Global bifurcation and chaos from automatic gain control loops

The dynamics of the automatic gain control (AGC) loops which employ variable-gain amplifiers with a square control law are studied. The selected loop filters are of second-order low-pass type. The existence of global homoclinic bifurcation and Smale horseshoe chaos are proved without the traditional small-signal model assumption. To investigate systems that are monitored during discrete-time intervals, sampled-data AGC loops are also considered. Under the same square gain-control law, the first-and second-order loop filters are studied. The period-doubling routes to chaos are verified for the first-order systems, and Hopf bifurcations for the second-order filters. Simulations are performed and the resultant homoclinic tangles, chaotic time waveforms, bifurcation diagrams, and Lyapunov exponents are illustrated to demonstrate the theoretical results.>