The primary objective is to investigate the applicability of spectral methods for designing feedback controllers for a closed loop system with an input shaper with time delays. The shaper is included in the feedback loop in order to pre-compensate low-damped oscillatory modes of a flexible subsystem. However, after inserting a shaper into the feedback loop, the closed loop dynamics becomes infinite dimensional. A robust controller design then requires guaranteeing that all the infinitely many poles of the closed loop system will safely be located in the left half of the complex plane. Besides, the closed loop dynamics need to be sufficiently fast in order to take over and keep filtering properties of the input shaper. For the spectral design of the controller, the recently developed spectral abscissa minimization approach for interconnected time delay systems is applied. The presented methods are tested on a case study simulation example, which is a multi-degree of freedom mechanical system.
This is joint work with Dan Pilbauer (KU Leuven) and Tomas Vyhlidal (Czech Technical University in Prague)