OPTIMAL DAMPING OF VIBRATIONS IN MULTIBODY SYSTEMS THROUGH EQUIVALENT FRICTION CONTROL LAWS

摘要

In the paper modelling and optimization of friction laws and energy exchange processes in multibody systems are considered. The multibody systems are regarded as chains of absolutely rigid bodies with compliance and friction concentrated at the connections. It is proposed to control the vibration level of such systems by introducing equivalent frictional forces. Such an approach enables modelling and optimization of passive and semi-active damping methods together with active control of vibrations in multibody systems within a unified framework. In particular, the equivalent friction laws can be regarded as controls minimizing deviations of the multibody system motion from the reference trajectory and used for total compensation of links cross interactions and stabilization of fast modes. The corresponding optimal vibration control problem is formulated and reduced to a constrained optimization one in order to determine the optimal friction laws dissipating the oscillation energy. For linear vibration control problems numerical methods based on solving matrix Lyapunov and Riccati equations are discussed. Additionally, an approach employing a global search mechanism, the genetic algorithm, and parallel processing techniques, to alleviate the problem of computational burden, is proposed to solve general control problems for optimal vibration damping. Two examples are presented in order to illustrate the proposed approach.