Adaptive acceleration waveform control of two-degree-of-freedom dual electrohydraulic shaking tables

Multi-degree-of-freedom multiple table systems are developed for seismic testing of large-span structures to spread the loads evenly on the tables. Synchronous control of multiple shaking tables is challenging because of coupling between different shaking tables and complex dynamics of the testing systems. This article presents an adaptive waveform control for a two-degree-of-freedom dual electrohydraulic shaking tables testing system to improve the acceleration tracking performance. Synchronous control of the two electrohydraulic shaking tables is transformed into the motion control of a two-degree-of-freedom overconstrained shaking table driven by 10 actuators. The force control loop based on the null space of the Jacobian matrix is developed to reduce the cross-coupling among the actuators. An adaptive acceleration waveform control method based on the DFP optimization algorithm in a complex domain is presented to improve the convergence and stability of the compensation algorithm in the outer control loop and replicate the acceleration reference waveforms accurately. Experimental results obtained in step responses, acceleration frequency responses measurement, and two-degree-of-freedom waveform replication tests are used to demonstrate the effectiveness of the proposed method.