Partial eigenvalue assignment for structural damage mitigation

In partial eigenvalue assignment, not all eigenvalues of the open loop system matrix are modified through a multiple input state or output feedback controller. This freedom available to assign selected eigenvalues of the closed loop system matrix has been widely used in design contexts such as to eliminate spillover effects in structural control problems. Similar approach is also required to modify damping and/or stiffness characteristics in selected eigenmodes of a damaged structure. When an external force acts on the damaged structure, partial eigenvalue assignment in this fashion will attempt to use minimal control effort and keep the structure active with safe operation. In this paper, a new approach to partial eigenvalue assignment and its application to structural damage mitigation are presented. A three mass spring-damper model with damage in one of the springs is illustrated with damping modifications at specific eigenmodes. The procedure is repeated for a second example, which is a cantilever beam modeled using two inputs and 10 state variables.