Shake table control method for nonlinear hysteretic systems

The shake table testing is an important experimental tool in order to reproduce the conditions of true effects of seismic motions by challenging complex structural and non-structural specimens. It is well known that as specimens are mounted on shake tables, the interaction between shake tables and specimens influence the system dynamics. In order to compensate the interaction, open loop feedforward compensation methods by using inverse transfer functions have been successfully used in current practice of table controls, assuming the controlled systems are linear. However, when flexible and heavy specimens experience nonlinear behaviour during shake table testing, unsatisfactory signal reproductions were observed. Based on stringent requirements of qualification testing where specific target motions are required, this study aims to develop more advanced control scheme for investigative and qualification purposes. This paper focuses on the development of adaptive tracking control scheme for which the feedback linearization control method is combined with the extended Kalman filter as estimator of state and parameter estimation in real time. The developed method has been implemented to a uniaxial shake table and a steel frame structure equipped with a friction damper at the University at Buffalo. The experimental setup and the initial results are discussed. Numerical simulations using identified system parameters demonstrate that the new method can be used to simulate target motions at desired locations of specimens having nonlinear hysteretic behaviour.