https://hal-polytechnique.archives-ouvertes.fr/hal-00828135v3Fliess, MichelMichelFliessLIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueAL.I.E.N. - ALgèbre pour Identification & Estimation NumériquesJoin, CédricCédricJoinAL.I.E.N. - ALgèbre pour Identification & Estimation NumériquesCRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche ScientifiqueModel-free controlHAL CCSD2013functional analysisoperational calculusheat partial differential equationsfault accommodationnon-minimum phase systemsdelay systemsflatness-based controlnoiseestimationPID controllersintelligent PID controllersintelligent PI controllersintelligent P controllersdifferential algebra[INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering[SPI.AUTO] Engineering Sciences [physics]/Automatic[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Fliess, Michel2021-02-05 22:34:212023-02-08 17:11:162021-02-10 07:30:32enJournal articleshttps://hal-polytechnique.archives-ouvertes.fr/hal-00828135v3/document10.1080/00207179.2013.810345https://hal-polytechnique.archives-ouvertes.fr/hal-00828135v2application/pdf3''Model-free control'' and the corresponding ''intelligent'' PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.