Zustandsregelung verteilt-parametrischer Systeme

Deutscher, Joachim

doi:10.1007/978-3-642-19559-4

Cited by 12 publications

(3 citation statements)

References 32 publications

(75 reference statements)

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“…Inserting Vuni and Vpar into (45) and subsequently Vflow into (43) leads to the closed loop state equation with modified velocity dependent state matrix Structures as shown in Fig. 2 are well known in control theory for the design of parametric feedback control systems [24]. In the considered scenario, the feedback structure serves a different purpose but its principle influence on the overall system behavior is similar.…”

Section: Closed Loop Transfer Function Modelmentioning

confidence: 99%

“…The representation in (64) is a compact description of the advection-diffusion process in the frequency domain and also allows an analysis of the process in terms of its spectrum. Transfer functions of the form of (64) are well known in linear operator and control theory, where they are referred to as resolvent operators that are used to study the spectral properties of linear operators [24], [26].…”

Section: G Interpretation In Terms Of Transfer Functionsmentioning

confidence: 99%

“…Then, the influence of laminar flow is incorporated via a feedback system that is attached to the open loop SSD to form a closed loop SSD. The design of feedback systems is well known in control theory, see e.g., [24]. Here, this approach is adopted to incorporate the influence of laminar flow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transfer Function Models for Cylindrical MC Channels With Diffusion and Laminar Flow

Schäfer

Wicke

Brand

et al. 2021

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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The analysis and design of advection-diffusion based molecular communication (MC) systems in cylindrical environments is of particular interest for applications such as micro-fluidics and targeted drug delivery in blood vessels. Therefore, the accurate modeling of the corresponding MC channel is of high importance. The propagation of particles in these systems is caused by a combination of diffusion and flow with a parabolic velocity profile, i.e., laminar flow. The propagation characteristics of the particles can be categorized into three different regimes: The flow dominant regime where the influence of diffusion on the particle transport is negligible, the dispersive regime where diffusion has a much stronger impact than flow, and the mixed regime where both effects are important. For the limiting regimes, i.e., the flow dominant and dispersive regimes, there are well-known solutions and approximations for particle transport. In contrast, there is no general analytical solution for the mixed regime, and instead, approximations, numerical techniques, and particle based simulations have been employed. In this paper, we develop a general model for the advection-diffusion problem in cylindrical environments which provides an analytical solution applicable in all regimes. The modeling procedure is based on a transfer function approach and the main focus lies on the incorporation of laminar flow into the analytical model. The properties of the proposed model are analyzed by numerical evaluation for different scenarios including the uniform and point release of particles. We provide a comparison with particle based simulations and the well-known solutions for the limiting regimes to demonstrate the validity of the proposed analytical model.

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Section: Closed Loop Transfer Function Modelmentioning

confidence: 99%

Section: G Interpretation In Terms Of Transfer Functionsmentioning

confidence: 99%