Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?

Michel Fliess (1, 2) , Cédric Join (2, 3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 ALIEN - Algebra for Digital Identification and Estimation
3 CRAN - Centre de Recherche en Automatique de Nancy

We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent'' PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments.

Keywords: differential algebra; linear systems; nonlinear systems; model-free control; control with a restricted model; predictive control; delay systems; PID; intelligent PID controllers; universal control; robustness; diagnosis; large-scale systems; anti-windup; numerical differentiators; frictions; non-minimum phase systems; differential algebra.

Domains: Automatic Control Engineering; Optimization and Control [math.OC]; Modeling and Simulation; Commutative Algebra [math.AC]; Numerical Analysis [cs.NA]; Classical Analysis and ODEs [math.CA]

Michel Fliess, Cédric Join. Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?. 15th IFAC Symposium on System Identification (SYSID 2009), IFAC, Jul 2009, Saint-Malo, France. ⟨inria-00372325v2⟩