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Nonlinear control

Abstract : Nonlinear behavior is the general rule in physics and nature. Linear models, obtained by linearization or identification, are in general crude approximations of nonlinear behaviors of plants in the neighbourhood of an operating point. However, in many cases such as startup, shutdown, or important transient regimes, study of batch and fed-batch processes, a linear model is insufficient to correctly reproduce the reality, and the resulting linear controller cannot guarantee stability and performance. Yet, because of the difficulty to cope with nonlinear control, linear models and linear controllers are by far dominant. Nevertheless, efficient methods exist that can be used with nonlinear models provided the end-users are willing to carry out some effort. Among existing theories, can be found backstepping, sliding mode control, [Khalil, 1996, Krstić et al., 1995, Slotine and Li, 1991], flatness based control [Fliess et al., 1995, 1997], and methods based on Lyapunov stability, nonlinear model predictive control [Alamir, 2006, Allgöwer and Zheng, 2000, Rawlings et al., 1994]. These methods are powerful and would deserve a long development. In this chapter, a particular method of nonlinear control, often called non-linear geometric control [Isidori, 1989, 1995, Jurdjevic, 1997, Khalil, 1996] will be presented and discussed. It is based on differential geometry but can be understood in simpler words. Differential geometry is devoted in particular to the theory of differential equations in relation with geometry, surfaces, manifolds.
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Jean Pierre Corriou. Nonlinear control. Sohrab Rohani. Coulson and Richardson’s Chemical Engineering: Volume 3B: Process Control Fourth Edition,, 2017, 978-0-08-101095-2. ⟨hal-02946767⟩

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