Summary
We present a systematic control design method for achieving non-collocated vibration suppression, with a focus on multi-frequency suppression. The objective is to suppress vibrations of various frequencies at a specific location while maximizing the closed-loop stability margin. This objective is translated into an optimization problem of minimizing the spectral abscissa of the closed-loop, subject to zero-location constraints. A simple output feedback controller is insufficient for multiple frequencies due to limited free parameters in the non-collocated setting. To address this, we propose a dynamic feedback controller with intentional delays applied to the measured output signal. By incorporating multiple delays and increasing the order of the dynamic controller, we aim to increase the number of free parameters for control. The design methodology involves remodelling the system of equations as a delay-differential algebraic equation (DDAE) and minimizing the spectral abscissa subject to zero-location constraints. Constraint elimination is used to impose the zero-location constraints, which is non-trivial in the case of dynamic feedback. We demonstrate that with the additional delays and dynamic feedback, we can achieve multi-frequency vibration suppression and closed-loop stabilization with a sufficient stability margin, even in cases where simple static output feedback is not feasible.
