Research ArticleRobust pole assignment using velocity-acceleration feedback for second-order dynamical systems with singular mass matrix

- The robust pole assignment problem by velocity-acceleration feedback for descriptor second-order system is solved.
- The necessary and sufficient conditions that ensure solvability are derived.
- Eigenstructure assignment problem for descriptor system is solved, then the robust solution is obtained.
- Problem is tackled in second-order form without transformation to first-order form.
- Illustrated examples are introduced to demonstrate the effectiveness of solution.
- Infinite eigenvalues for descriptor second-order system are relocated by finite one.

In this paper the robust pole assignment problem using combined velocity and acceleration feedback for second-order linear systems with singular mass matrix is illustrated. This is promising for better applicability in several practical applications where the acceleration signals are easier to obtain than the proportional ones. First, the explicit parametric expressions of both the feedback gain controller and the eigenvector matrix are derived. The parametric solution involves manipulations only on the original second-order model. The available degrees of freedom offered by the velocity-acceleration feedback in selecting the associated eigenvectors are utilized to improve robustness of the closed-loop system. Straight-forward computational algorithms are introduced to demonstrate the effectiveness of the proposed approach. These algorithms are applicable for a dynamical system with mass matrices that can be either singular or nonsingular. Numerical examples are provided to illustrate the application of the proposed procedure.