Numerical Strategies for Mixed-Integer Optimization of Power-Split and Gear Selection in Hybrid Electric Vehicles

This paper presents numerical strategies for a computationally efficient energy management system that co-optimizes the power split and gear selection of a hybrid electric vehicle (HEV). We formulate a mixed-integer optimal control problem (MIOCP) that is transcribed using multiple-shooting into a mixed-integer nonlinear program (MINLP) and then solved by nonlinear model predictive control. We present two different numerical strategies, a Selective Relaxation Approach (SRA), which decomposes the MINLP into several subproblems, and a Round-n-Search Approach (RSA), which is an enhancement of the known ‘relax-n-round’ strategy. Subsequently, the resulting algorithmic performance and optimality of the solution of the proposed strategies are analyzed against two benchmark strategies; one using rule-based gear selection, which is typically used in production vehicles, and the other using dynamic programming (DP), which provides a global optimum of a quantized version of the MINLP. The results show that both SRA and RSA enable about\ua03.6%\ua0cost reduction compared to the rule-based strategy, while still being within\ua01%\ua0of the DP solution. Moreover, for the case studied RSA takes about\ua035%\ua0less mean computation time compared to SRA, while both SRA and RSA being about\ua099\ua0times faster than DP. Furthermore, both SRA and RSA were able to overcome the infeasibilities encountered by a typical rounding strategy under different drive cycles. The results show the computational benefit of the proposed strategies, as well as the energy saving possibility of co-optimization strategies in which actuator dynamics are explicitly included

Gear shift strategies for automotive transmissions

The development history of automotive engineering has shown the essential role of transmissions in road vehicles primarily powered by internal combustion engines. The engine with its physical constraints on the torque and speed requires a transmission to have its power converted to the drive power demand at the vehicle wheels. Under dynamic driving conditions, the transmission is required to shift in order to match the engine power with the changing drive power. Furthermore, a gear shift decision is expected to be consistent such that vehicle can remain in the next gear for a period of time without deteriorating the acceleration capability. Therefore, an optimal conversion of the engine power plays a key role in improving the fuel economy and driveability. Moreover, the consequences of the assumptions related to the discrete state variable-dependent losses, e.g. gear shifting, clutch slippage and engine starting, and their e¿ect on the gear shift control strategy are necessary to be analyzed to yield insights into the fuel usage. The ¿rst part of the thesis deals with the design of gear shift strategies for electronically controlled discrete ratio transmissions used in both conventional vehicles and Hybrid Electric Vehicles (HEVs). For conventional vehicles, together with the fuel economy, the driveability is systematically addressed in a Dynamic Programming (DP) based optimal gear shift strategy by three methods: i) the weighted inverse of the power re¬serve, ii) the constant power reserve, and iii) the variable power reserve. In addition, a Stochastic Dynamic Programming (SDP) algorithm is utilized to optimize the gear shift strategy, subject to a stochastic distribution of the power request, in order to minimize the expected fuel consumption over an in¿nite horizon. Hence, the SDP-based gear shift strategy intrinsically respects the driveability and is realtime implementable. By per¬forming a comparative analysis of all proposed gear shift methods, it is shown that the variable power reserve method achieves the highest fuel economy without deteriorating the driveability. Moreover, for HEVs, a novel fuel-optimal control algorithm, consist-ing of the continuous power split and discrete gear shift, engine on-o¿ problems, based on a combination of DP and Pontryagin’s Minimum Principle (PMP) is developed for the corresponding hybrid dynamical system. This so-called DP-PMP gear shift control approach benchmarks the development of an online implementable control strategy in terms of the optimal tradeo¿ between calculation accuracy and computational e¿ciency. Driven by an ultimate goal of realizing an online gear shift strategy, a gear shift map design methodology for discrete ratio transmissions is developed, which is applied for both conventional vehicles and HEVs. The design methodology uses an optimal gear shift algorithm as a basis to derive the optimal gear shift patterns. Accordingly, statis¬tical theory is applied to analyze the optimal gear shift pattern in order to extract the time-invariant shift rules. This alternative two-step design procedure makes the gear shift map: i) respect the fuel economy and driveability, ii) be consistent and robust with respect to shift busyness, and iii) be realtime implementation. The design process is ¿exible and time e¿cient such that an applicability to various powertrain systems con¿gured with discrete ratio transmissions is possible. Furthermore, the study in this thesis addresses the trend of utilizing the route information in the powertrain control system by proposing an integrated predictive gear shift strategy concept, consisting of a velocity algorithm and a predictive algorithm. The velocity algorithm improves the fuel economy in simulation considerably by proposing a fuel-optimal velocity trajectory over a certain driving horizon for the vehicle to follow. The predictive algorithm suc¬cessfully utilizes a prede¿ned velocity pro¿le over a certain horizon in order to realize a fuel economy improvement very close to that of the globally optimal algorithm (DP). In the second part of the thesis, the energetic losses, involved with the gear shift and engine start events in an automated manual transmission-based HEV, are modeled. The e¿ect of these losses on the control strategies and fuel consumption for (non-)powershift transmission technologies is investigated. Regarding the gear shift loss, the study ¿rstly ever discloses a perception of a fuel-e¿cient advantage of the powershift transmissions over the non-powershift ones applied for commercial vehicles. It is also shown that the engine start loss can not be ignored in seeking for a fair evaluation of the fuel economy. Moreover, the sensitivity study of the fuel consumption with respect to the prediction horizon reveals that a predictive energy management strategy can realize the highest achievable fuel economy with a horizon of a few seconds ahead. The last part of the thesis focuses on investigating the sensitivity of an optimal gear shift strategy to the relevant control design objectives, i.e. fuel economy, driveability and comfort. A singu¬lar value decomposition based method is introduced to analyze the possible correlations and interdependencies among the design objectives. This allows that some of the pos¬sible dependent design objective(s) can be removed from the objective function of the corresponding optimal control problem, hence thereby reducing the design complexity

Fast Optimal Energy Management with Engine On/Off Decisions for Plug-in Hybrid Electric Vehicles

In this paper we demonstrate a novel alternating direction method of multipliers (ADMM) algorithm for the solution of the hybrid vehicle energy management problem considering both power split and engine on/off decisions. The solution of a convex relaxation of the problem is used to initialize the optimization, which is necessarily nonconvex, and whilst only local convergence can be guaranteed, it is demonstrated that the algorithm will terminate with the optimal power split for the given engine switching sequence. The algorithm is compared in simulation against a charge-depleting/charge-sustaining (CDCS) strategy and dynamic programming (DP) using real world driver behaviour data, and it is demonstrated that the algorithm achieves 90\% of the fuel savings obtained using DP with a 3000-fold reduction in computational time

Pedestrian-Aware Supervisory Control System Interactive Optimization of Connected Hybrid Electric Vehicles via Fuzzy Adaptive Cost Map and Bees Algorithm

Electrified vehicles are increasingly being seen as a means of mitigating the pressing concerns of traffic-related pollution. Due to the nature of engine-assisted vehicle exhaust systems, pedestrians in close proximity to these vehicles may experience events where specific emission concentrations are high enough to cause health effects. To minimize pedestrians’ exposure to vehicle emissions and pollutants nearby, we present a pedestrian-aware supervisory control system for connected hybrid electric vehicles by proposing an interactive optimization methodology. This optimization methodology combines a novel fuzzy adaptive cost map and the Bees Algorithm to optimize power-split control parameters. It enables the self-regulation of inter-objective weights of fuel and exhaust emissions based on the real-time pedestrian density information during the optimization process. The evaluation of the vehicle performance by using the proposed methodology is conducted on the realistic trip map involving pedestrian density information collected from the University College Dublin campus. Moreover, two bootstrap sampling techniques and effect of communication quality are both investigated in order to examine the robustness of the improved vehicle system. The results demonstrate that 14.42% mass of exhaust emissions can be reduced for the involved pedestrians, by using the developed fuzzy adaptive cost map

Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles

The primary objective of a hybrid electric vehicle (HEV) is to optimize the energy consumption of the automotive powertrain. This optimization has to be applied while respecting the operating conditions of the battery. Otherwise, there is a risk of compromising the battery life and thermal runaway that may result from excessive power transfer across the battery. Such considerations are critical if factoring in the low battery capacity and the passive battery cooling technology that is commonly associated with HEVs. The literature has proposed many solutions to HEV energy optimization. However, only a few of the solutions have addressed this optimization in the presence of thermal constraints. In this paper, a strategy for energy optimization in the presence of thermal constraints is developed for P2 HEVs based on battery sizing and the application of model predictive control (MPC) strategy. To analyse this approach, an electro-thermal battery pack model is integrated with an off-axis P2 HEV powertrain. The battery pack is properly sized to prevent thermal runaway while improving the energy consumption. The power splitting, thermal enhancement and energy optimization of the complex and nonlinear system are handled in this work with an adaptive MPC operated within a moving finite prediction horizon. The simulation results of the HEV SUV demonstrate that, by applying thermal constraints, energy consumption for a 0.9 kWh battery capacity can be reduced by 11.3% relative to the conventional vehicle. This corresponds to about a 1.5% energy increase when there is no thermal constraint. However, by increasing the battery capacity to 1.5 kWh (14s10p), it is possible to reduce the energy consumption by 15.7%. Additional benefits associated with the predictive capability of MPC are reported in terms of energy minimization and thermal improvement

Real-time distributed economic model predictive control for complete vehicle energy management

In this paper, a real-time distributed economic model predictive control approach for complete vehicle energy management (CVEM) is presented using a receding control horizon in combination with a dual decomposition. The dual decomposition allows the CVEM optimization problem to be solved by solving several smaller optimization problems. The receding horizon control problem is formulated with variable sample intervals, allowing for large prediction horizons with only a limited number of decision variables and constraints in the optimization problem. Furthermore, a novel on/off control concept for the control of the refrigerated semi-trailer, the air supply system and the climate control system is introduced. Simulation results on a low-fidelity vehicle model show that close to optimal fuel reduction performance can be achieved. The fuel reduction for the on/off controlled subsystems strongly depends on the number of switches allowed. By allowing up to 15-times more switches, a fuel reduction of 1.3% can be achieved. The approach is also validated on a high-fidelity vehicle model, for which the road slope is predicted by an e-horizon sensor, leading to a prediction of the propulsion power and engine speed. The prediction algorithm is demonstrated with measured ADASIS information on a public road around Eindhoven, which shows that accurate prediction of the propulsion power and engine speed is feasible when the vehicle follows the most probable path. A fuel reduction of up to 0.63% is achieved for the high-fidelity vehicle model.</p

Real-time distributed economic model predictive control for complete vehicle energy management

In this paper, a real-time distributed economic model predictive control approach for complete vehicle energy management (CVEM) is presented using a receding control horizon in combination with a dual decomposition. The dual decomposition allows the CVEM optimization problem to be solved by solving several smaller optimization problems. The receding horizon control problem is formulated with variable sample intervals, allowing for large prediction horizons with only a limited number of decision variables and constraints in the optimization problem. Furthermore, a novel on/off control concept for the control of the refrigerated semi-trailer, the air supply system and the climate control system is introduced. Simulation results on a low-fidelity vehicle model show that close to optimal fuel reduction performance can be achieved. The fuel reduction for the on/off controlled subsystems strongly depends on the number of switches allowed. By allowing up to 15-times more switches, a fuel reduction of 1.3% can be achieved. The approach is also validated on a high-fidelity vehicle model, for which the road slope is predicted by an e-horizon sensor, leading to a prediction of the propulsion power and engine speed. The prediction algorithm is demonstrated with measured ADASIS information on a public road around Eindhoven, which shows that accurate prediction of the propulsion power and engine speed is feasible when the vehicle follows the most probable path. A fuel reduction of up to 0.63% is achieved for the high-fidelity vehicle model.</p

Development of an Adaptive Efficient Thermal/Electric Skipping Control Strategy Applied to a Parallel Plug-in Hybrid Electric Vehicle

In recent years automobile manufacturers focused on an increasing degree of electrification of the powertrains with the aim to reduce pollutants and CO2 emissions. Despite more complex design processes and control strategies, these powertrains offer improved fuel exploitation compared to conventional vehicles thanks to intelligent energy management. A simulation study is here presented aiming at developing a new control strategy for a P3 parallel plug-in hybrid electric vehicle. The simulation model is implemented using vehicle modeling and simulation toolboxes in MATLAB/Simulink. The proposed control strategy is based on an alternative utilization of the electric motor and thermal engine to satisfy the vehicle power demand at the wheels (Efficient Thermal/Electric Skipping Strategy-ETESS). The choice between the two units is realized through a comparison between two equivalent fuel rates, one related to the thermal engine and the other related to the electric consumption. An adaptive function is introduced to develop a charge-blended control strategy. The novel adaptive control strategy (A-ETESS) is applied to estimate fuel consumption along different driving cycles. The control algorithm is implemented on a dedicated microcontroller unit performing a Processor-In-the-Loop (PIL) simulation. To demonstrate the reliability and effectiveness of the A-ETESS, the same adaptive function is built on the Equivalent Consumption Minimization Strategy (ECMS). The PIL results showed that the proposed strategy ensures a fuel economy similar to ECMS (worse of about 2% on average) and a computational effort reduced by 99% on average. This last feature reveals the potential for real-time on-vehicle applications

Heavy-Duty Vehicles Modeling and Factors Impacting Fuel Consumption.

A conventional heavy-duty truck PSAT model was validated and incorporated into the Powertrain System Analysis Toolkit (PSAT). The truck that was modeled was a conventional over-the-road 1996 Peterbilt tractor, equipped with a 550 hp Caterpillar 3406E non exhaust gas circulation (EGR) engine and an 18-speed Roadranger manual transmission. A vehicle model was developed, along with the model validation processes. In the engine model, an oxides of nitrogen (NOx) emissions model and a fuel rate map for the Caterpillar 3406E engine were created based on test data. In the gearbox model, a shifting strategy was specified and transmission efficiency lookup tables were developed based on the losses information gathered from the manufacturer. As the largest mechanical accessory model, an engine cooling fan model, which estimates fan power demand, was integrated into the heavy-duty truck model. Experimental test data and PSAT simulation results pertaining to engine fuel rate, engine torque, engine speed, engine power and NOx were within 5% relative error. A quantitative study was conducted by analyzing the impacts of various parameters (vehicle weights, coefficients of rolling resistance and the aerodynamic drag) on fuel consumption (FC) for the Peterbilt truck. The vehicle was simulated over five cycles which represent typical vehicle in-use behavior. Three contributions were generated. First, contour figures provided a convenient way to estimate fuel economy (FE) of the Peterbilt truck over various cycles by interpolating within the parameter values. Second, simulation results revealed that, depending on the circumstances and the cycle, it may be more cost effective to reduce one parameter value (such as coefficient of aerodynamic drag) to increase FE, or it may be more beneficial to reduce another (such as the coefficient of rolling resistance). Third, the amount of the energy consumed by auxiliary loads was found to be highly dependent upon the driving cycles. The ratios between average auxiliary power and average engine power were found to be 71.0%, 17.1%, 15.3%, 12.4% and 11.43% for creep, transient, UDDS, cruise and HHDDT_s cycles, respectively. A hybrid electric bus (HEB) also was modeled. The HEB that was modeled was a New Flyer bus with ISE hybrid system, a Cummins ISB 260H engine and a single-reduction transmission. Information and data were acquired to describe all major components of the HEB. The engine model was validated prior to modeling of the whole vehicle model. The load-following control strategy was utilized in the energy management system. Experimental data and PSAT simulated results were compared over four driving schedules, and the relative percent of errors of the FC, FE, CO2 and NOx were all within 5% except for the FE and NOx of the Manhattan cycle, which were 6.93% and 7.13%, respectively. The high fidelity of this model makes it possible to evaluate the FE and NOx emissions of series hybrid buses for subsequent PSAT users