## 5 Simulation Experiment and Result Analysis
### Simulation Experiment  
According to the feedforward-cascade compound control system scheme based on IPFC proposed in this paper, the simulation model is built in Simulink, as shown in Figure 8. The proposed compound control system based on the IPFC main controller (IPFC-PID) and the compound control system based on the PID main controller (PID-PID) are simulated and compared under the same conditions to observe the control effect. For the compound control system based on a PID main controller, the transfer function of the controlled object and the disturbance channel is consistent with that of the feedforward cascade compound control system based on IPFC. When the cascade control system reaches a stable state, the PID controller parameter in the inner loop is: \(k_{p}=0.1\), \(k_{i}=0.007\), \(k_{d}=0.01\), so: \(G_{c2}(s)=\left(0.1+\frac{0.007}{s}+0.01s\right)\). PID controller parameters in the main loop are \(P=7\), \(I=0.03\), \(D=3\). The transfer function of the feedforward controller of each channel can be obtained by substituting into the formula in the previous section: \(G_{ff1}(s)=\frac{0.717s^{2}+0.781s+0.00497}{0.01s^{2}+0.18s+0.007}\), \(G_{ff2}(s)=-0.16\frac{6.874s^{2}+1.358s+0.51}{0.715s^{2}+0.174s+0.19}\), \(G_{ff3}(s)=-0.28\frac{0.19^{2}+1.18s+0.007}{0.01s^{2}+0.18s+0.007}\). In the IPFC-PID algorithm, according to the principle of the control algorithm, the PID controller is used for inner loop control and the IPFC is used for outer loop control. The controlled objects of the inner loop and main loop are combined as the generalized controlled objects of IPFC. The system identification is simplified through fitting. The corresponding first-order addition hysteresis model is: \(G(s)=\frac{0.77}{1.825s+1}e^{-15.355s}\), This model is used as the  
Figure 8: Simulation model of Feedforward-cascade compound control system based on IPFC. prediction model for the external loop IPFC controller. The initialization parameters are as follows: First in the inner loop PID controller: \(k_{p}=0.3\), \(k_{i}=0.00001\), \(k_{d}=0.1\). In the main loop IPFC controller, the sampling period: \(t_{s}=0.1s\). System closed loop response time: \(t_{r}=0.6s\). Predictive optimization time domain: \(H=30\). \(k_{p}=10,k_{i}=10,k_{d}=1\). (1) Model matching  
Because there may be a variety of burst factors at the industrial site, the most representative disturbance can be decomposed into multiple sets of step signals when the system is running, and usually, the step input has the greatest impact on the system. To effectively reduce the influence of multi-source interference on the heat exchanger system, the output of the system is analyzed, and the step disturbance is given as the disturbance signal in this paper. After the system reached a stable state, step disturbance signals were added to the three channels, respectively, and the inhibition effect of the feedforward control scheme on disturbance was observed. When only the flow of hot fluid fluctuates, the other two channels are disconnected. At this time, a 0.5 step disturbance is added to interference channel 1 when the simulation reaches 200 s. The simulation effect is shown in Figure 9.  
When only the temperature of the hot fluid inlet fluctuates, the other two channels are disconnected. At this time, a 0.5 step disturbance is added to interference channel 2 when the simulation reaches 200 s. The simulation effect is shown in Figure 10.  
Figure 10: Simulation curve of system output under thermal fluid inlet temperature disturbance. Figure 9: Simulation curve of system output under thermal fluid flow disturbance. When only the temperature of the refrigerant inlet fluctuates, the other two channels are disconnected.