## 4 Linking the Two Approaches
### Application to the Multicopter Example  
In this section, the applicability of the expanded class diagram, which was developed to allow the integration of the IFM Framework into the engineering framework, is evaluated and tested by means of an application following the example of a product family of multicopters (see [49]), as shown in Figure 13 (adapted from [50]). Figure 12: UML class diagram for function modeling in DC43. From a mechanical point of view, a multicopter is a fairly simple technical system that receives its ability for stable flight primarily as a consequence of powerful control engineering. The simplest possible basic structure of a multicopter can be realized with a circular arrangement of four rotors, which are arranged within an angle of 90 degrees between each other (see Figure 13). The motors, which are driving these rotors, are usually mounted on a lightweight frame. This frame is usually equipped with a landing gear and appliances for fitting the electronics and the components of the power supply. It is possible to vary many parameters of the multicopter, such as rotor size and rotor blade pitch, motor torque and battery capacity. However, it is also possible to vary the number of rotors and motors and to create, for instance, hexacopters and octocopters. This multicopter product family was chosen in this paper as it combines mechanical and electrical design as well as control engineering, and has been used repeatedly in the past as a suitable example for digital modeling in design engineering. Additionally, the multicopter family serves as an example for investigating lightweight design development in GBDLs. The specific challenge with lightweight design is to develop, simulate and optimize geometries that dispose of a frame structure that is very rigid in order to be able to suppress oscillations and to enable enhanced flight control. For the purpose of deriving a superior design, this multicopter is modeled using GBDLs (see [47]) in order to allow the investigation of multiple configurations (e.g., octocopter) as well as of the performance of multi-domain simulations. For a functional representation of this multicopter family, it is mandatory to consider the fact that several use cases (starting, hovering, descending, etc.) have to be taken into account. The consideration of the use cases will initially allow the collection of necessary processes and will lead to the formulation of a list of processes. An example of a process is process 2, _\"distribute energy according to need\"_, that describes the distribution and control of the electricity for the electrical motors that drive the rotors of the multicopter; this description is abstract and is on a solution-neutral level. The different processes that are formulated in the function model of the multicopter are listed in Table 3.  
The developed IFM of the multicopter family is described in Figures 14-16. As explained in Section 3.1, the IFM Framework offers a maximum of five views on the technical system; Figure 14 illustrates an excerpt of the state view for the example of the multicopter. Figure 13: Basic structure of a multicopter, its CAD model and its concrete realization. Figure 14: State view of the IF model (excerpt). \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Number** & **Process** \\ \hline
1 & Starting system \\ \hline
2 & Distributing energy according to stated need \\ \hline
3 & Sending steering command \\ \hline
4 & Sending steering command via remote \\ \hline
5 & Calculating flightpath and motor engagement \\ \hline
6 & Increasing or decreasing rotation speed of drive motors \\ \hline
7 & Tracking left \\ \hline
8 & Tracking rate of ascent or descent \\ \hline
9 & Tracking roll rate and roll angle \\ \hline
10 & Holding position \\ \hline
11 & Landing multicopter \\ \hline
12 & Switching system off \\ \hline
13 & Distributing forces \\ \hline \hline \end{tabular}
\end{table} 
Table 3: IF model processes of the function model of the multicopter.