## 4 Coordinated Predictive Controller Design
### Coordinated Predictive Controller Design for the MGT-CCP System  
This section presents the coordinated predictive control strategy for the MGT-CCP system, as shown in Figure 5.  
Considering the physical characteristics of the MGT-CCP system, the MGT-CCP system was split into a power supply system and a cooling system. In view of the degree of nonlinearity of the two subsystems, the linear GPC is designed for the power generation system and the nonlinear Hammerstein-GPC is designed for the cooling system. The nonlinearity of the cooling system is effectively suppressed by nonlinear compensation, and the coupling between subsystems is effectively weakened by feedforward compensation. Besides, due to the inevitable modeling error, feedback correction is adopted in the proposed control strategy.  
The main calculation process of the GPC-HGPC coordinated control algorithm is summarized as follows:  
Figure 4: Structure of Hammerstein-GPC.  
Figure 5: Coordinated predictive control strategy for the MGT-CCP system.  
1. At time \(t\), the calculation of the linear GPC controller is performed, and the optimal input increment sequence \(\Delta U(1)=\left[\begin{array}{cccc}\Delta u_{t}(1)&\Delta u_{t+1}(1)&\cdots& \Delta u_{t+M-1}(1)\end{array}\right]^{T}\) of the fuel amount is calculated, and the optimal control variable \(u_{t}(1)=u_{t-1}(1)+\Delta u_{t}(1)\) of the MGT system is further obtained;
2. The intermediate control variable sequence \(\Delta\overline{U}(1)=\left[\begin{array}{cccc}\Delta\overline{u}_{t}(1)& \Delta\overline{u}_{t+1}(1)&\cdots&\Delta\overline{u}_{t+M-1}(1)\end{array} \right]^{T}\) is calculated by using the fuel quantity optimal input increment sequence \(\Delta U(1)=\left[\begin{array}{cccc}\Delta u_{t}(1)&\Delta u_{t+1}(1)& \cdots&\Delta u_{t+M-1}(1)\end{array}\right]^{T}\) and the nonlinear polynomial \(f_{1}(\cdot)\);
3. Adding the sequence \(\Delta\overline{U}(1)=\left[\begin{array}{cccc}\Delta\overline{u}_{t}(1)& \Delta\overline{u}_{t+1}(1)&\cdots&\Delta\overline{u}_{t+M-1}(1)\end{array} \right]^{T}\) as feedforward information to Equation (15) gives an output prediction of chilled water temperature: \[\begin{array}{rl}\hat{y}_{t+j}(2)&=g_{j,0}^{(2)}\Delta u_{t+j-1}(2)+g_{j,1 }^{(2)}\Delta u_{t+j-2}(2)+\cdots+g_{j,j-1}^{(2)}\Delta u_{t}(2)+l_{j}(t)\\ &\quad\quad+g_{j,0}^{(1)}\Delta u_{t+j-1}(1)+g_{j,1}^{(1)}\Delta u_{t+j-2}(1)+ \cdots+g_{j,j-1}^{(1)}\Delta u_{t}(1)\\ &=g_{j,0}^{(2)}\Delta u_{t+j-1}(2)+g_{j,1}^{(2)}\Delta u_{t+j-2}(2)+\cdots+g_{ j,j-1}^{(2)}\Delta u_{t}(2)+\widehat{l}_{j}(t)\end{array}\] (22) where \(\widehat{l}_{j}(t)=g_{j,0}^{(1)}\Delta u_{t+j-1}(1)+g_{j,1}^{(1)}\Delta u_{t+ j-2}(1)+\cdots+g_{j,j-1}^{(1)}\Delta u_{t}(1)+l_{j}(t)\). Note that \(\widehat{l}_{j}(t)\) is known at time \(t\);
4. Based on (22), using the linear GPC algorithm to calculate the intermediate control variable increment sequence \(\Delta\overline{U}(2)=\left[\begin{array}{cccc}\Delta\overline{u}_{t}(2)& \Delta\overline{u}_{t+1}(2)&\cdots&\Delta\overline{u}_{t+M-1}(2)\end{array} \right]^{T}\), and then obtain \(\overline{u}_{t}(2)=\overline{u}_{t-1}(2)+\Delta\overline{u}_{t}(2)\);
5. Using the intermediate control variable \(\overline{u}_{t}(2)\) and the inverse of the nonlinear polynomial \(f_{2}(\cdot)\) to obtain the refrigerant valve opening \(u_{t}(2)\);
6. Next sampling time, return to step (1), repeat steps (1) to (5).  
_Remark 2_: For the sake of simplicity, the proposed method uses the control model obtained by offline identification. If the actual MGT-CCP system has large time-varying characteristics, the performance of the proposed control algorithm will be attenuated. But this problem can be overcome by adding online identification of the control model.  
_Remark 3_: This algorithm can only eliminate the influence of external disturbance of the step type. For time-varying disturbances, adding on-line identification of the disturbance model to the proposed algorithm can improve control performance [31].