# Hierarchical Model Predictive Control for Hydraulic Hybrid Powertrain of a Construction Vehicle
## 5 Experimental Evaluation  
In the section, the proposed control strategy is verified by the experimental results carried out on a test platform indoors, as shown in Figure 14. The test platform consists of a power distribution unit, a load unit, and a control unit, where the electric motor is adjusted by the inverter to simulate the engine torque, and the load unit simulates the load torque by adjusting the pump pressure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**EMS+Engine Control** & **Final SOC Value** & **SOC Range** & **Fuel Economy (mpg)** \\ \hline +PID (without SOC) & - & - & 31.82 \\ RB+PID (practice) & 0.592 & 0.18–0.69 & 34.43 \\ RB+MPC & 0.592 & 0.18–0.69 & 35.15 \\ SDP+MPC & 0.608 & 0.21–0.82 & 37.18 \\ SMPC+PID & 0.607 & 0.37–0.90 & 36.26 \\ SMPC+MPC (proposed) & 0.607 & 0.37–0.90 & 37.85 \\ PMPC+MPC (benchmark) & 0.602 & 0.39–0.82 & 38.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation comparison of different algorithms in the second driving conditions. Figure 13: Lower-layer engine speed tracking control in the second driving conditions. The main parameters of the powertrain system on the test platform are shown in Table 4.  
The experiment process is briefly described below. First, the load, \(T_{p}\), of the entire vehicle is simulated by adjusting the pressure of the load unit to form the torque demand that is distributed by the EMS of the upper layer. The experimental data is obtained by PLC collecting sensors installed on the experimental platform. However, during the experiment, the electric motor only simulates the engine torque, therefore the fuel consumption is obtained by querying the Map table through the actual torque of the electric motor. The first driving conditions are considered in the experiment and three EMSs of the upper layer including the RB, the SDP, and the SMPC are carried out on the test platform, respectively. The experimental results are shown in Figure 15. Meanwhile, Table 5 shows the evaluation performance for the experimental results of the three EMS strategies. \begin{table}
\begin{tabular}{c c c} \hline \hline
**System Components** & **Parameter/(Uint)** & **Value** \\ \hline Electric motor (virtual engine) & rated power/(kW) & 30 \\ \hline Main pump & flow/(ml/r) & 28 \\  & max pressure/(Mpa) & 30 \\ \hline Hydraulic motor & flow/(ml/r) & 28 \\  & max pressure/(Mpa) & 30 \\ \hline  & rated volume/(L) & 18.9 \\ accumulator & working pressure/(Mpa) & [8,30] \\  & precharge pressure/(Mpa) & 5.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Powertrain system parameters. Figure 14: Structure of experiment platform. It can be seen from Table 5 and Figure 15:  
1. Three EMS control strategies can satisfy the pressure of the accumulator within the working range. The SOC value meets the work requirements. The range of SOC value changes is significantly  
Figure 15: Experimental results of three control strategies: (**a**) Results for the rule-based strategy, (**b**) results for SDP strategy, (**c**) results for SMPC strategy, and (**d**) comparison of engine operating points under three EMS. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters (unit)** & **RB** & **SDP** & **SMPC** \\ \hline Accumulator pressure range (MPa) & 8.5–22.5 & 9.1–20.8 & 9.1–20.3 \\ Final SOC value & 0.583 & 0.603 & 0.605 \\ SOC range & 0.22–0.65 & 0.34–0.76 & 0.39–0.77 \\ Motor speed bias (rad/s) & 4.9 & 5.1 & 5.2 \\ Fuel economy (mpg) & 33.62 & 34.98 & 35.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results. smaller as compared with the simulation results. This is because the leakage of the pipeline is not considered in the system model. 2. It can be observed that the SMPC strategy has better fuel economy than the SDP and RB strategies. The SMPC and SDP methods have improved fuel economy by 5.9% and 4%, respectively as compared with the RB strategy. This verifies the effectiveness and advantage of the proposed method. 3.