Robust pole placement in structures by the method of receptances

The problem of robust pole placement in structural vibration using receptance data is considered. Expressions are derived for the sensitivities of the eigenvalues to perturbations in the measurements and for robustness to measurement errors these sensitivity terms should be made as small as possible. A sequential multi-input state-feedback approach is described and by this procedure it is shown that a different eigenvalue may be assigned at each step without changing those eigenvalues assigned at previous steps. The columns of the force distribution matrix are chosen to excite easily the eigenvalue considered at the current step of the procedure. The sequential approach has the advantage of a characteristic equation that is linear in the control gains and is shown to be inherently more robust to measurement noise than the single-input method. The effects of sequential multi-input state feedback when combined with minimisation of eigenvalue sensitivity norms are investigated.