Exploration of instantaneous frequency for local control assessment in real-time hybrid simulation

Local control parameters such as instantaneous delay and instantaneous amplitude play an essential role in evaluating the performance and maintaining the stability of real-time hybrid simulation(RTHS). However, existing methods have limitations in obtaining this local assessment in either the time domain or frequency domain. In this study, the instantaneous frequency is introduced to determine local control parameters for actuator tracking assessment in a real-time hybrid simulation. Instantaneous properties, including amplitude, delay, frequency and phase, are then calculated based on analytic signals translated from actuator tracking signals through the Hilbert transform. Potential issues are discussed and solutions are proposed for calculation of local control parameters. Numerical simulations are first conducted for sinusoidal and chirp signals with time varying amplitude error and delay to demonstrate the potential of the proposed method. Laboratory tests also are conducted for a predefined random signal as well as the RTHS of a single degree of freedom structure with a self-centering viscous damper to experimentally verify the effectiveness of the proposed use of the instantaneous frequency. Results from the ensuing analysis clearly demonstrate that the instantaneous frequency provides great potential for local control assessment, and the proposed method enables local tracking parameters with good accuracy.