High‐gain control without identification: a survey

Abstract. We consider electrical circuits containing linear resistances, capacitances, inductances. The circuits can be described by differential-algebraic input-output systems, where the input consists of voltages of voltage sources and currents of current sources and the output consists of currents of voltage sources and voltages of current sources. We generalize a characterization of asymptotic stability of the circuit and give sufficient topological criteria for its invariant zeros being located in the open left half-plane. We show that asymptotic stability of the zero dynamics can be characterized by means of the interconnectivity of the circuit and that it implies that the circuit is high-gain stabilizable with any positive high-gain factor. Thereafter we consider the output regulation problem for electrical circuits by funnel control. We show that for circuits with asymptotically stable zero dynamics, the funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular that the transient behaviour of the output error can be prescribed and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illustrated by a simulation of a discretized transmission line.

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“…Altogether, we have that (4.6) is valid. We show that (ii) implies (4.6): From (4.7) we have 8) and by (4.5) we obtain…”

Section: Corollary 42 (Kernel and Generalized Eigenvalues) Let Se −mentioning

confidence: 55%

“…The aim is to achieve tracking of a reference trajectory by the output signal with prescribed transient behavior. The funnel controller resolves several problems of other control strategies such as the classical adaptive high-gain controller; see the survey [8].…”

Section: Funnel Control In This Section We Consider Funnel Control Fmentioning

confidence: 99%

Zero dynamics and funnel control for linear electrical circuits

Berger

Reis

2014

Journal of the Franklin Institute

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“…Further drawbacks are that (6.2) does not tolerate mild output perturbations, tracking would require an internal model and, most importantly, transient behaviour is not taken into account. These issues are discussed for ODE systems (with strictly proper transfer function of strict relative degree one and asymptotically stable zero dynamics) in the survey [22]. To overcome these drawbacks, the concept of "funnel control" is introduced (see [22] and the references therein): For any function ϕ belonging to…”

Section: Funnel Controlmentioning

confidence: 99%

Zero dynamics and funnel control of general linear differential-algebraic systems

Berger

2016

ESAIM: COCV

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We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the zero dynamics and tracking control. We use the concepts of autonomous zero dynamics and (E, A, B)-invariant subspaces to derive the so called zero dynamics form -which decouples the zero dynamics of the system -and exploit it for the characterization of system invertibility. Asymptotic stability of the zero dynamics is characterized and some implications for stabilizability in the behavioral sense are shown. A refinement of the zero dynamics form is then exploited to show that the funnel controller (that is a static nonlinear output error feedback) achieves -for a special class of right-invertible systems with asymptotically stable zero dynamics -tracking of a reference signal by the output signal within a pre-specified performance funnel. It is shown that the results can be applied to a class of passive electrical networks.

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“…Funnel control itself is based on ideas from high-gain control and λ-tracking (see for example the survey [2]). There have been several extensions of the funnel controller, e.g.…”

Section: Introductionmentioning

confidence: 99%

The bang-bang funnel controller

Liberzon

Trenn

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-A bang-bang controller is proposed which is able to ensure reference signal tracking with prespecified time-varying error bounds (the funnel) for nonlinear systems with relative degree one or two. For the design of the controller only the knowledge of the relative degree is needed. The controller is guaranteed to work when certain feasibility assumptions are fulfilled, which are explicitly given in the main results. Linear systems with relative degree one or two are feasible if the system is minimum phase and the control values are large enough.

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High‐gain control without identification: a survey

Cited by 111 publications

References 53 publications

Zero dynamics and funnel control for linear electrical circuits

Zero dynamics and funnel control for linear electrical circuits

Zero dynamics and funnel control of general linear differential-algebraic systems

The bang-bang funnel controller

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