A Servo-Clock Model for Chains of Transparent Clocks Affected by Synchronization Period Jitter

Industrial networks for distributed monitoring, control, and automation purposes require high-accuracy clock synchronization in topologies including long chains of cascaded nodes. Unfortunately, accuracy typically degrades as the number of devices and the distance from the synchronization reference node (i.e., the master or grandmaster) grows, because of the accumulation of multiple uncertainty contributions. To mitigate this problem, the so-called transparent clocks are used in some synchronization protocols, such as the precision transparent clock protocol used in PROFINET IO isochronous real time networks and the precision time protocol version 2, standardized as IEEE 1588-2008. In this paper, an optimal servo-clock in the mean square sense is proposed. The controller relies on both a Kalman filter that estimates the clock state difference with respect to the master and a static-state feedback assuring mean square stability even under the effect of significant fluctuations of the synchronization period. Several multiparametric simulation results in a case study based on the features of PROFINET IO devices confirm that excellent performance can be achieved with the proposed approach.