A graphical analysis method for piecewise linear dynamical systems

A wide range of systems today fall into the class of piecewise linear systems, particularly electrical and mechanical systems. Traditionally systems with nonlinearities such as dead-zones, saturation and relays would be classed as piecewise linear in nature. However, a wide range of controllers will contain logic in the form of rule-based control, gain schedulling or just 'anti-windup' in a simple PID. These types of system are generally not susceptible to classic methods of analysis, since the nonlinearities are usually distributed through the system and controller. However, industry often embeds logic into controllers via engineering intuition. This is OK for well understood systems, but as complexity increases, counter-intuitive results can occur with the interaction of logic and dynamics, particularly in fast systems ( e.g. the Anti-lock brakes in a car ). The talk presents an approach that aims to provide the designer with a visual understanding of the interaction of the logic and dynamics of the system by mapping the system into a directed graph.

N.Pettit
Control Systems Centre		email: Njal.Pettit@umist.ac.uk
UMIST, P.O.Box 88		Tel: +44-61-200-4668
Manchester, M60 1QD, U.K.	Fax: +44-61-200-4647