Unified Algebraic Framework for Centralized and Decentralized MIMO RST Control for Strongly Coupled Processes

Reliable multivariable control is critical for industrial sectors where processes exhibit severe nonlinearities and interactions. A Continuous Stirred Tank Reactor (CSTR) is a rigorous benchmark for testing control strategies addressing these complexities. This work first establishes a linear MIMO mathematical framework to define the specific structure of such interactive systems. Analysis via phase planes and steady-state analysis reveals low controllability, bistability, and strong coupling, leading to the collapse of traditional decoupled control schemes. To address these issues via multivariable control, we propose a centralized MIMO RST control structure synthesized via a Matrix Fraction Description (MFD) and the extended Bézout equation. Simulations for performance evaluation and comparison highlight the following key findings: (1) the centralized RST maintains stability and tracking precision in regions where decentralized RST loops fail; (2) it exhibits performance comparable to the Augmented State Pole Placement with Integral Action (ASPPIA) method and outperforms the standard Model-Based Predictive Control (MPC) baseline, particularly during critical equilibrium point transitions; and (3) it offers a robust yet computationally simple design that provides superior flexibility for pole placement, accommodating future identification-based models and adaptive tuning. These results validate our algebraic synthesis as a robust, computationally efficient solution for managing highly interactive nonlinear dynamics.