This paper presents the mechatronic design, mathematical modeling, parameter identification, and nonlinear position control of an open-architecture biaxial shake table capable of generating base acceleration along two orthogonal horizontal directions. The shake table is tailored for engineering research and education. Addressing the limitations of proprietary “black-box” systems, the platform is constructed using standard industrial components (HLTNC-CNC modules and NEMA 23 BLDC motors) to ensure reproducibility. A core contribution is the characterization of the system’s nonlinear dynamics to enhance tracking fidelity. The mathematical model, derived via the Euler–Lagrange formulation, incorporates viscous and Coulomb friction phenomena, which are critical for accurately reproducing zero-velocity crossings in seismic signals. System parameters are identified using the Recursive Least Squares (RLS) algorithm combined with State Variable Filters (SVFs) to process the regression vector. To enable precise closed-loop performance, a nonlinear state observer incorporating the identified friction dynamics is designed for velocity estimation. Furthermore, a Computed Torque Control (CTC) strategy is synthesized and compared against a conventional Proportional-Velocity (PV) controller. Experimental validations using historical ground motions, including the 1986 Colima earthquake, confirm that the CTC strategy reduces the maximum absolute tracking error by more than 75% compared to the PV approach, bounding the peak error to 0.36mm across both axes. Furthermore, in high-amplitude scenarios, the proposed model-based approach achieved an RMS tracking error reduction of more than 83%. These results validate the proposed platform as a reliable and accessible tool for structural dynamics testing.
Ramírez-Zúñiga et al. (Mon,) studied this question.