Modeling and prediction of nonlinear cable slab dynamics using Koopman operators

A novel approach for modeling the nonlinear dynamics of cable slabs using Koopman operator theory is presented. Cable slab dynamics are a critical challenge in precision motion systems, as the cables can induce undesired vibrations and disturbances on motion stages. To address this, a higher-dimensional state-space model with nonlinear observable functions is developed to approximate the cable slab dynamics. The proposed model achieves a prediction error within $\sim 1$% over the specified motion range and demonstrates robustness in predicting untrained, randomized, acyclic cable slab motions. A systematic evaluation of various observable functions was conducted to minimize the modeling errors, leading to an optimized model with fractional-order exponents. When compared with a neural network-based state-space model (NN-SS), the Koopman approach demonstrated faster training and better performance. For force prediction, the Koopman approach achieved a reduction of three-quarters in maximum error when compared with the NN-SS method. This work offers a concise and experimentally validated analytical framework specifically for developing accurate predictive models of nonlinear cable slab dynamics.