Eigenstructure assignment for second-order systems using velocity-plus-acceleration feedback

This paper presents an approach for solving the eigenstructure assignment problem using velocity-plus-acceleration feedback for second-order dynamic systems. In this work, the necessary and sufficient conditions that ensure solvability for second-order systems are derived. A complete parametric solution to the feedback gain controller that describes the available degrees of freedom offered by the velocity-plus-acceleration feedback in selecting the associated eigenvectors from an admissible class is developed. These freedoms can be utilized to improve robustness of the closed-loop system. The main advantage of the described approach is that the problem is tackled in the second-order form without transformation into the first-order form, and the computation is numerically stable as it uses only the singular value decomposition and simple matrix transformation. Finally, numerical examples are introduced to demonstrate the effectiveness of the proposed approach.