EIGENVALUE AND EIGENVECTOR ASSIGNMENT AND DISTURBANCE DECOUPLING UNDER DECENTRALIZED FEEDBACK
Abstract
The thesis develops a numerically implementable theory for the design of decentralized feedback controllers, specifically controllers which assigns a specified set of eigenvalues and eigenvectors. The underlying model is the component connection model (CCM). The CCM is a mathematical model which represents the interconnected system by two separate sets of equations. Under decentralized control each component has a local controller which is independent of all other local controllers. Little work has been done in the area decentralized control using eigenstructure assignment. Since most control problems such as tracking, disturbance decoupling and regulation can be expressed in terms of eigenstructure assignment, study of this area is important to field of control. The thesis provides a method for optimizing the norm of the feedback matrix which assigns a specified spectrum. It is based on the continuation method of eigenvalue assignment. A complete theoretical justification of the developed method is included in the thesis. In the area of eigenstructure assignment there are two basic types of problems. The first involves eigenstructure assignment under a specified set of eigenvalues. The thesis will review and fill in the gaps of the theory needed to handle this type of problem using global state and output feedback and extend the theory to include decentralized feedback. The second type of problem involves satisfying a set of constraints on the eigenvectors while requiring that the system maintains stability. In particular the goal is to characterize AB-invariant subspaces (a subspace whose basis is a set of eigenvectors) and controllability subspaces (an AB-invariant subspace which can have an arbitrary spectrum). The thesis completes the theory for eigenstructure assignment under global feedbacks and extends the theory to include decentralized feedback. On the practical side the thesis will solve the Disturbance Decoupling Problem under Decentralized Control with Internal Stability. Here the task is to eliminate input disturbances from the output while maintaining the system's stability.
Degree
Ph.D.
Subject Area
Electrical engineering
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