Robust Frequency-Adaptive Quadrature PLLs with Lyapunov-certified Global Stability

This work describes and compares two phaselocked- loop (PLL) algorithms aimed at tracking a biased sinusoidal signal with unknown frequency, amplitude and phase, with inherent robustness to dc-offset. The proposed methods endow Quadrature PLLs, renowned for their excellent tracking performance, with frequency-adaptation capability, while providing robust global stability certificates. The large-gain global stability, proven by Lyapunov-like arguments borrowed from adaptive control theory, represents a major benefit compared to conventional PLLs, whose convergence instead can be proven only locally by small-signal analysis or small-gain assumptions. In this connection, the proposed algorithms represent the first frequency-adaptive and DC-bias rejecting PLL-type architectures with Lyapunov-certified global stability. When used for signal tracking, the proposed methods are shown to outperform the adaptive observer, especially in noisy conditions. Moreover, they provide more accurate frequency estimates than existent frequency-adaptive PLLs, showing enhanced robustness in facing both phase-noise and measurement perturbations.