COMPARISON OF INTEGRATION ALGORITHMS FOR REAL-TIME HYBRID SIMULATION USING FREQUENCY DOMAIN-BASED ERROR INDICATORS

Real-time hybrid simulation (RTHS) is a testing method that combines computer simulation (i.e., analytical substructure) with physical testing (i.e., experimental substructure). This enables investigation of dynamic characteristics of load-rate dependent complex structures. To ensure reliable experimental results, even in the presence of sophisticated controllers and compensation methods, it is necessary to evaluate the accuracy of the success of the hydraulic actuators in imposing the command displacements. With recent developments in tracking error monitoring, new indicators have been proposed that are based on frequency domain analysis and can successfully uncouple phase (lag and lead) and amplitude (overshoot and undershoot) errors and quantify them. These new frequency-based error indicators are not structure-specific and can be reliably used to examine the effectiveness of each component of RTHS inner (i.e., servo-control) and outer (i.e., integration algorithm) loops. In this paper, frequency domain-based (FDB) error indicators are employed to evaluate the effectiveness of five commonly-used integration algorithms (i.e. central difference method, explicit Newmark method, discrete state space formulation with a zero-order hold and first-order hold, the state-space formulation by Zhang et al., and the alpha method) in different test scenarios. The applicability of the FDB error indicators to nonlinear systems is first verified through numerical simulations performed on a nonlinear system with predefined parameters. Then these indicators are used to post-process the experimental results obtained from RTHS’s with various integration algorithms. The experiments are carried out on a system with a nonlinear analytical substructure and a linear experimental substructure at the University of Toronto. Findings from numerical simulation and experimental results demonstrate that the FDB method is an efficient approach to compare performances of different integration algorithms.