# Hierarchical Model Predictive Control for Hydraulic Hybrid Powertrain of a Construction Vehicle
## 3 MPC-Based Hierarchical Control Scheme
### MPC-Based Lower-Layer Engine Speed Tracking Controller Design
It should be noted that the simulation operation is carried out under the closed-loop control for the whole HHV, thus, in the simulation verification, one of the four EMSs is used in the upper layer, meanwhile, the designed MPC tracking controller of the engine is also embedded into the lower layer. The simulation results are shown in Figure 9.  
Figure 8: First driving conditions. Moreover, to verify the effectiveness of the designed lower layer controller, the comparison results are presented between the designed MPC tracking controller and a PID controller of the conventional engineering control method. Consequently, in the simulation verification, the designed SMPC, RB, and SDP EMSs are used in the upper layer, respectively, and the designed MPC tracking controller and a PID controller are embedded into the lower layer, respectively. The simulation comparison results are shown in Figure 10.  
To facilitate comparative analysis of the control performance of various strategies, the simulation results are summarized, as listed in Table 2, where the different control strategies include: only PID lower-layer control for the conventional diesel engine driving construction vehicle (without  
Figure 10: Lower-layer engine speed tracking control under the first conditions. Figure 9: Simulation results of upper-layer energy management control strategy (EMS) under the first conditions. SOC); the upper-layer RB and the lower-layer PID that are adopted in practice (RB+PID), as well as the upper-layer RB and the lower-layer MPC (RB+MPC), the upper-layer SDP and the lower-layer MPC (SDP+MPC), the upper-layer SMPC and the lower-layer PID (SMPC+PID), the upper-layer SMPC and the lower-layer MPC (SMPC+MPC); and the upper-layer PMPC, and the lower-layer MPC (PMPC+MPC) for the benchmark. The evaluated control performance contains the final SOC, the variation range of SOC during the driving cycle, and the fuel economy expressed by miles per gallon (mpg). It is worth mentioning that although the final SOC is not the same for different control strategies, the corresponding fuel consumptions theoretically can be compared directly with each other due to very low accumulator capacity and the close final SOC of various strategies. From Table 2, it can be seen that at the end of the driving cycle, the SOC of the accumulator of all strategies is between 0.58 and 0.61, which means the energy of the accumulator is balanced. In addition, because a bladder accumulator is used, in order to extend the life of the bladder during the working process, it is necessary to avoid the contraction and expansion of the bladder from colliding with the bacteria valve at the lower end of the accumulator. From the variation range of SOC, various strategies meet the requirements for use. Fuel economy is the most concerned evaluation index of energy management strategy. It can be seen from Table 2 that compared with traditional engineering vehicles (without SOC), when the upper-layer control adopts the RB strategy (RB+PID), the fuel economy is improved by 9.1%, whereas when the lower-level controller uses the designed MPC tracking controller in this study instead of the PID controller (RB+MPC), fuel economy is further improved by 2.3%. Furthermore, when the upper layer uses the SDP (SDP+MPC) and the proposed SMPC (SMPC+MPC), the fuel economy is improved by 5.8% and 7.8% as compared with the RB+MPC strategy, respectively. Fuel economy of the PMPC+MPC strategy increases by 10.7% as compared with the RB+MPC strategy. It is worth mentioning that in the PMPC control strategy the entire driving conditions are regarded as completely known and the optimization solution is obtained by the DP, which is impossible to implement in practice and, in this study, is listed only for the benchmark. Therefore, from these results, we concluded that the proposed SMPC-EMS had much superiority in fuel economy. In addition, as compared with the SMPC+PID, the fuel economy of the SMPC+MPC is further improved by 2.2%.