On a linear input–output approach for the control of nonlinear flat systems

Abstract

ABSTRACTThe need for observers, or other means of state- or phase variables-on-line computations, is revisited from the perspective of structural integral reconstructors. The problem addressed is the regulation, via simplified pure integration dynamics, of the large class of static, or dynamic, feedback linearisable systems (i.e. differentially flat systems), subject to additive exogenous disturbances and where nonlinearities are purposefully neglected. Integral reconstructors of the simplified input-to-flat output dynamics, directly lead to generalised proportional integral controllers, which are also shown to be equivalent to classical compensation networks. Their robust version, addressed here as flat filters, are found to be quite useful in the approximate (i.e. practical) control of perturbed differentially flat systems. The controller design is based on their simplified, perturbed, and pure integration dynamics. Flat filters evade for the need of nonlinear asymptotic observers and other, on-line, explicit output time derivatives computations. Simulation and challenging experimental examples are provided to validate this linear approach to the control of nonlinear flat systems.