Global effects of controller saturation on closed-loop dynamics

Abstract

Global stability of a locally stable closed-loop set point is achieved when all other attracting states are removed from the state space. These extraneous states are introduced by system and controller nonlinearities and are hence impossible to analyse by linear theories. In this work, the multiplicity of equilibrium points in a closed-loop system with saturable controller is associated with certain topological features of the steady-state model. The bifurcation of these features is analysed and certain criteria are established which ensure the set point as the unique equilibrium point in the closed-loop system. For systems satisfying these criteria, global closed-loop instability can only be caused by the existence of higher order dynamic attractors such as limit-cycles and tori. These cases are relatively rare and one particular example is studied by a Poincare-map approach.