## 4 Identification Analysis of the Motor Parameters  
### Simulation Identification  
The motor parameter values used to simulate the identification algorithms are shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Motor Parameters** & **Value** & **Unit** \\ \hline Armature resistance \(R_{m}\) & 0.35 & \(\Omega\) \\ Armature inductance \(L_{m}\) & 0.001 & H \\ Motor back EMF constant \(K_{t}\) & 0.0433 & V\(\cdot\)s \\ Motor rotor inertia \(J_{m}\) & 0.00018 & kg\(\cdot\)m\({}^{2}\) \\ Hydraulic friction coefficient of Motor rotor \(B_{m}\) & 0.0034 & N\(\cdot\)m\(\cdot\)s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Motor parameters used in the simulations. The following transfer functions can be calculated by combining the motor transfer function in Equation (5) and Table 1:  
\[G_{0}(s)=\frac{1000s+18889}{s^{2}+368.8889s+6611.1} \tag{29}\]  
The sampling rate is very important for parameter estimation. A sampling rate of 800 Hz is the optimal sampling rate in this paper, as it satisfies the Nyquist theorem, allowing high precision in model parameter identification. In addition, the experiments were implemented at the different sampling rates in order to adopt the optimal sampling rate. From the above basic theoretical analysis of the proposed the algorithms, Equation (28) implemented in the MATLAB is used to estimate the motor transfer function at different sampling rates. The simulation results for the SRIV algorithm with a signal-to-noise ratio (SNR) of 30 dB and using different sampling rates are shown in Figure 2. The Bode plots using individual sampling rates of 300 Hz, 800 Hz and 10 kHz compared with the actual model are shown in Figure 2.  
A sampling rate of 300 Hz is too low to satisfy the Nyquist sampling theorem, and thus, the identification effect is not ideal. A sampling rate of 10 kHz satisfies the Nyquist sampling theorem but is too high, leading to a waste of memory space and long signal processing times. Using high-performance filters to filter the noise in the high frequency range leads to a high degree of control over system implementation cost. In addition, high-quality filters, fast processor speed and large memory capacity are necessary to respond to the high sampling rate. Without these, undesirable results, such as incorrect model parameter identification, would be obtained. According to this analysis, phase frequency characteristics of 300 Hz or 10 kHz are quite different from the actual one. In the simulation identification, the noises added to the system outputs are uncertain, and thus, the simulation outputs are different for every trial. The results also show that the identification result is unstable when the sampling rate is high. Using Equations (17), (22) and (28), the motor transfer function was estimated by three different algorithms. The Bode plots of the identification results using the SRIV, IVSVF and LSSVF algorithms are shown in Figure 3. These algorithms are appropriate for the actual model. The LSSVF algorithm is the simplest method for system parameter identification. The IVSVF algorithm reduces the bias of the LSSVF algorithm, whereas the SRIV algorithm is the optimal identification algorithm. Hence, the Bode plot of the SRIV algorithm is the most appropriate for the actual model, and the results obtained using the IVSVF algorithm are better than those obtained using the LSSVF algorithm, as confirmed in [31; 32]. Figure 2: Bode plots of the SRIV identification algorithm with a signal-to-noise ratio of 30 dB. To select an appropriate model structure, we utilized various criteria, such as the coefficient of determination (RT2), [PERSON]'s information criterion (YIC), the condition number (Cond), the Akaike information criterion (AIC), and _nb_, _nf_, and _nk_ denote the number of numerator and denominator parameters and number of samples for the delay of the system, which are shown in Table 2, in accordance with [31; 32]. Figure 4 shows the inputs of the motor during the identification simulation.