Observation of chaotic behavior in automatic tuning loops for continuous-time filters

The appropriate linear dynamic modeling of continuous-time filters (CTFs) with automatic tuning loops should be obtained to assure stability in case an improved design of the loop controllers is to be carried out. With this aim, starting from a general and systematic analysis in order to obtain an equivalent small-signal linearized incremental model, from which transfer functions between output variables and control voltages are derived, the subsequent design of compensated loops with enhanced stability and dynamic performance is required. This systematic procedure allows obtaining improved controllers for the two involved control loops. However, CTFs with automatic tuning loops are nonlinear feedback systems with potential instability. What is more, nonlinear phenomena, which cannot be predicted by a design-oriented small signal modeling approach, are observed in this kind of tuning systems. The purpose of this work is to highlight that when control parameters are varied, the system could present different kinds of dynamical nonlinear phenomena such as bifurcations and chaotic behavior, which cannot be predicted by the small signal design-oriented model.