An asymptotic analysis of the so called intelligent PID controller

Abstract

This note takes its origin from reading a paper by M. Fliess and C. Join, whose latest version is entitled Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control? that can be obtained at http://arxiv.org/abs/0904.0322 Unfortunately in that paper, the authors write that . . . it is impossible of course to give a complete description of it and that the usual mathematical criteria for robust control become . . . irrelevant. In the following, to obtain an usable description of a controller and to give some guarantees that it performs correctly, we interpret and materialize the ideas proposed in that paper. Of course, this is at the price of trivializing and likely also degrading them. Nevertheless, this allows us to present an elementary analysis using standard mathematical criteria although we know the authors claimed that this is irrelevant