Electrical and Electronic Engineering - Theses
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ItemRobust overlapping decentralised control of linear uncertain time-delay systems with application to power systemsAhmadi, Adel ( 2016)There are many real-life or man-made large scale systems comprise subsystems with overlapping parts. In other words, the subsystems are strongly coupled in the overlapping (shared) parts but weakly interconnected otherwise. Such systems are called to have overlapping structure. Feedback controller with the overlapping structure, which is consistent with structure of the system, has been used widely to control such systems. The controller with overlapping structure comprises of local controllers which are fed by local information in addition to shared (overlapping) information. The overlapping controller design is based on the mathematical framework called the inclusion principle. The design procedure has three steps. First, the expanded system (includes the original system) comprising interconnected subsystems is generated. Then, local controllers are designed for interconnected subsystems of the expanded system. The local controllers form a decentralised controller. Finally, the decentralised controller is contracted (transformed) to an overlapping controller for implementation on the original system. In this thesis, we will present a comprehensive study of the inclusion principle for linear systems. First, a necessary and sufficient condition for stabilisability of linear time-invariant systems with overlapping structure is presented. The conditions are related to minimality and the concept of quotient fixed modes (QFMs). Meanwhile, an iterative algorithm is presented to guarantee the contractibility of decentralised output feedback control law designed for the expanded system. Also, stabilisability of overlapping uncertain linear systems by overlapping static output feedback controllers is studied. Furthermore, stabilisability of linear state-delay systems with overlapping structure is investigated. An extension of the inclusion principle is presented to design robust overlapping output feedback controllers for linear state-delay systems. Non-commensurate communication delays are assumed to be constant and unknown but bounded by given values. First, the expanded system is generated using the extended inclusion principle. Then, an iterative algorithm is suggested to design robust local controllers for the interconnected subsystems. Finally, the designed decentralised controller which is formed by local controllers, is contracted to an overlapping controller. It is proven that stability and performance are preserved through the contraction process. From application viewpoint, a two-area interconnected power system experiencing communication delay and model uncertainties is studied. The power system is decomposed into two overlapping subsystems with tie-lines being the overlapping parts. Afterwards, the proposed overlapping design approach is used to design an overlapping Load Frequency Controller (LFC) for the case study. Simulation results and a quantitative criterion clearly demonstrate the improved performance obtained by the proposed overlapping LFC compared with existing ones under different scenarios for communication delays and uncertain parameters. Motivated by the load frequency control problem in the presence of network delays, the inclusion principle is used to design an overlapping output feedback controller for linear uncertain input-delay system. The network delays are unknown and time-varying but with bounded size and rate of change. Similar to before, the expanded system is generated at the first step. Then, robust local controllers are designed for the interconnected subsystems using a proposed iterative algorithm. The obtained decentralised control design is then contracted to an overlapping one for implementation on the original system. The preservation of stability and performance through contraction is proven. As an application, the inclusion principle is used to design a robust overlapping LFC for a three-area interconnected power system experiencing time-varying input delay. The simulation results and quantitative criteria with the proposed overlapping LFC are compared with those of existing decentralised LFCs.