An electro-hydraulic shaking table (EHST) is used for real-time replication of situations that occur in civil and architectural engineering, the automotive industry, and earthquake resistance testing. EHSTs are able to generate a large force at high speeds over a wide frequency range and this feature makes them invaluable in performing vibration tests. Unfortunately, due to the inherent dynamics of the EHST system’s hydraulics, the output response of an EHST system displays magnitude attenuation and phase delays in response to displacement and acceleration commands. A feedforward inverse model (FFIM) combined with adaptive inverse control (AIC) is proposed to improve the tracking performance of the EHST following specified displacement and acceleration commands. The proposed control strategy utilizes a FFIM to extend the EHST system’s frequency bandwidth and uses AIC based on a recursive least squares (RLS) algorithm to adaptively adjust the time domain drive signal of the EHST servo controller and improve the tracking accuracy. Experimental and simulation results demonstrate the effectiveness of the proposed combined control strategy.

A common approach for simplification analysis of complex dynamic model is presented, and the simplified dynamic model of a spatial 6-DOF parallel motion system with high computational efficiency is proposed for high real time control. By using Kane method, the full dynamic model of a spatial 6-DOF parallel motion system viewed as 13 rigid bodies is built. With rigid body decomposition, the full dynamic model is separated into several parts firstly, and then some separated parts are further divided into many dynamic components in terms of motion separation and the relationship with acceleration or velocity. The contribution of each dynamic term is analyzed for a specified spatial 6-DOF parallel motion system, and the simplified model is derived. Comparing with full dynamic model, the simplified error is analyzed, and the computational efficiency of the simplified model is discussed in a real-time industrial computer. The simplified strategy is confirmed in simulation. The simplified error is less than 8%, the simplified model can improve the computational efficiency by more than 70%, and the execution time is less than 0.1 ms, which can achieve the requirements of high real time control. The numerical results illustrate that the proposed approach is feasible and effective for simplification analysis of dynamics and the derived simplified dynamic model can be used in real-time control system with small simplified error.

In order to obtain direct solutions of parallel manipulator without divergence in real time, a modified global Newton-Raphson (MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom (DOF) parallel manipulator. Based on geometrical frame of parallel manipulator, the highly nonlinear equations of kinematics were derived using analytical approach. The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration. The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio .NET for implementation. The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed. Applying the MGNR algorithm, the real generalized pose of moving platform is solved by using the set of given positions of actuators. The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy (1×10 −9 m in linear motion and 1×10 −9 rad in angular motion), even the initial guess value is far from the root.

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