Accurate attitude tracking of six degree of freedom electrohydraulic shaking tables (EHSTs) is restricted by parameter uncertainty, nonlinearity, strong coupling, and external disturbances. Existing sliding mode control schemes are limited by fixed switching gains and the absence of integral compensation, which restrict steady-state accuracy and dynamic adaptability under nonlinear hydraulic effects and multi-axis coupling. An Adaptive Integral Sliding Mode Control (AISMC) scheme is developed to address these factors through two coordinated elements: an integral sliding surface that removes steady state deviation caused by static disturbances such as servo valve dead zones and hydraulic leakage, and an adaptive switching gain that regulates the reaching dynamics online without reliance on conservative bounds; a decay term in the gain update restrains parameter drift and keeps the adaptation bounded. Lyapunov analysis establishes closed loop stability and finite time convergence of the tracking error under bounded uncertainties and excitations. Simulation studies on a six degree of freedom EHST with a broadband random reference (0.1-10 Hz, 10 mm) compare AISMC with Sliding Mode Control (SMC) along X , Y , and Z . Pose tracking shows consistent gains, with the maximum value reduced by about 11.5-11.9 % and the root mean square (RMS) reduced by about 34.9-35.1 %. Pose error decreases from 0.392-0.396 mm to 0.035-0.036 mm in maximum value and from 0.175-0.177 mm to 0.015-0.016 mm in RMS. Acceleration tracking under AISMC approaches the reference in X and Z and improves in Y , while acceleration error decreases by about 83.5 % in X and Y and about 88 % in Z . The results indicate higher control precision, smoother transients with reduced chattering, and robust multi axis coordination suitable for practical vibration testing applications.
Liu et al. (Sat,) studied this question.
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