# Hierarchical Model Predictive Control for Hydraulic Hybrid Powertrain of a Construction Vehicle
###### Abstract
In particular, the relatively low energy density of a hydraulic accumulator requires a carefully designed control strategy in order for the fuel economy potential to be fully realized. In practice, the EMS for HHVs is usually designed as a rule-based (RB) control strategy because it is simple and has real-time implementable structure [6; 7; 8; 9; 10]. However, since its control performance depends heavily on rule-switching thresholds defined by the engineering experience, it actually cannot always provide good results during various driving conditions. Therefore, in order to achieve the best control performance possible during a driving cycle, an optimization-based control strategy has become a popular research topic for HHVs, as well as for HEVs. If the driving cycle is completely known, dynamic programming (DP) [11; 12; 13] should be the most popular optimization-based EMS. However, due to the uncertain real driving cycles, the EMS designed offline based on DP is not feasible in practice, although it is globally optimal in theory. Consequently, stochastic DP (SDP) [14] is a natural alternative to DP, which utilizes the probability distribution extracted from multiple historical driving cycles to deal with the uncertain driving cycles in practice. From the aspect of a real-time implementable EMS, the equivalent consumption minimization strategy (ECMS) [15] is a popular instantaneous optimization-based method. However, to be close to global optimization, it is a challenge to determine an appropriate adaptive equivalent factor for ECMS. Fortunately, EMS that uses a model predictive control (MPC) framework achieves both near-global optimization and real-time implementation provided the prediction model in the MPC is well processed and the real-time performance of the solution algorithm to the optimal control in the finite receding horizon is guaranteed. In this regard, a MPC-based control strategy is highly adoptable in the design of EMS for HHVs, and therefore more efforts have been directed at the model's prediction accuracy and a real-time optimal solution. More specifically, an MPC-based EMS is designed in [16] for a parallel HHV used in a passenger vehicle, in which the optimization objective is only a convex quadratic function that can be solved quickly to avoid the requirement of intense online computations. To improve the prediction performance, a type of predictive energy management approach with a learning drive cycle based on previous vehicle operations on the same route is presented in [17] for parallel hydraulic hybrid powertrain heavy vehicles used in garbage trucks or city buses. Moreover, in [18], the learned driving profiles for the prediction are associated with a particular vehicle's location. An MPC energy management method is studied in [19] for a series HHV based on the prediction of engine power by means of decrement of velocity tracking error. Additionally, an MPC-based EMS is presented in [20] for a type of parallel HHV based on the prediction model using the simplified powertrain dynamics to facilitate rapid online solutions to the optimization problem. However, it should be noted that, in practice, the uncertain driving cycles inevitably affect the accuracy of the prediction information and further affect the control performance of the MPC-based EMS. Therefore, stochastic model predictive control (SMPC) is a promising approach in an EMS, such as, in [21], where the velocity demand from the driver is expressed as a random Markov process and a SMPC strategy is developed for power management tailored for the series HHV. In a vehicle with a hybrid powertrain that involves an engine, the upper-layer EMS controls the power allocation between the engine and the additional power source which is undoubtedly crucial to reduce fuel consumption and exhaust emission; however, the lower-layer closed-loop control of the driving power source itself, especially the engine, is even more important to realize the effect of the EMS.