A fractional-order phase-locked loop with time-delay and its Hopf bifurcation
Yajuan Yu, Zaihua Wang
Abstract: A fractional-order phase-locked loop (PLL) with a time-delay is firstly proposed on the basis of the fact that a capacitor has memory. The existence of Hopf bifurcation of the fractional-order PLL with a time-delay is investigated by studying the root location of the characteristic equation, and the bifurcated periodic solution and its stability are studied simply by using pseudo-oscillator analysis. The results are checked by numerical simulation. It is found that the fractional-order PLL with a time-delay reduces the locking time, and it minimizes the amplitude of the bifurcated periodic solution when the order is properly chosen.
原文链接: https://iopscience.iop.org/article/10.1088/0256-307X/30/11/110201/meta
