Partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback

• A method for partial eigenstructure assignment is proposed for good dynamic performance.
• It uses acceleration and displacement feedback.
• It allows the control matrix to be specified beforehand and thus easy implementation of control strategy in practice.
• It leads to small-norm solutions of feedback gain matrices.

A new method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper. Firstly, a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged. Secondly, based on this condition, an algorithm for determining the required control gain matrices of acceleration and displacement feedback, which assign the desired eigenstructure, is developed. This algorithm is easy to implement, and works directly on the second-order system model. More importantly, the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices. Finally, some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm.