The focal point of this paper is to develop a measure of closedloop nonlinearity. In this work, the Vinnicombe metric and the quasi-linear parameter varying (quasi-LPV) representation of nonlinear systems are exploited for this purpose. The proposed measure can serve as a decision making tool for control engineers when deciding whether a linear or nonlinear control strategy should be employed to solve their control problems. A continuous stirred tank reactor (CSTR) simulation example is used to illustrate the proposed measure.
• Easy to interpret. The results obtained using the measure must be easy to interpret. Ideally, a scale between 0 and 1 is used, where 0 means "negligible closed-loop non-linearity", while 1 means "signifi cant closed-loop non-linearity". Over the past few decades, various linearity tests were proposed (Ramsey, 1969;Desoer and Wang, 1980;Billings and Voon, 1983;Brock et al., 1987;Nikolaou, 1993;Guay et al., 1995). Most of them are measuring open-loop non-linearity and are restricted to open-loop stable systems. However, in practice, feedback control is normally employed to handle uncertainty, plant/model mismatch and noise attenuation, and is also known to modify closed-loop non-linearity. Hence, measuring open-loop non-linearity gives little information on the severity of closedloop non-linearity.Closed-loop stabilities for non-linear systems admitting a linear parameter varying structure by using the Linear Matrix Inequality framework have also been described by Doyle et al. (1989) and Becker and Packard (1994). This approach is particularly useful for controller design and performance assessment.The focal point of this paper is to develop a measure of closed-loop non-linearity. In this work, the Vinnicombe metric and the Quasi-Linear Parameter Varying representation of a non-linear system are exploited for this purpose. It is expected that the proposed measure can serve as a decision making tool for control engineers when considering whether a linear or a non-linear control strategy should be employed to close the loop for a non-linear system operating in a prescribed range.Dans cet article, on vise à mettre au point une mesure de la non linéarité en boucle fermée. À cette fi n, on exploite dans ce travail la représentation des variations des paramètres quasi-linéaires et métriques de Vinnicombe pour un système non linéaire. On s'attend à ce que la mesure proposée puisse servir comme outil dans la prise de décisions pour les ingénieurs de contrôle au moment de considérer si une stratégie de contrôle linéaire ou non linéaire devrait être employée pour fermer la boucle pour un système non linéaire fonctionnant dans une gamme prescrite.
The focal point of this paper is to develop a measure of closed-loop nonlinearity. In this work, the Vinnicomhe metric and the Quasi-Linear Parameter Varying representation of a nonlinear system are exploited for this purpose. It is expected that the proposed measure can sene as a decision making tool for control engineers when considering whether a linear or a nonlinear control stratea should be employed to close the loop.
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