Comparison of Data-Driven Methods on Discovering the Dynamics of the Unforced Multi-axis Cart System
Data-driven system identification is essential for understanding the behavior of real-world systems. Since the dynamics of such systems are often complicated, complex, or intractable, estimating them is essential to developing a model and applying control. This chapter compares the performance of various data-driven identification methods on a candidate system, the multi-axis cart system (MACS). The MACS is a mass–spring–damper system consisting of four discrete masses arranged in two axes. These two axes are then coupled using a rigid massless link. While the MACS is simple in construction, it can be configured to be linear or nonlinear and exhibits modes with components in two axes. Understanding the dynamics of this simple system can help gain insight into the behavior of more complicated systems. This chapter compares the performance of four popular data-driven identification methods, SINDy, SINDy-PI, DMD, and Hankel DMD (HDMD). The models were trained using many trajectories tracking the states and derivatives over time. The data was generated by simulating the governing equations for the system which were derived using Lagrange’s equations. To make a more appropriate comparison to real-world measurements, which innately have sensor noise, proportional random Gaussian noise was added. In addition to the trajectory error, several implicit properties of the models were analyzed such as model sparsity and model stability.
