Modeling for control of an inflatable space reflector, the nonlinear 1-D case

Abstract

Modeling for control of an inflatable space reflector, the nonlinear 1-D case Voß, T.; Scherpen, J.M.A.; Onck, P.R. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Abstract-In this paper we develop a mathematical model of the dynamics for an inflatable space reflector, which can be used to design a controller for the shape of the inflatable structure. Inflatable structures have very nice properties, suitable for aerospace applications. We can construct e.g. a huge light weight reflector for a satellite which consumes very little space in the rocket because it can be inflated when the satellite is in the orbit. So with this technology we can build inflatable reflectors which are about 100 times bigger than solid ones. But to be useful for telescopes we have to actively control the surface of the inflatable to achieve the desired surface accuracy. The starting point of the control design is modeling for control, in the case port-Hamiltonian (pH) modeling. We will show how to derive a nonlinear infinite dimensional pH model of a 1-D Euler-Bernoulli beam with piezo actuation. In the future we will also focus on 2-D models.

A port-Hamiltonian model of liquid sloshing in moving containers and application to a fluid-structure system

“…Several contributions were presented in the last years for modeling beams as port-Hamiltonian systems (Cardoso-Ribeiro et al, 2016; Macchelli et al, , 2009Voss et al, 2008aVoss et al, , 2008bVoss and Scherpen, 2014;Morris and Ozer, 2013)). These included linear (Voss et al, 2008a) and non-linear (Voss et al, 2008b) Euler-Bernoulli beams, as well as the Timoshenko beam theory Voss and Scherpen, 2014). Here, a pHs model of a linear Euler-Bernoulli beam with distributed piezoelectric actuators is used (as in Cardoso-Ribeiro et al, 2016), for sake of simplicity.…”

“…Several contributions were presented in the last years for modeling beams as port-Hamiltonian systems [33,36,37,38,39,40,41,42]). These included linear [39] and non-linear [40] Euler-Bernoulli beams, as well as the Timoshenko beam theory [36,41].…”

“…Several contributions were presented in the last years for modeling beams as port-Hamiltonian systems [33,36,37,38,39,40,41,42]). These included linear [39] and non-linear [40] Euler-Bernoulli beams, as well as the Timoshenko beam theory [36,41]. Here, a pHs model of a linear Euler-Bernoulli beam with distributed piezoelectric actuators is used (as in [33]), for sake of simplicity.…”