Stability analysis of real‐time dynamic substructuring using delay differential equation models

Abstract

SUMMARYReal-time dynamic substructuring is an experimental technique for testing the dynamic behaviour of complex structures. It involves creating a hybrid model of the entire structure by combining an experimental test piece-the substructure-with a numerical model describing the remainder of the system. The technique is useful when it is impractical to experimentally test the entire structure or complete numerical modelling is insu cient.In this paper, we focus on the in uence of delay in the system, which is generally due to the inherent dynamics of the transfer systems (actuators) used for structural testing. This naturally gives rise to a delay di erential equation (DDE) model of the substructured system. With the case of a substructured system consisting of a single mass-spring oscillator we demonstrate how a DDE model can be used to understand the in uence of the response delay of the actuator. Speciÿcally, we describe a number of methods for identifying the critical time delay above which the system becomes unstable.Because of the low damping in many large structures a typical situation is that a substructuring test would operate in an unstable region if additional techniques were not implemented in practice. We demonstrate with an adaptive delay compensation technique that the substructured mass-spring oscillator system can be stabilized successfully in an experiment. The approach of DDE modelling also allows us to determine the dependence of the critical delay on the parameters of the delay compensation scheme. Using this approach we develop an over-compensation scheme that will help ensure stable experimental testing from initiation to steady state operation. This technique is particularly suited to sti structures or those with very low natural damping as regularly encountered in structural engineering.

Modelling and control issues of dynamically substructured systems: adaptive forward prediction taken as an example

“…Here, the estimated delay in equation (2.4) is parametrized by Figure 3. The over-compensation scheme of the AFP controller in [16].…”

“…With reference to [16,17], the adaptive laws of σ (t) and ρ(t) in equations (2.8) and (2.9) are expressed by horizontal delay correction:…”

“…compensating for the phase lag and gain modulation in the classic control sense, involve more concerns, such as the computational speed and numerical accuracy of the matrix inversion. Furthermore, in (d), information of Σ 2 and G TS models is usually required [16] in order to precisely parametrize the controller and to guarantee settling stability; this may degrade the benefit of using adaptive strategies. These two observations motivated the research into the efficacy of delay compensation and AFP techniques.…”

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

“…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.…”

Substructure Hybrid Simulation Boundary Technique Based on Beam/Column Inflection Points

“…Beginning in the 1990s, development and application of HS in Europe, Asia, and other regions grew significantly [5][6][7]. For structural systems with rate-dependent components, real-time HS testing was proposed and developed [8][9][10][11][12][13][14][15]. Moreover, HS also allows testing to be geographically distributed in multiple testing facilities.…”