Jie Feng

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.

Conventional floating bridge systems used during emergency repairs, such as during wartime or after natural disasters, typically rely on passive rubber bearings or semi-active control systems. These methods often limit traffic speed, stability, and safety under dynamic conditions, including varying vehicle loads and fluctuating water levels. To address these challenges, this study proposes a novel Hydraulic Self-Adaptive Bearing System (HABS). The system integrates real-time position closed-loop control and a flexible support compensation method to enhance stability and adaptability to environmental changes. A modified three-variable controller is introduced to optimise load response, while a multi-state observer control strategy effectively reduces vibrations and improves traffic smoothness. A 1:15 scale prototype was constructed, and a co-simulation model combining MATLAB/Simulink and MSC Adams was developed to simulate various operational conditions. Results from both experiments and simulations demonstrate the HABS’s ability to adapt to varying loads and environmental disturbances, achieving a 72% reduction in displacement and a 54% reduction in acceleration. These improvements enhance traffic speed, stability, and safety, making the system a promising solution for emergency and floating bridges, providing superior performance under challenging and dynamic conditions.

The adaptive iterative learning control method for electro-hydraulic shaking tables based on the complex optimization algorithm was proposed to overcome the potential stability problem of the traditional iteration control method. The system identification precision’s influence on convergence was analyzed. Based on the real optimization theory and the mapping relationship between real vector space and complex vector space, the complex Broyden optimization iterative algorithm was proposed, and its stability and convergence was analyzed. To improve the stability and accelerate the convergence of the proposed algorithm, the complex steepest descent algorithm was proposed to cooperate with the complex Broyden optimization algorithm, which can adaptively optimize the complex steepest gradient iterative gain and update the system impedance in real time during the control process. The shaking tables experiment system was designed, applying xPC target rapid prototype control technology, and a series of experimental tests were performed. The results indicated that the proposed control method can quickly and stably converge to the optimal solution no matter whether the system identification error is small or large, and, thus, verified that validity and feasibility of the proposed adaptive iterative learning method.