Platitude-based system control

The flatness property of a system is a relatively recent concept in Automatic Control, proposed and developed from 1992 onwards by M. Fliess, J. Lévine, P. Martin and P. Rouchon . This property, which makes it possible to parameterize the dynamic behavior of a system in a very simple way, is based on the identification of a set of fundamental variables of the system: its flat outputs. As we shall see, this point of view has many interesting consequences for system control.

First and foremost, this puts the notion of the trajectory the system must execute back at the heart of process control, i.e. the movement required of a system must first and foremost be achievable by that system. This avoids many of the problems faced by automation engineers. One of the first steps in platitude control is to generate a suitable desired trajectory that implicitly takes account of the system model.

Secondly, this control also implies the design of a feedback control that allows this trajectory to be pursued. This is one of the basic principles of the feedback loop: it essentially serves to compensate for the errors inherent in all modeling. We shall also see that, although the feedback loop uses the non-linear model of the process to be controlled, it is designed in a linear framework, with a view to asymptotic tracking of the trajectory to be achieved.

Last but not least, this type of control can be designed and applied from a strictly engineering point of view. Indeed, and we'll be focusing on this angle, this control, which can be implemented directly from the nonlinear model, or even in some cases, on models involving partial differential equations, significantly simplifies the design of system control without calling on the whole heavy panoply of tools usually used in the context of nonlinear systems . It thus allows us to turn to a more pragmatic, yet highly effective approach, which has given rise to numerous industrial applications in fields as diverse - and without claiming to be exhaustive here - as aeronautics, automotive, chemical engineering or food processing, in other words in...