Vinnicombe metric as a closed-loop nonlinearity measure

Tan, Guan Tien; Huzmezan, M.; Kwok, K.E.

doi:10.23919/ecc.2003.7085047

Cited by 8 publications

(7 citation statements)

References 26 publications

(28 reference statements)

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“…24 In model-based control design, it is desirable to check the adequacy of a linear model before any attempts to use a nonlinear controller are made. The Vinnicombe metric (-gap metric) has been advocated as a measure of closed-loop nonlinearity, 25 and attracted much attention particularly in robust control and system identification. 26,27 The main effort of this paper is the establishment of frame for surrogate modeling with the inspection of principal influence parameters.…”

Section: Introductionmentioning

confidence: 99%

Surrogate modeling of a 3D scramjet-powered hypersonic vehicle based on screening method IFFD

Chen

Liu

Shen

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part G:

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The emphasis of this paper lies in the development of an efficient approach to reproduce the behaviors of the scramjetpowered hypersonic system with high fidelity. The modeling of the dual-mode scramjet powered hypersonic vehicle dynamics with shock interaction, Ram-to-Scram transition, and finite rate chemistry reaction is firstly introduced. The structure of surrogate model is identified with the implement of iterative fractional factorial design (IFFD). In order to declare the reliability of the surrogate models, -gap metric is applied to distinguish the difference among these surrogate models in terms of closed-loop performance. The results show that the influence of Mach number on the aerodynamics should not be overlooked, and the effect of propulsion system to the aerodynamic pitch moment is dramatic. Further, the partial Kriging model appears to have the closest plants throughout the flight envelope compared with the full Kriging model and polynomials model. Nevertheless, considering the briefness of analytical expression, the polynomials model may be an alternative approach for design-oriented modeling.

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Section: Introductionmentioning

confidence: 99%

Surrogate modeling of a 3D scramjet-powered hypersonic vehicle based on screening method IFFD

Chen

Liu

Shen

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…Thus we can decide whether a linear controller is adequate for the system or a nonlinear controller is necessary according to the nonlinearity measures. In the past decades, researchers have made extensive studies on nonlinearity measures, and have proposed quite a few definitions and computational methods [1][2][3][4][5][6][7][8][9][10][11][12][13]. Most of them are defined as a distance between the nonlinear system and its best linear approximation [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the gap metric which was recognized as being more appropriate to measure the distance between two linear systems than a norm-based metric [17][18], has been employed to quantify the nonlinearity level of industrial processes. And several definitions have been developed [13][14][15][16]. The nonlinearity measures based on the gap metric are comparatively easier and simpler to compute and apply.…”

Section: Introductionmentioning

confidence: 99%

Control-relevant nonlinearity measure and integrated multi-model control

Johansen

2017

Journal of Process Control

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A control-relevant nonlinearity measure (CRNM) method is proposed based on the gap metric and the gap metric stability margin to measure the nonlinear degree of a system once a linear control strategy is selected. Supported by the CRNM method, an integrated multi-model control framework is developed, in which the multi-model decomposition and local controller design are closely integrated, model redundancy is avoided, computational load is reduced, and dependency on a prior knowledge is reduced. Besides, a 1/δ gap-based weighting method is put forward to combine the local controllers. On one hand, the 1/δ gap-based weighting method has merely one tuning parameter and can be computed off-line; on the other hand, it is sensitive to the tuning parameter, flexible and easy to tune. Two continuous stirred tank reactor (CSTR) systems are investigated. Closed-loop simulations validate the effectiveness and benefits of the proposed integrated multi-model control approach based on CRNM.

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“…Similar to induced norms is the relative error-like measure given in [3,7]. A different way to measure the distance between two systems is provided by the gap metric [8], and this metric can also be used to assess the nonlinearity of a system [9,10]. In [11] the curvature of the steady state map is introduced as a measure of nonlinearity and in [12] an extension of this approach to dynamic systems is discussed.…”

Section: Introductionmentioning

confidence: 99%

A robustness approach to linear control of mildly nonlinear processes

Schweickhardt

Allgöwer

2007

Intl J Robust & Nonlinear

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SUMMARYWe present a novel approach toward linear control of nonlinear systems. Combining robust control theory and nonlinearity measures, we derive a method to (i) assess the nonlinearity of a given control system, (ii) derive a suitable linear model (not necessarily equivalent to the local linearization), and (iii) design a linear controller that guarantees stability of the closed loop containing the nonlinear process. A distinctive feature of the approach is that the nonlinearity analysis, linear model derivation and linear controller synthesis can be done on an operating regime specified by the designer. Examples are given to illustrate the approach.

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Vinnicombe metric as a closed-loop nonlinearity measure

Cited by 8 publications

References 26 publications

Surrogate modeling of a 3D scramjet-powered hypersonic vehicle based on screening method IFFD

Surrogate modeling of a 3D scramjet-powered hypersonic vehicle based on screening method IFFD

Control-relevant nonlinearity measure and integrated multi-model control

A robustness approach to linear control of mildly nonlinear processes

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