Remote control of mechatronic systems over communication networks

Roesch, O.; Roth, Hubert

doi:10.1109/icma.2005.1626802

Cited by 32 publications

(13 citation statements)

References 2 publications

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“…Similar models with distributed delays and a particular gamma distributed delay kernel have been studied in Roesch et al (2005); Michiels et al (2007); Moraˇrescu et al (2007). The novelty of our work is an analytical bound for the modelling error, cf Mu¨nz et al (2007).…”

Section: Modeling Of Communication Channels Withmentioning

confidence: 99%

“…This avoids the pitfall of assuming that the delay is fixed which could wrongly predict instability, while the distributed delay model is stable and vice versa, cf Michiels, Assche, and Niculescu (2005). The use of a distributed delay framework to model packet-switched networks (PSN) has been suggested in the past by Roesch, Roth, and Niculescu (2005); Moraˇrescu, Niculescu, and Gu (2007). However, no conditions for the accuracy of the transformation have been given so far.…”

Section: Introductionmentioning

confidence: 99%

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Consensus reaching in multi-agent packet-switched networks with non-linear coupling

Münz

Papachristodoulou

Allgöwer

2009

International Journal of Control

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An important task for multi-agent systems (MAS) is to reach a consensus, e.g. to align their velocity vectors. Recent results propose appropriate consensus protocols to achieve such tasks, but most of them do not consider the effect of communication constraints such as the presence of time-delays in the exchange of information between the agents. In this article, we provide conditions for a non-linear, locally passive MAS of arbitrary size to reach a consensus, when the agents communicate over a packet-switched network that is characterised by a given topology. Both the cases of constant and switching topologies are considered. The nature of the communication channel imposes constraints that are modelled using stochastic delays of arbitrary distribution. We first embed this model in another, distributed but deterministic delay model and provide conditions for the error introduced by this simplification. In our main result, we provide conditions for the locally passive MAS with distributed delays to reach a consensus. In the case of a fixed topology, the underlying directed graph has to contain a spanning tree. In the case of a switching topology, only the union graph of all graphs that persist over time is required to contain a spanning tree. These conditions are independent of the distribution and the size of the packet delays. To show attractivity of the consensus set, we use an invariance principle for systems described by functional differential equations based on an appropriate Lyapunov-Razumikhin function. This methodological approach is the main contribution of this work and can also be applied to other consensus problems with delays. We illustrate our results by numerical simulations showing synchronisation of non-linear Kuramoto oscillators over a digital network.

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Section: Modeling Of Communication Channels Withmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consensus reaching in multi-agent packet-switched networks with non-linear coupling

Münz

Papachristodoulou

Allgöwer

2009

International Journal of Control

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“…However, there are only very few results for distributed input delays, e.g. [1], [11], which also assume undelayed inputs, and [24], which assumes a γ-distributed delay kernel. Distributed input delays appear, e.g., in networked control systems (NCS) where the digital communication channel with stochastic packet delay and loss is modeled using distributed delays, cf.…”

Section: Introductionmentioning

confidence: 99%

“…Distributed input delays appear, e.g., in networked control systems (NCS) where the digital communication channel with stochastic packet delay and loss is modeled using distributed delays, cf. [24].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of linear systems with distributed input delay

Goebel

Münz

Allgöwer

2010

Proceedings of the 2010 American Control Conference

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This paper presents linear matrix inequality (LMI) conditions to design stabilizing state-feedback controllers for linear systems with distributed input delays. A LyapunovKrasovskii functional approach is used and the obtained parametric matrix inequalities are reformulated as LMIs using the full-block S-procedure and a convex hull relaxation. These LMI conditions can be used, for example, to design stabilizing controller for networked control systems (NCS). In this setup, the kernel of the distributed input delay describes the probability density of the packet-delay in the communication channel. This controller design for NCS is illustrated in an example.Index Terms-Time delay systems, distributed input delay, stabilization, full-block S-procedure, convex hull relaxation, networked control systems.

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“…This makes some of the described results directly applicable to the emerging field of network controlled systems also, since the varying delays in communication networks are typically of a stochastic nature, yet knowledge is available about their distribution, see, for instance, [36,41] and the references therein.…”

Section: X(t) = A(ωt) X(t) + B(ωt) X(t − τ (T))mentioning

confidence: 99%

Mathematical and Computational Tools for the Stability Analysis of Time-Varying Delay Systems and Applications in Mechanical Engineering

Michiels¹,

Verheyden²,

Niculescu³

Applications of Time Delay Systems

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Summary. An overview of eigenvalue based tools for the stability analysis of linear periodic systems with delays is presented. It is assumed that both the system matrices and the delays are periodically varying. First the situation is considered where the time-variation of the periodic terms is fast compared to the system's dynamics. Then averaging techniques are used to relate the stability properties of the time-varying system with these of a time-invariant one, which opens the possibility to use frequency domain tools. As a special characteristic the averaged system exhibits distributed delays if the delays in the original system are time-varying. Both analytic and numerical tools for the stability analysis of the averaged system are discussed. Special attention is paid to the characterization of situations where a variation of a delay has a stabilizing effect. Second, the assumption underlying the averaging approach is dropped. It is described how exact stability information of the original, periodic system can be directly computed. The two approaches are briefly compared with respect to generality, applicability and computational efficiency. Finally the results are illustrated by means of two examples from mechanical engineering. The first example concerns a model of a variable speed rotating cutting tool. Based on the developed theory and using the described computational tools, both a theoretical explanation and a quantitative analysis are provided of the beneficial effect of a variation of the machine speed on enhancing stability properties, which was reported in the literature. The second example concerns the stability analysis of an elastic column, subjected to a periodic force.

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Remote control of mechatronic systems over communication networks

Cited by 32 publications

References 2 publications

Consensus reaching in multi-agent packet-switched networks with non-linear coupling

Consensus reaching in multi-agent packet-switched networks with non-linear coupling

Stabilization of linear systems with distributed input delay

Mathematical and Computational Tools for the Stability Analysis of Time-Varying Delay Systems and Applications in Mechanical Engineering

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