## 4 Simulation Experiments and Analysis Based on Error Sensitivity  
In the real application process of the system, those disturbances caused by UAV, environment factors such as wind, noises, etc., will all couple to the system pedestal base in the end. They are all integrated and defined as the base disturbances (BD) for simplicity. Apparently, in the normal working process of the system, BD is the strongest factor affecting the stability accuracy. That effect will be deteriorated by those modeled assembly errors. According to previous definitions in Section 3.2, the angular velocities of BD disturbances are denoted as \(\overrightarrow{\omega_{ib}}=\left[\omega_{ibx},\omega_{iby},\omega_{ibz} \right]^{T}\). By carrying out dynamic simulations, the effects caused by BD and the modeled assembly errors can be analyzed. The analysis results will provide valuable guidance for future possible improvements. For simulation study, according to Equation (1), the sampling period \(T_{s}\) is equal to the Simulink step size, and set as \(1 ms\). For other parameter settings: Total sampling time: \(t_{s}=30s\); Sampling number: \(n_{s}=30\),000. By referring to real measurement data of a newly developing system, the necessary parameters are predefined before the simulation experiments. Those parameters are listed in Table 1, and the prototype of the product is shown in Figure 15. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Descriptions** & **Values** & **Units** \\ \hline \(J_{ma}\) & Rotary inertia of the azimuth motor & 0.02 & kg\(\cdot\)m\({}^{2}\) \\ \(J_{La}\) & Rotary inertia of the azimuth load & 0.04 & kg\(\cdot\)m\({}^{2}\) \\ \(J_{mp}\) & Rotary inertia of the pitch motor & 0.01 & kg\(\cdot\)m\({}^{2}\) \\ \(I_{lp}\) & Rotary inertia of the pitch load & 0.02 & kg\(\cdot\)m\({}^{2}\) \\ \(R_{m}\) & Total resistor of the two armature circuits & 8.60 & \(\Omega\) \\ \(L_{m}\) & Total inductance of the armature circuits & 0.01 & H \\ \(D_{L}\) & Damping coefficient of the two motors & 10 & / \\ \(K_{L}\) & Elastic coefficient of the two motors & \(\approx\)100,000 & / \\ \(C_{e}\) & EMF coefficient of the two motors & 0.33 & / \\ \(C_{m}\) & Motor torque coefficient of the two motors & 0.33 & / \\ \(K_{p}\) & Amplification coefficient of the driving circuit & \(\approx\)20 & / \\ \(R_{s}\) & Resistor of the driving circuit & 0.4 & \(\Omega\) \\ \(K_{g}\) & Amplification coefficient of the gyroscopes & 15/\(\pi\) & / \\ \(\omega_{g}\) & Natural frequency of the gyroscopes & \(\approx\)200\(\pi\) & rad/s \\ \(\zeta_{g}\) & Damping coefficient of the gyroscopes & 0.7 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Necessary measured parameters before simulation experiments. Figure 15: The assembly prototype of the newly developing system. To study the sensitivity of the assembly error effect on the stability accuracy, the simulation experiments affected by each kind error source was carried out separately. Specifically, the simulations of each type of error source are carried out with other errors are equal to zero. The variables of each group of simulations will be the levels of each error source, and the disturbance frequencies of BD. The two variables are determined by referring to principles as follows: according to engineering experiences and the real conditions of manufacturing accuracies, the error source levels are set to range from \(1m^{\circ}\) to \(50m^{\circ}\). By referring to [25; 26], the angular velocities of the three axes of BD disturbances, specifically \(\overrightarrow{\omega}_{ib}=\left[\omega_{ibx},\omega_{iby},\omega_{ibz} \right]^{T}\), are all simulated as sinusoidal signals of low frequencies, and they range from \(1.5^{\circ}/0.5 Hz\) to \(1.5^{\circ}/4 Hz\). The simulation results of stability accuracy obtained \(\triangle\theta\) are presented with three decimal places, and listed in the central area of Tables 2-6. The results of each kind of BD disturbance are listed in a separate table.