Nonlinear Signal-Based Control for a Shake Table Supporting a Heavy Multi-Storey Nonlinear Structure

Abstract

Shake table control is greatly affected by an interaction with a heavy specimen, especially when it has severe nonlinear characteristics. Hence, to this fundamental and challenging issue in the experimentation, this study proposes a solution using nonlinear signal-based control (NSBC) and demonstrates its effectiveness in actual experiments. Moreover, an innovative controller design is presented in this paper: the bare condition referenced (BCR) approach relies on the bare table dynamics and the specimen's weight. It frees the design from the properties of the controlled system, in contrast to the orthodox approach, which uses the dynamics of a table supporting a specimen. Following numerical examinations including a stability analysis, experiments were carried out on NSBC with these approaches, with a table having a three-storey structure that was 2.5 times heavier than the table and had nonlinear characteristics. An inversion-based controller, using a feedforward controller only, did not perform well, even at small excitations, owing to the modelling gap and nonlinearity. NSBC, with the orthodox approach, accurately realised the expected acceleration on the table, despite the considerable interaction with the specimen and the nonlinearity of its collapse level. NSBC, with the BCR approach, performed as well or better than the orthodox approach, despite the obvious modelling gap and nonlinearity. NSBC with both approaches can solve the challenging control problem and has considerable potential for deployment in large experiments. Furthermore, the BCR approach is more advantageous than the orthodox approach, as it eliminates the need to identify the dynamics of the table supporting the specimen.