Controlled Vibration Suppression of Structural Telescopic Systems

Bending vibrations of telescopic systems of structural components are analyzed during extending and retracting motion. For a physical model, consisting of geometrically non-linear Timoshenko beams which are connected with some clearance in their contact areas, the governing boundary value problem is derived by applying Hamilton’s principle. Galerkin’s method based on admissible shape functions is used as a discretization procedure to generate a system of coupled, non-linear, time-varying, ordinary differential equations. Linearization about the static equilibrium position and model reduction by modal truncation for different telescopic lengths leads to a multiplicity of simple linear reduced models. On the basis of these models, an adaptive state regulator and an adaptive full state observer (Luenberger observer) are designed for vibration suppression using the Optimal Linear Quadratic Regulator (LQR). The adaptive controller and observer are applied to the significantly more complicated geometrically non-linear system with clearance so that the robustness of the controlled system can be studied during telescopic motions.