| In this dissertation, controller design and stability analysis of systems in matrix second order (MSO) form are proposed. Until now, in time-domain approaches, control designers had to choose between first order state space techniques and conservative MSO techniques, which are based on sufficiency conditions of stability with tighter assumptions (such as symmetry, positive definiteness) on system matrices. As most of the development in MSO approach took place with special applications, it lacked generalized framework, constraining its applicability to a small class of practical systems. This dissertation provides generalized, necessary, and sufficient conditions of stability for MSO systems. These conditions remove the conservatism in design and provide wider applicability of MSO techniques, thereby realizing full benefits of MSO approach including acceleration feedback, computational ease and physical insight. The systems, are classified as conservative/nonconservative, dissipative, nondissipative, gyroscopic/nongyroscopic, according the type of loadings acting on them. Practical examples of each type of loading are discussed and the corresponding necessary and sufficient conditions of stability are obtained. This contribution in theory gives sound mathematical basis for further design. A controller design in a second-order form is carried out for vibration control of piezoelectric flexible beam. Utilizing the inherent advantages of piezoelectric beam structure and flexibility obtained from derived conditions, two approaches, Independent Modal Space Control and Direct output feedback control are used to design control gain matrix. The closed loop system using the new approach is shown to be stable even in the presence of indefinite system matrices. It is shown that to stabilize an unstable system and/or to enhance the damping, the gains obtained using the new approach are of smaller value than using the traditional approach. The wider applicability of MSO techniques is used in analyzing an aeroelastic flutter problem in matrix second order form. Sufficiency conditions for avoiding flutter in a given flight envelope are given. These conditions, if satisfied, can eliminate the need for cumbersome numerical procedures in flutter analysis. Furthermore, the MSO framework has also been applied to stability robustness of systems. The design algorithms are applied to design a controller for suppressing vibrations of flexible structures.;This dissertation has both theoretical as well as practical contributions. The contributions will have a significant impact on practical controller design as it provides a bridge between somewhat separated areas, theory and practice. |
