Critical Delay Computation, Overlapping Interaction Selection and Output Feedback Design for Decentralized Control Systems.

Abstract

This thesis deals with Linear Time Invariant (LTI) control systems subjected to decentralized feedback, otherwise called as decentralized control systems. Such systems are well known to have modes that remain unchanged for any LTI decentralized controller. These modes are called as Decentralized Fixed Modes (DFMs) that play an important role in determining stabilizability of the system by a decentralized controller. A survey on characterization of DFMs is presented in this thesis.
A decentralized control system may have modes that are not explicit DFMs, but their behaviour is close to that of DFMs. In such a case, a small perturbation in the system parameters may result in one or more DFMs in the system. A perturbation measure in terms of DFM radius is used to determine how ‘close’ a system is from having at least one DFM. This thesis defines real DFM radius for decentralized control systems with input and output delays, and computing formulae are derived for the same using restricted real perturbation measures.
In addition to the above, a catalog of perturbation measures for critically delayed fixed mode radius that correspond to critical delays having minimum radius is introduced for systems with input and output delays. Computable formulas are derived using perturbation measures for both the centralized and the decentralized control systems.
Next problem considered in the thesis is the selection of overlapping control structure to remove decentralized fixed mode. This selection is proposed to be made through approximate decentralized fixed mode measure. Also, a framework for improving control cost of approximate decentralized fixed modes through overlapping control is given. The proposed selection method is demonstrated through the wide-area loop selection in electrical power systems.
Finally, the problem decentralized static output feedback controller design is considered. Static output feedback controller design even for centralized systems is well known to be an open problem, particularly in absence of computable necessary and sufficient conditions. New sufficient conditions in terms of linear matrix inequalities are derived to design static out put feedback controllers with H1 performance and regional pole placement constraint. The proposed method is shown to yield less conservative controller than some existing methodologies.