Nonstationary Robust Control of Flexible Structures Using Frequency-Shaped Time-Varying Criterion Function

Abstract

In the positioning control of flexible structures, it is important to develop a nonstationary robust control method for nonstationary uncertainty perturbations. At the same time, it is important to take account of influences of such unstructured uncertainties as ignored high-order vibration modes in order to suppress the spillover instability. This paper presents a nonstationary robust control method for flexible structures taking account of the structured and unstructured uncertainties influences by using a frequency-shaped time-varying criterion function. In order to avoid influences of unstructured uncertainties, in this method, a low-pass property is given to the controller from a frequency-shaped part of the criterion function. Moreover, an integrated design of both the H₂ control for little influences of structured uncertainties and the H_∞ control for large influences is carried out by applying a time-varying part of the criterion function.
In this paper, as an example, a positioning control problem of flexible inverted pendulum possessing infinity vibration modes is adopted. In this problem, the influences of structured uncertainties of Coulomb friction and parameter variations are generally severer in the period after positioning than in the period during positioning. In comparison with the former methods proposed by the authors, the usefulness of the present nonstationary robust control was verified by numerical calculations and experiments.