# Hierarchical Model Predictive Control for Hydraulic Hybrid Powertrain of a Construction Vehicle
###### Abstract
To this end, several researchers have focused on the lower-layer control design of an engine and pump/motor to achieve the power split for HHVs. For example, in [22], the engine on/off control strategy based on compensation of the used accumulator power is investigated and the effect of control parameters on the performance and efficiency of the hybrid power train is analyzed for improvement of fuel economy. The design and evaluation of the linear MPC method is presented in [23] applied to the tracking problem in a hydraulic hybrid powertrain system. A strategy that combined steady-state feedforward control with an MPC-based dynamic control is designed in [24] to calculate the control input sequence of engine torque and hydraulic variable pump displacement for a heavy commercial vehicle. However, it is worth mentioning that the influence of uncertainties of the system structure and parameters, as well as external disturbance, is not ignored on the transient and static performance of the closed-loop control of the subsystems of the HHVs. Motivated by the analysis above, in this study, we focus on a hierarchical control including upper-layer EMS and lower-layer engine closed-loop control to implement optimal engine control with high efficiency and low fuel consumption for a hydraulic hybrid powertrain used in an example of a spray-painting construction vehicle. The structural feature of the HHV uses a hydraulic bridge and one accumulator to achieve two-way energy collection, which is different from the usual structure of most HHVs that use two accumulators with high and low pressures. Considering the uncertain acceleration and deceleration driving cycles of the construction vehicle studied, the uncertain nonlinear characteristics of engine and external disturbance, as well as the actuator constraints, a hierarchical MPC strategy is designed to achieve reasonable distribution of engine power and obtain better performance of setpoint tracking of engine torque. The main highlights of the proposed control strategy include three aspects. First, the uncertain driving cycle derived from the randomness of drivers' driving patterns of construction vehicles and considered and a SMPC-EMS is proposed, to predict the acceleration of the vehicle using the Markov chain according to the statistical information of driving condition data for the actual construction vehicle to ensure the prediction accuracy of the load torque demand. Second, considering the real time of the optimization solution, to avoid intense online computations, a scenario-based enumeration approach is used to solve a multistage stochastic optimization problem in the SMPC-EMS of the upper layer. Third, focusing on the nonlinear characteristics and uncertain parameters of the engine and external disturbance, an estimator of the total disturbance is combined with the MPC torque tracking controller of the engine in a closed-loop control of the lower layer to ensure the robustness of the tracking performance for the distributed torque from the upper-layer SMPC-EMS, and therefore the diesel engine operates quickly and stably in a high-efficiency fuel zone. The remainder of this paper is organized as follows: The description of the studied system and the control problem are introduced in Section 2. Section 3 presents the design of the upper-layer SMPC energy management controller and the lower-layer engine fast speed tracking MPC controller are designed for the torque coupling system. The effectiveness and adaptability of the proposed method are verified using both simulation and the experiment test platform in Sections 4 and 5, respectively. In addition, the comparison results with the existing strategies are also presented. The conclusions of this paper are drawn in Section 6.