Robust Control of a Lightweight Structure for Digital Fabrication

Abstract

For a material efficient construction process of lightweight concrete shells, tensioned cable nets can be used as a supporting formwork. In order to guarantee the mechanical stability of the shells, tight tolerances in their form need to be met. To this end, methods have recently been proposed to readjust the form of the cable net on the construction site. This paper proposes a novel view on the cable net model as a dynamical system and derives robust control approaches based on H∞ and μ synthesis. Both approaches can account for input uncertainties and external disturbances. The μ controller additionally is robust against the uncertain model parameters, which makes their precise identification unnecessary. The μ synthesis also provides a priori bounds on the allowable fabrication tolerances of the cable net in order to guarantee robust performance of the closed-loop system. The resulting LTI controllers can be applied to the system without expert knowledge about the system model or the underlying optimization. The effectiveness of the controllers is demonstrated in numerical experiments.