Truncation Problems in the Dynamics and Control of Flexible Mechanical Systems

Abstract The distributed deformation coordinates of flexible mechanical systems are commonly discretizised by means of a truncated series expansion (Ritz-method). After a short explanation of the governing equations, a mathematical justification of the truncation is given applying singular perturbation theory. The truncated model is compared with the exact, infinite-dimensional model. Easy to evaluate error bounds for the substantial eigenvalues are developped. It is shown under which conditions the control system design basing on the truncated model is admissible. Effects of control spillover are discussed. The results are corroborated by the application to the test model of a flexible manipulator arm.