Bifurcations and chaos in simple control systems

An analysis of the dynamical behavior of second-order linear plants controlled with conventional controllers is presented. The control signal is passed through classical non-linearities before being applied to the plant. Existence, stability, and some bifurcations occurring in some control schemes are analyzed. Existence of periodic and homoclinic orbits is also discussed. Using the Melnikov/Smale and Genesio/Tesi methods some conditions about existence of strange invariant sets are established. Numerical and experimental results support the analysis presented.