Physics-based and data-driven modeling for linear systems using moment matching

First-principle models often fail to accurately capture system dynamics due to modeling simplifications and parameter uncertainties. This article introduces a data-driven technique for linear systems, enhancing baseline first-principle state-space models with black-box models obtained from experimental steady-state data. The proposed method parameterises models that achieve moment matching by integrating a known baseline model with a black-box component. Tools are provided to enforce a known interconnection structure or other physical knowledge. A mass-spring-damper system demonstrates the effectiveness of the technique.