Experimentally investigating the influence of changing payload stiffness on outer loop iterative learning control strategies with shaking table tests

Shaking tables are widely used across numerous engineering research and industrial sectors, including mechanical (e.g. automotive and aerospace testing), electrical (e.g. instrumentation testing) and civil (e.g. structural and geotechnical testing) engineering. It is commonly required to replicate the shake table motions accurately and precisely. Iterative learning control algorithms can be used to complement traditional proportional-integral-differential feedback control algorithms to optimize drive signals using a test payload prior to the real experiment. Historically, the design of these test payloads has focused on matching the mass of the actual payload and neglected its dynamic response. In this study, experimental results from shake table tests using multiple geotechnical containers with dry and saturated beds that exhibit a range of stiffnesses and material damping when shaken are presented. Errors between the demanded and achieved motions are explored and compared to the changing secant stiffness abstracted from the dynamic shear stress-strain loops of the payload. A clear trend emerges that demonstrates increased errors as the payload stiffness deviates from the constant stiffness test payload originally used with the open loop iterative learning control, and further the errors are not necessarily bounded by test payloads significantly softer or stiffer than the actual specimen. The findings support that in cases where repeatable, accurate and precise shake table motions are required for payloads that exhibit a complex material response that is not readily modelled mathematically, it may be necessary to reproduce the specimen's overall dynamic response during the iterative learning control process.