The rapid global proliferation of Battery EV Cars, while alleviating reliance on fossil fuels and reducing tailpipe emissions, presents a persistent and critical challenge: limited driving range. Maximizing the utilization of every available energy source is paramount. A significant opportunity lies in reclaiming the kinetic energy dissipated as heat during conventional braking. Regenerative braking systems convert this otherwise wasted energy back into electrical energy, storing it in the vehicle’s battery, thereby extending its range. Studies indicate that effective regenerative braking can increase the driving range of a Battery EV Car by 15% to 35%. The core of this technology lies in an intelligent control strategy that seamlessly blends regenerative braking with hydraulic friction braking to ensure safety, stability, and optimal energy recovery under diverse driving conditions.
Traditional control strategies, such as rule-based or fixed-ratio methods, often fail to fully exploit the regenerative potential. They may not adequately consider real-time variables like the Battery EV Car’s speed, state of charge (SOC), brake pedal application rate, and motor-generator efficiency characteristics. This leads to suboptimal energy recuperation. This paper proposes a sophisticated Braking Energy Recovery Control System for Battery EV Cars, utilizing a Fuzzy Neural Network (FNN) to achieve precise braking force distribution and signal recognition, ultimately enhancing the vehicle’s overall energy efficiency and driving range.
Vehicle Dynamics and Braking Force Analysis
To design an effective control system, a fundamental understanding of the forces acting on a Battery EV Car is essential. The longitudinal dynamics during braking are governed by the equilibrium between inertia, driving/braking forces, and various resistive forces. The key resistive forces include rolling resistance \( F_r \), aerodynamic drag \( F_w \), and grade resistance \( F_g \).
The total resistance \( F_{resist} \) opposing the motion of the Battery EV Car is given by:
$$F_{resist} = F_r + F_w + F_g$$
Where:
- Rolling Resistance: \( F_r = mg f_r \cos(\alpha) \). Here, \( m \) is the vehicle mass, \( g \) is gravitational acceleration, \( f_r \) is the rolling resistance coefficient, and \( \alpha \) is the road gradient.
- Aerodynamic Drag: \( F_w = \frac{1}{2} \rho A_f C_D (v + v_w)^2 \). Here, \( \rho \) is air density, \( A_f \) is frontal area, \( C_D \) is drag coefficient, \( v \) is vehicle speed, and \( v_w \) is wind speed (headwind positive).
- Grade Resistance: \( F_g = mg \sin(\alpha) \).
During braking, the total braking force \( F_{b\_total} \) required to decelerate the Battery EV Car at a rate \( a \) is derived from the equation of motion:
$$F_{b\_total} = m a + F_{resist}$$
The total braking torque \( T_{b\_total} \) at the wheels is:
$$T_{b\_total} = F_{b\_total} \cdot r_d$$
where \( r_d \) is the dynamic tire radius.
The maximum regenerative braking torque \( T_{regen\_max} \) that the electric motor can provide is a function of motor speed (related to vehicle speed) and the battery’s ability to accept charge (related to SOC and temperature). The control system’s primary task is to allocate the total braking demand \( T_{b\_total} \) between the regenerative torque \( T_{regen} \) (where \( 0 \leq T_{regen} \leq T_{regen\_max} \)) and the friction brake torque \( T_{friction} \), such that:
$$T_{b\_total} = T_{regen} + T_{friction}$$
This allocation must prioritize regenerative braking to save energy while ensuring the friction brakes supply any shortfall to meet the driver’s demand and maintain vehicle stability.
Fuzzy Neural Network for Braking Signal Recognition and Control
The proposed system employs a five-layer Fuzzy Neural Network architecture to intelligently manage this force distribution. The FNN combines the interpretability of fuzzy logic with the learning capability of neural networks, making it ideal for handling the non-linearity and uncertainty inherent in braking scenarios for a Battery EV Car.
The structure of the FNN controller is as follows:
- Layer 1 (Input Layer): Receives crisp input signals. The chosen inputs are critical for determining the optimal regenerative braking level:
- Vehicle Speed (\( v \)): Determines the motor’s operating point and available regenerative capability.
- Brake Pedal Application Rate (\( \dot{S}_{brk} \)): Indicates driver intent (gentle stop vs. emergency brake).
- Battery State of Charge (\( SOC \)): Determines the battery’s capability to safely accept regenerative charge.
- Layer 2 (Fuzzification Layer): Converts crisp inputs into fuzzy linguistic variables using membership functions. For example:
$$ \mu_{Low}(v), \mu_{Medium}(v), \mu_{High}(v) $$
$$ \mu_{Slow}(\dot{S}_{brk}), \mu_{Moderate}(\dot{S}_{brk}), \mu{Fast}(\dot{S}_{brk}) $$
$$ \mu_{Low}(SOC), \mu_{Medium}(SOC), \mu_{High}(SOC) $$ - Layer 3 (Rule Layer): Each node represents a fuzzy IF-THEN rule. A typical rule base for the Battery EV Car is formulated, e.g.:
IF Speed is High AND Brake Pedal Rate is Moderate AND SOC is Medium, THEN Regenerative Torque Ratio is High.
The firing strength \( \omega_i \) of rule \( i \) is computed, often using the product operator:
$$ \omega_i = \mu_{A_i}(v) \cdot \mu_{B_i}(\dot{S}_{brk}) \cdot \mu_{C_i}(SOC) $$ - Layer 4 (Normalization Layer): Normalizes the firing strengths of all rules.
$$ \bar{\omega}_i = \frac{\omega_i}{\sum_{j=1}^{N} \omega_j} $$ - Layer 5 (Output Layer): Produces the crisp output, which is the desired regenerative braking torque ratio (\( \lambda_{regen} \)), where \( 0 \leq \lambda_{regen} \leq 1 \). This is achieved through defuzzification, often using a weighted sum of consequent parameters (\( p_i \)):
$$ T_{regen\_cmd} = \lambda_{regen} \cdot T_{regen\_max} = \frac{\sum_{i=1}^{N} \bar{\omega}_i p_i}{\sum_{i=1}^{N} \bar{\omega}_i} \cdot T_{regen\_max}(v, SOC) $$
The commanded friction torque is then: \( T_{friction\_cmd} = T_{b\_total} – T_{regen\_cmd} \).
The FNN parameters (membership function shapes and consequent parameters \( p_i \)) are optimized through a hybrid training strategy. An initial offline training phase uses historical driving cycle data to establish a baseline. This is followed by an online adaptation phase, where a small correction is applied based on real-time performance error to fine-tune the system for the specific driving patterns of the Battery EV Car and its driver. The error function for learning is defined as:
$$ E = \frac{1}{2} (T_{regen\_desired} – T_{regen\_cmd})^2 $$
Parameters are adjusted via gradient descent methods to minimize this error.
Implementation of the Control System for the Battery EV Car
The proposed Braking Energy Recovery Control System is implemented using a distributed electronic architecture, crucial for the modern Battery EV Car. The system consists of two primary hardware modules communicating via a high-speed Controller Area Network (CAN) bus, as shown in the structure below.
1. Data Acquisition and Control Module: This module is responsible for gathering real-time vehicle signals and executing the FNN-based braking control algorithm.
- Input Signal Processing: Acquires analog/digital signals including brake pedal position (two-stage for light and hard braking), accelerator pedal position, battery pack voltage, battery current, and motor speed.
- Core Control Logic: Hosts the embedded FNN algorithm. It calculates the total braking demand, infers the optimal regenerative torque ratio using the current inputs, and outputs command signals.
- Output Command: Sends the regenerative torque command to the Motor Control Unit (MCU) via CAN and sends the friction brake pressure command to the Electro-Hydraulic Braking (EHB) system.
2. Communication and Display Module (HMI): This module manages the human-machine interface and external communication for the Battery EV Car.
- Vehicle CAN Gateway: Interfaces with other vehicle ECUs (e.g., VCU, BMS) to obtain and display data like remaining range, total mileage, and system status.
- Data Display: Presents key information such as real-time energy flow (charging/recovering), battery SOC, instantaneous energy recovery power, and cumulative recovered energy on an LCD screen.
- External Communication: Provides a diagnostic interface (e.g., via a PC) for monitoring and calibrating the control system parameters.
The CAN bus protocol ensures robust and real-time data exchange between modules. The process for sending a braking data frame is standardized: setting the message identifier, data length code, payload data, and initiating transmission.
Simulation Results and Performance Analysis
The performance of the proposed FNN-based system was evaluated through co-simulation using MATLAB/Simulink for the control model and AVL CRUISE for the high-fidelity model of the Battery EV Car. The key parameters of the simulated vehicle are listed in Table 1.
| Component | Parameter | Value |
|---|---|---|
| Vehicle | Curb Mass | 1480 kg |
| Wheel Radius | 0.321 m | |
| Wheelbase | 2.93 m | |
| Drag Coefficient (\(C_D\)) | 0.28 | |
| PMSM Motor | Peak Power | 78 kW |
| Peak Torque | 260 Nm | |
| Battery Pack | Nominal Voltage | 310 V |
| Capacity | 280 Ah |
The proposed FNN strategy was compared against two other methods from recent literature: a rule-based regenerative braking strategy (Method A) and a braking mode fuzzy recognition strategy (Method B). The comparison focused on braking performance and energy recovery efficiency under different initial speeds. Table 2 shows the time taken to decelerate from various initial speeds to a safe low speed.
| Control Method | Braking Time (seconds) | ||
|---|---|---|---|
| Initial Speed: 40 km/h | Initial Speed: 80 km/h | Initial Speed: 120 km/h | |
| Method A (Rule-based) | 1.55 | 2.74 | 3.87 |
| Method B (Mode Fuzzy) | 0.93 | 1.96 | 2.49 |
| Proposed FNN Method | 0.71 | 1.44 | 2.40 |
Table 3 presents the reduction in braking distance achieved by each strategy compared to a baseline without regenerative braking. A shorter stopping distance indicates more effective utilization of the available road-tire friction, contributing to safety.
| Control Method | Braking Distance Reduction (meters) | ||
|---|---|---|---|
| Initial Speed: 40 km/h | Initial Speed: 80 km/h | Initial Speed: 120 km/h | |
| Method A (Rule-based) | 2.13 | 6.25 | 8.51 |
| Method B (Mode Fuzzy) | 2.49 | 6.74 | 8.76 |
| Proposed FNN Method | 2.57 | 7.11 | 9.82 |
The results clearly demonstrate the superiority of the proposed FNN method. It achieves the shortest braking times and the greatest reduction in braking distance across all tested speeds, particularly at higher velocities. This is attributed to its dynamic and optimal distribution of braking force, maximizing regenerative contribution without compromising deceleration performance.
The ultimate goal is to improve the driving range of the Battery EV Car. This was evaluated by simulating a standard urban driving cycle. Figure 1 illustrates the change in Battery State of Charge (SOC) over the driving distance for the three methods, starting from an initial SOC of 47.5%.
The analysis reveals that after completing the 1800-meter driving cycle, the proposed FNN-based system retained the highest final SOC of 45.6%. Method A ended at 45.3%, and Method B at 45.2%. This translates to the FNN system recovering more kinetic energy and consuming less net energy from the battery, directly contributing to an extended driving range for the Battery EV Car.
Conclusion
This paper presented the design and implementation of an advanced Braking Energy Recovery Control System for Battery EV Cars based on a Fuzzy Neural Network. By intelligently processing critical real-time inputs—vehicle speed, brake pedal application rate, and battery SOC—the FNN controller generates an optimal regenerative braking torque ratio. This strategy ensures that the Battery EV Car maximizes energy recuperation during deceleration while fully meeting the driver’s braking demand and maintaining vehicle stability through coordinated friction braking.
The system was implemented via a distributed architecture with dedicated data acquisition and display modules communicating over a CAN bus. Simulation results confirmed the system’s effectiveness, demonstrating superior performance in reducing braking time and distance compared to other contemporary methods. Most importantly, the proposed system achieved the highest energy recovery efficiency, as evidenced by the smallest depletion of battery SOC over a driving cycle. This work provides a practical and intelligent control solution that enhances the energy efficiency, driving range, and overall performance of Battery EV Cars, contributing to their wider adoption and sustainability.