## 4 Identification Analysis of the Motor Parameters
### Identification Experiment  
In this subsection, the identification experiment for the motor parameters based on the recorded voltage and current of the motor is presented. The mathematical model of the motor is obtained using different identification algorithms with different conditions. Before the motor identification experiment, the load motor is shortened, and the electromagnetic clutch of the load motor is supplied with a 24 V direct source, so it can provide the load torque when the assist motor is rotated. In the experiment, when the starting command is received by the upper computer, the PRBS in the motor control module will circulate until the end of the experiment. At the same time, the data acquisition system will measure the current, the terminal voltage of the assist motor and the load current. The upper computer can change the amplitude and the clock time of the PRBS in the motor control module through the CAN bus, and can also change the sampling rate of the data acquisition system. Figure 6 highlights the step response for identifying the motor model using different sampling rates. The conditions for the sampling rates of 1 kHz and 900 Hz are 20% and 50% pulse width modulation (PWM) duty cycle (motor only rotates clockwise) with a time of 20 ms, respectively. When the sampling rate is 800 Hz, the identification condition of the model is 60% (positive and negative, clockwise and anticlockwise) PWM duty cycle. The identification model yields the most accurate identification under this condition. The step response of the motor model, identified at different sampling rates, takes 20 ms to reach steady-state mode. The step response curve of the motor model identified by the experiments is also analyzed. Considering the transfer function of the motor, there are five motor parameters: the motor resistance, inductance, back EMF constant, rotor inertia and rotor friction coefficient. Only 4 parameters can be identified in the motor model structure when _nb_ and _nf_ are equal to 2. Hence, in the identification test, only two parameters of the motor (the motor resistance and inductance) can be identified; the other parameters can be obtained through an identification experiment in which the motor voltage is the input and the motor speed is the output. Table 3 shows that when the sampling rate is too  
Figure 5: Comparison of the simulation data and test data using the SRIV algorithm. high, the parameters of the motor are clearly not consistent with the actual physical parameters of the motor. Therefore, a reasonable choice of sampling rate is critical for an accurate motor parameter identification. The results show the motor resistance (R = 0.281) and inductance (L = 0.0015). Figure 7 compares the experimental and identification results at a sampling rate of 800 Hz. When the sampling rate is 800 Hz, the motor model parameters can be obtained with a high level of accuracy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Identification Results** & \multicolumn{4}{c}{**Motor Parameter**} \\ \hline
**Sampling Rate (Hz)** & **Amplitude (\%)** & **Clock Time (ms)** & **Resistance (\(\Omega\))** & **Inductance (H)** \\ \hline
10k & 20 50 & 200 & \(-\)0.374 & 0.0020 \\
5k & 20 50 & 200 & \(-\)0.759 & 0.0023 \\
1k & 20 60 & 200 & 0.096 & 0.0015 \\
800 & 20 60 & 200 & 0.101 & 0.0014 \\
800 & \(-\)60 60 & 500 & 0.281 & 0.0015 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Identification of the motor parameters under different identification conditions. Figure 6: Step response for identifying the motor model at different sampling rates. Figure 7: Comparison of the experimental and identification results at sampling rate of 800 Hz. Table 4 shows the values of RT2 and YIC identified by the SRIV identification algorithm under different identification conditions. Figure 8 illustrates the Bode plots of the identified motor at different sampling rates.