Lyapunov based Time Varying Subregional Control of System with Distributed Parameters

An increased size of optical reflective elements, e.g., in the trend of large telescopes, requires thin structures to maintain a little mass for regaining performance in a change of orientation for example. However, exciting such a compliant structure leads to vibrations. Often, the whole surface is actively damped, although only a subregion might be exposed. Thus, a state feedback for the control of a subregion is derived by utilizing a Lyapunov function, deduced from mechanical energy. The method is then extended towards a time varying subregion. A simulation of a vibrating thin circular plate shows that the proposed method outperforms a linear quadratic regulator and that the time varying feedback law renders the closed loop stable.