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A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode’s ideal transfer function based automobile cruise control system

Abstract

This paper considers the development of a novel hybrid metaheuristic algorithm which is proposed to achieve an optimum design for automobile cruise control (ACC) system by using a proportional-integral-derivative (PID) controller based on Bode’s ideal transfer function. The developed algorithm (AOA-NM) adopts one of the recently published metaheuristic algorithms named the arithmetic optimization algorithm (AOA) to perform explorative task whereas another well-known local search method known as Nelder–Mead (NM) simplex search to perform exploitative task. The developed hybrid algorithm was initially tested on well-known benchmark functions by comparing the results with only its original version since AOA has already been shown to be better than other state-of-the-art algorithms. The statistical results obtained from benchmark functions have demonstrated better capability of AOA-NM. Furthermore, a PID controller based on Bode’s ideal transfer function was adopted to regulate an ACC system optimally. Statistical, convergence rate, time domain and frequency domain analyses were performed by comparing the performance of AOA-NM with AOA. The respective analyses have shown better capability of the proposed hybrid algorithm. Moreover, the capability of the proposed AOA-NM based PID control scheme was compared with other available approaches in the literature by using time domain analysis. The latter case has also confirmed enhanced capability of the proposed approach for regulating an ACC system which further verified the ability of the proposed AOA-NM algorithm. Lastly, other recently reported and effective metaheuristic algorithms were also used to assess the performance of the proposed approach. The obtained comparative results further confirmed the AOA-NM to be a greater tool to achieve more successful results for ACC system.

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References

  1. Abdel-Basset M, Mohamed R, Mirjalili S (2021) A novel Whale Optimization Algorithm integrated with Nelder-Mead simplex for multi-objective optimization problems. Knowledge-Based Syst 212:106619. https://doi.org/10.1016/j.knosys.2020.106619

    Article  Google Scholar 

  2. Abualigah L, Diabat A, Mirjalili S et al (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609. https://doi.org/10.1016/j.cma.2020.113609

    MathSciNet  Article  MATH  Google Scholar 

  3. Ali AF, Tawhid MA (2016) A hybrid cuckoo search algorithm with Nelder Mead method for solving global optimization problems. Springerplus 5:473. https://doi.org/10.1186/s40064-016-2064-1

    Article  Google Scholar 

  4. Barbosa RS, Machado JAT, Ferreira IM (2004) Tuning of PID controllers based on Bode’s ideal transfer function. Nonlinear Dyn 38:305–321. https://doi.org/10.1007/s11071-004-3763-7

    Article  MATH  Google Scholar 

  5. Blondin MJ, Trovão JP (2019) Soft-computing techniques for cruise controller tuning for an off-road electric vehicle. IET Electr Syst Transp 9:196–205. https://doi.org/10.1049/iet-est.2019.0008

    Article  Google Scholar 

  6. Bonabeau E, de Marco RDF, Dorigo M et al (1999) Swarm intelligence: from natural to artificial systems. Oxford University Press

    Book  Google Scholar 

  7. Chelouah R, Siarry P (2003) Genetic and Nelder-Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions. Eur J Oper Res 148:335–348. https://doi.org/10.1016/S0377-2217(02)00401-0

    MathSciNet  Article  MATH  Google Scholar 

  8. Demirören A, Ekinci S, Hekimoğlu B, Izci D (2021) Opposition-based artificial electric field algorithm and its application to FOPID controller design for unstable magnetic ball suspension system. Eng Sci Technol Int J 24:469–479. https://doi.org/10.1016/j.jestch.2020.08.001

    Article  Google Scholar 

  9. Dorf RC (2011) Modern control systems, 12th edn. Pearson, Boston, London

    MATH  Google Scholar 

  10. Eker E, Kayri M, Ekinci S, Izci D (2021) A new fusion of ASO with SA algorithm and its applications to MLP training and DC motor speed control. Arab J Sci Eng 46:3889–3911. https://doi.org/10.1007/s13369-020-05228-5

    Article  Google Scholar 

  11. Ekinci S, Hekimoğlu B, Izci D (2021) Opposition based Henry gas solubility optimization as a novel algorithm for PID control of DC motor. Eng Sci Technol an Int J 24:331–342. https://doi.org/10.1016/j.jestch.2020.08.011

    Article  Google Scholar 

  12. Frank AA, Liu SJ, Liang SC (1989) Longitudinal control concepts for automated automobiles and trucks operating on a cooperative highway. SAE Trans 98:1308–1315

    Google Scholar 

  13. Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using Firefly Algorithm. Comput Struct 89:2325–2336. https://doi.org/10.1016/j.compstruc.2011.08.002

    Article  Google Scholar 

  14. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35. https://doi.org/10.1007/s00366-011-0241-y

    Article  Google Scholar 

  15. Gulzar MM, Sharif B, Sibtain D et al (2019) Modelling and controller design of automotive cruise control system using hybrid model predictive controller. In: 2019 15th International Conference on Emerging Technologies (ICET). pp 1–5

  16. Hekimoğlu B (2019) Sine-cosine algorithm-based optimization for automatic voltage regulator system. Trans Inst Meas Control 41:1761–1771. https://doi.org/10.1177/0142331218811453

    Article  Google Scholar 

  17. 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. https://doi.org/10.1016/j.engappai.2020.103731

    Article  Google Scholar 

  18. 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

  19. Izci D, Ekinci S, Demiroren A, Hedley J (2020) HHO algorithm based PID controller design for aircraft pitch angle control system. In: 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA). IEEE, pp 1–6

  20. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-International Conference on Neural Networks. IEEE, pp 1942–1948

  21. 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

    MathSciNet  Article  MATH  Google Scholar 

  22. Lewis PH, Houghton Y (1997) Basic control systems engineering. Prentice Hall, Upper Saddle River, NJ (United States), United States

    Google Scholar 

  23. Li X, Wang Y, Li N et al (2017) Optimal fractional order PID controller design for automatic voltage regulator system based on reference model using particle swarm optimization. Int J Mach Learn Cybern 8:1595–1605. https://doi.org/10.1007/s13042-016-0530-2

    Article  Google Scholar 

  24. Li S, Chen H, Wang M et al (2020) Slime mould algorithm: a new method for stochastic optimization. Futur Gener Comput Syst 111:300–323. https://doi.org/10.1016/j.future.2020.03.055

    Article  Google Scholar 

  25. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowledge-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

    Article  Google Scholar 

  26. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  27. Mirjalili SZ, Mirjalili S, Saremi S et al (2018) Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48:805–820. https://doi.org/10.1007/s10489-017-1019-8

    Article  Google Scholar 

  28. 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

    MathSciNet  Article  MATH  Google Scholar 

  29. Nematollahi AF, Rahiminejad A, Vahidi B (2020) A novel meta-heuristic optimization method based on golden ratio in nature. Soft Comput 24:1117–1151. https://doi.org/10.1007/s00500-019-03949-w

    Article  Google Scholar 

  30. Osman K, Rahmat MF, Ahmad MA (2009) Modelling and controller design for a cruise control system. In: 2009 5th International Colloquium on Signal Processing & Its Applications. pp 254–258

  31. Pradhan R, Majhi SK, Pradhan JK, Pati BB (2017) Performance evaluation of PID controller for an automobile cruise control system using ant lion optimizer. Eng J 21:347–361. https://doi.org/10.4186/ej.2017.21.5.347

    Article  Google Scholar 

  32. Pradhan R, Majhi SK, Pradhan JK, Pati BB (2018) Antlion optimizer tuned PID controller based on Bode ideal transfer function for automobile cruise control system. J Ind Inf Integr 9:45–52. https://doi.org/10.1016/j.jii.2018.01.002

    Article  Google Scholar 

  33. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (NY) 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  34. Rout MK, Sain D, Swain SK, Mishra SK (2016) PID controller design for cruise control system using genetic algorithm. In: 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT). pp 4170–4174

  35. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713. https://doi.org/10.1109/TEVC.2008.919004

    Article  Google Scholar 

  36. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328

    MathSciNet  Article  MATH  Google Scholar 

  37. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  38. Xin-She Y, Amir HG (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29:464–483. https://doi.org/10.1108/02644401211235834

    Article  Google Scholar 

  39. Xu J, Yan F (2019) Hybrid Nelder-Mead algorithm and dragonfly algorithm for function optimization and the training of a multilayer perceptron. Arab J Sci Eng 44:3473–3487. https://doi.org/10.1007/s13369-018-3536-0

    Article  Google Scholar 

  40. Yang X-S, Karamanoglu M, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46:1222–1237. https://doi.org/10.1080/0305215X.2013.832237

    MathSciNet  Article  Google Scholar 

  41. Yang Y, Chen H, Heidari AA, Gandomi AH (2021) Hunger games search: visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Syst Appl 177:114864. https://doi.org/10.1016/j.eswa.2021.114864

    Article  Google Scholar 

  42. Yildiz AR, Kurtulus E, Demirci E et al (2016) Optimization of thin-wall structures using hybrid gravitational search and nelder-Mead algorithm. Mater Test 58:75–78. https://doi.org/10.3139/120.110823

    Article  Google Scholar 

  43. Yumuk E, Güzelkaya M, Eksin İ (2019) Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay. ISA Trans 91:196–206. https://doi.org/10.1016/j.isatra.2019.01.034

    Article  Google Scholar 

  44. Zhang D-L, Tang Y-G, Guan X-P (2014) Optimum design of fractional order PID controller for an AVR system using an improved artificial bee colony algorithm. Acta Autom Sin 40:973–979. https://doi.org/10.1016/s1874-1029(14)60010-0

    MathSciNet  Article  Google Scholar 

  45. Zhao W, Wang L, Zhang Z (2020a) Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm. Neural Comput Appl 32:9383–9425. https://doi.org/10.1007/s00521-019-04452-x

    Article  Google Scholar 

  46. Zhao W, Zhang Z, Wang L (2020b) Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300. https://doi.org/10.1016/j.engappai.2019.103300

    Article  Google Scholar 

  47. Zhuo-Yun N, Yi-Min Z, Qing-Guo W et al (2020) Fractional-order PID controller design for time-delay systems based on modified Bode’s ideal transfer function. IEEE Access 8:103500–103510. https://doi.org/10.1109/ACCESS.2020.2996265

    Article  Google Scholar 

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Correspondence to Davut Izci.

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Izci, D., Ekinci, S., Kayri, M. et al. A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode’s ideal transfer function based automobile cruise control system. Evolving Systems (2021). https://doi.org/10.1007/s12530-021-09402-4

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Keywords

  • Arithmetic optimization algorithm
  • Nelder–Mead simplex search
  • Bode’s ideal transfer function
  • PID controller
  • Automobile cruise control system