Parametrizing mechanical systems using matrix fraction descriptions: with application to spatio-temporal identification

Identifying accurate Linear Parameter Varying models of flexible mechanical systems is crucial for the inference and control of unmeasured performance variables in high-performance mechatronic systems. A succesfull grey-box strategy to obtain accurate models through a local approach is to directly identify canonical mechanical systems, whose parameters can subsequently be interpolated in a physically motivated manner. Estimating these generally nonlinear-in-the parameter modal models from Frequency Response Function data through gradient-based techniques suffers from the potential of converging to sub-optimal estimates. In this research proposes a novel Matrix-Fraction Description parametrisation that is shown to be equivalent to the relevant class of modal mechanical systems. This parametrisation enables the formulation of the Sanathanan-and-Koerner and Instrumental Variables estimators which are known to attain the global optimum upon convergence.
The proposed parametrisation is successfully employed to directly estimate a large set of local models of various position-dependent motion systems, thereby confirming that proposed the identification method is well-suited for practical applications.