Jean-Marc Biannic's CoursesONERA/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...
RemarkIn 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. |