Funnel control for nonlinear systems with known strict relative degree

Berger, Toby; Lê, Huy Hoàng; Reis, Timo

doi:10.1016/j.automatica.2017.10.017

Cited by 159 publications

(252 citation statements)

References 30 publications

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“…We may show the following result: The generator (2.1) of the new reference signal is incorporated as a dynamic part into the controller design and the funnel controller from [18] is applied to system (1.1) with new output y new . The final controller design is given by:…”

Section: Trackability and Controllermentioning

confidence: 99%

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Funnel control for linear non‐minimum phase systems

Berger

2019

Proc Appl Math and Mech

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We consider tracking control for linear non-minimum phase systems with known relative degree. For a given reference signal we design a low-complexity controller which achieves that the tracking error evolves within a prescribed performance funnel. We present a novel approach where a new output is constructed, with respect to which the system has a higher relative degree, but the unstable part of the internal dynamics is eliminated. Using recent results in funnel control, we then design a controller for this new output, which also incorporates a new reference signal. The original output stays within a prescribed performance funnel around the original reference trajectory and all signals in the closed-loop system are bounded.We consider linear systems given bẏ( 1.1) where x(0) = x 0 ∈ R n , A ∈ R n×n and B, C ∈ R n×m . We assume that (1.1) has strict relative degree r ∈ N, that isWe do not assume that (1.1) is minimum phase or, equivalently, its zero dynamics (cf. [1][2][3][4]) are asymptotically stable, which would mean that rk A−λIn B C 0

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Section: Trackability and Controllermentioning

confidence: 99%

“…A suitable redefinition of the reference signal then guarantees that the funnel controller developed in the recent work [18] may be applied. A suitable redefinition of the reference signal then guarantees that the funnel controller developed in the recent work [18] may be applied.…”

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confidence: 99%

Funnel control for linear non‐minimum phase systems

Berger

2019

Proc Appl Math and Mech

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“…The solution to this control objective was proposed in [1], see also the survey [2]. more general feedback gain [3], input constraints [4][5][6][7][8], higher relative degree [9][10][11][12][13], for differential-algebraic equations [14,15] and is also included in the engineering textbook [16]. more general feedback gain [3], input constraints [4][5][6][7][8], higher relative degree [9][10][11][12][13], for differential-algebraic equations [14,15] and is also included in the engineering textbook [16].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic tracking with funnel control

Trenn

2019

Proc Appl Math and Mech

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Funnel control is a strikingly simple control technique to ensure model free practical tracking for quite general nonlinear systems. It has its origin in the adaptive control theory, in particular, it is based on the principle of high gain feedback control. The key idea of funnel control is to chose the feedback gain large when the tracking error approaches the prespecified error tolerance (the funnel boundary). It was long believed that it is a theoretical limitation of funnel control not being able to achieve asymptotic tracking, however, in this contribution it will be shown that this is not the case.

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“…In a recent paper by Berger et al a funnel controller for nonlinear systems with arbitrary known relative degree is developed, which resolves the longstanding open problem of how to handle relative degree higher than one in high‐gain adaptive control, cf the works Ilchmann and Ryan and Morse . Earlier works suggested a “backstepping” procedure in conjunction with an input filter, see the works of Ilchmann et al, or a bang‐bang funnel controller, see the work of Liberzon and Trenn .…”

Section: Introductionmentioning

confidence: 99%

“…Earlier works suggested a “backstepping” procedure in conjunction with an input filter, see the works of Ilchmann et al, or a bang‐bang funnel controller, see the work of Liberzon and Trenn . Drawbacks are the backstepping procedure in the works of Ilchmann et al that is quite complicated and impractical since it involves high powers of a gain function that typically takes large values, cf Section 4.4.3 in the work of Hackl, and the approaches in the works of Berger et al and Liberzon and Trenn that require availability of the output derivatives, which means, in practice, that measurements have to be differentiated. The latter is an ill‐posed problem particularly in the presence of noise, see, eg, Section 1.4.4 in the work of Hackl …”

Section: Introductionmentioning

confidence: 99%

The funnel pre‐compensator

Berger

Reis

2018

Intl J Robust & Nonlinear

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Summary We introduce the funnel pre‐compensator as a novel and simple adaptive pre‐compensator of “high‐gain type”. We show that this pre‐compensator is feasible for a large class of signal pairs, which satisfy a certain relationship. We show that the funnel pre‐compensator guarantees prescribed transient behavior of the compensator error, it is of low complexity and inherently robust since its design is model‐free. As an application in adaptive control of nonlinear systems, a cascade of funnel pre‐compensators is exploited to obtain an artificial output with explicitly known derivatives, which tracks the system output with prescribed transient behavior. In some important cases the interconnection of the system with the pre‐compensator cascade is shown to have input‐to‐state stable internal dynamics. This guarantees feasibility of a novel funnel controller that consists of a funnel pre‐compensator cascade in conjunction with a recently developed funnel controller for systems with arbitrary relative degree. We illustrate the application of this interconnection for some mechanical systems.

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Funnel control for nonlinear systems with known strict relative degree

Cited by 159 publications

References 30 publications

Funnel control for linear non‐minimum phase systems

Funnel control for linear non‐minimum phase systems

Asymptotic tracking with funnel control

The funnel pre‐compensator

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