Delay systems: open loop control techniques.

Dr. Nicolas Petit, California Institute of Technology, Control and Dynamical Systems

First we will show that the delay operator plays a crucial role in the dynamics of many real life systems. This will be enlighted by several industrial realizations, including the world's largest polypropylene reactor. The realizations serve to compare real-time and simulated signals, where the models are defined by a few differential equations with delays.

Next, we will give some efficient open loop control techniques following the ideas of flatness, i.e. computation of the reference trajectories between two operating points. This is quite straightforward for ODEs with punctual delays and yields very good dynamical performance when combined with a stabilizing feedback controller.

PDEs that model waves can also be considered as delay systems, but in this casethe delays form a finite continuous interval whose width depends on the waves velocity. We will show how to control these systems using the previous methods for controlling ODEs. We will use some complex analysis arguments (Paley-Wiener theorem) to derive a controllability property of these systems. Further, we will illustrate our open loop methodology on mechanical systems and a signal processing system.