| This dissertation is concerned with the relevant research in developing finite dimensional indirect adaptive schemes to control vibrations in flexible smart structures based on the finite element approximation of the infinite dimensional system. The advantage of this type of modeling is that the dominant modes of vibrations wherein the total energy is concentrated are accommodated thereby avoiding the so-called "spillover" phenomenon. Further, the mass, stiffness and damping coefficients associated with each element appear explicitly in the model facilitating the derivation of the ARMA parametric representation which is suitable for on-line estimation of the structural parameters.; The state-space representation of the finite dimensional model is used to design an indirect linear quadratic self tuning regulator algorithm using the parameter estimation, indicated above. Further, a method to choose the control and state weighting matrices (required to design the controller) to yield a stable closed-loop system, is presented. Simulation results demonstrating the performance of the adaptive control system are presented.; Another algorithm based on the model reference technique is also developed by considering the discrete time approximation of the finite dimensional model. This control algorithm in conjunction with the parameter estimation constitute an indirect model reference adaptive control system. Simulation results are presented to demonstrate the effect of the reference model parameters, which may impose certain constraints on the force requirements causing actuator saturation and thereby affecting the stability of the closed-loop system.; In order to overcome the problem of using bulky and expensive sensors to measure transverse displacement and velocity, a new spatial recursive technique to estimate these variables alternatively by using a distributed set of (measured) strain data, is developed. Relevant algorithm enables the use of smart materials to sense the strain developed at various locations along the length of the structure leading to the development of flexible smart structures. Experimental results on the personal computer based control of vibrations in an aluminum beam using patches of polyvinyldene fluoride (PVDF), and lead zirconate titanate (PZT) as sensors and control actuators respectively, are furnished to demonstrate the feasibility of real-time implementation of the above mentioned control algorithms. |
