Structural Analysis and Stability Conditions of Decentralized Control Systems

Abstract

Stability analysis in decentralized control systems relies heavily on steady state tools such as the relative gain array and the Niederlinski index. However, only necessary stability conditions are provided by these tools and their usefulness lies essentially solely in eliminating unstable pairings. In this paper, upon structurally decomposing a decentralized control system into completely equivalent individual dynamic single input−single output loops with interactions explicitly embedded, system structure and main properties, such as right half plane (RHP) zeros, RHP poles, integrity, and stability, are analyzed in a systematic and transparent way. The intrinsic connections among these properties are elucidated. New important insights into the effects of loop interaction due to the process and the controller on the closed loop system are offered. Various necessary and sufficient conditions to prevent interaction from inducing undesirable behavior, such as nonminimum phase, lack of integrity, and instability, are developed. Significant implications for variable pairing and controller tuning are presented.