Model and controller reduction of large-scale structures based on projection methods
The design of low-order controllers for high-order plants is a challenging problem theoretically as well as from a computational point of view. Frequently, robust controller design techniques result in high-order controllers. It is then interesting to achieve reduced-order models and controllers while maintaining robustness properties. Controller designed for large structures based on models obtained by finite element techniques yield large state-space dimensions. In this case, problems related to storage, accuracy and computational speed may arise. Thus, model reduction methods capable of addressing controller reduction problems are of primary importance to allow the practical applicability of advanced controller design methods for high-order systems. A challenging large-scale control problem that has emerged recently is the protection of civil structures, such as high-rise buildings and long-span bridges, from dynamic loadings such as earthquakes, high wind, heavy traffic, and deliberate attacks. Even though significant effort has been spent in the application of control theory to the design of civil structures in order increase their safety and reliability, several challenging issues are open problems for real-time implementation. This dissertation addresses with the development of methodologies for controller reduction for real-time implementation in seismic protection of civil structures using projection methods. Three classes of schemes are analyzed for model and controller reduction: nodal truncation, singular value decomposition methods and Krylov-based methods. A family of benchmark problems for structural control are used as a framework for a comparative study of model and controller reduction techniques. It is shown that classical model and controller reduction techniques, such as balanced truncation, modal truncation and moment matching by Krylov techniques, yield reduced-order controllers that do not guarantee stability of the closed-loop system, that is, the reducedorder controller implemented with the full-order plant. A controller reduction approach is proposed such that to guarantee closed-loop stability. It is based on the concept of dissipativity (or positivity) of linear dynamical systems. Utilizing passivity preserving model reduction together with dissipative-LQG controllers, effective low-order optimal controllers are obtained. Results are shown through simulations.