Content area
Abstract
This research focuses on the applications of center manifold and normal form theories to design nonlinear control strategies for vibration suppression in flexible structures. The proposed method utilizes the coupling terms in the set of the equations of the system to design the nonlinear control strategy.
We show that center manifold and normal form theories provide a systematic and powerful means for controlling oscillatory systems. Using normal form we develop a new Modal Coupling Controller (MCC) which utilizes the concept of energy transfer between the plant and controller. The transfer of energy between the systems is thoroughly investigated and the general form of the coupling terms resulting in maximum transfer of energy are derived. We also extend the results obtained in the study of free vibration and introduce a new approach for control of forced vibrations.
In earlier research the center manifold theory was solely used in the study of feedback stabilization in nonlinear systems with eigenvalues on the imaginary axis (degenerate linearization). In this dissertation we extend the previous work to regulation problems and introduce a method to select the optimal controller parameters.
To corroborate the theoretical work, the proposed controller technique is applied to an experimental flexible beam with piezo-ceramic actuators. The comparison of theoretical and experimental results indicate the validity of the research.
