Internal Variable and Temperature Modeling Behavior of Viscoelastic Structures -- A Control Analysis
Silva, Luciano Afonso
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Most of the methodologies dealing with viscoelastic damping focused exclusively on the frequency dependence behavior of the material. Only a few looked into the temperature dependence of the model, although none of them has taken a more serious investigation on the control design subjected to temperature disturbances. The general purpose of this work is to develop and investigate structures with damping modeled by means of internal variables. Thermodynamic principles are used to develop models, which are based on a generalized Maxwell element. Initially, studies are conducted to verify how the method of reduced variables can be applied to account for temperature dependence, as well as to evaluate the number of internal variables necessary for good accuracy of material properties representation. Lumped and finite element models are characterized and validated against other methods. A constrained layer damping model is experimentally validated for many temperatures. A control analysis is carried out on the models with the purpose to identify the role played by the internal variables on the control design. The results show that moving the internal poles is very expensive in terms of control energy. It is also shown that it is not always possible to eliminate the internal coordinates in the reduced order model if the system is highly damped. The problem of having the internal pole moved is solved by applying partial pole placement. This technique shows similar performance as compared to the linear quadratic Gaussian regulator. The control designs are implemented and it is shown that good regulation can be achieved for a fixed temperature. It is further shown that the controller will lose its performance when the model is subjected to temperature changes. To investigate the behavior of the model under different temperatures, a linear temperature-dependent model is developed, which clearly shows how the temperature affects the time response of the model. This model is used as a baseline to develop an adaptive and a time-varying controllers. With the aid of the shift factor, the eigenvalue variation with temperature is used as a time-varying function in the design. The results show that good track performance and regulation can be achieved with a control law that is capable of compensating for temperature variations.
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