Distributed integral controllability for non-square processes: A comprehensive study and numerical analysis

Distributed control systems offer significant benefits such as enhanced flexibility, improved failure tolerance, and simplified system design compared to centralized systems. While the controllability of linear square systems under decentralized structures incorporating integral action is well-explored, challenges arise when dealing with non-square processes, which are prevalent in various control and optimization scenarios. Traditionally, non-square systems are manipulated into square configurations by adjusting inputs and outputs to apply decentralized integral controllability (DIC) analysis, potentially affecting the system’s reliability and controller flexibility. To address this issue, we propose a direct application of decentralized integral controllability to non-square processes, termed DIC-NSQ. We approach this problem by representing the system through a state space description, transforming it into standard singular perturbation form, and subsequently establishing its necessary as well as sufficient conditions using singular perturbation analysis. Through numerical examples, we demonstrate that DIC-NSQ effectively maintains offset-free tracking and ensures robust performance, even in the presence of actuator failures. This contribution marks an advancement in the field of distributed control systems, particularly for applications involving non-square processes.