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zbMATH Open
Article . 2013
Data sources: zbMATH Open
SIAM Journal on Control and Optimization
Article . 2013 . Peer-reviewed
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DBLP
Article . 2013
Data sources: DBLP
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Funnel Control for Systems with Relative Degree Two

Funnel control for systems with relative degree two
Authors: Christoph M. Hackl; Norman Hopfe; Achim Ilchmann; Markus Mueller 0002; Stephan Trenn;

Funnel Control for Systems with Relative Degree Two

Abstract

Summary: Tracking of reference signals \(y_{\text{ref}}(\cdot)\) by the output \(y(\cdot)\) of linear (as well as a considerably large class of nonlinear) single-input, single-output systems is considered. The system is assumed to have strict relative degree two with (weakly) stable zero dynamics. The control objective is tracking of the error \(e=y-y_{\text{ref}}\) and its derivative \(\dot{e}\) within two prespecified performance funnels, respectively. This is achieved by the so-called funnel controller \(u(t)=-k_0(t)^2e(t)-k_1(t)\dot{e}(t)\), where the simple proportional error feedback has gain functions \(k_0\) and \(k_1\) designed in such a way to preclude contact of \(e\) and \(\dot{e}\) with the funnel boundaries, respectively. The funnel controller also ensures boundedness of all signals. We also show that the same funnel controller (i) is applicable to relative degree one systems, (ii) allows for input constraints provided a feasibility condition (formulated in terms of the system data, the saturation bounds, the funnel data, bounds on the reference signal, and the initial state) holds, (iii) is robust in terms of the gap metric: if a system is sufficiently close to a system with relative degree two, stable zero dynamics, and positive high-frequency gain, but does not necessarily have these properties, then for small initial values the funnel controller also achieves the control objective. Finally, we illustrate the theoretical results by experimental results: the funnel controller is applied to a rotatory mechanical system for position control.

Country
United Kingdom
Keywords

Adaptive or robust stabilization, output feedback, Stabilization of solutions to ordinary differential equations, gap metric, input saturation, linear systems, robustness, tracking, 510, functional differential equations, Linear systems in control theory, transient behavior, Control of mechanical systems, Sensitivity (robustness), relative degree two, nonlinear systems, funnel control, Control/observation systems governed by ordinary differential equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
111
Top 1%
Top 1%
Top 10%
bronze