In recent years, the rapid advancement of electric vehicle technology, particularly in China EV markets, has highlighted the importance of distributed drive systems for improving energy efficiency and vehicle dynamics. As a researcher focused on sustainable transportation, I have developed a composite braking control strategy that integrates yaw stability and braking energy recovery for distributed drive electric vehicles. This approach leverages the independent control of four-wheel motor braking torque and friction braking torque, addressing key challenges in electric vehicle performance. The strategy employs a hierarchical control framework, where an upper-layer controller manages longitudinal speed tracking and yaw moment, while a lower-layer controller optimizes torque distribution to maximize tire utilization and energy regeneration. Through extensive simulations, I demonstrate that this method not only ensures braking stability under various conditions but also enhances energy recovery, contributing to the broader goals of China EV development in reducing emissions and improving economic viability.
The core of my research lies in the hierarchical control structure, which consists of two main components. The upper-layer controller includes a proportional-integral-derivative (PID) based longitudinal speed tracking controller and a model predictive control (MPC) based yaw moment controller. The PID controller calculates the required longitudinal braking force by comparing the target and actual vehicle speeds, using the following equation for braking intensity $z$:
$$ z = K_p (v_d – v) + K_i \int (v_d – v) \, dt + K_d \frac{d(v_d – v)}{dt} $$
where $K_p$, $K_i$, and $K_d$ are the proportional, integral, and derivative gains, respectively, $v_d$ is the target speed, and $v$ is the current speed. The longitudinal force $F_x$ is then derived as $F_x = z m g$, with $m$ being the vehicle mass and $g$ the gravitational acceleration. This simple yet effective approach ensures accurate speed tracking, which is crucial for maintaining control in electric vehicle systems.
For yaw stability, I utilize an MPC controller that minimizes deviations from the ideal yaw rate and sideslip angle. The ideal values are derived from a two-degree-of-freedom vehicle model, expressed as:
$$ \beta_d = \frac{amv_x^2}{k_r(a+b) – b m v_x^2} \delta \quad \text{and} \quad \gamma_d = \frac{v_x}{a+b} \delta $$
where $\beta_d$ is the ideal sideslip angle, $\gamma_d$ is the ideal yaw rate, $a$ and $b$ are distances from the center of mass to the front and rear axles, $v_x$ is the longitudinal velocity, $k_f$ and $k_r$ are the cornering stiffnesses of the front and rear axles, and $\delta$ is the steering angle. The MPC formulation involves a discrete state-space model:
$$ x(t+1) = A x(t) + B_1 u(t) + B_2 \psi(t) $$
$$ y(t) = C x(t) $$
with $x = [\beta, \gamma]^T$ as the state vector, $u = M_z$ as the control input (yaw moment), and $\psi(t)$ representing disturbances. The performance index minimizes the error between actual and ideal states while penalizing control effort:
$$ J = \sum_{k=1}^{N_p} (y(t+k) – w(t+k))^T Q (y(t+k) – w(t+k)) + \sum_{k=0}^{N_c-1} \Delta u(t+k)^T R \Delta u(t+k) $$
where $N_p$ is the prediction horizon, $N_c$ is the control horizon, $Q$ and $R$ are weighting matrices, and $w(t)$ is the reference input. This ensures robust handling of yaw dynamics, a critical aspect for electric vehicle safety in scenarios like cornering braking.
The lower-layer controller focuses on optimal torque distribution across the four wheels, with the objective of minimizing tire utilization, defined as:
$$ J = \sum_{i=\text{fl, fr, rl, rr}} \left( \frac{F_{xi}^2 + F_{yi}^2}{(\mu F_{zi})^2} \right) $$
where $F_{xi}$ and $F_{yi}$ are the longitudinal and lateral forces on each wheel, $\mu$ is the friction coefficient, and $F_{zi}$ is the vertical load. Since lateral forces are uncontrollable in this context, the optimization simplifies to longitudinal force distribution. The constraints include satisfying the total longitudinal force and yaw moment demands:
$$ \sum F_{xi} = F_x \quad \text{and} \quad \sum (F_{xi} \cdot d_i) = M_z $$
where $d_i$ represents the moment arm for each wheel. Additionally, forces are bounded by tire adhesion limits and motor capabilities:
$$ |F_{xi}| \leq \mu F_{zi} \quad \text{and} \quad |T_{\text{motor},i}| \leq T_{\text{max}} $$
I solve this quadratic programming problem using the active-set method for efficiency. To maximize energy recovery in the electric vehicle, I design a motor braking force ratio coefficient $k$ that considers braking intensity $z$, battery state of charge (SOC), and vehicle speed $v$. The coefficient is computed as:
$$ k = k_1 \cdot k_2 \cdot k_3 $$
where $k_1$ depends on braking intensity and motor torque limits, $k_2$ on SOC constraints to protect battery health, and $k_3$ on speed thresholds for efficient regeneration. Specifically:
$$ k_1 = \begin{cases}
1 & \text{if } z \leq 0.7 \text{ and } T_{\text{max}} \geq T_{\text{need}} \\
\frac{T_{\text{max}}}{T_{\text{need}}} & \text{if } z \leq 0.7 \text{ and } T_{\text{max}} < T_{\text{need}} \\
0 & \text{if } z > 0.7
\end{cases} $$
$$ k_2 = \begin{cases}
0 & \text{if } \text{SOC} \geq 0.8 \\
1 & \text{if } \text{SOC} < 0.8
\end{cases} $$
$$ k_3 = \begin{cases}
0 & \text{if } v \leq 5 \, \text{km/h} \\
0.2v – 1 & \text{if } 5 < v < 10 \, \text{km/h} \\
1 & \text{if } v \geq 10 \, \text{km/h}
\end{cases} $$
The motor braking torque for each wheel is then $T_{\text{motor},i} = k \cdot F_{xi} \cdot R_w$, where $R_w$ is the wheel radius, and the remaining torque is supplied by friction brakes. This approach prioritizes electric vehicle energy recovery without compromising stability, aligning with the innovation trends in China EV sectors.
To validate my strategy, I conducted co-simulations using MATLAB/Simulink and CarSim under cornering braking conditions. The vehicle parameters are summarized in the table below, which highlights key aspects relevant to electric vehicle design, such as mass distribution and motor specifications. These parameters are typical for compact electric vehicles in China EV applications, ensuring realism in the analysis.
| Parameter | Value |
|---|---|
| Mass (m) | 1230 kg |
| Wheel Radius (R_w) | 0.31 m |
| Distance to Front Axle (a) | 1.04 m |
| Distance to Rear Axle (b) | 1.56 m |
| Rolling Resistance Coefficient | 0.018 |
| Yaw Inertia (I_z) | 1343.1 kg·m² |
| Parameter | Value |
|---|---|
| Rated Power | 7 kW |
| Peak Power | 15 kW |
| Rated Torque | 200 Nm |
| Peak Torque | 350 Nm |
| Rated Speed | 450 rpm |
| Peak Speed | 1250 rpm |
In the first simulation scenario, I applied a constant braking intensity of 0.2 on a circular path with a radius of 100 m and a friction coefficient of 0.8, starting from an initial speed of 50 km/h. The battery SOC was initialized at 0.6. The results showed that my optimization-based分配 strategy allocated higher motor braking torques compared to a proportional分配 method, leading to better energy recovery. For instance, the SOC increased by 0.103 in my approach versus 0.095 in the proportional method. Moreover, the yaw rate tracking was more accurate, with a maximum deviation of only 0.31 deg/s from the ideal value, compared to 0.93 deg/s in the proportional case. This underscores the effectiveness of the hierarchical control in enhancing electric vehicle stability and efficiency.
The torque distribution over time can be described by the following equations for the optimization approach:
$$ T_{\text{motor,fl}} = k \cdot F_{x,\text{fl}} \cdot R_w, \quad T_{\text{friction,fl}} = F_{x,\text{fl}} \cdot R_w – T_{\text{motor,fl}} $$
and similarly for other wheels, where the forces $F_{x,i}$ are optimized to minimize tire utilization. The cumulative energy recovery $E_{\text{regen}}$ is approximated as:
$$ E_{\text{regen}} = \sum_{i} \int T_{\text{motor},i} \cdot \omega_i \cdot \eta \, dt $$
where $\omega_i$ is the wheel angular velocity and $\eta$ is the regeneration efficiency. This formulation highlights how the electric vehicle system maximizes energy recapture during deceleration.
In a second scenario with variable braking intensity, the initial braking intensity of 0.2 was increased to 0.7 after 2 seconds, starting from 72 km/h. My strategy adapted smoothly, with motor braking dominating at lower intensities and friction brakes engaging more at higher intensities. The yaw rate deviation remained within 1.88 deg/s, whereas the proportional method failed to track the ideal yaw rate effectively. The SOC increased by 0.09 in my approach, compared to 0.05 in the proportional method, demonstrating superior energy recovery. The table below summarizes the key outcomes, emphasizing the advantages for China EV applications where both safety and economy are prioritized.
| Control Strategy | SOC Increase | Max Yaw Rate Deviation (deg/s) |
|---|---|---|
| Proportional Allocation | 0.095 (constant), 0.05 (variable) | 0.93 (constant), N/A (variable) |
| Optimization-Based Allocation | 0.103 (constant), 0.09 (variable) | 0.31 (constant), 1.88 (variable) |
These results confirm that my composite braking control strategy effectively balances yaw stability and energy recovery in distributed drive electric vehicles. The use of MPC for yaw moment control and quadratic programming for torque distribution ensures robust performance under dynamic conditions. Furthermore, the incorporation of real-world constraints like SOC and speed enhances the practicality of this approach for mass-produced electric vehicles, particularly in the rapidly growing China EV market. Future work will involve real-world testing to validate these findings and explore adaptations for other vehicle types, such as hybrid electric systems, to broaden the impact on sustainable transportation.
In conclusion, the integration of advanced control theories with practical energy management strategies represents a significant step forward for electric vehicle technology. My research demonstrates that through careful design and optimization, it is possible to achieve both stability and efficiency in braking systems, contributing to the global advancement of electric vehicles. As China EV manufacturers continue to innovate, approaches like this will play a crucial role in shaping the future of mobility, reducing environmental impact while enhancing driver safety and comfort.