Citation: Kozáková, A.; ˇ Cápková, R.; Kozák, Š. Decentralized QFT Controller Design Based on the Equivalent Subsystems Method. Electronics 2023, 12, 3658. https:// doi.org/10.3390/electronics12173658 Academic Editor: Cheng Siong Chin Received: 7 August 2023 Revised: 27 August 2023 Accepted: 28 August 2023 Published: 30 August 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). electronics Article Decentralized QFT Controller Design Based on the Equivalent Subsystems Method Alena Kozáková 1, * ,† , Romana ˇ Cápková 1,† and Štefan Kozák 2 1 Institute of Automotive Mechatronics Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkoviˇ cova 3, 812 19 Bratislava, Slovakia; romana.capkova@stuba.sk 2 Faculty of Informatics, Pan-European University, Tematínska 3246/10, 851 05 Bratislava, Slovakia; stefan.kozak@paneurouni.com * Correspondence: alena.kozakova@stuba.sk † These authors contributed equally to this work. Abstract: Since the 1970s various decentralized control methodologies have been developed to deal with the challenge of controlling complex and/or spatially distributed systems with multiple inputs and multiple outputs (MIMO), e.g., chemical plants, power systems, water systems, etc. In general, the use of distributed information and control structures requires the synthesis of control laws in a constrained (decentralized) information structure. The article presents a novel frequency domain robust decentralized controller design method that is appropriate for uncertain dynamic MIMO systems with equal numbers of input and output variables, which consist of interconnected physical subsystems and are given as a set of square transfer function matrices. The main framework of the proposed method provides the Equivalent Subsystems Method (ESM), whereby the overall closed- loop system under a decentralized controller is stable if, and only if, all the individual closed-loop equivalent subsystems are stable. By generating equivalent subsystems for all transfer matrices, which describe the uncertain MIMO system, the individual uncertain equivalent subsystems are obtained as sets of respective frequency responses. Such representation allows the application of the QFT (quantitative feedback theory) approach to independently design local single-input single-output (SISO) robust controllers which constitute the resulting decentralized controller implemented in real subsystems. The designed controller ensures robust stability of the overall closed-loop system and the required performance as specified by the standard QFT performance specification types in both the equivalent subsystems and the overall closed-loop system. Compared to the existing method and references therein, the proposed method reduces the conservatism of the robust stability conditions and enables the exploitation of the benefits by the SISO QFT approach in the independent design of the robust decentralized controller. The developed design procedure is verified and illustrated in a case study on the robust decentralized level controller design of the quadruple tank process. Keywords: decentralized control; frequency domain; independent design; MIMO system; parametric uncertainty; robust performance; robust stability; Equivalent Subsystems Method (ESM); quantitative feedback theory (QFT) 1. Introduction Since it appeared in the 1970s, decentralized control has been an important practice- oriented advanced control approach. Various decentralized control methodologies have been developed to deal with the challenge of controlling complex and/or spatially dis- tributed systems with multiple inputs and multiple outputs (MIMO systems), such as chemical plants, interconnected electrical power systems with strong interactions, water treatment plants, etc. Typically, complex systems are made up of several mutually interacting subsystems, whereby each subsystem operates relatively independently, with its own sub-objective Electronics 2023, 12, 3658. https://doi.org/10.3390/electronics12173658 https://www.mdpi.com/journal/electronics