In the rapidly evolving landscape of automotive technology, the safety and performance of battery electric vehicles during critical maneuvers such as emergency braking have become paramount concerns. As a researcher focused on advancing vehicle dynamics control, I have observed that the emergency braking process in a battery electric vehicle often introduces complex challenges, including the risk of skidding, tail swing, and loss of control. These phenomena significantly compromise driving safety, primarily due to the intricate interplay between rapid deceleration demands and the vehicle’s torque response. Traditional control methodologies, particularly conventional Proportional-Integral-Derivative (PID) strategies, frequently fall short in meeting the high-precision, fast-response requirements necessary for effective torque management during such transient events. The core difficulty lies in the complex analysis of speed parameter expectations during emergency braking, a factor that profoundly influences the torque control loop and often results in extended braking distances. This limitation underscores the urgent need for more sophisticated control paradigms that can adapt to the dynamic and unpredictable conditions faced by a battery electric vehicle.
The pursuit of enhanced braking performance has led to considerable interest in intelligent adaptive control strategies. These strategies integrate artificial intelligence techniques, such as fuzzy logic and neural networks, to enable real-time tuning and optimization of PID controller parameters. This adaptive capability allows the control system to respond more effectively to the multifaceted and variable operational states of a battery electric vehicle. In my work, I propose a comprehensive intelligent adaptive PID control strategy specifically tailored for torque regulation during the emergency braking of a battery electric vehicle. This approach aims to ensure rapid deceleration and stoppage within a minimized distance, thereby mitigating collision risks. The strategy is built upon a foundation of calculating speed expectation gains under emergency conditions, establishing a precise electromagnetic torque equation for the vehicle’s motor, and implementing a fuzzy PID control framework. Through this methodology, the control system gains the ability to intelligently adjust its parameters based on real-time vehicle state and braking demand, enhancing both dynamic response speed and stability.
The design of this torque control technology begins with a critical step: calculating the desired speed expectation gain during emergency braking for a battery electric vehicle. When a driver initiates an emergency stop, the vehicle must generate sufficient braking force responsively. The vehicle’s dynamic behavior during such an event is primarily characterized by parameters like the yaw rate and the sideslip angle at the center of mass. To analyze this, I consider a simplified model where aerodynamic drag is neglected and the drivetrain of the battery electric vehicle is treated as a linear system. A three-dimensional Cartesian coordinate system (x, y, z) is established with its origin at the geometric center of the contact points between the vehicle’s four tires and the road surface. Based on this framework and adhering to higher-order generalized theory, the vertical force boundaries for the vehicle tires in the x and y axial directions are computed. The formulation is as follows:
$$ F_{\text{avg}} = 1 – \exp\left[ -\Phi – E \Phi^2 – \left( \frac{E^2 + 1}{a} \right) \Phi^3 \right] $$
$$ F_x = F_{\text{avg}} \frac{\Phi_x}{\Phi} \mu_x F_z $$
$$ F_y = F_{\text{avg}} \frac{\Phi_y}{\Phi} \mu_y F_z $$
Here, $F_{\text{avg}}$ represents the average tire vertical force boundary for the battery electric vehicle. $F_x$ and $F_y$ denote the vertical force boundary components along the x and y axes, respectively. $\Phi$ is the dimensionless total slip ratio, with $\Phi_x$ and $\Phi_y$ being its components along the x and y axes. $E$ is a curvature factor that varies with the vehicle load, $a$ is the road surface adhesion coefficient, $\mu_x$ and $\mu_y$ are the lateral slip friction coefficients for the respective axes, and $F_z$ is the longitudinal vertical force along the z-axis.
Using these parameters, the tire slip angles are calculated. The total tangential condition under emergency braking is defined to satisfy a second-order derivative constraint of the slip ratio, allowing for the computation of the tire slip angle at the adhesion limit:
$$ \alpha_1 = \arctan\left( \frac{F_x}{F_y} \left( \frac{V_y + a_y}{V_x – \frac{c}{2} \gamma} \right) \right) – \delta $$
$$ \alpha_2 = \arctan\left( \frac{F_x}{F_y} \left( \frac{V_y + a_y}{V_x – \frac{c}{2} \gamma} \right) \right) – \delta $$
$$ \alpha_3 = \arctan\left( \frac{F_x}{F_y} \left( \frac{V_y + \beta_y}{V_x – \frac{c}{2} \gamma} \right) \right) $$
$$ \alpha_4 = \arctan\left( \frac{F_x}{F_y} \left( \frac{V_y + \beta_y}{V_x – \frac{c}{2} \gamma} \right) \right) $$
In these equations, $\alpha_1$ and $\alpha_2$ correspond to the front wheels of the battery electric vehicle, while $\alpha_3$ and $\alpha_4$ correspond to the rear wheels. $J$ symbolizes the moment of inertia, $V_x$ and $V_y$ are the instantaneous velocities along the x and y axes just before emergency braking, $c$ is a tire pressure distribution concavity-convexity factor during braking, $\gamma$ is a distribution factor, $\delta$ is a uniformity factor, and $\beta$ represents the tire adhesion limit constraint.
By calculating the tire slip angles, the saturation state of the tires can be analyzed. Subsequently, within a two-degree-of-freedom model for the battery electric vehicle, appropriate transfer functions are constructed. The ideal gain parameters for both the yaw rate and the sideslip angle at the center of mass during emergency braking are then solved independently:
$$ G_{\theta1} = \frac{2 \mu_x K m L – a V_x}{\mu_y (1 – K V_y)^2} $$
$$ G_{\theta2} = \frac{(-a K_f + b) – m V_y^2}{r^2 L^2 (1 – K V_x)^2} $$
$$ G_{\omega1} = \frac{V_x}{L (1 – K V_x^2) r} $$
$$ G_{\omega2} = \frac{V_x (K + m a)^2}{2 L^2 (1 – K V_y)^2} $$
Here, $\theta$ denotes the sideslip angle at the center of mass, and $\omega$ represents the yaw rate. $G_{\theta1}$ and $G_{\theta2}$ are the transfer function gains for the sideslip angle at the front and rear wheels, respectively. $G_{\omega1}$ and $G_{\omega2}$ are the corresponding gains for the yaw rate. $K$ is a gradient coefficient, $m$ is the vehicle load mass, $r$ is a damping coefficient, $L$ is the maximum braking distance, $a$ is the instantaneous vehicle acceleration, and $b$ is a differential coefficient. The results from these calculations provide the speed expectation gain analysis under emergency braking conditions for the battery electric vehicle, characterized by both yaw rate and sideslip angle.
To further refine the torque control strategy towards an ideal state, a precise understanding of the motor’s internal dynamics is essential. Therefore, I proceed to establish the electromagnetic torque equation for the motor in a battery electric vehicle. This equation elucidates the electromagnetic relationships and kinetic characteristics crucial for torque control. To simplify the derivation, the following assumptions are made:
| Assumption Number | Description |
|---|---|
| 1 | Magnetic hysteresis and eddy current losses in the motor are neglected. |
| 2 | Iron core magnetic saturation is not considered; the system is treated as linear. |
| 3 | The motor air gap distribution is uniform and follows a sinusoidal pattern. |
| 4 | The stator windings are symmetric across all phases. |
| 5 | The rotor permanent magnets have zero electrical conductivity, and there are no damping windings. |
Under these assumptions, a three-phase coordinate system for the motor is constructed. Within this system, the phase voltage equations for the motor stator are defined:
$$ u_{sA} = R_s i_{sA} + \frac{d\psi_{sA}}{dt} $$
$$ u_{sB} = R_s i_{sB} + \frac{d\psi_{sB}}{dt} $$
$$ u_{sC} = R_s i_{sC} + \frac{d\psi_{sC}}{dt} $$
In these equations, the subscript $s$ refers to the stator. $u_{sA}$, $u_{sB}$, and $u_{sC}$ represent the three-phase voltages of the stator. $i_{sA}$, $i_{sB}$, and $i_{sC}$ are the corresponding stator phase currents. $\psi_{sA}$, $\psi_{sB}$, and $\psi_{sC}$ denote the three-phase stator flux linkages. $R_s$ is the equivalent stator resistance, and $dt$ signifies the time differential.
The stator flux linkage is calculated from the mutual and self-inductance coefficients of the stator windings. The self-inductance includes both main and leakage inductances, assumed constant. The mutual inductance coefficients can be negative due to the 120-degree electrical radian offset between the stator winding axes. Based on this, the stator flux linkage expressions are defined:
$$ \psi_{sA} = L_{AA} i_{sA} + M_{AB} i_{sB} + M_{AC} i_{sC} + \psi_f \cos \theta $$
$$ \psi_{sB} = M_{BA} i_{sA} + L_{BB} i_{sB} + M_{BC} i_{sC} + \psi_f \cos (\theta – 120^\circ) $$
$$ \psi_{sC} = M_{CA} i_{sA} + L_{CB} i_{sB} + M_{CC} i_{sC} + \psi_f \cos (\theta + 120^\circ) $$
Here, $L_{AA}$, etc., represent stator self-inductance coefficients; $M_{AB}$, etc., denote mutual inductance coefficients; $\psi_f$ is the stator flux linkage due to the permanent magnet; and $\theta$ is the stator flux linkage angle.
Building upon these definitions, the concept of a load angle is introduced into the phase voltage equations. During the transient state of emergency braking in a battery electric vehicle, the rotational speed of the stator flux linkage vector is coupled with the rotor’s rotational speed. By regulating the load angle based on the correlation between these two speeds, the motor’s electromagnetic torque can be adjusted. Consequently, the electromagnetic torque expression for the motor is formulated as:
$$ T = P_n \left[ \frac{J \psi_f \Omega}{L \times M} \sin \rho + \frac{(L – M)}{2 L \times M} \eta_\rho^2 \sin 2\rho \right] $$
In this equation, $T$ represents the electromagnetic torque of the battery electric vehicle’s motor. $P_n$ is the number of motor pole pairs. $\Omega$ is the mechanical angular velocity of the motor torque. $\rho$ is a differential operator (often representing the load angle in this context), and $\eta_\rho$ signifies the motor’s synchronous speed.
With the ideal gain parameters for torque control under emergency braking conditions now analyzed, I integrate a fuzzy PID control method to precisely adjust the PID parameters. This integration is vital for a battery electric vehicle as it enhances control precision and stability, improves system robustness and disturbance rejection, and better adapts to the complex scenarios of emergency braking. The fuzzy PID controller intelligently modulates the electromagnetic torque to achieve effective torque control. The design involves constructing a linear control architecture where the input is the given rotational speed command for the battery electric vehicle’s torque, and the output is the calculated optimal rotational speed parameter. The proportional, integral, and derivative actions are incorporated within this architecture. The transfer function for the fuzzy PID control is defined as:
$$ G(q) = k \left( 1 + \frac{1}{S_1 q} + S_2 q \right) $$
Here, $q$ represents the input signal to the fuzzy PID controller. $G(q)$ is the corresponding transfer function. $k$ is the proportional coefficient, $S_1$ is the integral time constant, and $S_2$ is the derivative time constant.
The ideal gain parameters derived earlier are incorporated into the fuzzy PID control framework to define its membership function. This function is expressed as:
$$ \lambda(q) = \exp\left[ -\frac{(q – G)^2}{\sigma^2} \right], \quad (\sigma > 0) $$
In this membership function, $\lambda(q)$ denotes the degree of membership. $G$ represents the composite value of the ideal gain parameters, obtained by summing the four fundamental gain terms ($G_{\theta1}$, $G_{\theta2}$, $G_{\omega1}$, $G_{\omega2}$). $\sigma$ is the Gaussian kernel width. By employing this Gaussian-type membership function and combining it with the established electromagnetic torque equation for the battery electric vehicle, the final torque fuzzy PID control law is generated:
$$ u(t) = k \left( e(t) T + \frac{1}{S} \int_0^t e(t) \, dt + S_2 \frac{de(t)}{dt} \right) \lambda(q) $$
Here, $u(t)$ represents the torque control law for the battery electric vehicle at time $t$. $e(t)$ signifies the error term in the fuzzy PID control loop. This control law yields the optimal parameters for torque control in the battery electric vehicle. These parameters are then fed as output signals into the vehicle’s drivetrain control unit, thereby executing precise torque regulation during emergency braking events.
To validate the efficacy of the proposed intelligent adaptive PID control strategy for a battery electric vehicle, a series of simulation tests were conducted. The emergency braking parameters were set as follows: a maximum braking distance of 1.5 meters, an initial speed of 60 km/h, a left-side road adhesion coefficient of 0.56, a right-side coefficient of 0.79, and a brake pedal pressure of 1 MPa. Under these conditions, the feasibility of the fuzzy PID control technology was assessed by analyzing the longitudinal speed characteristics of the vehicle’s tires before and after control implementation. The results demonstrated a marked improvement in deceleration efficiency. Prior to applying the control strategy, the battery electric vehicle required approximately 3 seconds to reduce its travel speed to 0 m/s, implying a considerably long braking distance that could lead to collisions in real-world emergency scenarios. After implementing the proposed control, the longitudinal speed of the tires reached zero roughly 1.3 seconds faster, substantially shortening the braking distance. The vehicle’s longitudinal displacement was reduced by approximately 7.2 meters. This outcome preliminarily confirms that the control technique can effectively manage torque during emergency braking for a battery electric vehicle and significantly decrease the stopping distance, showcasing strong practical applicability.
To further benchmark the performance of this method against existing approaches, comparative experiments were performed under identical operational parameters. Several alternative control methods from contemporary research were selected as benchmarks. Multiple test rounds were executed with consistent parameters to minimize experimental error. The simulated driving data for the battery electric vehicle under each control method was recorded, with braking distance serving as the key performance indicator. The comparative results are summarized in the table below:
| Control Method | Description of Approach | Braking Distance at Low Initial Speed (~30 km/h) | Braking Distance at High Initial Speed (~60 km/h) | Adaptability to Variable Conditions |
|---|---|---|---|---|
| Method A (Genetic Algorithm-based) | Utilizes a non-dominated sorting genetic algorithm for torque distribution optimization. | Relatively long, similar to uncontrolled case | Very long, poor performance | Limited due to potential loss of population diversity |
| Method B (Model-based Trajectory Circle) | Employs a trajectory circle model to analyze torque and flux linkage fluctuations. | Relatively long, similar to uncontrolled case | Very long, poor performance | Highly dependent on precise motor parameters, vulnerable to model inaccuracy |
| Method C (Fuzzy PID with Sliding Mode) | Combines fuzzy PID control with a sliding mode variable structure for switched reluctance motors. | Short (within ~2 meters) | Significantly increases, control efficacy drops | Relies heavily on empirical rules, struggles with high-speed,多变 conditions |
| Proposed Intelligent Adaptive PID | Integrates fuzzy logic with PID, using calculated speed gains and electromagnetic torque model. | Short (within ~2 meters) | Remains short (minimized distance) | High, due to real-time parameter adaptation and model-based foundation |
The data clearly indicates that while some methods perform adequately at lower initial speeds for a battery electric vehicle, their effectiveness deteriorates markedly as speed increases. In contrast, the proposed intelligent adaptive PID control strategy maintains a consistently short braking distance across different speed regimes. This robustness stems from its ability to dynamically adjust control parameters in response to real-time vehicle state and the analytically derived gain expectations, making it particularly suitable for the demanding conditions of emergency braking in a battery electric vehicle.
In conclusion, the development and implementation of an intelligent adaptive PID control strategy for torque management during emergency braking represent a significant advancement for battery electric vehicle safety. This strategy addresses the inherent limitations of traditional control methods by incorporating fuzzy logic to enable real-time, context-aware tuning of PID parameters. The theoretical foundation, comprising the calculation of speed expectation gains under emergency conditions, the establishment of a detailed electromagnetic torque equation, and the synthesis of a fuzzy PID control law, provides a comprehensive framework for understanding and controlling the complex dynamics at play. Simulation tests confirm the practical viability of this approach, demonstrating a substantial reduction in braking distance—by approximately 7.2 meters in the tested scenario—which directly translates to enhanced collision avoidance capability. For the future of battery electric vehicles, integrating such adaptive, intelligent control systems will be crucial not only for improving emergency braking performance but also for advancing overall vehicle stability, safety, and reliability in diverse driving conditions. The continuous evolution of these strategies, potentially incorporating deeper neural networks or reinforcement learning, promises to further elevate the safety standards of battery electric vehicles, ensuring they meet the stringent demands of modern transportation ecosystems.