## 2 Dynamics and Nonlinearity Analysis of MGT-CCP
### Dynamic Analysis  
Suppose the system is running at operating point #3 in Table 1. At 500 s and 3000 s, a +10% step signal of the corresponding steady-state value is added to the fuel and the refrigerant valve opening, respectively. The response of the plant is shown in Figure 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Operating Points** & \(y_{1}(\mathrm{kw})\) & \(y_{2}(^{\circ}C)\) \\ \hline \#1 & 80 & 8 \\ \#2 & 76.85 & 8.2 \\ \#3 & 73.5 & 8.5 \\ \#4 & 69.69 & 8.8 \\ \#5 & 65.18 & 9.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Typical operating points of MGT-CCP system.  
Figure 2 shows that the power output responds very quickly to the fuel step command because it has very fast dynamic response characteristics. In addition, Figure 2 shows that as the fuel step increases, the chilled water temperature slowly decreases to a constant value. The reason for the slow response of the chilled water is caused by exhaust gas transport and heat transfer in the chiller. It is easy to understand that the more fuel entering the MGT and the more exhaust gas entering the chiller, the greater the power of the chiller. Therefore, when the fuel is increased, the chilled water temperature is lowered. At 3000 s, the refrigerant valve opening increases, resulting in a decrease in exhaust gas entering the chiller, thus causing a decrease in chilled water temperature. As seen from Figure 1, the chiller is located behind the MGT, so the power output does not change when the refrigerant valve opening changes.  
The large inertia of the chilled water temperature is due to the exhaust gas transmission and thermal transferring process in the chiller. First the lithium bromide solution is heated in the generator by the exhaust gas which is a desorption process of solution. The vapour out of the solution condenses into the refrigerant water by releasing its heat to the cooling water in the condenser. The refrigerant  
Figure 2: Step response of MGT-CCP system: Fuel and valve openings increased by 10% at 500 s and 3000 s, respectively.  
water flows through the throttle valve and then evaporates in the evaporator and absorbs heat from the chilled water and cools it down. All these processes in the flowchart of the chiller, shown in Figure 1, contributes to a large inertial from the fuel change to the variation of chilled water temperature. Another input the refrigerant valve is a bypass valve for the exhaust gas to the chiller, thus it influences the chilled water temperature in the same direction slowly.  
To conclude, the power output is affected only by fuel, so for the safety and flexibility of MGT-CCP, a separate controller is designed for the control loop of power output. The chilled water temperature is affected by both fuel and refrigerant valve opening. There is a strong coupling between the variables. Therefore, when designing the control loop of the chilled water temperature \(y_{2}\), it is necessary to coordinate the control with the control loop of the power output \(y_{1}\). In addition, the chilled water temperature response has a large inertia, so it is necessary to study advanced control methods to replace the traditional PID control.