{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:28:51Z","timestamp":1765960131265,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T00:00:00Z","timestamp":1606694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Simple and easy to use methods are of great practical demand in the design of Proportional, Integral, and Derivative (PID) controllers. Controller design criteria are to achieve a good set-point tracking and disturbance rejection with minimal actuator variation. Achieving satisfactory trade-offs between these performance criteria is not easily accomplished with classical tuning methods. A particle swarm optimization technique is proposed to design PID controllers. The design method minimizes a compromise cost function based on both the integral absolute error and control signal total variation criteria. The proposed technique is tested on an Arduino-based Temperature Control Laboratory (TCLab) and compared with the Grey Wolf Optimization algorithm. Both TCLab simulation and physical data show that satisfactory trade-offs between the performance and control effort are enabled with the proposed technique.<\/jats:p>","DOI":"10.3390\/a13120315","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T10:26:12Z","timestamp":1606731972000},"page":"315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Swarm-Based Design of Proportional Integral and Derivative Controllers Using a Compromise Cost Function: An Arduino Temperature Laboratory Case Study"],"prefix":"10.3390","volume":"13","author":[{"given":"P. B.","family":"de Moura Oliveira","sequence":"first","affiliation":[{"name":"Department of Engineering, University of Tr\u00e1s-os-Montes and Alto Douro (UTAD), 5000-801 Vila Real, Portugal"},{"name":"Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), Campus da Faculdade de Engenharia da Universidade do Porto (FEUP), 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5535-5277","authenticated-orcid":false,"given":"John D.","family":"Hedengren","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3224-4926","authenticated-orcid":false,"given":"E. J.","family":"Solteiro Pires","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Tr\u00e1s-os-Montes and Alto Douro (UTAD), 5000-801 Vila Real, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.ifacol.2015.11.213","article-title":"An Industry Sponsored Video Course for Control Engineering Practitioners","volume":"48","author":"Starr","year":"2015","journal-title":"IFAC PapersOnLine"},{"key":"ref_2","unstructured":"(2018, January 9\u201311). PID-18. Proceedings of the 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control, Ghent, Belgium. Available online: https:\/\/www.sciencedirect.com\/journal\/ifac-papersonline."},{"key":"ref_3","first-page":"759","article-title":"Optimum settings for automatic controllers","volume":"31","author":"Ziegler","year":"1942","journal-title":"Trans. ASME"},{"key":"ref_4","first-page":"4","article-title":"Anti-windup, bumpless, and conditioned transfer techniques for PID controllers","volume":"16","author":"Peng","year":"1996","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_5","unstructured":"\u00c5str\u00f6m, K.J., and H\u00e4gglund, T. (2006). Advanced PID Control, ISA."},{"key":"ref_6","unstructured":"Seborg, D., Edgar, T.F., Mellichamp, D.A., and Doyle, F.J. (2017). Process Dynamics and Control, Wiley. [4th ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Visioli, A., and Vilanova, R. (2012). PID Control in the Third Millennium: Lessons Learned and New Approaches, Springer.","DOI":"10.1007\/978-1-4471-2425-2"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Rossiter, A., Zakova, K., Huba, M., Serbezov, A., and Visioli, A. (2020, January 11\u201317). A First Course in Feedback, Dynamics and Control: Findings from 2019 Online Survey of the International Control Community. Proceedings of the IFAC-2020 World Congress, Berlin, Germany.","DOI":"10.1016\/j.ifacol.2020.12.1803"},{"key":"ref_9","unstructured":"Holland, J.H. (1975). Adaptation in Natural and Artificial Systems, The University of Michigan Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/3477.484436","article-title":"Ant system: Optimization by a colony of cooperating agents","volume":"26","author":"Dorigo","year":"1996","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_11","unstructured":"Koza, J.R. (1990). Genetic Programming: A Paradigm for Breeding Populations of Computers Programs to Solve Problems, Stanford University. Technical Report STAN-CS-90-1314."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential Evolution\u2014A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Global Optim."},{"key":"ref_13","unstructured":"Kennedy, J., and Eberhart, R.C. (December, January 27). Particle swarm optimization. Proceedings of the International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Yang, X.-S., and Deb, S. (2009, January 8\u201310). Cuckoo Search via L\u00e9vy Flights. Proceedings of the World Congress on Nature & Biologically Inspired Computing (NaBIC), Coimbatore, India.","DOI":"10.1109\/NABIC.2009.5393690"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bramer, M., Ellis, R., and Petridis, M. (2010). Firefly Algorithm, L\u00e9vy Flights and Global Optimization. Research and Development in Intelligent Systems XXVI, Springer.","DOI":"10.1007\/978-1-84882-983-1"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.3233\/MGS-2006-2301","article-title":"Glowworm swarm based optimization algorithm for multimodal functions with collective robotics applications","volume":"2","author":"Krishnanand","year":"2006","journal-title":"Multiagent Grid Syst. Int. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","article-title":"GSA: A Gravitational Search Algorithm","volume":"179","author":"Rashedi","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey wolf optimizer","volume":"69","author":"Seyedali","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_19","first-page":"239","article-title":"Grey Wolf, Gravitational Search and Particle Swarm Optimizers: A Comparison for PID Controller Design","volume":"Volume 402","author":"Vrancic","year":"2016","journal-title":"CONTROLO 2016"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4243","DOI":"10.1007\/s00500-016-2291-y","article-title":"Grey Wolf Optimization for PID Controller Design with Prescribed Robustness Margins","volume":"20","author":"Freire","year":"2016","journal-title":"Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5329","DOI":"10.3233\/JIFS-169815","article-title":"Controller design for Doha water treatment plant using grey wolf optimization","volume":"35","author":"Rathore","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"194","DOI":"10.19101\/IJATEE.2016.324005","article-title":"Elephant herding optimization based PID controller tuning","volume":"3","author":"Gupta","year":"2016","journal-title":"Int. J. Adv. Technol. Eng. Explor."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jones, A.H., and De Moura Oliveira, P.B. (1995, January 12\u201314). Genetic Auto-Tuning of PID Controllers. Proceedings of the First IEE Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications (GALESIA\u201995), Sheffield, UK.","DOI":"10.1049\/cp:19951039"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1016\/S0967-0661(02)00081-3","article-title":"Evolutionary algorithms in control systems engineering: A survey","volume":"10","author":"Fleming","year":"2002","journal-title":"Control Eng. Pract."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.compag.2005.08.003","article-title":"Greenhouse Air Temperature Control using the Particle Swarm Optimisation Algorithm","volume":"49","author":"Coelho","year":"2005","journal-title":"Comput. Electron. Agric."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2338","DOI":"10.1177\/0142331220909010","article-title":"Review of Nature and Biologically Inspired Metaheuristics for Greenhouse Environment Control","volume":"42","author":"Pinho","year":"2020","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/j.ejor.2006.06.034","article-title":"A hybrid simplex search and particle swarm optimization for unconstrained optimization","volume":"181","author":"Zahara","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Fan, S.-K.S., and Jen, C.-H. (2019). An Enhanced Partial Search to Particle Swarm Optimization for Unconstrained Optimization. Mathematics, 7.","DOI":"10.3390\/math7040357"},{"key":"ref_29","unstructured":"Irigoyen, E., Larzabal, E., and Priego, R. (2013, January 28\u201330). Low-cost platforms used in Control Education: An educational case stud. Proceedings of the 10th IFAC Symposium Advances in Control Education, Sheffield, UK."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.ifacol.2015.11.223","article-title":"A low-cost open source hardware in control education. Case study: Arduino-Feedback MS-150","volume":"48","author":"Reguera","year":"2015","journal-title":"IFAC PapersOnLine"},{"key":"ref_31","unstructured":"McLoone, S.C., and Maloco, J. (September, January 31). A Cost-effective Hardware-based Laboratory Solution for Demonstrating PID Control. Proceedings of the UKACC 11th International Conference on Control (CONTROL), Belfast, UK."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.proeng.2017.03.085","article-title":"Heat Transfer Lab Kit using Temperature Sensor based Arduino TM for Educational Purpose","volume":"170","author":"Prima","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Rossiter, J.A., Pope, S.A., Jones, B.L., and Hedengren, J.D. (2019, January 7\u20139). Evaluation and demonstration of take-home laboratory kit, Invited Session: Demonstration and poster session. Proceedings of the 12th IFAC Symposium on Advances in Control Education, Philadelphia, PA, USA.","DOI":"10.1016\/j.ifacol.2019.08.124"},{"key":"ref_34","unstructured":"Juchem, J., Chevalier, A., Dekemele, K., and Loccu, M. (2020, January 11\u201317). Active learning in control education: A pocket-size PI(D) setup. Proceedings of the IFAC-2020 World Congress, Berlin, Germany."},{"key":"ref_35","unstructured":"Hedengren, J.D. (2020, September 20). Temperature Control Lab Kit. Available online: https:\/\/apmonitor.com\/heat.htm."},{"key":"ref_36","unstructured":"Hedengren, J.D., Martin, R.A., Kantor, J.C., and Reuel, N. (2019, January 10\u201315). Temperature Control Lab for Dynamics and Control. Proceedings of the AIChE Annual Meeting, Orlando, FL, USA."},{"key":"ref_37","unstructured":"Park, J., Patterson, C., Kelly, J., and Hedengren, J.D. (April, January 31). Closed-Loop PID Re-Tuning in a Digital Twin by Re-Playing Past Setpoint and Load Disturbance Data. Proceedings of the AIChE Spring Meeting, New Orleans, LA, USA."},{"key":"ref_38","first-page":"6","article-title":"Benchmark Temperature Microcontroller for Process Dynamics and Control","volume":"135","author":"Park","year":"2020","journal-title":"J. Comp. Chem. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Moura Oliveira, P.B., and Hedengren, J.D. (2019, January 10\u201313). An APMonitor Temperature Lab PID Control Experiment for Undergraduate Students. Proceedings of the 24th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), Zaragoza, Spain.","DOI":"10.1109\/ETFA.2019.8869247"},{"key":"ref_40","unstructured":"Moura Oliveira, P.B., Hedengren, J.D., and Rossiter, J.A. (2020, January 11\u201317). Introducing Digital Controllers to Undergraduate Students using the TCLab Arduino Kit. Proceedings of the IFAC-2020 World Congress, Berlin, Germany."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1007\/s12555-015-0271-0","article-title":"From Single to Many-objective PID Controller Design using Particle Swarm Optimization","volume":"15","author":"Freire","year":"2017","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Bansal, J.C., Singh, P.K., Saraswat, M., Verma, A., Jadon, S.S., and Abraham, A. (2011, January 19\u201321). Inertia Weight Strategies in Particle Swarm Optimization. Proceedings of the IEEE Third World Congress on Nature and Biologically Inspired Computing, Salamanca, Spain.","DOI":"10.1109\/NaBIC.2011.6089659"},{"key":"ref_43","first-page":"827","article-title":"Theoretical consideration of retarded control","volume":"75","author":"Cohen","year":"1953","journal-title":"Trans. ASME"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/12\/315\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:39:36Z","timestamp":1760179176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/12\/315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,30]]},"references-count":43,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["a13120315"],"URL":"https:\/\/doi.org\/10.3390\/a13120315","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2020,11,30]]}}}