Abstract
To enhance the economic performance of electric vehicles, this study presents an optimized braking energy recovery control strategy. Taking a specific electric vehicle as the research object, I developed a front-rear axle braking force distribution scheme based on ECE-R13 regulations. Considering battery charge-discharge limits and motor constraints, I designed a fuzzy controller with three inputs (braking intensity, vehicle speed, state of charge [SOC]) and one output (regenerative braking force ratio). Through co-simulation using Cruise and MATLAB/Simulink, the strategy’s effectiveness was verified by comparing it with Cruise’s official control strategy. The results show that the proposed strategy optimizes braking force distribution, reducing energy consumption per 100 km by 23.4% under the FTP75 cycle, thus extending the driving range. This study provides a reference for subsequent research on electric vehicle energy recovery.
1. Introduction
With the global energy crisis and growing environmental awareness, the automotive industry has increasingly focused on new energy vehicles. Electric vehicles (EVs) stand out due to their zero emissions, low energy consumption, and low noise. However, limitations in battery technology—such as short driving range, inconvenient charging, and long charging times—hinder their widespread adoption.
During vehicle braking, the motor of an EV operates in a generating state, converting kinetic energy into electrical energy stored in batteries or other energy storage devices. Studies show that only 10%–30% of braking energy can be recovered, with the rest dissipating as heat. Therefore, optimizing braking energy recovery is crucial to improving energy efficiency and extending the range of EVs.
Vehicle braking combines mechanical braking and regenerative braking. The key challenge is to distribute braking force between the axles and between mechanical and regenerative systems to maximize energy recovery while ensuring braking safety. Previous studies have explored fuzzy control strategies, multi-parameter allocation, and co-simulation methods to address this. For example, Li et al. designed regenerative braking force ratios under different braking intensities using fuzzy control based on ECE curves and I curves. Geng et al. proposed a two-layer control strategy integrating mechanical and regenerative braking for higher energy efficiency.
In this study, I aim to further optimize the braking energy recovery control strategy for EVs. By designing a fuzzy controller with multi-factor inputs (braking intensity, speed, SOC) and following ECE-R13 regulations for safety, I seek to improve energy recovery efficiency and reduce energy consumption.
2. Braking Force Distribution Strategy
2.1 Vehicle Parameters
The EV studied employs front-wheel drive, and key parameters are listed in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Full-load mass m (kg) | 1580 | Rolling resistance coefficient f | 0.09 |
| Distance from centroid to front axle a (m) | 1.2 | Tire radius r (m) | 0.287 |
| Distance from centroid to rear axle b (m) | 1.267 | Main reducer ratio i | 6.14 |
| Centroid height \(h_g\) (m) | 0.5 | Gravitational acceleration g (m/s²) | 9.8 |
| Wheelbase L (m) | 2.467 | Braking intensity z | – |
| Frontal area A (m²) | 1.97 | Front axle braking force \(F_{uf}/F_{u1}\) (N) | – |
| Drag coefficient \(C_D\) | 0.284 | Rear axle braking force \(F_{ur}/F_{u2}\) (N) | – |
Table 1. Related Parameter Table
2.2 Braking Force Distribution Principles
The braking force distribution strategy flowchart is shown in Figure 1 (conceptual). Based on ECE regulations and the I-curve, I designed force distribution for light, moderate, and emergency braking conditions, considering motor and battery constraints to ensure stability and recovery efficiency.
For safety, braking stability zones are defined: front wheel lock without rear lock, simultaneous front-rear lock (stable), and rear wheel lock without front lock (unstable, to be avoided). The braking force distribution curve (OABCD) is set within the safe zone defined by ECE (M-curve), I-curve, and f-curve.
2.3 Front-Rear Axle Braking Force Allocation
- Light braking (\(0 < z < 0.12\)): All braking force is borne by the front axle, with regenerative braking maximizing energy recovery:\(\begin{cases} F_{uf} = mgz \\ F_{ur} = 0 \end{cases}\)
- Moderate braking (\(0.120 < z < 0.525\)): Composite braking (mechanical + regenerative) with force distribution:\(\begin{cases} F_{uf} = \frac{0.95G \times (z + 0.07) \times (b + z \times h_g)}{0.85L} \\ F_{ur} = z \times G – F_{uf} \end{cases}\) where \(G = mg\) (vehicle gravity).
- High braking (\(0.525 < z < 0.665\)): Increasing mechanical braking proportion, with regenerative braking gradually decreasing:\(\begin{cases} F_{uf} = \frac{0.665G \times (b + z \times h_g)}{L} \\ F_{ur} = \frac{(L – 0.665h_g) \times F_{uf}}{0.665h_g} – \frac{Gb}{h_g} \end{cases}\)
- Emergency braking (\(z > 0.665\)): Only mechanical braking is used, with no energy recovery:\(\begin{cases} F_{uf} = \frac{z \times G \times (b + z \times h_g)}{L} \\ F_{ur} = \frac{z \times G \times (a – z \times h_g)}{L} \end{cases}\)
To prevent unstable braking, the brake force distribution follows the ODC segment to track the I-curve closely.
3. Fuzzy Control-Based Regenerative Braking Simulation Model
3.1 Mandani Fuzzy Controller Design
I developed a Mandani-type fuzzy controller with three inputs: braking intensity z, speed v, and SOC. The output is the regenerative braking ratio coefficient k.
- Input Variables:
- Braking intensity z: Universe [0, 1], fuzzy subsets {Low (L), Medium (M), High (H)}.
- Speed v: Universe [0, 100] (km/h), fuzzy subsets {L, M, H}.
- SOC: Universe [0, 1], fuzzy subsets {L, M, H}.
- Output Variable:
- Regenerative braking ratio k: Universe [0, 1], fuzzy subsets {Very Low (VL), Low (L), Medium (M), High (H), Very High (VH)}.
Triangle and trapezoid membership functions were used, aligned with motor external characteristics (Figure 2, conceptual). The fuzzy control rules, based on expert experience and experiments, are shown in Table 2.
| Rule No. | v | SOC | z | k | Rule No. | v | SOC | z | k |
|---|---|---|---|---|---|---|---|---|---|
| 1 | L | H | L | VL | 15 | M | M | H | VL |
| … | … | … | … | … | … | … | … | … | … |
Table 2. Fuzzy Control Rule Table
3.2 Simulation Model Setup
Using MATLAB/Simulink, I built two control strategies:
- Strategy A: Proposed fuzzy control-based braking energy recovery strategy.
- Strategy B: Cruise’s official strategy without force distribution and fuzzy control.
The models were compiled into DLL files and integrated into the Cruise vehicle model for co-simulation (Figure 3, conceptual). The simulation covered NEDC and FTP75 driving cycles (Figure 4, conceptual).
4. Simulation Results and Analysis
4.1 Energy Consumption Comparison
Table 3 shows the energy consumption per 100 km for both strategies under NEDC and FTP75 cycles.
| Parameter | NEDC Cycle | FTP75 Cycle |
|---|---|---|
| Control Strategy A (kW·h) | 11.71 | 9.95 |
| Control Strategy B (kW·h) | 13.62 | 12.99 |
| Efficiency Improvement (%) | +14.00 | +23.40 |
Table 3. Electrical Consumption per 100 Kilometers
4.2 Result Discussion
- NEDC Cycle: Energy consumption decreased from 13.62 kW·h to 11.71 kW·h, a 14% improvement. The strategy effectively recovers energy during light and moderate braking phases.
- FTP75 Cycle: Energy consumption dropped from 12.99 kW·h to 9.95 kW·h, a 23.4% improvement. The FTP75 cycle’s frequent acceleration-deceleration allows more regenerative braking opportunities, highlighting the strategy’s advantage in dynamic conditions.
The results confirm that the fuzzy control-based strategy outperforms the baseline in energy recovery, primarily because:
- The multi-factor fuzzy controller adapts regenerative braking ratio to real-time braking intensity, speed, and SOC, optimizing force distribution.
- Following ECE regulations ensures braking safety while maximizing energy recovery in non-emergency braking.
5. Conclusion
In this study, I proposed an optimized braking energy recovery control strategy for electric vehicles, integrating ECE-R13-based braking force distribution and a three-input fuzzy controller. Key findings include:
- The strategy optimizes front-rear axle braking force distribution, balancing safety and energy efficiency.
- The fuzzy controller, considering braking intensity, speed, and SOC, dynamically adjusts regenerative braking ratio, improving recovery efficiency.
- Co-simulation results show 14% (NEDC) and 23.4% (FTP75) reductions in energy consumption, extending the driving range.
This work provides a practical reference for developing energy-efficient braking systems in electric vehicles. Future research may explore real-time adaptive control and integration with other vehicle systems for further optimization.