Bifurcation analysis of a feedback system with dead zone and saturation

An experimental example has been presented showing how nonlinearities affect the dynamic behavior of a DC servomechanism controlled by a proportional controller. The analysis has been developed using tools supplied by classical methods for feedback system analysis based on the describing function method. The case studied is a very good and simple example of a feedback system where a saddle-node bifurcation of periodic orbits occurs. This bifurcation is very interesting because it explains the coexistence of a stable equilibrium at the operating point with a stable limit cycle for large perturbations. The major advantage of the bifurcation analysis developed is that it supplies a single unified framework for representing all the different behavior modes the system can display. Finally, these results have been tested using laboratory equipment