Research And Application On Phase-locked Loop Chaos Characteristic

Phase-locked loop (PLL) is a nonlinear closed-loop control system, which has beenwidely used in many fields, such as modern communication, remote sensing and controland intelligent instruments. All the time, all the researches are mainly with the help ofapproximate analysis. Few are focus on the process from the out-of-lock state to thein-lock state about the PLL.Chaos theory is an important part of the non-linear science,which can be used to analyze the characteristics of the PLL system and is excepted toin-depth interpret the complex process of PLL. Meanwhile, it has an important guidingsignificance for better understanding and application of the PLL.Firstly, Based on the Melnikov method, we analyze the second-order PLL on whetherit has chaotic characteristics or not. Some approaches, such as the bifurcation diagram,phase trajectories, power spectrum, Lyapunov exponent, Poincare mapping and so on, arecomprehensively utilized to further prove the second-order PLL having the law of motionof the chaotic system.Secondly, Through analysis of the stability of the stationary point in the PLL system,the corresponding relation between the out-of-lock state or in-lock state of thesecond-order PLL and the chaotic state or the periodic state are illustrated. Beside, weexplain the reason for the phenomenon of cycle slippery due to the out-of-lock. By usingthe least squares method and the incremental harmonic method, we obtain approximatesolutions of second-order PLL system, and take advantage of the Floquet theory to analyzethe stability of the solution. Then a qualitative description of the phase noise immunity tothe second-order PLL is illustrated at the condition of nonlinear state.Thirdly, Linear variable feedback control and sliding mode variable structure controlmethod are employed to realize chaos control of the second-order PLL system. The Linearvariable feedback control is mainly achieved by setting the feedback coefficient of control.Whereas the sliding mode variable structure control determine the desire state of systemby selecting the appropriate sliding plane, which is in purpose of achieving the chaoticstate turning into a cycle state of the PLL system, and then reach the in-lock state. Simulation experiments are carried out to demonstrate the feasibility of the approach.At last, The application of PLL in the detection of frequency modulation (FM) isstudied. A stable cycle state deriving from chaotic state can be obtained by chaos controlmethod, and the modulated frequencies in FM are achieved by power spectrum method.By combination of linear variable feedback control method and the extreme points, weestimate the modulation index of FM signal in the cycle state. Simulation experiments arecarried out to show the feasibility and efficiency of the above two methods.