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.

Iterative Method for Tuning Multiloop PID Controllers Based on Single Loop Robustness Specifications in the Frequency Domain

“…As there are no previous controllers in the first iteration, expressions (3) or (4) cannot be used for the first EOP calculation. In this work, it was proposed to use the reduced equivalent open loop process (REOP) in (25) as the initial EOP g 0 i (s), where controller terms are excluded [29]. Since PID controllers have integral action, assuming a closed loop perfect control, the REOPs can be approximated from the structural decomposition in (3) as follows:…”

“…They are a key concept of the proposed methodology because they allow one to decompose the control system into equivalent SISO control loops to be designed. Then, the stability of a decentralized control system can be achieved if the characteristic equation of each equivalent single loop, as shown in (5), does not contain zeros in the right half plane [25].…”

“…Once the algorithm enters the iterative procedure of the flow diagram in Figure 4, the n EOPs g m i (jω) are already calculated from the previous iteration m − 1. Then, a PID controller is tuned for each EOP by means of the linear programming problem in (25). Next, the new EPO g m+1 i (jω) of each loop is updated using these new sets of PID controllers.…”

Design of multi-loop ADRC controllers based on the effective open-loop transfer function method

“…It aims at taking into account the cross-coupling, and then completely decomposing a multivariable control system into a number of equivalent independent single loops. Thus, the effects of the process and controller on the loop interaction and subsequent system properties, such as right half plane (RHP) zeroes and poles, integrity, and stability, are elucidated [14] . Moreover, the well-known of dynamic relative gain array (DRGA) is also used for the multi-loop controller design.…”

The design of an IMC-PID controller based on MEOTF and its application to non-square processes with time delay

“…In recent years, control methods for multi-variable systems based on the application of effective open-loop transfer function theory have become increasingly popular: in particular, Vu and Lee (2010), He et al (2005), Zhu (1996), Huang et al (2003) and Xiong and Cai (2006) put forward controller design methods for square control systems, which have produced better results. In the current paper, we develop a new controller design method that can be used for non-square control systems.…”