## 2 Materials and Methods
### Data-Driven System Identification  
Data-driven system identification is another widely used modelling approach. The model is constructed based on the information extracted from the experimental data. This allows high-fidelity models to be delivered from observations without relying on a detailed prior knowledge of geometry and physics involved in the dynamics of the controlled plant. The derived models are often directly applicable for the subsequent step of model-based control design. On the other hand, they often offer a limited insight into physical properties of the system under study. This may be necessary for qualified predictions regarding machine design changes made in the early phases of the development cycle. Moreover, a prototype has to be built physically to allow execution of experiments for data acquisition. In our approach, we consider two different scenarios in which the data-driven identification may be used as a complement to the physics-based modelling:  
1. **Experimental identification for direct derivation of a control-relevant model** The first scenario is relevant for the final phases of machine construction, assembly and control system commissioning. The data gathered from an experiment with the real plant may often offer more information than first-principle models. This is due to several factors usually not taken into consideration when developing the analytical and FEM models such as actuator/sensor dynamics and noise characteristics, unknown material properties or construction tolerances, and varying assembly conditions, e.g., clamping, tightening, and friction forces. The first-principle models may be used to derive a proper structure of the control-relevant model, e.g., by estimating a number of oscillatory modes in the target bandwidth range. The data-driven identification provides parameters for the assumed model structure. The result is used for the subsequent control algorithm design. 2. **Experimental identification as a means for improving quality of the physics-based models** This scenario involves early stages of development that often use various testbeds and prototype designs for the validation of predictions made by physics-based models. Employment of the experiments allows the geometrical or analytical models to be further refined. The location and damping of the eigenmodes acquired from the experiments may be used to tune material and geometrical properties in the first-principle models, extending their predictive and extrapolation capabilities. In this way, the amount of model uncertainty can be vastly reduced. We focused mainly on the second scenario, which combines physics- and data-driven modelling approaches together. Our goal was to compare the results obtained from the analytical, FEM, and experimental models and provide some guidelines to the ways of incorporating the experimental results in the modelling process. Section 3 summarises our findings and recommendations in this context. As for the data-driven identification, there is a wide variety of well-developed, tried and tested methods and algorithms available in the linear systems theory [1; 2; 3] that can be applied for this purpose. We opted for the frequency-domain modelling and identification framework outlined in [2], which provides some inherent advantages when used for flexible motion systems:  
* Utilisation of deterministic periodic excitation signals for the experiments allowing to employ powerful averaging techniques to mitigate measurement noise and transient dynamics effects;
* Derivation of non-parametric frequency response function (FRF) as an intermediate step that may serve for model validation, providing a description of the oscillatory dynamics in a more natural way than time-domain models;
* Possibility of derivation of non-parametric noise models allowing model uncertainty to be evaluated;
* Numerically robust algorithms available for synthesis of the parametric transfer function models.