{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:06:44Z","timestamp":1767650804963,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T00:00:00Z","timestamp":1648252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the kinematics of an inverted pendulum. Several researchers have investigated the structure and design of PID controllers for high-order systems during the last decade. The designs were always concerned with the enhanced response, robustness, model reduction and performance of PID controllers. An accurate tuning process of such a controller depends on the engineer\u2019s experience level. This is due to the number of variables and hyperparameters tuned during the process. An adaptive genetic algorithm (AGA) is utilized to optimize the MS-PID controllers for controlling the quadrotor in this study. The proposed method optimizes the offline-planned approach, providing several possibilities for adapting the controllers with various paths and or varying weather conditions. The MS-PID parameters are optimized in parallel, as every PID controller affects the other controller\u2019s behavior and performance. Furthermore, the proposed AGA generates new chromosomes for \u201cnew solutions\u201d by randomly developing new solutions close to the previous best values, which will prevent any local minima solution. This study intends to investigate the design and development of a highly tuned robust multi-stage PID controller for a symmetrical multirotor UAV. The work presents a model for a non-referenced inertial frame multirotor UAV (quadcopter). Once the model is defined, a robust multi-stage PID controller for the non-inertial referenced frame symmetrical multirotor UAV is designed, tuned, and tested. A genetic algorithm (GA) will be used to tune the MS-PID controller. Finally, the performance comparison between the proposed and conventional methods is presented. The results show that the proposed method provides stability improvement, better transient response, and power consumption.<\/jats:p>","DOI":"10.3390\/sym14040689","type":"journal-article","created":{"date-parts":[[2022,3,27]],"date-time":"2022-03-27T21:31:25Z","timestamp":1648416685000},"page":"689","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Robust Nonlinear Non-Referenced Inertial Frame Multi-Stage PID Controller for Symmetrical Structured UAV"],"prefix":"10.3390","volume":"14","author":[{"given":"Faruk","family":"Takao\u011flu","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, \u0130stanbul Ayd\u0131n University, Istanbul 34295, Turkey"}]},{"given":"Ali","family":"Alshahrani","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Arab Open University, Riyadh 11681, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5116-8933","authenticated-orcid":false,"given":"Naim","family":"Ajlouni","sequence":"additional","affiliation":[{"name":"Department of Software Engineering, Istanbul Atlas University, Istanbul 34408, Turkey"}]},{"given":"Firas","family":"Ajlouni","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Lancashire college of Further Education, Accrington BB5 OHJ, UK"}]},{"given":"Basil","family":"Al Kasasbah","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Arab Open University, Riyadh 11681, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5375-1826","authenticated-orcid":false,"given":"Adem","family":"\u00d6zyava\u015f","sequence":"additional","affiliation":[{"name":"Department of Software Engineering, Istanbul Atlas University, Istanbul 34408, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,26]]},"reference":[{"key":"ref_1","first-page":"340","article-title":"PID parameter optimization of a UAV longitudinal Flight control system","volume":"45","author":"Turkoglu","year":"2008","journal-title":"World Acad. Sci. Eng. Technol."},{"key":"ref_2","unstructured":"Turkoglu, K., and Jafarov, E.M. (2006, January 16\u201317). Hinf loop shaping robust control vs. classical PI(D) control: A case study on the longitudinal dynamics of hezarfen UAV. Proceedings of the 2nd WSEAS International Conference on Dynamical Systems and Control, Bucharest, Romania."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dawes, J., Ng, L., Dorf, R., and Tam, C. (1994, January 24\u201326). Design of Deadbeat Robust Systems. Proceedings of the IEEE International Conference on Control and Applications, Glasgow, UK.","DOI":"10.1109\/CCA.1994.381478"},{"key":"ref_4","unstructured":"Lockheed Martin (2015). Kestrel Autopilot System: User Guide, Copyright\u00a9 2004\u20132008, Procerus\u00ae Technologies."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kumar, P.V., Challa, A., Ashok, J., and Narayanan, G.L. (2015, January 18\u201320). GIS based fire rescue system for industries using Quad copter\u2014A novel approach. Proceedings of the International Conference on Microwave, Optical and Communication Engineering (ICMOCE), Bhubaneswar, India.","DOI":"10.1109\/ICMOCE.2015.7489693"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dallal Bashi, O.I., Wan Hasan, W.Z., Azis, N., Shafie, S., and Wagatsuma, H. (2017, January 23\u201325). Quadcopter sensing system for risky area. Proceedings of the IEEE Regional Symposium on Micro and Nanoelectronics (RSM), Batu Ferringhi, Malaysia.","DOI":"10.1109\/RSM.2017.8069152"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Saha, H., Basu, S., Auddy, S., Dey, R., Nandy, A., Pal, D., Roy, N., Jasu, S., Saha, A., and Chattopadhyay, S. (2018, January 8\u201310). A low cost fully autonomous GPS (Global Positioning System) based quad copter for disaster management. Proceedings of the 8th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA.","DOI":"10.1109\/CCWC.2018.8301782"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"320526","DOI":"10.1155\/2014\/320526","article-title":"A Survey of Modelling and Identification of Quadrotor Robot","volume":"2014","author":"Zhang","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.proeng.2014.12.139","article-title":"Mathematical Modelling and Parameter Identification of Quadrotor (a survey)","volume":"96","author":"Fico","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_10","unstructured":"Bouabdallah, S., Noth, A., and Siegwart, R. (October, January 28). PID vs LQ control techniques applied to an indoor micro quadrotor. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No. 04CH37566), Sendai, Japan."},{"key":"ref_11","first-page":"1","article-title":"PID Controller Tuning Optimization with Genetic Algorithms for a Quadcopter","volume":"5","author":"Khuwaja","year":"2018","journal-title":"Recent Innov. Mech."},{"key":"ref_12","unstructured":"Luukkonen, T. (2011). Modeling and Control of Quadcopter. Independent Research Project in Applied Mathematics, Aalto University. Available online: https:\/\/sal.aalto.fi\/publications\/pdf-files\/eluu11_public.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s11044-018-9620-0","article-title":"Perspectives on Euler angle singularities, gimbal lock, and the orthogonality of applied forces and applied moments","volume":"44","author":"Hemingway","year":"2018","journal-title":"Multibody Syst. Dyn."},{"key":"ref_14","unstructured":"Valavanis, K., and Vachtsevanos, G. (2018). Analysis of Safety Requirements for Small Unmanned Aerial Systems (sUAS). Handbook of Unmanned Aerial Vehicles, Springer."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cai, G., Chen, B.M., and Lee, T.H. (2011). Unmanned Rotorcraft Systems. Advances in Industrial Control, Springer.","DOI":"10.1007\/978-0-85729-635-1"},{"key":"ref_16","first-page":"1087","article-title":"Nonlinear PID controller design for a 6-DOF UAV quadrotor system","volume":"22","author":"Najm","year":"2019","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_17","unstructured":"David, H. (2014). Quadcopter Dynamic Modeling and Simulation for Control System Design, Drexel University. Available online: www.mathworks.com\/academia\/student-challenge\/spring-2014.html."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1108\/ir.2006.33.5.403.1","article-title":"Robot Modeling and Control","volume":"33","author":"Spong","year":"2006","journal-title":"Ind. Robot."},{"key":"ref_19","first-page":"66","article-title":"Techniques for Quadcopter Modelling & Design: A review","volume":"5","author":"Musa","year":"2017","journal-title":"J. Unmanned Syst. Technol."},{"key":"ref_20","unstructured":"Cano, J.M. (2013). Quadrotor UAV for Wind Profile Characterization. [Master\u2019s Thesis, Universidad Carlos III de Madrid]. Available online: https:\/\/e-archivo.uc3m.es\/bitstream\/handle\/10016\/18105\/PFC_Javier_Moyano_Cano.pdf?isAllowed=y&sequence=1."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Dikmen, I.C., Arisoy, A., and Temeltas, H. (2009, January 11\u201313). Attitude control of a quadrotor. Proceedings of the 2009 4th International Conference on Recent Advances in Space Technologies, Istanbul, Turkey.","DOI":"10.1109\/RAST.2009.5158286"},{"key":"ref_22","first-page":"4805","article-title":"Mathematical modeling of hexacopter","volume":"7","author":"Artale","year":"2013","journal-title":"Appl. Math. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/689\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:44:04Z","timestamp":1760136244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/689"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,26]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["sym14040689"],"URL":"https:\/\/doi.org\/10.3390\/sym14040689","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,3,26]]}}}