Online learning compensation control of an electro-hydraulic shaking table using Echo State Networks

Electro-hydraulic shaking table (EHST) is widely used to simulate earthquake excitation in structural seismic tests. However, the nonlinear characteristics of the EHST, such as oil flow, friction, and dead zone, often lead to the distortion of seismic wave acceleration tracking and even cause the failure of the test. This paper describes the first application of Echo-State Networks (ESNs) to achieve high-precision seismic acceleration tracking of the EHST. The nonlinear control ability of the conventional three-variable control (TVC) algorithm in the EHST is discussed. An online learning compensation control framework using ESNs for "Transfer System" (The "Transfer System" denotes the nonlinear EHST controlled by TVC) is proposed. The least mean square (LMS) algorithm based on filtered-X is used to train the "ESN-Controller" online, and the initial transients of the "ESN-Controller" are reduced by using an estimation model of the actual "Transfer System" and a conditional switch. The offline iterative control (OIC) and nonlinear signal-based control (NSBC) are taken as the baseline algorithms of the proposed online learning compensation control. Simulation results show that the proposed online learning compensation control achieved excellent control with Pearson correlation coefficients of reference and responses above 99.6%, whereas the OIC and NSBC provided insufficient control. Moreover, the proposed online learning compensation control can also reduce the control error caused by the non-optimal TVC gains in the linear part of the EHST. This work throws new light on the study of the online learning control algorithm of the EHST.