## 5 Simulation Analysis
### System Parameters for Fault Scenarios
#### 5.1.2 Single Fault Effect Analysis under Closed-Loop System Conditions  
It can be seen from Figure 5(b) that, the changing law of Fault-1, Fault-3 and Fault-4, shows consistency, while the changing law of Fault-2 shows nonlinear characteristics with an obvious inflection point. Therefore, two sets of simulation results, before and after the inflection point are performed. By using the performance evaluation algorithm shown in Equations (18) and (19), to calculate the quantized value, the start and end times are set as \(t_{1}=0\) and \(t_{2}=8\), all evaluation results are shown in Table 4. The increasing of the \(e_{\text{perf}}(t)\) value indicates the gradual fault effectiveness of the system performance degradation. It can be figured out that the oil leakage of the cylinder is a fault type with the greatest impact. The system state response when only a single fault occurs is given in Figure 7. Compared with the normal state, among the four fault modes, the Fault-1 can have the greatest effect on the system performance (see Figure 6(a)): Under this type fault condition, in order to track the given step signal command order, even as the motor speed reaches its maximum value (see Figure 6(d)), the cylinder pressure can only reach a low level (see Figure 6(c)), leading the system output velocity to slow down to the slowest degree (see Figure 6(b)); The Fault-2 can have a secondary effect on the system performance (see Figure 6(a)): in order to track the given step signal command order, the motor speed also reaches a high level (see Figure 6(d)); however, since the motion damping increases, the cylinder pressure reaches the highest level due to the reverse motion damping caused force (see Figure 6(c)), \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Types** & \(e_{\text{perf}}(t)\) & \(\boldsymbol{e_{\text{perf}}}(t)\) & \(\boldsymbol{e_{\text{perf-max}}}\) \\ \hline Normal & 0.2723 & 0.0001429 & 0.03 \\ Fault-1 & 0.3631 & 0.0002581 & 0.03 \\ Fault-2 & 0.3142 & 0.0001954 & 0.03 \\ Fault-3 & 0.2728 & 0.0001432 & 0.03 \\ Fault-4 & 0.2865 & 0.0001598 & 0.03 \\ \hline \hline \end{tabular} Only the final output displacement is used to evaluate the tracking performance here.  
\end{table} 
Table 4: System performance evaluation values under different single fault conditions without FTC (before the inflection point of fault-3 pole position trajectory). Figure 6: Pole position analysis for the open-loop system: (**a**) Pole positions in different conditions; (**b**) Relationship between pole position and system single fault. but can only have a faster system output velocity (see Figure 7b); The Fault-4 can also have obvious effect on the system performance (see Figure 7a): the EHA motor resistance increases due to heat production caused high temperature, leading to the motor speed decreasing significantly (see Figure 7d), and the cylinder pressure and the system output velocity also decrease eventually (see Figure 7b,c); The Fault-3 have the minimal effect on the system performance (see Figure 7a): Figure 7a,b,d show that the system output state almost have the same performance level as the system under normal state conditions. However, the cylinder pressure is at a low level due to the bulk modulus changes caused by oil deterioration (see Figure 7c). To analyze the nonlinear characteristic of the Fault-3 effect, another set of simulation results is shown in Figure 8 with the evaluation results in Table 5, in which the remaining fault modes (Fault-1, 2 and 4) are set as the same with the first simulation scenarios. When the Fault-3 dominant pole position across the inflection point, leading the bulk modulus value to the lowest level, the motor speed and the final system displacement output have slight performance degradation compared with the system under normal state (see Figure 8a,d and Table 5, in which the \(e_{\text{perf}}(t)\) value changed to 0.2757 compared with the original 0.2728 in Table 4).