature control using natural ventilation. Agronomy 10:1327. https://doi.org/10.3390/agronomy10091327

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Batman University, 72100, Batman, Turkey

    Serdar Ekinci

  2. Department of Computer Engineering, Batman University, 72100, Batman, Turkey

    Davut Izci

  3. Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan

    Laith Abualigah

  4. Faculty of Information Technology, Middle East University, Amman, 11831, Jordan

    Laith Abualigah

  5. School of Computer Sciences, Universiti Sains Malaysia, 11800, Pulau Pinang, Malaysia

    Laith Abualigah

  6. Computer Science Department, Prince Hussein Bin Abdullah Faculty for Information Technology, Al al-Bayt University, 25113, Mafraq, Jordan

    Laith Abualigah

  7. Center for Engineering Application & Technology Solutions, Ho Chi Minh City Open University, Ho Chi Minh, Viet Nam

    Laith Abualigah

  8. Applied Science Research Center, Applied Science Private University, 11931, Amman, Jordan

    Laith Abualigah

Authors
  1. Serdar Ekinci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Davut Izci
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laith Abualigah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Davut Izci.

Ethics declarations

Conflict of interests

All authors declare that they have no conflict of interest.

Additional information

Technical Editor Mario Eduardo Santos Martins.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ekinci, S., Izci, D. & Abualigah, L. A novel balanced Aquila optimizer using random learning and Nelder–Mead simplex search mechanisms for air–fuel ratio system control. J Braz. Soc. Mech. Sci. Eng. 45, 68 (2023). https://doi.org/10.1007/s40430-022-04008-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-022-04008-6

Keywords

Search

Navigation