Jean-Marc Biannic's Courses

ONERA/DCSD - Flight Dynamics and Control Department

Analysis & Control of  Saturated Systems



Linear control theory has now reached a high level of maturity although there still remain unsolved problems in this field.  Quite interestingly, linear-oriented tools and their classical  extensions (gain-scheduling techniques, LPV control method, dynamic inversion techniques with a  linear robustifying loops) permit to design controllers for a large class of nonlinear systems. But their remain ubiquitous and hard nonlinearities such as magnitude and rate saturations which require a specific attention.

The course is organized in two parts.

Part I : Phase plane techniques & Describing function methods

In this first part of the course (10 hours), one focuses on analysis and design techniques for linear systems in feedback loop with a single static nonlinearity (saturation, deadzone, relay). The impact of saturations is first analyzed by a rigourous (but limited to second-order systems) in the phase plane. Then one focuses on limit-cycles characterization thanks to the first harmonic approximation approach

Part II : Lyapunov techniques & stability regions

In this second and more advanced part of the course a specific attention is devoted to the characterization of regional stability domains via Lyapunov-based techniques. In this case, the nonlinear operator is characterized through polytopic models or local sector conditions. The proposed techniques are no longer restricted to a single nonlinearity, but conservatism grows fast with the number of saturations...

Remark

In both parts, the proposed analysis methods are used to optimize anti-windup compensators in order to alleviate the adverse effects of saturations in control systems.