Complex dynamics in classical control systems

Abstract

An analysis of the complex dynamical behavior of second-order linear plants controlled with conventional controllers is presented. The control signal is passed through a classical nonlinearity before being applied to the plant. Existence of periodic and homoclinic orbits is discussed. Using the Melnikov/Smale and Genesio/Tesi methods some conditions about the existence of invariant strange sets are also established. It is shown that simple classical control schemes with typical nonlinearities can exhibit chaotic dynamics in a certain range of the controller parameters. Numerical and experimental results support the analysis presented.