Abstract
Pole assignment problems are special algebraic inverse eigenvalue problems. In this paper, we research numerical methods of the robust pole assignment problem for second-order systems. The problem is formulated as an optimization problem. Depending upon whether the prescribed eigenvalues are real or complex, we separate the discussion into two cases and propose two algorithms for solving this problem. Numerical examples show that the problem of the robust eigenvalue assignment for the quadratic pencil can be solved effectively.
Highlights
Pole assignment problems are special algebraic inverse eigenvalue problems 1, 2
The properties of systems of secondorder differential equation are governed by its associated quadratic eigenvalue problem QEP
Consider the following second-order matrix differential equation: Mzt Czt Kz t 0, 1.1 where the dots denote differentiation with respect to time, and M, C, and K are n × n real symmetric matrices; M is positive definite denoted by M > 0
Summary
Pole assignment problems are special algebraic inverse eigenvalue problems 1, 2. It is desirable to choose the feedback to ensure that the eigenstructure of closed-loop system is as robust, or insensitive to perturbation in the system matrices M, C − BFT , and K − BGT , as possible to the following inverse eigenvalue problem, known as the robust quadratic eigenvalue assignment problem. Datta and Sarkissian 6 proposed a direct partial modal approach to solve the partial eigenvalue assignment problem for second-order systems. It is “direct,” because the solutions are obtained directly in the second-order system without any types of reformulations; It is “partial modal,” because only a part of spectral data is needed for the solution.
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