## 5 Identification Analysis and Test Bench Simulation of the EPS System
### Identification Experiment for the EPS System  
For the identification experiment of the EPS, the input signal is the steering wheel torque provided by the driver. Unlike the motor identification experiment, the input signal of the motor is provided by programming the PRBS. Hence, when the driver is manipulating the steering wheel, the torque frequency and amplitude should be varied over a large range to ensure the continuity of the input signal. The input torque from the driver varies linearly with the output voltage signal of the torque sensor. In the experimental process, the data acquisition system is used to collect and save the current of the voltage signal of the torque main, assist motor and current of the load motor. The voltage range of the main and sub-main output of the torque sensor is 0.5 V. When the steering wheel has no input torque, the main and sub-main voltage is 2.5 V; when the steering wheel input torque is positive, the main voltage is greater than 2.5 V; and when the input torque of the steering wheel is negative, the main voltage is less than 2.5 V.  
In contrast to the identification simulation of the EPS system, the input torque and rack displacement in the EPS identification experiment cannot be measured directly. Hence, the system structure of the actual model will also differ from the theoretical analysis of the structure of simulation model [1 4 0]. Based on transfer function of the EPS system in Equation (10) combining the experiment data, the EPS system parameters include torsional stiffness, steering wheel damping and rack damping, which affect significantly response of the system. It is a very necessary to identify these parameters. The structure of the EPS by experimental identification can be obtained by comparing the RT2 and YIC values of different system structures at different sampling rates and selecting the best system structure. The SRIV identification algorithm is used at sampling rates of 100 Hz, 500 Hz, 800 Hz, 900 Hz and 1 kHz. The structure of the actual model [3 4 0] appears in the optimal system structure. Table 9 shows the evaluation using the [3 4 0] structure and different sampling rates. According to Table 9, the value of YIC is the most negative when the sampling rate is 800 Hz. In contrast, the value of RT2 is the largest when the sampling rate is 800 Hz. According to the comparative analysis of data, the structure [3 4 0] is  
Figure 17: Comparison of the SRIV simulation data and test data. selected as the main structure of the EPS system with a sampling rate of 800 Hz. The results show the torsional stiffness (\(K_{c}=103.6\)), steering wheel damping (\(B_{c}=0.438\)) and rack damping (\(B_{r}=702.4\)). Figure 18 shows the step response of the EPS system obtained at sampling rates of 800 Hz and 1 kHz, where the steady-state response of the system is a constant negative value. When the input torque of the system is stable, the speed of the load motor and the current produced is constant, which corresponds with the response of the actual system. Table 10 shows the evaluation parameters for three different identification algorithms, illustrating that the SRIV identification algorithm has the highest identification resolution, followed by the IVSVF identification algorithm and then the LSSVF algorithm. Figure 19 illustrates the EPS Bode plot obtained using different identification algorithms under an 800 Hz sampling rate. The Bode plot of the LSSVF identification algorithm fluctuates at a low frequency. The evaluation parameters in Table 10 illustrate that the highest identification accuracy is the SRIV identification algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Identification Algorithm** & **RT2** & **MSE** & **FIT (\%)** \\ \hline SRIV & 0.981 & 0.204 & 86.28 \\ IVSVF & 0.970 & 0.475 & 79.07 \\ LSSVF & 0.929 & 0.765 & 73.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Evaluation parameters using three different identification parameters. Figure 18: Step response of EPS for sampling rates of 800 Hz and 1 kHz.