## 5 Identification Analysis and Test Bench Simulation of the EPS System
### Identification Experiment for the EPS System
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure of the EPS System** & **Sampling Rate (Hz)** & **RT2** & **YIC** \\ \hline  & 100 & 0.975 & \(-\)9.990 \\  & 500 & 0.965 & \(-\)10.014 \\ \(nb=3\), \(nf=4\), \(nk=0\) & 800 & 0.984 & \(-\)12.265 \\  & 900 & 0.981 & \(-\)12.251 \\  & 1000 & 0.981 & \(-\)11.155 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Evaluation parameters at different sampling rates. Through the comparisons and analysis of the different identification conditions and identification results, the optimal identification algorithm and identification conditions are the SRIV identification algorithm and a sampling rate of 800 Hz. Figure 20 shows the identification of the input and output signals for the system, where the change in the input torque is reflected in the change in the main voltage of the torque sensor. The line in the starting position shows no input torque at this time, and the main and sub-main voltage is 2.5 V. The amplitude and frequency of the main road vary considerably, satisfying the requirement of the identifying input signal. Unlike the input signal of the motor identification experiment, the EPS identification input signal is from the driver turning the steering wheel. Therefore, the identification input signal is different each time. Data from several EPS identification experiments are needed to adequately identify the system. The identification data and experiment data coincide except for the peak position. Hence, the EPS model was identified by the SRIV algorithm at a sampling rate of 800 Hz. Figure 21 presents the verification result of the EPS identification model. The input signal between 23 and 28 s is considered in the identification model to obtain the identification data. The identification data is compared with the output signal of the original test to verify the accuracy of the identification model. Figure 19: Bode plot of the EPS using different identification algorithms. Figure 20: Input and output of the EPS identification system. The identification data even follow the trend of the test data in the peak and trough positions, which further confirms that the identified EPS model produces highly accurate identification results using the SRIV identification algorithm and a sampling rate of 800 Hz. The aim of this paper is to design a control algorithm for the EPS system that ensures that the curve of the desired assist characteristic tracks the curve of the actual assist characteristic at different vehicle velocities. This curve is established according to the correlation between the drive torque (\(T_{d}\)) and vehicle speed (\(v\)), which is obtained from the vehicle manufacturer. Figure 22 shows the assist torque characteristic curves versus the driver torque with respect to different vehicle speeds. Figure 22 illustrates that the assist torque is proportional to the steering wheel torque, with the assist torque (\(T_{a}\)) increasing with decreasing vehicle velocity to ensure maneuverability. In contrast, when the vehicle velocity increases, the assist torque decreases while maintaining the system stability.