Funnel control for overhead crane model. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Berger, Thomas; Lê, Huy Hoàng; Reis, Timo
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800041
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: We consider an overhead crane whose control variables are the length of the rope and force/velocity at the gantry. The output consists of the position of the load. The objective is to design a closed‐loop tracking controller which also takes into account the transient behavior. First we show that this system has no well‐defined relative degree, which unfortunately does not allow to apply established methods for adaptive control to achieve the objective. To circumvent this problem, we design a dynamic state feedback which results in a system with relative degree four. Thereafter, we apply a funnel controller to this feedback system. We show that our approach can be used to move loads from one to another given position in the situation where there are several obstacles which have to be circumnavigated.