Proportional–Integral Synchronization for Nonidentical Wireless Packet-Coupled Oscillators With Delays

Precise timing among wireless sensor nodes is a key enabling technology for time-sensitive industrial wireless sensor networks (WSNs). However, the accuracy of timing is degraded by manufacturing tolerance, aging of crystal oscillators, and communication delays. This article develops a framework of packet-coupled oscillators (PkCOs) to characterize the dynamics of communication and time synchronization of clocks in WSNs. The nonidentical clock is derived to describe the embedded clock's behavior accurately. A proportional-integral (PI) packet coupling scheme is proposed for synchronizing networked embedded clocks, while, scheduling wireless Sync packets to different slots for transmission. It also possesses the feature of automatically eliminating the effects of unknown processing delay, which further improves the synchronization performance. The rigorous theoretical analysis of PI-based PkCOs is presented via studying a closed-loop time synchronization system. The performance of PI-based PkCOs is evaluated on a hardware testbed of IEEE 802.15.4 WSN. The experimental results show that the precision of the proportional-integral PkCOs protocol is as high as 60 μs (i.e., 2 ticks) for 32.768 kHz crystal oscillator-based clocks.