Implementation and stability study of phase-locked-loop nonlinear dynamic measurement systems

We study the stability and convergence of a phase-locked-loop applied to a nonlinear system. It has been shown through numerical simulations by previous investigators that nonlinearity gives rise to oscillatory instability. By applying the method of averaging to the nonlinear system, we found that the nonlinear system has the identical criterion for stability as the linear system. However, the stable equilibrium has a shrinking domain of attraction as the nonlinearity increases. We show this by examining the feedback function. Moreover, we propose a nonlinear feedback which has faster convergence rate.