Dimension reduction and control of nonlinear distributed parameter systems

Controlling torsional vibrations of nonlinear driven distributed parameter systems requires a good understanding of the dynamics as well as low dimensional models. Singular value analysis and proper orthogonal decomposition are employed for dimension analysis and dimension reduction of a one-dimensional continuous system. The structure of an active damping system based on the reduced model is presented and the theoretical findings are verified with an experimental set-up of an extremely slender torsional string. Considerable improvements of the system dynamics are observed.