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

Reis

2014

Self Cite

We study the zero dynamics and funnel control for linear passive electrical circuits. We show that asymptotic stability of the zero dynamics can be characterized by criteria on the circuit topology. 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 result can be relaxed to the case of non-autonomous zero dynamics by requiring the reference trajectory to evolve within a certain subspace.

Section: Zero Dynamicsmentioning

confidence: 99%

“…The concept of funnel control has been introduced in [4] and investigated for linear DAEs recently in [6,9,[12][13][14] which provide the basis for the investigation in the present paper; nonlinear DAEs have also been treated in [15].…”

Section: Funnel Controlmentioning

confidence: 99%

Funnel control for electrical circuits

Reis

2014

Self Cite

“…

We consider tracking control for linear non-minimum phase systems with known relative degree. [1][2][3][4]) are asymptotically stable, which would mean that rk A−λIn B C 0

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.…”

mentioning

confidence: 99%

“…[1][2][3][4]) are asymptotically stable, which would mean that rk A−λIn B C 0 [1][2][3][4]) are asymptotically stable, which would mean that rk A−λIn B C 0…”

mentioning

confidence: 99%

See 1 more Smart Citation

Funnel control for linear non‐minimum phase systems

2019

Self Cite

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

Controlled invariance for DAEs

2015

We study the concept of locally controlled invariant submanifolds for nonlinear descriptor systems. In contrast to classical approaches, we define controlled invariance as the property of solution trajectories to evolve in a given submanifold whenever they start in it. It is then shown that this concept is equivalent to the existence of a feedback which renders the closed‐loop vector field invariant in the descriptor sense. This result is motivated by a preliminary consideration of the linear case. Local controlled invariance leads to the concept of output zeroing submanifolds. We show that the outcome of the differential‐algebraic version of the zero dynamics algorithm yields a locally maximal output zeroing submanifold. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)