Stability analysis of SDOF real‐time hybrid testing systems with explicit integration algorithms and actuator delay

Abstract

SUMMARYReal-time hybrid testing is a method that combines experimental substructure(s) representing component(s) of a structure with a numerical model of the remaining part of the structure. These substructures are combined with the integration algorithm for the test and the servo-hydraulic actuator to form the real-time hybrid testing system. The inherent dynamics of the servo-hydraulic actuator used in real-time hybrid testing will give rise to a time delay, which may result in a degradation of accuracy of the test, and possibly render the system to become unstable. To acquire a better understanding of the stability of a real-time hybrid test with actuator delay, a stability analysis procedure for single-degree-of-freedom structures is presented that includes both the actuator delay and an explicit integration algorithm. The actuator delay is modeled by a discrete transfer function and combined with a discrete transfer function representing the integration algorithm to form a closed-loop transfer function for the real-time hybrid testing system. The stability of the system is investigated by examining the poles of the closed-loop transfer function. The effect of actuator delay on the stability of a real-time hybrid test is shown to be dependent on the structural parameters as well as the form of the integration algorithm. The stability analysis results can have a significant difference compared with the solution from the delay differential equation, thereby illustrating the need to include the integration algorithm in the stability analysis of a real-time hybrid testing system.

An overview of seismic hybrid testing of engineering structures

“…Chen and Ricles [61] developed an unconditionally stable explicit integration algorithm for RTHT using a discrete transfer function approach (known as the CR method).…”

Experimental evaluation of the seismic performance of steel MRFs with compressed elastomer dampers using large-scale real-time hybrid simulation

“…In the real-time hybrid simulations presented herein, u d and ω where assumed equal to the expected damper deformation from the SDP and the first mode cyclic frequency of the building, respectively. Preliminary real-time hybrid simulations showed that the response results where insensitive to small variations of the selected values of u d and ω. Chen and Ricles [32] showed that it is necessary to include the damping and stiffness of the complete structure in Eq. (3) to ensure that the integration parameters result in maintaining a stable solution.…”

“…This time delay is usually referred to as actuator delay and will result in a desynchronization between the measured restoring forces from the experimental substructure(s) and the integration algorithm in a real-time hybrid simulation. Studies on the effect of actuator delay [31,32] show that actuator delay is equivalent to creating negative damping, which can destabilize a real-time hybrid simulation if not compensated properly.…”

“…These values were established by Chen by conducting parametric studies of the servo-hydraulic systems at the RTMD [32].…”

Use of Real-Time Hybrid Simulation to Evaluate the Performance-Based Seismic Design of Steel MRFs with Compressed Elastomer Dampers

“…This time delay is usually referred to as actuator delay and will result in a desynchronization between the measured restoring forces from the experimental substructures and the integration algorithm in a real-time hybrid simulation. Studies on the effect of actuator delay (Wallace et al 2005, Chen andRicles 2008b) have shown that actuator delay is equivalent to creating negative damping and can destabilize a real-time hybrid simulation if not compensated properly.…”