# The Development of an Optimal Control Strategy for a Series Hydraulic Hybrid Vehicle
## 4 Simulation and Results
### The DP-Based Control Strategy  
Although the optimal control inputs derived by applying DP cannot to be applied to the forward-facing simulation system, they can be functioned as the references. When using a rule-based control strategy, such as thermostatic and modulated-pressure strategies, the reference values of engine torque and engine speed are derived based on the accumulator pressure.  
Figure 15: Modulated-Pressure and Thermostatic Control Strategies Comparison.  
Under the Japan 1015 cycle, the results for DP show that the optimal power threshold is about 20 kW and lower and upper threshold pressures are 150 bar and 270 bar, respectively. These values were used as the thresholds to derive the improved thermostatic control strategy. The difference between the initial and the DP-based thermostatic strategies can be seen from the trajectories for the pressure in the accumulator, as shown in Figure 16.  
For HWFET, the effectiveness of different estimations of the reference pressure is shown in Figure 17. It is seen that when the pressure remains constant, the accumulator has a reduced capacity as an energy buffer. The output power of the engine fluctuates more significantly because of the variation in the power demand. For the modulated-pressure strategy, the accumulator is used as an energy buffer. Therefore, the engine operates at its highest efficiency Figure 18.  
Figure 16: Pressure Trajectories with Primary and DP-Based Thermostatic.  
Figure 17: Pressure Trajectories with Primary and DP-Based Modulated-Pressure Strategies.  
Using DP, an optimal benchmark solution was estimated. The fuel economy figures for the proposed SHHV using DP and DP-based control strategies are listed in Table 4. Using DP, the proposed system shows a respective improvement of 98.91% and 68.79% over a conventional vehicle for the Japan 1015 and HWFET driving cycles. These gains come from effective regenerative braking and highly efficient operation of the components.  
However, because driving cycles must be known _a priori_ to allow DP, the optimal control rules that are derived from DP cannot be directly applied to the forward-facing system. Instead, the DP results must be studied and used to improve the initial rule-based control strategies.  
The results for the use of DP show that the optimal power threshold is around a value of 20 kW and the optimal range of pressure in the accumulator is from 150 bar to 270 bar. These values were used as the parameters for the thermostatic control strategy, which is DP-based. The respective improvements in the fuel economy for the system are 71.53% and 56.78%, for Japan 1015 and HWFET.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Control Strategy**} & \multicolumn{2}{c}{**Japan 1015**} & \multicolumn{2}{c}{**HWFET**} \\ \cline{2-5}  & **Fuel Economy** & **Fuel Economy** & **Fuel Economy** & **Fuel Economy** \\  & **(km/L)** & **Improvement (\%)** & **(km/L)** & **Improvement (\%)** \\ \hline Conventional & 10.08 & - & 11.57 & - \\ DP & 20.05 & 98.91 & 19.53 & 68.79 \\ \hline DP-Based & \multirow{2}{*}{17.29} & \multirow{2}{*}{71.53} & \multirow{2}{*}{-} & \multirow{2}{*}{-} \\ Thermostatic & & & & \\ \hline DP-Based & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{18.14} & \multirow{2}{*}{56.78} \\ Modulated-pressure & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fuel Economy Estimation with Dynamic Programming (DP) and DP-Based Control Schemes.  
Figure 18: Number of Occurrence of Engine Operating Points on BSFC map.