Concurrent Active Control and Dynamic Structural Modification in the Design and the Optimization of Vibrating Systems

Abstract

The simultaneous optimization of the mechanical design and of the controller in vibrating systems is of great importance in order to improve the system dynamic performances. Due to the mutual interaction, the two tasks should be performed in a concurrent way. In order to overcome the limitations of traditional decoupled approaches, this paper proposes a method for the simultaneous synthesis of the state feedback controller and of the modifications of the inertial and elastic parameters. The performance optimization is obtained by assigning some desired eigenvectors and eigenvalues to the controlled systems, so that a desired dynamic behaviour is featured. Indeed, the eigenvalues determine damping and speed of response, while the eigenvectors set the sensitivity of the eigenvalues and the spatial shape of the vibration. By properly combining active control and structural modification, the capability to assign the desired eigenpairs is enlarged since passive control shapes the allowable subspace so that the desired eigenpairs can be assigned through active control. The numerical results show the effectiveness of the proposed method and the great potential advantages of the concurrent use of structural modification and active control over traditional design methods.