Proportional-Integral Synchronisation for Non-identical 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, ageing of crystal oscillators, and communication delays. This paper develops a framework of Packet-Coupled Oscillator (PkCOs) to characterise the dynamics of communication and time synchronisation of clocks in WSNs. A non-identical clock is derived to describe the embedded clock's behaviour accurately. The Proportional-Integral (PI) packet coupling scheme is proposed for synchronising networked embedded clocks, meanwhile, 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 synchronisation performance. The rigorous theoretical analysis of PI-based PkCOs is presented via studying a closed-loop time synchronisation 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 60us (i.e., 2 ticks) for 32.768kHz crystal oscillator-based clocks.