A new unconditional stability criterion and its application on decentralized integral controllability analysis

Decentralized integral control, such as multi-loop PI/PID control, is one of the most popular control strategies used in practice. An important issue associated with this strategy is the analysis of Decentralized Integral Controllability (DIC). Campo and Morari showed that for a process, if its steady state gain matrix is not critically D-stable, its DIC can be determined by using its steady state gain matrix only. This paper investigates decentralized integral control with a special focus on the DIC analysis of processes whose steady state gain matrices are critically D-stable. Firstly, this paper proposes a new unconditional stability criterion by using singular perturbation theory and eigenvalue sensitivity analysis, and shows that DIC analysis of such processes can be simplified by using unconditional stability analysis. Then, we presented a multi-loop PI control design method, which gives an explicit low bound of the proportional coefficient to achieve decentralized unconditional stability for 3 × 3 processes.