# Improvement of Hexacopter UAVs Attitude Parameters Employing Control and Decision Support Systems
## 5 FEM Decision Support
### Dynamic Analysis and Hover Stability  
The dynamic analysis focused on both the modal analysis and a drop test simulation to verify the stability and the structural integrity of the hexacopter at impact, as detailed in Figure 40.  
Figure 38: Drag and lift forces -numerical vs. analytic computation.  
Figure 39: Maximum displacements on Y axis after 0.25s hover flight time.  
The purpose of the modal analysis is to determine the eigenvalues for the drone's structural elements and the propeller in order to design the hexacopter control system accordingly, to ensure the structural stability of the drone for the operational rotational speed of the propellers in surveillance, photography or recording operations. An orthotropic elastic epoxy carbon woven (230 GPa) prepreg material (Tsai-Wu) was employed for the hexacopter structural elements and the rotors. For reaching a realistic behaviour of the system, the mass of the assemblies and individual components of the hexacopter were carefully checked as recorded in Table 1.  
Figure 41 illustrates an efficient model in terms of computational time and mesh quality, based on shells and beams processed in the ANSA preprocessing system in order to combine different advanced discretization strategies.  
The structure has two symmetry planes, and this is underlined in the modal response. In Figure 42, only relevant eigenvalues have been processed. Thus, the first mode shapes are bending modes in the vertical plane, followed by bending modes in the vertical plane combined with torsion in the horizontal plane. Participation factors were analysed to select the dominant vibration modes. For this purpose, ten mode shapes were calculated, with the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hexacopter Component** & **Mass (kg)** \\ \hline Frame & 0.833 \\ Brushless electric motor & 0.082 \\ Electronic speed controller & 0.026 \\
13\({}^{\prime\prime}\) Propeller & 0.014 \\ Avionics and accessories & 0.763 \\
12 Ah Battery 12 Ah & 1.080 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mass of the hexacopter components.  
Figure 40: Hexacopter dynamic analysis using FEM.  
normalization of the eigenvectors in respect to unity. The modal analysis of the hexacopter main structural components proves that there are no eigenfrequencies in the operational range; therefore, no problems arise from this point of view for controlling the attitude or position of the drone.  
The study also confirms that the amplitude peak at 47 Hz (Figure 34, Section 5) corresponding to 2820 rpm is caused by the natural frequency of the propellers that are overlapping the manoeuvring frequency. This can lead to high stresses at the propeller hub and may cause them to exceed the material yield strength or simply reduces the fatigue strength of the rotors. Considering that the manoeuvring speed range [58.34 Hz/3500 rpm--66.67 Hz/4000 rpm] is at least 24% higher than the rotor eigenvalues, it can be assumed that no resonances can occur for the manoeuvring regime of the hexacopter, but only for the fixed-point stationary regime. The maximum rotor speeds for different flight conditions in the range [6500-8000 rpm] should be mindfully chosen, as resonances may occur on the third and fourth rotor eigenvalues, but the amplitudes are expected to be low.  
The resonant rotational speeds have to be avoided and can be taken into account when monitoring the hover flight parameters. High-order frequencies may interfere with the flight parameters in manoeuvring mode, but this was not observed during the experiments.  
The hexacopter performance can also be improved by removing the resonances induced by the drives rotation from the operational range using dynamic harmonic notch filters.