Block-decoupling vibration control using eigenstructure assignment

• Decoupling vibration control is presented for vibration isolation.
• The methodology is based on eigenstructure assignment using the method of receptances.
• It is suitable for use with systems having diagonal or banded mass matrices.
• The number of actuators may be reduced to the dimension of the bandwidth for banded system matrices.

A theoretical study is presented on the feasibility of applying active control for the purpose of vibration isolation in lightweight structures by block diagonalisation of the system matrices and at the same time assigning eigenvalues (natural frequencies and damping) to the chosen substructures separately. The methodology, based on eigenstructure assignment using the method of receptances, is found to work successfully when the eigenvalues of the open-loop system are controllable and the open- and closed-loop eigenvalues are distinct. In the first part of the paper results are obtained under the restriction that the mass matrix is diagonal (lumped). This is certainly applicable in the case of numerous engineering systems consisting of discrete masses with flexible interconnections of negligible mass. Later in the paper this restriction is lifted to allow bandedness of the mass matrix. Several numerical examples are used to illustrate the working of the proposed algorithm.