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Tuning PI controller in non-linear uncertain closed-loop systems with interval analysis. (English) Zbl 1432.93132

André, Étienne (ed.) et al., 2nd international workshop on synthesis of complex parameters, SynCoP’15, April 11, 2015, London, UK. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. OASIcs – OpenAccess Ser. Inform. 44, 91-102 (2015).
Summary: The tuning of a PI controller is usually done through simulation, except for few classes of problems, e.g., linear systems. With a new approach for validated integration allowing us to simulate dynamical systems with uncertain parameters, we are able to design guaranteed PI controllers. In practical, we propose a new method to identify the parameters of a PI controller for nonlinear plants with bounded uncertain parameters using tools from interval analysis and validated simulation. This work relies on interval computation and guaranteed numerical integration of ordinary differential equations based on Runge-Kutta methods. Our method is applied to the well-known cruise-control problem, under a simplified linear version and with the aerodynamic force taken into account leading to a nonlinear formulation.
For the entire collection see [Zbl 1392.68009].

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93C41 Control/observation systems with incomplete information
93C10 Nonlinear systems in control theory
93-08 Computational methods for problems pertaining to systems and control theory
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Software:

GRKLib; VERICOMP
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Full Text: DOI

References:

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