Advanced controls of large scale structural systems using linear matrix inequality methods

As more advanced aerospace systems emerge, the requirements for better performance, higher reliability and lower cost are becoming more stringent. It requires further theoretical and technical developments in many different disciplines. In this thesis we present method for the Hinfinity control of collocated structural systems, the fault identification and fault tolerant control of smart structures and the sub-optimal Hinfinity model reduction of symmetric systems.; We first examine the Hinfinity norm analysis and static output feedback control synthesis problems for structural systems with collocated sensors and actuators. Using a particular solution of the Bounded Real Lemma for an open loop collocated structural system we obtain an explicit expression to compute an upper bound of the Hinfinity norm of such systems. Then, for the corresponding output feedback Hinfinity control synthesis problem we obtain an explicit parametrization of the output feedback control gains that achieve a desired Hinfinity norm bound. These results have obvious computational advantages for large scale systems where standard Hinfinity analysis and control design methods are computationally intractable. Numerical examples demonstrate the advantages of the proposed method. This approach is also verified experimentally on a cantilevered aluminum beam with two collocated pairs of piezoceramic patches that serve as sensors and actuators. The finite element model of this beam is developed. The static output feedback controller that suppresses the vibration of the beam is designed using the proposed approach. Simulations show a drop of 6 dB in the Hinfinity norm of the closed loop system. Experimental results match the simulated results and demonstrate the effectiveness of this method.; The second part of the thesis focus on the development and application of an Hinfinity fault detection and isolation (FDI) filter and fault tolerant controller (FTC) for linear systems. A linear matrix inequality (LMI) formulation is obtained to design the full order robust Hinfinity filter to estimate the faulty input signals. A fault tolerant Hinfinity controller is designed for the combined system of plant and filter which minimizes the control objective selected in the presence of disturbances and faults. A cantilevered flexible beam attached with piezoceramic patches is used in the validation of the FDI filter and FTC controller design. The residuals obtained from the filter through experiments clearly identify the fault signals. The experimental results of the proposed FTC controller show its effectiveness for the vibration suppression of the beam for the faulty system.; The last part of the thesis investigates the Hinfinity suboptimal model reduction problem for state-space symmetric systems. Inherent in state-space symmetric property there exist some particular solutions of the corresponding non-convex constraint sets. An explicit parametrization of all reduced-order models and the solution to the zeroth-order Hinfinity approximation problem are obtained using these particular solutions. The infimum of the Hinfinity norm between the original and the obtained reduced order model is provided. These results are developed using the linear matrix inequality formulations of the Hinfinity control synthesis problem by employing simple matrix algebraic tools. Both the continuous and discrete-time cases are considered. Numerical examples demonstrate the effectiveness of the theoretical results.