When is the discretization of a spatially distributed system good enough for control?

Jones, Bernard J. T.; Kerrigan, Eric C.

doi:10.1016/j.automatica.2010.06.001

Cited by 27 publications

(23 citation statements)

References 16 publications

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“…There is therefore the risk that a control system, designed upon the former, will fail to stabilise the latter, owing to a phenomenon known as 'spillover' (Balas 1978), whereby a controller excites unmodelled plant dynamics. Jones & Kerrigan (2010) developed an alternative method for obtaining low-order control models of spatially distributed systems, that circumvented each of the problems described above. The method involved computing a sequence of ν-gaps between low-order plant-models of successively finer spatial resolution, starting from a coarsely discretised (and thus low-order) model.…”

Section: Model Refinement and Knowing When A Spatial Discretisation Imentioning

confidence: 99%

“…The rate at which the sequence converges to zero is dependent upon the flow, the control objective and the method of spatial discretisation, but can be very great. Establishing the rate of convergence enables the construction of an upper bound on the ν-gap between the models in the computed sequence and the infinite dimensional plant, which then informs the selection of a suitable low-order model (Jones & Kerrigan 2010). This enables the synthesis, on low-order models, of robust controllers that are guaranteed to stabilise the actual plant, a feature not shared by model reduction methods where the gap between the high-order model (e.g.…”

Section: Model Refinement and Knowing When A Spatial Discretisation Imentioning

confidence: 99%

“…Then, provided the robust stability margin of a H ∞ loop-shaping controller (synthesised from P n0,W ) exceeds this bound by a reasonable margin, then robust closedloop performance is guaranteed. The assumptions and technical details underpinning this process are fully discussed in Jones & Kerrigan (2010), and a sketch of the procedure is shown in Figure 7. The model refinement method embodies the fact that sensibly designed feedback control systems are insensitive to unmodelled dynamics occurring at frequencies above the Figure 7.…”

Section: Model Refinement and Knowing When A Spatial Discretisation Imentioning

confidence: 99%

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Modelling for robust feedback control of fluid flows

et al. 2015

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This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H ∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl's theory of sheared turbulence. To illustrate the application of these techniques, a H ∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall-shear stress in plane channel flow. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller.

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Section: Model Refinement and Knowing When A Spatial Discretisation Imentioning

confidence: 99%

Section: Model Refinement and Knowing When A Spatial Discretisation Imentioning

confidence: 99%

Section: Model Refinement and Knowing When A Spatial Discretisation Imentioning

confidence: 99%

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Modelling for robust feedback control of fluid flows

et al. 2015

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“…As in the dual control design problems, what is often done is to extract a low-order approximation of the system using model reduction [15], [16] or via successively finer spatial discretization of systems described by PDEs [17]. Using these low-order models, [17] designs low-order controllers with performance guarantees around the full-order model. Similarly, we base our filter design on such low-order models and with closed-loop L 2 error attenuation guarantees around the full-order model.…”

Section: Lower-order H ∞ Filter For Bilinear Systemsmentioning

confidence: 99%

Lower-Order <formula formulatype="inline"><tex Notation="TeX">$H_{\infty} $</tex></formula> Filter Design for Bilinear Systems With Bounded Inputs

Abraham

Kerrigan

2015

IEEE Trans. Signal Process.

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We propose an optimization-based method for designing a lower-order Luenberger-type state estimator, while providing L 2 -gain guarantees on the error dynamics when the estimator is used with the higher-order system. Suitable filter parameters can be computed by modelling the bilinear system as a linear differential inclusion and solving a set of bilinear matrix inequality constraints. Since these constraints are non-convex, in general, we also show that one can solve a suitably-defined semi-definite program to compute a bound on the level of sub-optimality. The design method also allows one to explicitly take account of linear parameter uncertainties in order to provide a priori robustness guarantees. The H-infinity estimator not only has lower real-time computational requirements compared to a Kalman filter, but also does not require knowledge of the noise spectrum.For a numerical example, we consider the estimation of the radiation force for a wave energy converter, where a low-order model is used to approximate the radiation dynamics.

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“…Due to the mathematical complexity, their analysis is more difficult, and possible applications are more limited than in the case of the finitedimensional models. Therefore, in order to enable the implementation of the developed over the years techniques for the synthesis of control systems, the infinite-dimensional DPS models are usually replaced by their finitedimensional approximations [3,4,9,12,16]. Nevertheless, regardless of the approximation method used, the starting point for the synthesis of a control system should be based on the possibly most accurate description of the DPS, taking into account its infinite-dimensional nature, e.g.…”

Section: Introductionmentioning

confidence: 99%

Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

Bartecki

2014

Heat Mass Transfer

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This paper discusses irrational transfer function representation for a typical thick-walled double pipe heat exchanger. Closed-form analytical expressions for the individual elements of 2 9 2 transfer function matrix are derived both for the parallel-and the counter-flow configurations using the Laplace transform method. Based on the transfer function representation, its frequency responses are demonstrated both in the form of three-dimensional graphs as well as classical, two-dimensional Bode and Nyquist plots. Finally, steady-state temperature profiles are presented and compared for both flow arrangements considered.

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When is the discretization of a spatially distributed system good enough for control?

Cited by 27 publications

References 16 publications

Modelling for robust feedback control of fluid flows

Modelling for robust feedback control of fluid flows

Lower-Order <formula formulatype="inline"><tex Notation="TeX">$H_{\infty} $</tex></formula> Filter Design for Bilinear Systems With Bounded Inputs

Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

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