Suppression of undesired inputs of linear systems by eigenspace assignment

In this paper, a method using output feedback is proposed to suppress the response of linear systems to undesired inputs and, in particular, to reduce the vibration response of flexible structures to these inputs. This method does not need to measure undesired inputs (or external forces). The analysis assumes that the location of the undesired inputs are known, although the general time dependency is unknown. The feedback gain matrix is calculated to assign the eigenvalues and left-hand eigenvectors of the closed-loop system to specified values. The effect of the undesired inputs on a closed-loop system can be altered or significantly reduced by properly choosing the left-hand eigenvectors of the system. The stability of the control system is guaranteed by properly choosing the output matrix, which can decouple the controlled modes from the uncontrolled modes. An example of forced vibration of a simple flexible structure is presented to demonstrate the proposed method.

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