## 4 A Feedforward-Cascade Compound Control Scheme Based on IPFC  
### Feedforward-Cascade Compound Control System  
Feedforward control, as an open-loop control system, is based on the measurable disturbance as the input of the controller, which then compensates for the deviation between the controlled variable and the set value and restores the controlled variable to a stable state according to the change in the disturbance quantity. A single feedforward is not very good at compensating interference, and there are many limitations. For example, a single feedforward control has no feedback link, and the compensation effect cannot be tested. As a result, when the feedforward fails to eliminate the deviation, the system cannot get the message for verification. In the actual industrial site, there are often many interference  
Figure 4: IPFC control scheme constrained by the control signal.  
Figure 3: IPFC structure of heat exchanger outlet temperature control system.  
factors. If feedforward is used to compensate one by one, it is necessary to design multiple feedforward channels, which consumes money and power. Therefore, to solve these limitations, feedforward control and feedback control are generally combined [31].  
For the heat exchanger outlet temperature control system, the common control scheme takes the refrigerant flow as the control variable to control the thermal fluid outlet temperature stability. Aiming at the typical feedforward feedback control system of the heat exchanger, its working principle is to superimpose the output value of the feedforward controller on the output value of the feedback controller and send it to the control valve together. This replaces the desired relationship between hot fluid flow and refrigerant flow with that between hot fluid flow and valve head pressure. To make the accuracy of feedforward compensation finer, a control valve with higher control quality is needed to meet the requirements of sensitivity, linearity, and minimal hysteresis, and the pressure difference before and after the control valve is required to remain unchanged. To solve the problem just mentioned, cascade control is adopted in the feedback loop, and refrigerant flow regulation is added in the secondary loop. The output effect of the feedforward controller is superimposed on that of the main loop controller as the given value of refrigerant flow regulation, which forms the feedforward-cascade compound control scheme.  
The feedforward-cascade compound control system of the heat exchanger is shown in Figure 5 [32]. The simplified corresponding block diagram is shown in Figure 6 [33].  
According to Figure 6, the transfer function of the system is listed as follows:  
\[\frac{T_{1o}(s)}{F(s)}=\frac{G_{PD}(s)+G_{ff}(s)G_{\rm{P2}}^{\prime}(s)G_{PC}( s)}{1+G_{\rm{c}}(s)G_{\rm{P2}}^{\prime}(s)G_{PC}(s)} \tag{57}\]  
Figure 5: The compound control system of feedforward and cascade heat exchanger.  
Figure 6: Block diagram of feedforward-cascade compound control system.  
where, \(G^{\prime}_{p2}(s)\) is the transfer function of the equivalent object of the secondary loop:  
\[G^{\prime}_{p2}(s)=\frac{G_{c2}(s)G_{p2}(s)}{1+G_{c2}(s)G_{p2}(s)} \tag{58}\]  
According to the invariance condition:  
\[F(s)\
eq 0\text{ and }T_{1o}(s)\equiv 0 \tag{59}\]  
The transfer function of \(G_{ff}\) can be obtained by substituting it into Formula (57):  
\[G_{ff}(s)=-\frac{G_{pp}(s)}{G^{\prime}_{p2}(s)G_{PC}(s)} \tag{60}\]