Dynamic modeling of a smart materials robot

Abstract

Three dynamic models of a smart materials robot are presented. First, Hamilton's approach is adopted to derive an accurate model expressed in partial differential equations, which is too complicated to be applicable in engineering practice. Based on the partial differential equations model, the assumed modes method and the finite element method are employed to derive two finite dimensional models in the forms of ordinary differential equations, which are readily usable for controller design. All of the models show that the model of a smart materials robot cannot be simply taken to be the same as that of a pure flexible robot, and the parameters of the smart materials robot should be properly chosen to avoid the divergent open-loop responses. For completeness, both mechanical dynamics and electrical dynamics are explicitly included in all of these models, although it is shown analytically and numerically that the latter dynamics can be omitted in engineering applications. Comparative studies between the assumed modes method model and the finite element method model are carried out by numerical simulations in both time and frequency domains to verify the correctness of the models and to analyze the performance of the system.