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Dissertation zugänglich unter
URN: urn:nbn:de:gbv:18-97118
URL: http://ediss.sub.uni-hamburg.de/volltexte/2019/9711/


Funnel control for systems with known vector relative degree

Funnel-Control für Systeme mit bekanntem Vektorrelativgrad

Le, Huy Hoang

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 Dokument 1.pdf (1.839 KB) 


Freie Schlagwörter (Englisch): Control theory , Closed-loop control , Differential-algebraic systems
Basisklassifikation: 30.10 , 31.44
Institut: Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Dissertation
Hauptberichter: Reis, Timo (Prof. Dr.)
Sprache: Englisch
Tag der mündlichen Prüfung: 18.04.2019
Erstellungsjahr: 2018
Publikationsdatum: 29.04.2019
Kurzfassung auf Englisch: The present dissertation examines funnel control which is a type of output feedback control for system with known vector relative degree. The goal of funnel control is to construct a simple controller for tracking the errors, which are the gap between system outputs y(t) and an arbitrary given smooth enough reference signals y_{ref}(t), within a prespecified performance funnel, and therefore, all involved quantities are bounded. This study addresses a number of questions concerned funnel control problem.

Firstly, it provides a normal form for linear differential-algebraic systems. A new definition of vector relative degree is proposed and based on that a normal form for linear differential-algebraic systems is introduced. The advantage of this normal form is not only placed on its simplicity but also the ability to design a new funnel controller tracking the error, e(t)=y(t)-y_{ref}(t), within a prespecified performance funnel.

Secondly, this research proposes a feasible funnel control law for system with higher strict relative degree. We consider tracking control for non-linear multi-input, multi-output systems which have arbitrary strict relative degree and input-to-state stable internal dynamics. To this end, we introduce a new controller which involves the first $r-1$ derivatives of the tracking error, where r is the strict relative degree of the system. We derive an explicit bound for the resulting input and discuss the influence of the controller parameters. We further present some simulations where our funnel controller is applied to a mechanical system with higher relative degree and a two-input, two-output robot manipulator. The controller is also compared with other approaches.

Moreover, we contribute a feasible funnel controller for non-linear multi-input, multi-output systems with input-to-state stable internal dynamics and known vector relative degree r=(r_1,r_2,...,r_m). To address the funnel control problem, a new funnel controller involving the first r_i-1 of the derivatives of each i-th element of the tracking error e(t), is proposed. Furthermore, simulations are presented to demonstrate the work of this funnel controller in a number of examples.

As an application, we consider an overhead crane model whose control variables are the velocities of trolley and rope length respectively. The position of the load is considered as the output of the system. The objective is to design a closed-loop tracking controller which also takes into account the transient behaviour. Unfortunately, this system is shown that has no well-defined vector relative degree. Therefore, this does not allow us to apply established methods directly for adaptive control to achieve the objective. To overcome this problem, a dynamic state feedback is proposed, which results in a system with strict relative degree four, and then we can apply a funnel controller to this feedback system. Consequently, we made a simulation to 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.

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