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 in...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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10825207the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘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.
