A dual-motor coupling-propulsion electric bus (DMCPEB) is modeled, and its optimal control strategy is studied in this paper. The necessary dynamic features of energy loss for subsystems is modeled. Dynamic programming (DP) technique is applied to find the optimal control strategy including upshift threshold, downshift threshold, and power split ratio between the main motor and auxiliary motor. Improved control rules are extracted from the DP-based control solution, forming near-optimal control strategies. Simulation results demonstrate that a significant improvement in reducing energy loss due to the dual-motor coupling-propulsion system (DMCPS) running is realized without increasing the frequency of the mode switch.
The application of battery electric vehicle in public transport field is a good way to improve the increasing air pollution and shortage of oil resources problems. Developing the electric bus has significant meanings for energy saving, emission reduction, and the electric vehicle (EV) industry development. The control of high-power drive system is one of the key technologies for electric bus. Dual-motor drive coupled by planetary gear is an effective way to realize the high-power drive system. Owing to the dual-power source nature, the control strategy of DMCPEB is typically more complicated than that of traditional engine based vehicle. Therefore, system-level vehicle simulation methodology is often applied to implement accurate sizing and matching studies and to develop effective energy control method, before the final design and physical prototyping.
The power control strategy for electric vehicle can be roughly classified into three categories (see [
In this paper, dynamic programming (DP) technique is applied to solve the optimal control strategy problem of a DMCPEB. The optimal control strategy solution over a driving cycle is obtained by minimizing a defined cost function. Two cases are solved: an energy-loss-only case and an energy-loss/shifting-frequency case. The comparison of these two cases provides insight into the change needed when the additional objective of riding comfort is included. However, the DP control actions are not implementable due to their preview nature and heavy computational requirement. They are, on the other hand, a good design tool to analyze, assess, and adjust other control strategies. After studying the behavior of the dynamic programming solution carefully, we extract implementable rules. These rules are used to improve a simple, intuition-based algorithm. It was found that the performance of the rule-based algorithm can be improved significantly.
The paper is organized as follows. In Section
The target vehicle is a conventional bus whose engine and part transmission were replaced by a DMCPS developed by Beijing Institute of Technology [
Basic parameters of the vehicle and DMCPS.
Name | Value | Unit |
---|---|---|
Vehicle mass ( |
18000 | kg |
Tire radius ( |
0.4785 | m |
Rolling resistance coefficient ( |
0.015 | Null |
Windward area ( |
7.5438 | m2 |
Air resistance coefficient ( |
0.8 | Null |
Final drive ratio |
6.34 | Null |
Maximum torque of the motor |
410 | Nm |
Maximum rotate speed of the motor |
6000 | rpm |
Characteristic parameter of PGT ( |
3.5 | Null |
The dual-motors coupling-propulsion electric bus modeling configuration.
Compared with HEV, BEV’s power management strategy seems much simpler, as most of BEVs only have one driving motor which means that the output power of motor is directly determined by the driver’s power requirement. For two-motor coupled driving system, there are four possible operating modes: one-motor driving, two-motor driving, one-motor regenerative braking, and two-motor regenerative braking. In order to reduce the energy loss, the power management controller has to decide which operating mode to use and determine the proper power split between the two power sources while meeting the driver’s demand. When the system is working in two-motor condition, the situation can be classified into torque coupling and speed coupling according to the structure of the driving system. For torque coupling driving system, the power split of power sources can be realized by determining the torque split, while, for the speed coupling driving system, the power split of power sources can be realized by determining the speed split between the two sources. The simple rule-based power management strategy was developed on the basis of engineering intuition and simple analysis of vehicle’s driving characteristics and vehicle’s dynamic requirements [
The speed discrepancy
where
Compared with rule-based algorithms, the dynamic optimization approach can find the best control strategy relying on a dynamic model (see [
In the discrete-time format, a model of the battery electric vehicle can be expressed as
The detailed DMCPS and DMCPEB models are not suitable for dynamic optimization due to their high number of states. Thus, a simplified but sufficiently complex vehicle model is developed. This DMCPS is a speed coupling system and can be calssified into two working modes (one-motor working mode and two-motor working mode). As the two aspects are the main influence factors when the DMCPS’s parameters are determined, it was decided that only these two state variables needed to be kept: the two motors’ speed ratio and DMCPS’s working mode. The simplifications of the subsystems motors, vehicle, transmission, battery, and the planetary gear train are described below.
Efficiency map of the electric motor.
where
where
where state
The DP technique is based on Bellman’s Principle of Optimality, which states that the optimal policy can be obtained if we first solve a one stage subproblem involving only the last stage and then gradually extend to subproblems involving the last two stages, last three stages
Step
Step
As the DMCPS is a nonlinear system, this DP has to be solved numerically by some approximations. A standard way to solve (
The DP procedure described above produces an optimal, time-varying, state-feedback control law. In the following, two cases are presented: energy-loss-only problem and energy-loss/ mode-change problem.
When optimizing for only fuel economy, the weighting
The rotating speed of the two motors.
The output torque of the two motors.
Energy-loss distribution.
From Figure
To study the tradeoff between energy loss and shifting frequency the weight factors are varied
The trend of the energy loss and number of shifts with the change of
From Figure
Energy-loss distribution for
The DP control policy is not implementable in real driving conditions because it requires knowledge of future speed and load profile. Nonetheless, analyzing its behavior provides useful insight into possible improvement of the rule-based controller. Based on the above discussion simulation results, here we abstract the shift control strategy including upshift and downshift strategy and power split strategy.
The working mode shift is crucial to the reduction of energy loss and riding comfort. In the original DP results the DMCPS needs frequent shifting to reduce the energy loss, which may influence the riding comfort, and when
Abstracting of shifting strategy.
New shifting strategy.
In this section, we study how power split control of the preliminary rule-based algorithm can be improved by analyzing the DP results when
Two working modes are defined: single motor working mode (
New power split strategy.
After incorporating the working mode shift control and power split control outlined in the previous sections, the improved rule-based controller is evaluated using Chinese typical city drive cycle. Table
Comparison of different control strategy in energy loss.
Loss type | Main motor (KJ) | Auxiliary motor (KJ) | Coupling box (KJ) | Total (KJ) | Improvement in total (%) |
---|---|---|---|---|---|
Preliminary rule-based | 5302 | 2781 | 2158 | 10240 | 0% |
New rule-based | 2938 | 3017 | 2030 | 7987 | 22% |
DP ( |
1848 | 2691 | 1922 | 6461 | 36.9% |
Comparison of different control strategy in shifting number.
Shifting number | Improvement in total (%) | |
---|---|---|
Preliminary rule-based | 26 | 0% |
New rule-based | 26 | 0% |
DP ( |
22 | 15.34% |
Based on the simplified model, DP is applied to solve the globally optimal control strategy. Designing the control strategy for DMCPEB by extracting rules from the dynamic programming results has the clear advantage of being near optimal, accommodating multiple objectives, and systematic. Depending on the overall objective, one can easily develop control laws that emphasize low energy loss and riding comfort. By analyzing the DP results the approximate optimal upshift threshold, downshift threshold, and power split ratio were determined. The improved rule-based control strategy can reduce the energy loss by about 22%, while the DP (
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Grant no. 51175040) and the Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20111101110037).