A novel internal force decoupling control algorithm under varying eccentric loads in vertically redundant shaking tables

Abstract Large-scale vertically redundant shaking tables are critical for indoor structural testing, yet internal forces within the system have long been regarded as redundant. However, decoupling internal forces becomes highly complex and challenging as the position and weight of the load/specimen vary. In this study, the spherical hinge is modeled as a spring–damper system, and a general force coupling model—incorporating mechanical, geometric, and deformation coupling—is proposed by considering the load’s position and mass. A novel descending internal force (DIF) algorithm based on the matrix form of the force coupling model is then proposed, and its effectiveness is validated by simulation. Finally, validation experiments with varying eccentric loads were conducted on a scaled model, an electric shaking table. The results show that the maximum error of the proposed coupling model is within 3.2%. The DIF algorithm can significantly reduce internal forces, from [141.0, −142.6, 145.6, −144.5 ] T N to [−1.9, 1.5, 1.6, −0.4] T N. The proposed method achieves decoupling of internal forces in vertically redundant mechanisms under varying eccentric loads, enjoying the advantages of high accuracy, high efficiency, and rapid response.