## 4 Results and Discussion
### Stability Analysis of Control System
#### 4.2.2 Perturbation Stability Test  
In order to verify the stability of the designed control system, the system responses under four different transient perturbations at the nominal power level are investigated: positive and negative reactivity insertion, and an increase and decrease in the fuel mass flow rate.  
Perturbation case 1 : The system responses to a positive reactivity insertion transient are shown in Figure 9. At t = 50 s, as a positive reactivity of 30 pcm is inserted into the core, the thermal power is increased by 19%, and then the control rod is inserted into the core by the servo to introduce negative reactivity to compensate for the inserted positive reactivity. In addition, as the fuel temperature rises due to higher thermal power, extra negative reactivity is introduced due to the negative feedback coefficient of the fuel temperature. At t = 53 s, as the thermal power becomes lower than the nominal power, the control system withdraws the control rod to introduce positive reactivity in order to increase the thermal power. After 20 s, the system reaches a new steady state, and the steam outlet temperature is almost constant during the whole transient. The inserted reactivity is compensated by that introduced by the control rod. There is no significant change in the fuel temperature.  
Figure 5: The transient responses of the nonlinear model and reference model for 50 pcm negative reactivity perturbation without the control system.  
Figure 6: The transient responses of the nonlinear model and reference model for a flow-rate reduction of 10% in the secondary salt loop without the control system.  
Figure 7: Nyquist diagram of the power control system after linearization.  
Perturbation case 2: The system responses to a negative reactivity insertion transient are shown in Figure 10. At t = 50 s, as a negative reactivity of \(-\)30 pcm is inserted into the core, the thermal power is reduced by 14%, and the control rod is moved up by the servo to introduce positive reactivity to compensate for the inserted negative reactivity. In addition, extra positive reactivity is introduced due to the decreased fuel temperature. The control system works in a similar way to the previous case and adjusts the system to the  
Figure 8: Nyquist diagram of the steam temperature control system after linearization: (**a**) full view; (**b**) zoomed in (\(-\)1, 0).  
Figure 9: System responses to a positive reactivity perturbation transient: 30 pcm.  
steady state, which has the same thermal power and steam temperature as those before the transient.  
Perturbation case 3: The system responses to a transient triggered by increasing the fuel mass flow rate by 10% are shown in Figure 11. At t = 50 s, as the fuel mass flow rate is increased by 10%, the fuel temperature is slightly decreased, which introduces positive reactivity due to the negative feedback coefficient. In order to counteract this effect, the control system starts to bring in negative reactivity. The inlet temperature is increased by 7 K, and the outlet temperature is 7 K lower compared to its value before the transient. The decreased temperature difference ensures that the same amount of heat can be removed by the salt with a higher mass flow rate.  
Perturbation case 4: The system responses to a transient triggered by decreasing the fuel mass flow rate by 10% are shown in Figure 12. At t = 50 s, the fuel mass flow rate is decreased by 10%. In a similar way, the system reaches a new steady state after 20 s. There is a higher temperature difference between the inlet and outlet temperatures, which ensures an equal heat removal capacity with a lower mass flow rate.