Modeling, analysis, and control of flexible and smart structures

Smart structure has become an increasingly common term describing a structure embedded or bonded with a large number of light weight active electro-mechanical sensors and actuators. In this thesis, we consider the dynamic modeling and control of flexible structures with piezoceramic actuators. The proposed model has the following advantages: it correctly predicts the frequency response of the system close to the actuator and away from it, it can be represented in a state-space form, it is based on the natural modes of vibration of the system, and experimental damping can be easily included in the model.; In this thesis, we consider controller design based on the concept of passivity. Passivity based control has long been used in the vibration control of flexible structures. These controllers provide robust stability even in the presence of unmodeled dynamics of the system. For an input/output pair of a flexible structure to be passive, the input map and the output map have to be the dual of each other. This requires the collocation of an actuator and a rate sensor. Furthermore, the structure should have equal number of inputs and outputs (i.e., the system should be square).; Due to their lower weight, simpler implementation, cheaper cost etc., typical flexible structures frequently have more sensors than actuators. Therefore, the passive controller can at best utilize only a subset of the available sensors. We propose a design procedure for synthesizing a fictitious passive output as a linear combination of all the available outputs subject to some additional performance considerations. The problem of obtaining the synthesized passive output is cast as a set of Linear Matrix Inequalities (LMIs) which can be efficiently solved by the LMI toolbox in Matlab. In the case of flexible structures, we apply this procedure with the assumption that the sensors provide both the position and velocity information. We show that the passive controllers can be implemented without the use of velocity information.; We present experimental validation of our model and the proposed control strategy using the single-link flexible beam test-bed at the Control Laboratory for Mechanical Structures. We show that by using synthesized passive outputs in addition to naturally occurring passive outputs, we can enhance the overall system performance.