Nuances in modeling and impedance-inspired control of shake tables for tracking ground-motion trajectories

Servo-hydraulic shake tables are widely used for simulating earthquake shaking in a laboratory environment. Control procedures for shake-table testing and the associated mathematical models are well documented. An evaluation of such models revealed nuances regarding actuator control, which led to the development of the simple, easy to implement, robust shake-table controller described in this paper. This controller design recognizes that (i) differential pressure feedback in actuator control is highly beneficial in reducing the consequences of hydraulic-related nonlinearities and other modeling uncertainties, (ii) the bandwidth over which differential pressure feedback is useful is limited by the sampling frequency of the chosen digital controller, (iii) a linear model predicts shake-table response with high fidelity across a broad frequency range for a carefully chosen differential pressure gain and a sufficiently large controller sampling frequency, and (iv) shake-table transfer functions derived from such a linear model are highly effective in designing a feedforward controller. Further, and perhaps most importantly, the controller utilizes real-time feedback of the reaction force from the test article to account for table-test article interaction. The three clear advantages of the proposed shake-table controller are (i) the test-article dynamics are decoupled from the control design, (ii) the need for offline/online iterative tuning, which is often ground motion- and test article-specific, is minimized, and (iii) control procedures for shake tables can be standardized, all of which are validated in this paper through a series of experiments performed on a uniaxial hydraulic shake table.