Efficient Newton method for optimal viscous dampers design

Passive control is a known method for vibrations damping in many mechanical systems, including civil structures. The simplicity and reliability of passive damping devices makes them a worthy candidate in many practical problems. However, despite of its practical simplicity, the optimal design of passive controller is quite hard computational problem. In this work, an enhanced optimal viscous passive dampers design method is proposed. The optimization is done with relation to performance index consists of ||H||₂ system norm and quadratic gains norm. An algorithm is suggested for the look after a candidate optimum. It is based on Newton's optimization method with a new and effective calculation method for the Hessian matrix. Numerical tests of the suggested method shows a very fast convergence rate with relation to known ones.