{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T02:05:44Z","timestamp":1767924344080,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T00:00:00Z","timestamp":1669334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"VIT-AP University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A decentralized PI\/PID controller based on the frequency domain analysis for two input two output (TITO) coupled tank systems is exploited in this paper. The fundamentals of the gain margin and phase margin are used to design the proposed PI\/PID controller. The basic objective is to keep the tank at the predetermined level. To satisfy the design specifications, the control algorithm is implemented for decoupled subsystems by employing a decoupler. First-order plus dead time (FOPDT) models are obtained for the decoupled subsystems using the model-reduction technique. In addition, the control law is realized by considering the frequency domain analysis. Further, the robustness of the controller is verified by considering multiplicative input and output uncertainties. The proposed method is briefly contrasted with existing techniques. It is envisaged that the proposed control algorithm exhibits better servo and regulatory responses compared to the existing techniques.<\/jats:p>","DOI":"10.3390\/s22239165","type":"journal-article","created":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T08:13:09Z","timestamp":1669623189000},"page":"9165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Frequency Domain Specifications Based Robust Decentralized PI\/PID Control Algorithm for Benchmark Variable-Area Coupled Tank Systems"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5421-1634","authenticated-orcid":false,"given":"Achu","family":"Govind K.R.","sequence":"first","affiliation":[{"name":"School of Electronics Engineering, VIT-AP University, Amaravati 522237, Andhra Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3717-2634","authenticated-orcid":false,"given":"Subhasish","family":"Mahapatra","sequence":"additional","affiliation":[{"name":"School of Electronics Engineering, VIT-AP University, Amaravati 522237, Andhra Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhou, J., Xue, L., Li, Y., Cao, L., and Chen, C. (2022). A Novel Fuzzy Controller for Visible-Light Camera Using RBF-ANN: Enhanced Positioning and Autofocusing. Sensors, 22.","DOI":"10.3390\/s22228657"},{"key":"ref_2","first-page":"102147","article-title":"A dynamic reconfiguration method based on neuro-fuzzy control algorithm for partially shaded PV arrays","volume":"52","year":"2022","journal-title":"Sustain. Energy Technol. Assess."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Torres-Salinas, H., Rodr\u00edguez-Res\u00e9ndiz, J., Cruz-Miguel, E.E., and \u00c1ngeles-Hurtado, L. (2022). Fuzzy Logic and Genetic-Based Algorithm for a Servo Control System. Micromachines, 13.","DOI":"10.3390\/mi13040586"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1016\/j.jart.2017.05.004","article-title":"Online tuning of fuzzy logic controller using Kalman algorithm for conical tank system","volume":"15","author":"Tamilselvan","year":"2017","journal-title":"J. Appl. Res. Technol."},{"key":"ref_5","first-page":"3","article-title":"Combining fractional order operators and adaptive passivity-based controllers: An application to the level regulation of a conical tank","volume":"19","author":"Beytia","year":"2017","journal-title":"J. Control Eng. Appl. Inform."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/j.measurement.2017.11.007","article-title":"Smart controller for conical tank system using reinforcement learning algorithm","volume":"116","author":"Ramanathan","year":"2018","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42452-019-0754-3","article-title":"Optimal tuning of FOPID controller based on PSO algorithm with reference model for a single conical tank system","volume":"1","author":"Rajesh","year":"2019","journal-title":"SN Appl. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1007\/s42835-021-00891-6","article-title":"Optimal Design of PID Controller for the analysis of Two TANK System Using Metaheuristic Optimization Algorithm","volume":"17","author":"Maruthupandi","year":"2022","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1222042","DOI":"10.1080\/23311916.2016.1222042","article-title":"Synthesis of fuzzy sliding mode controller for liquid level control in spherical tank","volume":"3","author":"Sreepradha","year":"2016","journal-title":"Cogent Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lakshmanan, M., Chitra, K., Kamatchi, K.V., and Srinivasan, S. (2020, January 15\u201317). Online Tuning of PI Controller for Spherical Tank System Using Root Locus Technique with Regulatory Operation. Proceedings of the 2020 Second International Conference on Inventive Research in Computing Applications (ICIRCA), Coimbatore, India.","DOI":"10.1109\/ICIRCA48905.2020.9182957"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.isatra.2019.04.006","article-title":"Evaluation of gap-metric based multi-model control schemes for nonlinear systems: An experimental study","volume":"94","author":"Prasad","year":"2019","journal-title":"ISA Trans."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1016\/B978-0-12-818634-3.50238-1","article-title":"Design of multi model fractional controllers for nonlinear systems: An experimental investigation","volume":"Volume 46","author":"Prasad","year":"2019","journal-title":"Computer Aided Chemical Engineering"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1504\/IJBIC.2012.048065","article-title":"Particle swarm optimisation applied to real time control of spherical tank system","volume":"4","author":"Priya","year":"2012","journal-title":"Int. J. Bio-Inspired Comput."},{"key":"ref_14","first-page":"2319","article-title":"Study of Different Controller\u2019s Performance for a Real Time Non-Linear System","volume":"3","author":"Soni","year":"2014","journal-title":"Int. J. Adv. Electron. Electr. Eng. ISSN"},{"key":"ref_15","first-page":"18","article-title":"Modelling and Simulation of Non Linear Spherical Tank Level Process","volume":"6","author":"Reshma","year":"2016","journal-title":"Asian J. Res. Soc. Sci. Humanit."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pradeepkannan, D., and Sathiyamoorthy, S. (2014, January 8\u201310). Control of a non-linear coupled spherical tank process using GA tuned PID controller. Proceedings of the 2014 IEEE International Conference on Advanced Communications, Control and Computing Technologies, Ramanathapuram, India.","DOI":"10.1109\/ICACCCT.2014.7019324"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.jprocont.2009.10.010","article-title":"Properties and control of the quadruple-tank process with multivariable dead-times","volume":"20","author":"Shneiderman","year":"2010","journal-title":"J. Process. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"13546","DOI":"10.3182\/20110828-6-IT-1002.01235","article-title":"Sliding-mode state-feedback control of non-minimum phase quadruple tank system using fuzzy logic","volume":"44","author":"Mirakhorli","year":"2011","journal-title":"IFAC Proc. Vol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.compeleceng.2015.04.012","article-title":"Fractional-Order sliding mode controller design for a modified quadruple tank process via multi-level switching","volume":"45","author":"Sutha","year":"2015","journal-title":"Comput. Electr. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1504\/IJSPM.2015.070474","article-title":"Bond-graph-based controller design for the quadruple-tank process","volume":"10","author":"Nacusse","year":"2015","journal-title":"Int. J. Simul. Process. Model."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107827","DOI":"10.1016\/j.compchemeng.2022.107827","article-title":"Practical implementable controller design with guaranteed asymptotic stability for nonlinear systems","volume":"163","author":"Rajhans","year":"2022","journal-title":"Comput. Chem. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.1109\/ACCESS.2021.3139214","article-title":"Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming","volume":"10","author":"Garrido","year":"2021","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8433","DOI":"10.1007\/s13369-014-1366-2","article-title":"Adaptive decentralized PI controller for two conical tank interacting level system","volume":"39","author":"Ravi","year":"2014","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2601","DOI":"10.1016\/j.proeng.2012.06.306","article-title":"Dynamic Matrix Control of a Two Conical Tank Interacting Level System","volume":"38","author":"Ravi","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.cogsys.2019.07.005","article-title":"Optimal tuning of decentralized fractional order PID controllers for TITO process using equivalent transfer function","volume":"58","author":"Lakshmanaprabu","year":"2019","journal-title":"Cogn. Syst. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1080\/00051144.2022.2061818","article-title":"A metaheuristic approach for interval type-2 fuzzy fractional order fault-tolerant controller for a class of uncertain nonlinear system","volume":"63","author":"Patel","year":"2022","journal-title":"Automatika"},{"key":"ref_27","first-page":"2031","article-title":"Real time implementation of gain scheduled controller design for higher order nonlinear system using LabVIEW","volume":"6","author":"Chakravarthi","year":"2014","journal-title":"Int. J. Eng. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"102948","DOI":"10.1016\/j.micpro.2019.102948","article-title":"Novel fuzzy fractional order PID controller for non linear interacting coupled spherical tank system for level process","volume":"72","author":"Jegatheesh","year":"2020","journal-title":"Microprocess. Microsystems"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Balakrishnaa, A., and Arun, N. (2022, January 27\u201329). Liquid Level Control of Interacting Coupled Spherical Tank System using PI and Fuzzy PI Controller. Proceedings of the 2022 3rd International Conference for Emerging Technology (INCET), Belgaum, India.","DOI":"10.1109\/INCET54531.2022.9824570"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1080\/00194506.2020.1852977","article-title":"Multi-model cascade control strategy design based on gap metric for nonlinear processes","volume":"64","year":"2022","journal-title":"Indian Chem. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.measurement.2013.10.011","article-title":"Distributed multiparametric model predictive control design for a quadruple tank process","volume":"47","author":"Kirubakaran","year":"2014","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1016\/j.ifacol.2016.07.313","article-title":"Robust PID auto-tuning for the quadruple tank system","volume":"49","author":"Ionescu","year":"2016","journal-title":"IFAC-PapersOnLine"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.jprocont.2019.01.006","article-title":"Design of sliding mode control for quadruple-tank MIMO process with time delay compensation","volume":"76","author":"Shah","year":"2019","journal-title":"J. Process. Control."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jprocont.2021.05.009","article-title":"Parameter estimation based robust liquid level control of quadruple tank system\u2014Second order sliding mode approach","volume":"104","author":"Gurjar","year":"2021","journal-title":"J. Process. Control"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.isatra.2021.04.021","article-title":"Disturbance observer-based feedback linearization control for a quadruple-tank liquid level system","volume":"122","author":"Meng","year":"2022","journal-title":"ISA Trans."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Olejnik, P., and Awrejcewicz, J. (2022). Intelligent Mechatronics in the Measurement, Identification, and Control of Water Level Systems: A Review and Experiment. Machines, 10.","DOI":"10.3390\/machines10100960"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"156857","DOI":"10.1109\/ACCESS.2021.3127795","article-title":"Decentralized PID controller tuning based on nonlinear optimization to minimize the disturbance effects in coupled loops","volume":"9","author":"Yamashita","year":"2021","journal-title":"IEEE Access"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.jprocont.2020.08.004","article-title":"SISO approaches for linear programming based methods for tuning decentralized PID controllers","volume":"94","author":"Yamashita","year":"2020","journal-title":"J. Process Control"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2008","DOI":"10.1021\/acs.iecr.5b03738","article-title":"A practical multivariable control approach based on inverted decoupling and decentralized active disturbance rejection control","volume":"55","author":"Sun","year":"2016","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.isatra.2011.01.001","article-title":"An analytical method for PID controller tuning with specified gain and phase margins for integral plus time delay processes","volume":"50","author":"Hu","year":"2011","journal-title":"ISA Trans."},{"key":"ref_41","first-page":"242","article-title":"Real time implementation of multivariable centralised FOPID controller for TITO process","volume":"10","author":"Lakshmanaprabu","year":"2018","journal-title":"Int. J. Reason.-Based Intell. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4774","DOI":"10.1016\/j.ifacol.2020.12.1004","article-title":"Analytical Triangular Decoupling Internal Model Control of a Class of Two-Input, Two-Output (TITO) Systems with Delays","volume":"53","author":"Ogunba","year":"2020","journal-title":"IFAC-PapersOnLine"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0959-1524(01)00025-7","article-title":"Relay feedback auto-tuning of process controllers\u2014A tutorial review","volume":"12","author":"Hang","year":"2002","journal-title":"J. Process. Control"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"106690","DOI":"10.1016\/j.compeleceng.2020.106690","article-title":"Level control of a conical tank using the fractional order controller","volume":"87","author":"Vavilala","year":"2020","journal-title":"Comput. Electr. Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"72","DOI":"10.3182\/20120619-3-RU-2024.00084","article-title":"Decentralized robust control of mimo systems: Quadruple tank case study","volume":"45","author":"Rosinova","year":"2012","journal-title":"IFAC Proc. Vol."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Osman, A., Kara, T., and Ar\u0131c\u0131, M. (2021). Robust adaptive control of a quadruple tank process with sliding mode and pole placement control strategies. IETE J. 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