Basic examination of two substructuring schemes for shake table tests

Abstract

Summary This study examines two basic substructuring schemes for shake table tests where the dynamics of the table is significantly affected by a specimen. The hybrid simulation (HS) scheme, commonly adopted in substructuring experiments, directly uses the output of a numerical substructure as an input signal to a physical substructure. The dynamical substructuring system (DSS) scheme, developed long after HS, uses feedforward and feedback controllers to minimise the control error produced by the outputs of numerical and physical substructures. Before examining these two schemes, this study introduces a systematic formulation for dividing a multi‐degree‐of‐freedom emulate system into a numerical substructure and a physical substructure with a shake table. Then, controller designs for HS and DSS are discussed for the substructures. The two schemes with basic control approaches were numerically examined through substructuring tests for a linear 3DOF emulate system. DSS with stability was powerful even under a control condition with a pure time delay and inaccurate estimation of the table dynamics, whereas these factors degraded the HS performance. In additional simulations in which nonlinear characteristics were considered, the performance of DSS (HS) was degraded mainly by the nonlinear (inaccurate estimation of the table dynamics). It was found that the stability of substructures with nonlinear characteristics could be roughly assessed by the Nyquist stability criterion. These simulations with/without nonlinear characteristics clarified the performances of the HS and DSS schemes through basic control approaches and stability analysis under practical conditions.

Nonlinear substructuring control for simultaneous control of acceleration and displacement in shake table substructuring experiments

“…NLSC was developed as an enhancement of LSC for nonlinear systems, and it has been applied to substructuring experiments using hydraulic actuators. 43,44 According to a basic study of shake table substructuring experiments, 21 the block diagram of a shake table experiment using LSC is depicted as Figure 1. In shake table experiments, the shake table dynamics is significantly influenced by the specimen and its structural conditions.…”

“…In this experiment, the output signal at the top storey of the numerical substructure is the reference signal to be realised on the shake table, and the output signal of the shake table, which is part of the physical substructure, is the controlled signal. Since the DSS scheme is insensitive to the variation of a pure time delay, 21 shake table substructuring experiments using NLSC are discussed on the basis of a constant delay.…”

“…Shake table substructuring experiments using NLSC require linear models of the substructures for its implementation, and the substructuring form basically follows that of LSC 21 . This section introduces the linear model design and formulation to extract the substructures from an emulate system.…”

“…4,14,25,26 Such experiments are now performed by shake tables, which are more complicated than actuators. Currently, the development of shake table substructuring experiment 21,[27][28][29][30] is of great interest in earthquake and structural engineering. The current development of shake table substructuring experiment is mainly limited to displacement control.…”

“…In addition, the DSS scheme regards the set of two substructures together with actuation systems as the controlled system, and the controller design requires the entire dynamics of the substructures and actuation systems 4 . As demonstrated by a basic examination of HS and DSS schemes, 21 the reflection of the entire dynamics into the DSS controller design makes its control accuracy insensitive to a pure time delay once the stability is maintained. Therefore, the DSS scheme can be freed from the requirements of a very accurate identification of the delay and its compensation, which are fundamentally important in the HS scheme.…”