High-fidelity Tracking Control of Electric Shaking Tables ⋆

This paper proposes a design method of tracking control for electric shaking tables via the stochastic optimal control theory with preview action based on a third-order model with respect to the jerk, acceleration, velocity and displacement of the table. The reaction force caused by the dynamic motion of a test structure subjected to seismic disturbances can be regarded as a random disturbance for the shaking table. The mission of our tracking controller is accurately to reproduce the earthquake ground motions using the derived third-order model and the preview information of the displacement of the ground motions. An augmented discretetime stochastic system of an incremental state and an incremental tracking error corresponding to the shaking table is constructed. This system is subject to the sum of the reaction force of the test structure and its derivative which is modeled by a white Gaussian noise. Combining this system with a command generator for making the preview information, a stochastic optimal tracking control based on the noisy observation data is constructed for the resultant system.