Robust and Minimum Norm Partial Pole Assignment in Vibrating Structures with Aerodynamics Effects

The paper considers a practical solution of the partial eigenvalue assignment problem in a cubic matrix polynomial arising from modeling of vibrating structures with aerodynamics effects, with a special attention to numerically robust feedback design and obtaining feedback matrices with minimum norms. To this end, a direct parametric method that works exclusively with the coefficient matrices of the cubic polynomial without requiring transformation to a standard state-space form is proposed first. The computational requirements of the method are minimal -all thatare needed are solutions of a small Sylvester equation and a small linear algebraic system, both of the same order as the number of eigenvalues to be reassigned. The parametric nature of the method is then exploited to deal with the issues of robustness and minimum feedback norms, by formulating the problem as an unconstrained optimization problem. The numerical effectiveness of the method is demonstrated by results of a numerical experiment performed on simulated data obtained from the Boeing Company.