## 5 Identification Analysis and Test Bench Simulation of the EPS System  
### Identification Analysis of the EPS System  
The identification simulation of the EPS is similar to the motor identification simulation. Because the input is the torque from the steering wheel and the output is the displacement of the rack,  
Figure 12: Time profiles of the assist motor current and voltage. Figure 13: Verification of the identification model. the EPS system can be regarded as a single-input single-output (SISO) system. The input signal and sampling rate selection is consistent with the relevant contents in the previous section. Table 7 shows the parameter value used in the analysis of the EPS simulation. The transfer function of the EPS system is obtained from the previous section as shown in Equation (10). Combining Table 7, the transfer function of the EPS system is shown in Equation (30):  
\[ \begin{split} G_{1}(s)&=\frac{p_{r}(s)}{T_{d}(s)}= \frac{1}{\frac{T}{K_{c}}(Ls^{2}+B_{s}s+K_{c})(M_{s}s^{2}+B_{s}s+\frac{K_{c}}{r_{p }^{2}}+K_{r})-\frac{K_{c}}{r_{p}}}\\ &=\frac{1.1518\times 10^{4}}{s^{4}+29.438s^{3}+6.497\times 10^{4}s^{2 }+6.175\times 10^{5}s+8.181\times 10^{6}}\end{split}  \tag{30}\]  
Figure 14 shows the Bode plot of the EPS obtained using the SRIV identification algorithm at an SNR of 30 dB and different sampling rates. The identified model is the closest to the real model when the sampling rate is 800 Hz. The Bode plot illustrates that for a sampling rate of 70 Hz, the identified model is not suitable as the actual model. Figure 15 shows the EPS Bode plot using different identification algorithms based on an SNR of 30 dB and a sampling rate of 800 Hz. The SRIV algorithm identification model clearly has the best identification resolution. The phase frequency characteristics of the IVSVF and LSSVF identification models deviate considerably from the phase frequency characteristics of the actual model. Table 8 presents the evaluation of different model structures using the SRIV algorithm with an SNR of 30 dB and a sampling rate of 800 Hz. The evaluation parameters of the optimal model structure are also listed in Table 8. According to the data in Table 8, when \(nb=1\), \(nf=4\) and \(nk=0\), the structure of the model is the structure of the actual model. RT2 is the largest value, and the YIC value is the most negative (\(-18.755\)), indicating the identification conditions and the feasibility of the algorithm. Figure 16 shows the input signal of the identification simulation, which is \begin{table}
\begin{tabular}{c c c} \hline \hline
**EPS Parameters** & **Value** & **Unit** \\ \hline Steering wheel moment of inertia \(l_{c}\) & 0.04 & kg\(\cdot\)m\({}^{2}\) \\ Torsional stiffness \(K_{c}\) & 115 & N\(\cdot\)m/rad \\ Steering wheel damping \(B_{c}\) & 0.325 & N\(\cdot\)m/(rad/s) \\ Rack and wheel assembly mass \(M_{r}\) & 32 & kg \\ Rack damping \(Br\) & 653.2 & N\(\cdot\)(m/s) \\ Tire or rack centring spring rate \(K_{r}\) & 91,061 & N\(\cdot\)m \\ Pinion radius \(r_{p}\) & 0.0071 & m \\ \hline \hline \end{tabular}
\end{table} 
Table 7: EPS parameters. Figure 14: Bode plot of the EPS using different sampling rates. the 8-level shift register. The overlap of the coarse lines is caused by the high frequency of the PRBS. Figure 17 shows a comparison of the simulation and test data identified by the SRIV algorithm when \(nb=1\), \(nf=4\) and \(nk=0\). As shown in Figure 17, there are more burrs in the curve of the test data. This trend is related to the sampling noise in the test. When the test is identified, the input signal must be filtered to eliminate the effect of noise on the test data. The simulation result of the SRIV algorithm is relatively smooth, and the degree of coincidence between them is relatively high, illustrating a high identification resolution. Through the simulation analysis of the EPS model, the SRIV identification algorithm obtains a good identification result under the simulation conditions of an 800 Hz sampling rate and an  
Figure 16: Input signal of the identification simulation.