Data Synchronization for Offline and Online Identification of Dynamic Systems

System dynamics identification has an important role in engineering, whether it is for used for modeling dynamic objects or mechanisms, controller design, or simulation of dynamic systems. The accuracy of estimation certainly depends on how the input variables used for estimation are obtained and synchronized in time. For systems such as actuators where usually only position is measured, the velocity and acceleration input variables are obtained in discrete-time domain through difference equations that shift the signals in time. In this way, the incorrect data synchronization in time might become an issue; likewise in online identification where filters used might cause significant phase delay. In this paper, the effect of discrete data synchronization for offline and online identification of dynamic systems is studied. The identification process is performed utilizing the widely-known batch Least Squares (LS) method and Recursive LS for off-line and on-line identification processes. Four possible combinations of backward difference and forward difference techniques are utilized for computing velocity and acceleration. Simulations of linear-time-invariant mass-damper-spring system for ten sets of system parameters are used to identify the best way to synchronize the data within the four possible differentiation options. The performance of the four options are evaluated in terms of parameter convergence and force prediction in the root mean square error sense. The results are discussed and guidelines are presented.