Koopman Operator-Based Modeling of Cable Slab Nonlinear Dynamics

This paper presents a higher-dimensional state-space model for predicting the nonlinear dynamics of a cable slab using Koopman operators. Currently, cable slab dynamics is a problem in precision motion systems, as the cable can impart unwanted vibrations or disturbances onto the motion stage. Currently, there is no definitive analytical model of the cable slab dynamics. The development process involved systematically evaluating various Koopman observable functions to minimize tracking errors. The model achieves an error margin of approximately ±1% for the given motion range and is robust enough to predict the movement of untrained acyclic randomized cable slab motions. Through a Koopman Operator approach the analytical formulation of the nonlinear cable slab dynamics is approximated. The model is verified through experimental results.