Abstract This manuscript introduces an optimal detuning approach for designing a centralized PI control system for multi-input multi-output (MIMO) processes. Based on the approach, two multivariable PI controller designs are proposed in this manuscript. The proposed approach formulates the centralized PI controller design problem in an optimization framework and transforms it into an equivalent detuning parameter(s) design problem. While the centralized controller design with the proposed 1-Optimal Detuning Parameter (ODP) method is carried out as a multi-stage problem, the proposed 2-ODP method formulates the controller design as a single-stage optimization problem. An effective transfer function (ETF) parameterization followed by controller synthesis using the IMC theory and further the optimal detuning comprises the various stages in 1-ODP design. In this regard, a novel ETF parameterization procedure for large scale processes or systems with higher-order elements is presented in this manuscript. Contrary to the centralized controller design in the k p , k i space, where the dimensionality of the optimization problem blows at O( 2 n 2 ), the proposed 1-ODP and 2-ODP design methods always aim at solving a uni- and bi-dimensional optimization problem, respectively, irrespective of the dimensionality of the MIMO process. Hence, the proposed method is easily applicable even to high-dimensional MIMO processes. Several illustrative industrial MIMO systems are considered to demonstrate the applicability of the proposed methods to highly interacting and large scale processes. The simulation studies show that the proposed methods performs better as compared to the other centralized PI controller designs. Even with parameter variations, the proposed methods give satisfactory closed-loop performance. Further, robust stability analysis for the proposed designs is performed by considering multiplicative input and output uncertainties.

中文翻译：

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基于最优解调方法的MIMO过程集中控制设计

摘要 本文介绍了一种用于设计多输入多输出 (MIMO) 过程的集中式 PI 控制系统的最佳解调方法。基于该方法，本文提出了两种多变量 PI 控制器设计。所提出的方法在优化框架中制定集中式 PI 控制器设计问题，并将其转换为等效的失谐参数设计问题。虽然采用所提出的 1-最优失谐参数 (ODP) 方法的集中控制器设计是作为一个多阶段问题进行的，但所提出的 2-ODP 方法将控制器设计制定为一个单阶段优化问题。有效传递函数 (ETF) 参数化，然后使用 IMC 理论进行控制器综合，进一步优化失谐，包括 1-ODP 设计中的各个阶段。在这方面，本手稿介绍了一种用于具有高阶元素的大规模过程或系统的新型 ETF 参数化程序。与 kp , ki 空间中的集中控制器设计相反，其中优化问题的维数为 O( 2 n 2 )，所提出的 1-ODP 和 2-ODP 设计方法始终旨在解决一个维度优化问题，分别与 MIMO 过程的维度无关。因此，所提出的方法甚至很容易适用于高维 MIMO 过程。几个说明性的工业 MIMO 系统被认为证明了所提出的方法对高度交互和大规模过程的适用性。仿真研究表明，与其他集中式 PI 控制器设计相比，所提出的方法性能更好。即使有参数变化，所提出的方法也能提供令人满意的闭环性能。此外，通过考虑乘法输入和输出的不确定性，对所提出的设计进行稳健的稳定性分析。