## 1 Introduction  
Mathematical modelling has become the cornerstone of many technical disciplines. Models generally allow us to gain insight, answers, and guidance when analysing and predicting the behaviour of complex systems. Model-based engineering methods also provide essential tools in the field of mechatronics. Derivation of relevant models enables the optimisation of machine design before physical prototype assembly. This may help to avoid costly build-and-test cycles, speeding up the whole development process considerably. A high-fidelity model is a necessary prerequisite for employing modern control engineering methods and algorithms. It can be said that the achievable performance of a motion system is directly proportional to the predictive and explanatory power of the model used for the controller synthesis. On the other hand, an excessively complex model, albeit well suited for numerical simulations and predictions, may turn out to be useless for the process of control algorithms design. High-order nonlinear models are generally incompatible with well-established and generally applicable control design methods working mainly in the linear domain. Therefore, a general rule of thumb is to use a control-relevant model that is as simple as possible while capturing the significant features of the physical plant's dynamics essential for achieving formulated design requirements. Mathematical models of dynamic mechanical systems can be generally derived in two distinct ways. First-principles (or physics-based, white-box) approaches use all the available prior knowledge about the subject of study for the derivation of the equations of motion. This involves information about the system structure and geometry, basic laws of physics, mechanics, and other domains necessary to cover all the aspects of the system behaviour. The model parameters usually have an exact physical meaning and are closely related to the properties of the system under study. On the other hand, a data-driven (or black-box) approach uses quite a limited amount of a priori knowledge regarding the system and tries to deduce its dynamical properties indirectly by observing available input and output variables [1]. The model parameters often do not have a clear physical interpretation. They result from the specifically used data processing method and chosen model structure. The white-box method usually requires extensive knowledge about the physical system that may not be available in practice. Considerable effort is often required for the model derivation. The advantage is that the model may be inferred without having to construct and assemble a physical device. Therefore, such models may provide valuable insight when designing new systems that do not physically exist yet. On the other hand, the black-box approach is relatively simple to use when employing well-established methods available in the field of system identification [1; 2; 3]. Much less prior knowledge about the system is required, and high-fidelity models can be acquired from experimental data with less effort. However, back-box modelling typically depends on an extensive amount of the input-output data which have to be obtained from the experiments with the physical plant. A combination of both approaches can be used forming a grey-box modelling concept. In this case, the model properties and its structure are at least partially known in advance and particular parameters are derived from experimental data. The role of the model is being emphasised and changed at the same time significantly with the introduction of the Digital Twin concept [4; 5; 6; 7]. There is a fundamental shift in the understanding of what the model represents and how it can interact with its physical counterpart in the form of a device or machine to be designed and built.