460 research outputs found

    On Robustness in the Gap Metric and Coprime Factor Uncertainty for LTV Systems

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    In this paper, we study the problem of robust stabilization for linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV Hankel operator, and in which case singular values and vectors can be used to compute the time-varying stability margin and TV controller. A connection between robust stabilization for LTV systems and an Operator Corona Theorem is also pointed out.Comment: 20 page

    Worst-case analysis of identification - BIBO robustness for closed loop data

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    This paper deals with the worst-case analysis of identification of linear shift-invariant (possibly) infinite-dimensional systems. A necessary and sufficient input richness condition for the existence of robustly convergent identification algorithms in l1 is given. A closed-loop identification setting is studied to cover both stable and unstable (but BIBO stabilizable) systems. Identification (or modeling) error is then measured by distance functions which lead to the weakest convergence notions for systems such that closed-loop stability, in the sense of BIBO stability, is a robust property. Worst-case modeling error bounds in several distance functions are include

    BIBO stability robustness in the presence of coprime factor perturbations

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    Cover title.Includes bibliographical references (leaf 8).Research supported by the Center for Intelligent Control Systems under an Army Research Office grant. DAAL03-86-K-0171 Research supported by the NSF. 8810178-ECSM.A. Dahleh

    Robustness analysis for power systems based on the structured singular value tools and the [nu] gap metric

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    Modern power systems are operated more stressed than ever because of the advent of deregulation and competition. One of the important issues in the design of controllers for a stressed system is to evaluate the stability of the controlled system over a range of operating conditions.;The conventional controllers are designed to make the system stable under certain conditions of operation. The time consuming time domain simulation is then used to evaluate the controllers for a few selected operating conditions around which the controllers are designed. Such a design and evaluation procedure cannot guarantee robustness of the controller over the whole range of operating conditions.;In this dissertation, practical algorithms to perform robustness analysis based on two tools, structured singular value and the nu gap metric, are investigated. The power system stabilizer is used as the controller and small signal stability is of interest.;The robustness problem in the SSV framework is set up for the multimachine power system. In this formulation, an improved uncertainty characterization has been used to capture the effect of parameter variations in terms of the varying elements of the linearized system matries, which are derived from the component differential equations and the network algebraic equations separately. SVD decomposition is used to reduce the size of the problem. Based on the resulting framework, a branch and bound scheme is proposed to intelligently select frequency intervals on which the frequency sweep test can be performed further to find the peak of mu. Instead of blindly choosing frequency intervals to sweep, which could ignore important frequency points on the mu plots, this scheme provides searching under guidance. The analysis procedure accurately predicts the range of stable operating conditions which are verified by repeated eigenvalue analysis.;Fir the robustness in terms of nu gap metric, we set up the feedback configuration for multimachine power system. The frequency response of the nu gap metric is plotted and its relationship with that of the stability margin is used to determine the stability of the perturbed systems. A weighted nu gap metric is defined and its frequency domain interpretation is explored to further reduce the conservatism of the results.;Finally, a feedback configuration is carefully developed to carry out the McFarlane and Glover Hinfinity loop shaping design procedure. The effect of the damping controller on improving system dynamic performance is also examined.;Comparisons are made between the two major analysis tools via the results on the same test systems with the same scenarios

    Modelling for Robust Feedback Control of Fluid Flows

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    This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. 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 theory assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. Linearisation, where appropriate, overcomes the first disparity, but attempts to reconcile the remaining two have proved difficult. This paper addresses these two problems as follows. Firstly, a numerical approach is used to project the governing equations onto a divergence-free basis, thus converting a system of differential-algebraic equations into one of ordinary differential equations. This dispenses with the need for analytical velocity-vorticity transformations, and thus simplifies the modelling of boundary sensing and actuation. Secondly, this paper presents a novel and straightforward approach for obtaining suitable low-order models of fluid flows, from which robust feedback controllers can be synthesised that provide~\emph{a~priori} guarantees of robust performance when connected to the (infinite-dimensional) linearised flow system. This approach overcomes many of the problems inherent in approaches that rely upon model-reduction. To illustrate these methods, a perturbation shear stress controller is designed and applied to plane channel flow, assuming arrays of wall mounted shear-stress sensors and transpiration actuators. 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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