Robust pole placement for second-order linear systems using velocity-plus-acceleration feedback

This paper considers the robust pole assignment problem using combined velocity and acceleration feedbacks for matrix second-order linear systems. The necessary and sufficient conditions which ensure solvability are derived. Based on recently developed parametric solution to the eigenstructure assignment problem by velocity-plus-acceleration feedback, a new technique is described to perform robust pole placement for second-order systems. The available degrees-of-freedom offered by the velocity-plus-acceleration feedback in selecting the associated eigenvectors are utilised 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. Finally, several examples are introduced to demonstrate the effectiveness of the proposed approach.