Abstract
This paper presents a new metaheuristic algorithm by enhancing one of the recently proposed optimizers named Aquila optimizer (AO). The enhanced AO (enAO) algorithm is constructed by employing a novel modified opposition-based learning (OBL) mechanism and Nelder-Mead (NM) simplex search method. The novel modified OBL aids the AO in further diversification while the NM method increases the intensification. The enAO algorithm is first demonstrated to have more extraordinary ability than the original AO algorithm by employing challenging benchmark functions from the CEC 2019 test suite. The constructed enAO algorithm is proposed to design a PID plus second-order derivative (PIDD2) controller used in an automatic voltage regulator (AVR) system. To reach better efficiency, a novel objective function is also proposed in this paper. Initially, the proposed enAO-PIDD2 approach is demonstrated to be superior in terms of transient and frequency responses along with robustness and disturbance rejection compared to other available and best performing PID, fractional order PID (FOPID), PID acceleration (PIDA), and PIDD2 controllers tuned with different practical algorithms. Moreover, the superior performance of the proposed approach is also demonstrated comparatively using other available techniques for the AVR system reported in the last six years.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
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
Abualigah L, Diabat A, Elaziz MA (2021a) Improved slime mould algorithm by opposition-based learning and Levy flight distribution for global optimization and advances in real-world engineering problems. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-021-03372-w
Abualigah L, Diabat A, Mirjalili S et al (2021b) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609. https://doi.org/10.1016/j.cma.2020.113609
Abualigah L, Yousri D, Abd Elaziz M et al (2021c) Aquila Optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250. https://doi.org/10.1016/j.cie.2021.107250
AlRassas AM, Al-qaness MAA, Ewees AA et al (2021) Optimized ANFIS model using aquila optimizer for oil production forecasting. Processes 9:1194. https://doi.org/10.3390/pr9071194
Altbawi SMA, Bin MAS, Jumani TA et al (2021) Optimal design of fractional order PID controller based automatic voltage regulator system using gradient-based optimization algorithm. J King Saud Univ - Eng Sci. https://doi.org/10.1016/j.jksues.2021.07.009
Ayas MS (2019) Design of an optimized fractional high-order differential feedback controller for an AVR system. Electr Eng 101:1221–1233. https://doi.org/10.1007/s00202-019-00842-5
Ayas MS, Sahin E (2021) FOPID controller with fractional filter for an automatic voltage regulator. Comput Electr Eng 90:106895. https://doi.org/10.1016/j.compeleceng.2020.106895
Bhullar AK, Kaur R, Sondhi S (2020a) Optimization of fractional order controllers for AVR system using distance and levy-flight based crow search algorithm. IETE J Res. https://doi.org/10.1080/03772063.2020.1782779
Bhullar AK, Kaur R, Sondhi S (2020b) Enhanced crow search algorithm for AVR optimization. Soft Comput 24:11957–11987. https://doi.org/10.1007/s00500-019-04640-w
Bingul Z, Karahan O (2018) A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system. J Franklin Inst 355:5534–5559. https://doi.org/10.1016/j.jfranklin.2018.05.056
Bourouba B, Ladaci S, Schulte H (2019) Optimal design of fractional order PIλDμ controller for an AVR system using Ant Lion Optimizer. IFAC-PapersOnLine 52:200–205. https://doi.org/10.1016/j.ifacol.2019.11.304
Celik E (2018) Incorporation of stochastic fractal search algorithm into efficient design of PID controller for an automatic voltage regulator system. Neural Comput Appl 30:1991–2002. https://doi.org/10.1007/s00521-017-3335-7
Çelik E, Durgut R (2018) Performance enhancement of automatic voltage regulator by modified cost function and symbiotic organisms search algorithm. Eng Sci Technol an Int J 21:1104–1111. https://doi.org/10.1016/j.jestch.2018.08.006
Çelik E, Öztürk N (2018) A hybrid symbiotic organisms search and simulated annealing technique applied to efficient design of PID controller for automatic voltage regulator. Soft Comput 22:8011–8024. https://doi.org/10.1007/s00500-018-3432-2
Chatterjee S, Mukherjee V (2016) PID controller for automatic voltage regulator using teaching–learning based optimization technique. Int J Electr Power Energy Syst 77:418–429. https://doi.org/10.1016/j.ijepes.2015.11.010
Chen C, Yu L (2020) A hybrid ant lion optimizer with improved Nelder-Mead algorithm for structural damage detection by improving weighted trace lasso regularization. Adv Struct Eng 23:468–484. https://doi.org/10.1177/1369433219872434
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 an Int J 24:469–479. https://doi.org/10.1016/j.jestch.2020.08.001
Dhargupta S, Ghosh M, Mirjalili S, Sarkar R (2020) Selective opposition based grey wolf optimization. Expert Syst Appl 151:113389. https://doi.org/10.1016/j.eswa.2020.113389
Duman S, Yörükeren N, Altaş IH (2016) Gravitational search algorithm for determining controller parameters in an automatic voltage regulator system. Turkish J Electr Eng Comput Sci 24:2387–2400. https://doi.org/10.3906/elk-1404-14
Ekinci S, Hekimoglu B (2019) Improved kidney-inspired algorithm approach for tuning of PID controller in AVR system. IEEE Access 7:39935–39947. https://doi.org/10.1109/ACCESS.2019.2906980
Ekinci S, Demiroren A, Zeynelgil H, Hekimoğlu B (2020a) An opposition-based atom search optimization algorithm for automatic voltage regulator system. J Fac Eng Archit Gazi Univ 35:1141–1158. https://doi.org/10.17341/gazimmfd.598576
Ekinci S, Izci D, Hekimoğlu B (2021a) Optimal FOPID speed control of DC motor via opposition-based hybrid manta ray foraging optimization and simulated annealing algorithm. Arab J Sci Eng 46:1395–1409. https://doi.org/10.1007/s13369-020-05050-z
Ekinci S, Izci D, Kayri M (2021b) An effective controller design approach for magnetic levitation system using novel improved manta ray foraging optimization. Arab J Sci Eng. https://doi.org/10.1007/s13369-021-06321-z
Ekinci S, Izci D, Hekimoglu B (2020b) Henry gas solubility optimization algorithm based FOPID Controller Design for Automatic Voltage Regulator. In: International Conference on Electrical, Communication, and Computer Engineering (ICECCE). IEEE, pp 1–6
Elsisi M (2020a) New design of robust PID controller based on meta-heuristic algorithms for wind energy conversion system. Wind Energy 23:391–403. https://doi.org/10.1002/we.2439
Elsisi M (2020b) Optimal design of nonlinear model predictive controller based on new modified multitracker optimization algorithm. Int J Intell Syst 35:1857–1878. https://doi.org/10.1002/int.22275
Elsisi M (2021) Optimal design of non-fragile PID controller. Asian J Control 23:729–738. https://doi.org/10.1002/asjc.2248
Elsisi M (2022) Improved grey wolf optimizer based on opposition and quasi learning approaches for optimization: case study autonomous vehicle including vision system. Artif Intell Rev. https://doi.org/10.1007/s10462-022-10137-0
Elsisi M, Tran M-Q, Hasanien HM et al (2021) Robust model predictive control paradigm for automatic voltage regulators against uncertainty based on optimization algorithms. Mathematics 9:2885. https://doi.org/10.3390/math9222885
Gong C (2019) Jaya Algorithm-optimized PID controller for AVR system. In: Xhafa F, Patnaik S, Tavana M (eds) Advances in Intelligent Systems and Computing. Springer International Publishing, Cham, pp 382–393
Gozde H (2020) Robust 2DOF state-feedback PI-controller based on meta-heuristic optimization for automatic voltage regulation system. ISA Trans 98:26–36. https://doi.org/10.1016/j.isatra.2019.08.056
Guvenc U, Yigit T, Isik AH, Akkaya I (2016) Performance analysis of biogeography-based optimization for automatic voltage regulator system. Turkish J Electr Eng Comput Sci 24:1150–1162
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
Hekimoğlu B, Ekinci S (2018) Grasshopper optimization algorithm for automatic voltage regulator system. In: 2018 5th International Conference on Electrical and Electronics Engineering, ICEEE 2018. pp 152–156
Houssein EH, Mahdy MA, Fathy A, Rezk H (2021) A modified Marine Predator Algorithm based on opposition based learning for tracking the global MPP of shaded PV system. Expert Syst Appl 183:115253. https://doi.org/10.1016/j.eswa.2021.115253
Ismail MM, Bendary AF, Elsisi M (2020) Optimal design of battery charge management controller for hybrid system PV/wind cell with storage battery. Int J Power Energy Convers 11:412. https://doi.org/10.1504/IJPEC.2020.110018
Izci D, Ekinci S (2021) Comparative performance analysis of slime mould algorithm for efficient design of proportional–integral–derivative controller. Electrica 21:151–159. https://doi.org/10.5152/electrica.2021.20077
Izci D, Ekinci S, Kayri M, Eker E (2021) A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode’s ideal transfer function based automobile cruise control system. Evol Syst. https://doi.org/10.1007/s12530-021-09402-4
Izci D, Ekinci S, Zeynelgil HL, Hedley J (2022a) Performance evaluation of a novel improved slime mould algorithm for direct current motor and automatic voltage regulator systems. Trans Inst Meas Control 44:435–456. https://doi.org/10.1177/01423312211037967
Izci D, Hekimoğlu B, Ekinci S (2022b) A new artificial ecosystem-based optimization integrated with Nelder-Mead method for PID controller design of buck converter. Alexandria Eng J 61:2030–2044. https://doi.org/10.1016/j.aej.2021.07.037
Izci D, Ekinci S, Eker E, Kayri M (2020) Improved Manta Ray Foraging Optimization Using Opposition-based Learning for Optimization Problems. In: 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA). IEEE, pp 1–6
Jaradat MA, Sawaqed LS, Alzgool MM (2020) Optimization of PIDD2-FLC for blood glucose level using particle swarm optimization with linearly decreasing weight. Biomed Signal Process Control 59:101922. https://doi.org/10.1016/j.bspc.2020.101922
Jumani TA, Mustafa MW, Hussain Z et al (2020) Jaya optimization algorithm for transient response and stability enhancement of a fractional-order PID based automatic voltage regulator system. Alexandria Eng J 59:2429–2440. https://doi.org/10.1016/j.aej.2020.03.005
Khan IA, Alghamdi AS, Jumani TA et al (2019) Salp Swarm optimization algorithm-based fractional order PID controller for dynamic response and stability enhancement of an automatic voltage regulator system. Electronics 8:1472. https://doi.org/10.3390/electronics8121472
Kiran HU, Tiwari SK (2021) Hybrid BF-PSO Algorithm for Automatic Voltage Regulator System. In: Gupta D, Khanna A, Bhattacharyya S, et al. (eds) Advances in Intelligent Systems and Computing. Springer Singapore, Singapore, pp 145–153
Kose E (2020) Optimal control of AVR system with tree seed algorithm-based PID controller. IEEE Access 8:89457–89467. https://doi.org/10.1109/ACCESS.2020.2993628
Kumar M, Hote YV (2021a) Maximum sensitivity-constrained coefficient diagram method-based PIDA controller design: application for load frequency control of an isolated microgrid. Electr Eng. https://doi.org/10.1007/s00202-021-01226-4
Kumar M, Hote YV (2021b) Real-time performance analysis of PIDD2 controller for nonlinear twin rotor TITO aerodynamical system. J Intell Robot Syst 101:55. https://doi.org/10.1007/s10846-021-01322-4
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
Lahcene R, Abdeldjalil S, Aissa K (2017) Optimal tuning of fractional order PID controller for AVR system using simulated annealing optimization algorithm. In: 2017 5th International Conference on Electrical Engineering - Boumerdes (ICEE-B). IEEE, pp 1–6
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
Mandal B, Roy PK (2013) Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization. Int J Electr Power Energy Syst 53:123–134. https://doi.org/10.1016/j.ijepes.2013.04.011
Micev M, Ćalasan M, Oliva D (2020) Fractional order PID controller design for an AVR system using chaotic yellow saddle goatfish algorithm. Mathematics 8:1182. https://doi.org/10.3390/math8071182
Micev M, Ćalasan M, Ali ZM et al (2021a) Optimal design of automatic voltage regulation controller using hybrid simulated annealing – Manta ray foraging optimization algorithm. Ain Shams Eng J 12:641–657. https://doi.org/10.1016/j.asej.2020.07.010
Micev M, Ćalasan M, Oliva D (2021b) Design and robustness analysis of an automatic voltage regulator system controller by using equilibrium optimizer algorithm. Comput Electr Eng 89:106930. https://doi.org/10.1016/j.compeleceng.2020.106930
Mokeddem D, Mirjalili S (2020) Improved Whale optimization algorithm applied to design PID plus second-order derivative controller for automatic voltage regulator system. J Chinese Inst Eng 43:541–552. https://doi.org/10.1080/02533839.2020.1771205
Mosaad AM, Attia MA, Abdelaziz AY (2018) Comparative performance analysis of AVR controllers using modern optimization techniques. Electr Power Components Syst 46:2117–2130. https://doi.org/10.1080/15325008.2018.1532471
Mosaad AM, Attia MA, Abdelaziz AY (2019) Whale optimization algorithm to tune PID and PIDA controllers on AVR system. Ain Shams Eng J 10:755–767. https://doi.org/10.1016/j.asej.2019.07.004
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
Oliva D, Esquivel-Torres S, Hinojosa S et al (2021) Opposition-based moth swarm algorithm. Expert Syst Appl 184:115481. https://doi.org/10.1016/j.eswa.2021.115481
Pachauri N (2020) Water cycle algorithm-based PID controller for AVR. COMPEL - Int J Comput Math Electr Electron Eng 39:551–567. https://doi.org/10.1108/COMPEL-01-2020-0057
Padiachy V, Mehta U, Azid S et al (2021) Two degree of freedom fractional PI scheme for automatic voltage regulation. Eng Sci Technol an Int J. https://doi.org/10.1016/j.jestch.2021.08.003
Paliwal N, Srivastava L, Pandit M (2021) Equilibrium optimizer tuned novel FOPID-DN controller for automatic voltage regulator system. Int Trans Electr Energy Syst. https://doi.org/10.1002/2050-7038.12930
Price K V, Awad NH, Ali MZ, Suganthan PN (2018) Problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. In: Technical Report. Nanyang Technological University
Raju M, Saikia LC, Sinha N (2016) Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller. Int J Electr Power Energy Syst 80:52–63. https://doi.org/10.1016/j.ijepes.2016.01.037
Rizk-Allah RM, Hassanien AE (2022) A hybrid Harris hawks-Nelder-Mead optimization for practical nonlinear ordinary differential equations. Evol Intell 15:141–165. https://doi.org/10.1007/s12065-020-00497-3
Sahib MA (2015) A novel optimal PID plus second order derivative controller for AVR system. Eng Sci Technol an Int J 18:194–206. https://doi.org/10.1016/j.jestch.2014.11.006
Shekhawat S, Saxena A (2020) Development and applications of an intelligent crow search algorithm based on opposition based learning. ISA Trans 99:210–230. https://doi.org/10.1016/j.isatra.2019.09.004
Sikander A, Thakur P (2020) A new control design strategy for automatic voltage regulator in power system. ISA Trans 100:235–243. https://doi.org/10.1016/j.isatra.2019.11.031
Sikander A, Thakur P, Bansal RC, Rajasekar S (2018) A novel technique to design cuckoo search based FOPID controller for AVR in power systems. Comput Electr Eng 70:261–274. https://doi.org/10.1016/j.compeleceng.2017.07.005
Tang Y, Zhao L, Han Z et al (2016) Optimal gray PID controller design for automatic voltage regulator system via imperialist competitive algorithm. Int J Mach Learn Cybern 7:229–240. https://doi.org/10.1007/s13042-015-0431-9
Tizhoosh HR (2005) Opposition-Based Learning: A New Scheme for Machine Intelligence. In: International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC’06). IEEE, pp 695–701
Verma M, Sreejeth M, Singh M (2021) Application of hybrid metaheuristic technique to study influence of core material and core trench on performance of surface inset PMSM. Arab J Sci Eng. https://doi.org/10.1007/s13369-021-06017-4
Wang H, Wu Z, Rahnamayan S et al (2011) Enhancing particle swarm optimization using generalized opposition-based learning. Inf Sci (ny) 181:4699–4714. https://doi.org/10.1016/j.ins.2011.03.016
Wang S, Jia H, Abualigah L et al (2021a) An improved hybrid aquila optimizer and harris hawks algorithm for solving industrial engineering optimization problems. Processes 9:1551. https://doi.org/10.3390/pr9091551
Wang W, Xu L, Chau K et al (2021b) An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization. Eng Comput. https://doi.org/10.1007/s00366-020-01248-9
Yu X, Xu W, Li C (2021) Opposition-based learning grey wolf optimizer for global optimization. Knowledge-Based Syst 226:107139. https://doi.org/10.1016/j.knosys.2021.107139
Zhao X, Feng S, Hao J et al (2021) Neighborhood opposition-based differential evolution with Gaussian perturbation. Soft Comput 25:27–46. https://doi.org/10.1007/s00500-020-05425-2
Zheng R, Jia H, Abualigah L et al (2021) Deep ensemble of slime mold algorithm and arithmetic optimization algorithm for global optimization. Processes 9:1774. https://doi.org/10.3390/pr9101774
Zhou Y, Miao F, Luo Q (2019a) Symbiotic organisms search algorithm for optimal evolutionary controller tuning of fractional fuzzy controllers. Appl Soft Comput 77:497–508. https://doi.org/10.1016/j.asoc.2019.02.002
Zhou Y, Zhang J, Yang X, Ling Y (2019b) Optimization of PID controller based on water wave optimization for an automatic voltage regulator system. Inf Technol Control 48:160–171. https://doi.org/10.5755/j01.itc.48.1.20296
Zhou G, Li J, Tang Z et al (2020) An improved spotted hyena optimizer for PID parameters in an AVR system. Math Biosci Eng 17:3767–3783. https://doi.org/10.3934/mbe.2020211
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no confict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ekinci, S., Izci, D., Eker, E. et al. An effective control design approach based on novel enhanced aquila optimizer for automatic voltage regulator. Artif Intell Rev 56, 1731–1762 (2023). https://doi.org/10.1007/s10462-022-10216-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-022-10216-2