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A controller perturbation technique for transferring closed-loop stability between systems

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Abstract

This brief paper presents a perturbation technique with which a controller stabilizing one plant may be modified so that it stabilizes a second, related plant. The proposed technique produces an internally stable loop for a broad class of linear systems without requiring any further calculations on the part of the designer. Four seemingly different examples are described in terms of this result.

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... A variation of the model identification problem is the case in which an initial model is available, and data is used to refine the initial model to obtain an improved 1 fit to the data, specifically, by identifying poorly modeled dynamics. This problem has been extensively studied within the context of finite element modeling [6,7,8], and has received some attention within the systems and control literature [9,10,11]. The goal is to update θ based on the residual between the truth system and the model. ...
... Next, assume that the frequency Θ does not coincide with any zeros of G FIR . Furthermore, assume that (2.5) reaches harmonic steady state for all ν, and assume thatû(k) − u * (k) → 0 as k → ∞ and that η(k) is chosen such that η(k) → 0, as k → ∞, which implieŝ z(k) → 0, as k → ∞, (see Fact. 9. 5.2) then if ...
... Under these conditions, the performance z(k) tends to zero and the state x(k) of the real system is bounded. 9.5.1 Sufficient Conditions for z(k) −ẑ(k) → 0 as k → ∞ Consider the retrospective system ...
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... In [2] to preserve the structure of the structural model, the parameters of the model are updated directly by using connectivity constraints. Furthermore, in [5] a method is outlined for modifying an existing controller based on knowledge of deviations in the plant. However, the aim of [5] is not to correct the model itself, but rather to correct the controller such that it handles deviations in the plant. ...
... Furthermore, in [5] a method is outlined for modifying an existing controller based on knowledge of deviations in the plant. However, the aim of [5] is not to correct the model itself, but rather to correct the controller such that it handles deviations in the plant. ...
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First principle models and empirical models are necessarily approximate. In this paper we develop two empirical approaches that use a delta model to modify an initial model by means of cascade, parallel or feedback augmentation. A sub-space based nonlinear identification algorithm and an adaptive disturbance rejection algorithm are both used to construct the delta model. Three classes of errors in the initial model, i.e. unmodeled dynamics, parametric errors and initial condition errors are considered. Some illustrative examples are presented
... A two dimensional loop-shaping technique for industrial CD controllers has been implemented in many paper mills as part of a commercial product Stewart et al. (2003a) and Stewart et al. (2003b). A technique for modifying the CD controllers designed through two-dimensional loop-shaping to handle edge effects is presented in Mijanovic (2004) and Mijanovic et al. (2003). In Gorinevsky et al. (2008), designing a controller for steady-state performance and robustness in spatially distributed feedback systems was proposed. ...
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... The identification task is then to use available data to refine the available model, thereby improving its accuracy. This task is variously known as model correction, model refinement, or model updating [2,3,4,5,8,10]. ...
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... With this initial model as a starting point, our goal is to use additional measurements to refine the model. This problem is known as model correction, empirical correction, model refinement, or model updating; relevant literature includes finite-element modeling, 1-4 meteorology, 5-7 feedback control, 8,9 applications to health monitoring, 13 and algorithms. [10][11][12] This literature is surprisingly sparse given the potential benefits of using data to improve models. ...
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Multivariable feedback control: Analysis and design Closer control of loops with dead time
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  • I Postlethwaite
Skogestad, S., & Postlethwaite, I. (1996). Multivariable feedback control: Analysis and design. New York: Wiley. Smith, O. J. M. (1957). Closer control of loops with dead time. Chemical Engineering Progress, 53(5), 217–219.