{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T19:14:00Z","timestamp":1722885240555},"reference-count":50,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Coordination for the Improvement of Higher Education Personnel","award":["001"]},{"name":"Brazilian National Council for Scientific and Technological Development","award":["40558\/2018-5","315298\/2020-0"]},{"DOI":"10.13039\/501100004612","name":"Araucaria Foundation","doi-asserted-by":"publisher","award":["51497"],"id":[{"id":"10.13039\/501100004612","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"This work aims to analyze two metaheuristics optimization techniques, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), with six variations each, and compare them regarding their convergence, quality, and dispersion of solutions. The optimization target is the Gaussian Adaptive PID control (GAPID) to find the best parameters to achieve enhanced performance and robustness to load variations related to the traditional PID. The adaptive rule of GAPID is based on a Gaussian function that has as adjustment parameters its concavity and the lower and upper bound of the gains. It is a smooth function with smooth derivatives. As a result, it helps avoid problems related to abrupt increases transition, commonly found in other adaptive methods. Because there is no mathematical methodology to set these parameters, this work used bio-inspired optimization algorithms. The test plant is a DC motor with a beam with a variable load. Results obtained by load and gain sweep tests prove the GAPID presents fast responses with very low overshoot and good robustness to load changes, with minimal variations, which is impossible to achieve when using the linear PID.<\/jats:p>","DOI":"10.3390\/s22166094","type":"journal-article","created":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T03:44:03Z","timestamp":1660621443000},"page":"6094","source":"Crossref","is-referenced-by-count":3,"title":["Metaheuristics-Based Optimization of a Robust GAPID Adaptive Control Applied to a DC Motor-Driven Rotating Beam with Variable Load"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-8358-2469","authenticated-orcid":false,"given":"F\u00e1bio Galv\u00e3o","family":"Borges","sequence":"first","affiliation":[{"name":"Graduate Program in Electrical Engineering (PPGEE), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0679-6957","authenticated-orcid":false,"given":"M\u00e1rcio","family":"Guerreiro","sequence":"additional","affiliation":[{"name":"Graduate Program in Industrial Engineering (PPGEP), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-8228-2245","authenticated-orcid":false,"given":"Paulo Eduardo Sampaio","family":"Sampaio Monteiro","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering (PPGEE), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8215-4510","authenticated-orcid":false,"given":"Frederic Conrad","family":"Janzen","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-4907-0395","authenticated-orcid":false,"given":"Fernanda Cristina","family":"Corr\u00eaa","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering (PPGEE), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"},{"name":"Electrical Engineering Department, Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-4783-5350","authenticated-orcid":false,"suffix":"Jr.","given":"Sergio Luiz","family":"Stevan","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering (PPGEE), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"},{"name":"Electrical Engineering Department, Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-1278-4602","authenticated-orcid":false,"given":"Hugo Valadares","family":"Siqueira","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering (PPGEE), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"},{"name":"Graduate Program in Industrial Engineering (PPGEP), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"},{"name":"Electrical Engineering Department, Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-7687-1297","authenticated-orcid":false,"given":"Mauricio dos Santos","family":"Kaster","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering (PPGEE), Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"},{"name":"Electrical Engineering Department, Federal University of Technology\u2014Paran\u00e1 (UTFPR), R. Dr. Washington Subtil Chueire, 330, Jardim Carvalho, Ponta Grossa 84017-220, PR, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TCYB.2019.2895319","article-title":"Optimization Tools Based on Metaheuristics for Performance Enhancement in a Gaussian Adaptive PID Controller","volume":"50","author":"Puchta","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_2","unstructured":"Atherton, D.P., and Majhi, S. (1999, January 2\u20134). Limitations of PID controllers. Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), San Diego, CA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2596","DOI":"10.1021\/ie960090+","article-title":"Limitations and countermeasures of PID controllers","volume":"35","author":"Sung","year":"1996","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Palanikumar, A., Saikumar, N., and HosseinNia, S.H. (2018, January 12\u201315). No more differentiator in PID: Development of nonlinear lead for precision mechatronics. Proceedings of the 2018 European Control Conference (ECC), Limassol, Cyprus.","DOI":"10.23919\/ECC.2018.8550088"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hsia, T. (1986, January 7\u201310). Adaptive control of robot manipulators\u2014A review. Proceedings of the 1986 IEEE International Conference on Robotics and Automation, San Francisco, CA, USA.","DOI":"10.1109\/ROBOT.1986.1087696"},{"key":"ref_6","unstructured":"Astrom, K.J., and Wittenmark, D.B. (2008). Adaptive Control, Dover Publications. [2nd ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0165-0114(98)00052-9","article-title":"Fuzzy adaptive control of multivariable nonlinear systems","volume":"111","author":"Shaocheng","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/S0165-0114(02)00279-8","article-title":"Stable indirect fuzzy adaptive control","volume":"137","author":"Golea","year":"2003","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hunt, K.J. (1996). Neural Adaptive Control Technology, World Scientific.","DOI":"10.1142\/9789812819451_0001"},{"key":"ref_10","unstructured":"Dracopoulos, D.C. (2013). Evolutionary Learning Algorithms for Neural Adaptive Control, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Xu, H., Mirmirani, M., and Ioannou, P. (2003, January 11\u201314). Robust neural adaptive control of a hypersonic aircraft. Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, TX, USA.","DOI":"10.2514\/6.2003-5641"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s00521-007-0124-8","article-title":"Neural adaptive control for a class of nonlinear systems with unknown deadzone","volume":"17","author":"Wang","year":"2008","journal-title":"Neural Comput. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jinli, L. (2012, January 23\u201325). Adaptive Fuzzy PID Control for Boiler Deaerator. Proceedings of the 2012 International Conference on Industrial Control and Electronics Engineering, Xi\u2019an, China.","DOI":"10.1109\/ICICEE.2012.157"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Korkmaz, M., Aydogdu, O., and Dogan, H. (2012, January 2\u20134). Design and performance comparison of variable parameter nonlinear PID controller and genetic algorithm based PID controller. Proceedings of the 2012 International Symposium on Innovations in Intelligent Systems and Applications, Trabzon, Turkey.","DOI":"10.1109\/INISTA.2012.6246935"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Qi, W.M., Cai, W.Y., Ji, Q.L., and Cheng, Y.C. (2006, January 16\u201318). A Design of Nonlinear Adaptive PID Controller Based on Genetic Algorithm. Proceedings of the 2006 Chinese Control Conference, Harbin, China.","DOI":"10.1109\/CHICC.2006.280846"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Lucas, R., Oliveira, R.M., Nascimento, C.B., and Kaster, M.S. (2015, January 3\u20135). Performance analysis of an adaptive Gaussian nonlinear PID control applied to a step-down CC-CC converter. Proceedings of the 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE), Rio de Janeiro, Brazil.","DOI":"10.1109\/ISIE.2015.7281612"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Puchta, E.D.P., Lucas, R., Ferreira, F.R.V., Siqueira, H.V., and Kaster, M.S. (2016, January 20\u201323). Gaussian adaptive PID control optimized via genetic algorithm applied to a step-down DC-DC converter. Proceedings of the 2016 12th IEEE International Conference on Industry Applications (INDUSCON), Curitiba, Brazil.","DOI":"10.1109\/INDUSCON.2016.7874509"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Guerreiro, M.T., Guerreiro, E.M.A., Barchi, T.M., Biluca, J., Alves, T.A., de Souza Tadano, Y., Trojan, F., and Siqueira, H.V. (2021). Anomaly Detection in Automotive Industry Using Clustering Methods\u2014A Case Study. Appl. Sci., 11.","DOI":"10.3390\/app11219868"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tao, L., Yang, X., Zhou, Y., and Yang, L. (2021). A novel transformers fault diagnosis method based on probabilistic neural network and bio-inspired optimizer. Sensors, 21.","DOI":"10.3390\/s21113623"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Santos, P., Macedo, M., Figueiredo, E., Santana, C.J., Soares, F., Siqueira, H., Maciel, A., Gokhale, A., and Bastos-Filho, C.J. (2017, January 8\u201310). Application of PSO-based clustering algorithms on educational databases. Proceedings of the 2017 IEEE Latin American Conference on Computational Intelligence (LA-CCI), Arequipa, Peru.","DOI":"10.1109\/LA-CCI.2017.8285690"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zivkovic, M., Stoean, C., Chhabra, A., Budimirovic, N., Petrovic, A., and Bacanin, N. (2022). Novel improved salp swarm algorithm: An application for feature selection. Sensors, 22.","DOI":"10.3390\/s22051711"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7709","DOI":"10.1007\/s00521-019-04441-0","article-title":"A hybrid firefly algorithm with particle swarm optimization for energy efficient optimal cluster head selection in wireless sensor networks","volume":"32","author":"Pitchaimanickam","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Devan, P.A.M., Hussin, F.A., Ibrahim, R.B., Bingi, K., Nagarajapandian, M., and Assaad, M. (2022). An arithmetic-trigonometric optimization algorithm with application for control of real-time pressure process plant. Sensors, 22.","DOI":"10.3390\/s22020617"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lin, J., Zheng, R., Zhang, Y., Feng, J., Li, W., and Luo, K. (2022). CFHBA-PID Algorithm: Dual-Loop PID Balancing Robot Attitude Control Algorithm Based on Complementary Factor and Honey Badger Algorithm. Sensors, 22.","DOI":"10.3390\/s22124492"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Huba, M., and Vrancic, D. (2022). Performance Portrait Method: An Intelligent PID Controller Design Based on a Database of Relevant Systems Behaviors. Sensors, 22.","DOI":"10.3390\/s22103753"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Kang, C., Park, B., and Choi, J. (2021). Scheduling PID Attitude and Position Control Frequencies for Time-Optimal Quadrotor Waypoint Tracking under Unknown External Disturbances. Sensors, 22.","DOI":"10.3390\/s22010150"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"110106","DOI":"10.1016\/j.envres.2020.110106","article-title":"Air pollution epidemiology: A simplified Generalized Linear Model approach optimized by bio-inspired metaheuristics","volume":"191","author":"Belotti","year":"2020","journal-title":"Environ. Res."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Puchta, E.D.P., Bassetto, P., Biuk, L.H., Itaborahy Filho, M.A., Converti, A., Kaster, M.S., and Siqueira, H.V. (2021). Swarm-inspired algorithms to optimize a nonlinear gaussian adaptive PID controller. Energies, 14.","DOI":"10.3390\/en14123385"},{"key":"ref_29","unstructured":"Puchta, E.P., Lucas, R., Siqueira, H.V., and Kaster, M.S. (2016, January 3\u20137). Application of a Nonlinear Gaussian Adaptive PID with PSO Optimization to a Buck Conveter. Proceedings of the Congresso Brasileiro de Automatica. Sociedade Brasileira de Automatica, Vitoria, Brazil."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bassetto, P., Puchta, E.D.P., Biuk, L.H., Itaborahy Filho, M.A., Kaster, M.S., and Siqueira, H.V. (2021, January 15\u201318). Metaheuristic-based optimization applied to GAPID controller. Proceedings of the 2021 14th IEEE International Conference on Industry Applications (INDUSCON), Sao Paulo, Brazil.","DOI":"10.1109\/INDUSCON51756.2021.9529388"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Janzen, F.C., Tusset, A.M., and Balthazar, J.M. (2016, January 21\u201324). Positioning Control of a Flexible Slewing Structure by Applying Sliding Mode Control. Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Charlotte, NC, USA.","DOI":"10.1115\/DETC2016-59363"},{"key":"ref_32","first-page":"43","article-title":"Simplified dynamic model of rotating beam","volume":"14","author":"Hein","year":"2013","journal-title":"Diagnostika"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1177\/1077546307085212","article-title":"Vibration Control of a Structure and a Rotor Using One-sided Magnetic Actuator and a Digital Proportional-derivative Control","volume":"15","author":"Nandi","year":"2009","journal-title":"J. Vib. Control"},{"key":"ref_34","unstructured":"Sarkar, S., Nandi, A., and Neogy, S. (2010, January 13\u201315). Control of Simulink Based Jeffcott Rotor Model. Proceedings of the 6th International Conference on Vibration Engineering and Technology on Machinery (VETOMAC 2010), New Delhi, India."},{"key":"ref_35","first-page":"1911","article-title":"Modeling the coupled flexural and torsional vibrations in rotating machines in transient states","volume":"16","author":"Matyja","year":"2014","journal-title":"J. Vibroeng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Ippoliti, E. (2014). Heuristic Reasoning, Springer.","DOI":"10.1007\/978-3-319-09159-4"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s11047-008-9098-4","article-title":"A survey on metaheuristics for stochastic combinatorial optimization","volume":"8","author":"Bianchi","year":"2009","journal-title":"Nat. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems, MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.engappai.2019.04.007","article-title":"Swarm intelligence for clustering\u2014A systematic review with new perspectives on data mining","volume":"82","author":"Figueiredo","year":"2019","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs, Springer.","DOI":"10.1007\/978-3-662-03315-9"},{"key":"ref_41","unstructured":"Castro, L.N. (2006). Fundamentals of Natural Computing: Basic Concepts, Algorithms and Applications, Chapman & Hall\/CRC."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Goldberg, D. (2002). The Design of Innovation (Genetic Algorithms and Evolutionary Computation), Springer.","DOI":"10.1007\/978-1-4757-3643-4"},{"key":"ref_43","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks IV, Perth, Australia."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The particle swarm-explosion, stability, and convergence in a multidimensional complex space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_45","unstructured":"Janzen, F.C. (2016). Positioning and Vibration Control of a Flexible Structure in Slewing Motion by Applying Shape Memory Alloys. [Ph.D. Thesis, Universidade Estadual Paulista]."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Siqueira, H., Belotti, J.T., Boccato, L., Luna, I., Attux, R., and Lyra, C. (2020). Recursive linear models optimized by bioinspired metaheuristics to streamflow time series prediction. Int. Trans. Oper. Res.","DOI":"10.1111\/itor.12908"},{"key":"ref_47","unstructured":"Eberhart, R.C., and Shi, Y. (2000, January 16\u201319). Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No. 00TH8512), La Jolla, CA, USA."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Khan, T.A., Taj, T.A., Asif, M.K., and Ijaz, I. (2012, January 18\u201320). Modeling of a standard Particle Swarm Optimization algorithm in MATLAB by different benchmarks. Proceedings of the Second International Conference on the Innovative Computing Technology (INTECH 2012), Casablanca, Morocco.","DOI":"10.1109\/INTECH.2012.6457817"},{"key":"ref_49","unstructured":"Pololu (2019, May 17). Pololu Dual VNH5019 Motor Driver Shield for Arduino. Available online: https:\/\/www.pololu.com\/product\/2507."},{"key":"ref_50","unstructured":"Instruments, N.N. (2019, May 22). CompactRIO Systems. Available online: http:\/\/www.ni.com\/pt-br\/shop\/compactrio.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6094\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,3]],"date-time":"2024-08-03T22:30:52Z","timestamp":1722724252000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,15]]},"references-count":50,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22166094"],"URL":"https:\/\/doi.org\/10.3390\/s22166094","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,8,15]]}}}