Regularization-based output-trajectory preshaping of a high-speed flexiblebeam against ill-conditioned stable inversion

In this paper we consider the problem of mitigating actuator high-frequency saturation due to ill-conditioned stable inversion for exact output tracki ng control of a high-speed flexible beam. For this purpose, the regularizat ion-based frequency shaping approach is used to preshape the reference outp ut-trajectory so that the calculated torque through stable inversion is smo oth enough without high-frequency saturation. The output-trajectory preshap ing task is formulated by the regularized output least square problem, from which a regularization-based preshaping filter is well-defined explicitly. To make the regularization-based preshaping approach viable, the practical implementation of a regularization-based preshaping filter, including the specification of the stabilizing functional and the choice of the regulariz ation parameter, is discussed analytically. The time-domain computation for an output-trajectory preshaping task is also addressed. Numerical simulati on studies are presented to assess the validity of the method proposed in t his paper.