Fast frequency and phase synchronization of high-stability oscillators with 1 PPS signal from satellite navigation systems

Abstract In this paper, we propose a novel algorithm for fast frequency and phase synchronization of high-stability oscillators synchronized with 1 PPS signal from satellite navigation systems. The algorithm uses a model of a control object in the space of state variables and controls the frequency of an oscillator operating in a phase-locked loop. A new element is the introduction to the theoretical analysis and the design process, the time of entering synchronization. Currently, the literature lacks theoretical analysis and design methodology that considers the impact of the synchronization time on the choice of the steering algorithm and its parameters. All the data needed to determine the numerical values of the model were found experimentally for three different classes of control objects. Short synchronization times, a detailed description of the design methodology, and the use of values measured in the real system distinguish the proposed algorithm from the solutions described in the literature. The effect of optimization was achieved thanks to the algorithm’s two-stage operation. In the first stage, the algorithm aims to minimize the phase error quickly. The best solution for this stage is Sliding Mode Control (SMC). In the second stage, the algorithm strives to maximize the control quality, understood as minimizing the values of Maximum Time Interval Error (MTIE) and Time Deviation (TDEV). The Model Predictive Control (MPC) and Linear-Quadratic Regulator (LQR) optimal control algorithms were used at this stage. The paper also investigated the influence of the tuning parameters of these algorithms (weights as a function of cost) on the long-term behavior of the control system.