A Fractional-Order Phase-Locked Loop with Time-Delay and Its Hopf Bifurcation
YU Ya-Juan1,2, WANG Zai-Hua1,3**
1State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 2School of Mathematics and Physics, Changzhou University, Changzhou 213164 3Institute of Science, PLA University of Science and Technology, Nanjing 211101
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.
2013, Vol. 30 
