In the context of global efforts to mitigate climate change, the aviation industry faces increasing pressure to reduce carbon emissions. Electric aircraft, with their zero-emission and low-noise characteristics, have emerged as a promising solution. As a researcher in this field, I have focused on the thermal management of power battery packs for electric aircraft, which is critical for ensuring safety, performance, and longevity. The core of this study is to address the limitations of traditional PID control in handling the nonlinear and time-varying thermal dynamics of EV battery packs under variable operating conditions. Here, I present a comprehensive investigation into a fuzzy PID-based temperature control strategy for liquid cooling systems, leveraging co-simulation and experimental validation to demonstrate its superiority.
The performance of lithium-ion batteries, commonly used in EV battery packs, is highly temperature-sensitive. Excessive temperatures can lead to capacity degradation, reduced cycle life, and even thermal runaway, posing significant safety risks. Therefore, effective thermal management is paramount. Among cooling methods—air cooling, liquid cooling, and phase change material cooling—liquid cooling offers superior heat transfer coefficients and temperature uniformity, making it ideal for high heat generation rates in electric aircraft applications. However, the dynamic nature of flight profiles demands a control strategy that can adapt to rapid changes in heat dissipation requirements. Traditional PID controllers, while simple and effective for linear systems, often exhibit response lag and poor parameter adaptability in such scenarios. This study proposes a fuzzy PID algorithm to enhance the adaptive control of pump speed in a liquid cooling system, ensuring precise temperature regulation for EV battery packs.
To build a realistic model, I started with a square ternary lithium-ion power battery cell used in a small electric aircraft. The basic parameters of the cell are summarized in Table 1. These parameters form the foundation for modeling the EV battery pack, which consists of 60 cells arranged in four modules, each with 15 cells in series, resulting in a total voltage of 216 V and a capacity of 50 Ah.
| Parameter | Value |
|---|---|
| Rated Capacity (Ah) | 50 |
| Dimensions (L × W × H, mm) | 148 × 27 × 97 |
| Mass (kg) | 0.86 ± 0.01 |
| Rated Voltage (V) | 3.6 |
| Operating Voltage Range (V) | 2.8–4.2 |
| Maximum Allowable Charge Temperature Range (°C) | -10–55 |
| Maximum Allowable Discharge Temperature Range (°C) | -30–60 |
The geometric model of the EV battery pack liquid cooling system includes battery modules, thermal pads, and cold plates. The cells are placed on a bottom-integrated liquid cold plate, with thermal pads acting as interfaces to enhance heat conduction. The thermal properties of key components are detailed in Table 2, where Kx, Ky, and Kz represent the thermal conductivity coefficients along the x, y, and z axes, respectively.
| Component | Density (kg/m³) | Specific Heat Capacity (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Battery Cell | 2219 | 1060 | Kx = Ky = 31; Kz = 0.8 |
| Thermal Pad | 2000 | 900 | 2 |
| Cold Plate | 2690 | 900 | 201 |
The heat generation model is based on the Bernardi equation, which accounts for both Joule heating and entropic heat. The heat generation rate Q1 and the heat absorption rate Q2 are given by:
$$ Q_1 = I^2 R_j + I T \frac{\partial U_{ocv}}{\partial T} $$
$$ Q_2 = m C_b \frac{dT}{dt} $$
where I is the discharge current, Rj is the Joule resistance, Uocv is the open-circuit voltage, T is temperature, m is mass, Cb is specific heat capacity, and t is time. Under adiabatic conditions, Q1 = Q2, allowing derivation of the heat generation power. Through experimental testing at various discharge rates (0.5C, 1.0C, 1.5C, 2.0C), I collected temperature data and fitted a linear relationship between the temperature change rate per current and the discharge current:
$$ \frac{dT}{I dt} = 2.041 \times 10^{-6} I + 2.868 \times 10^{-5} $$
From this, the equivalent specific heat capacity was calculated as 1060 J/(kg·K), leading to the heat generation power formula:
$$ Q = m C_b \frac{dT}{dt} = 1.861 \times 10^{-3} I^2 + 2.615 \times 10^{-2} I $$
The heat generation rates for different discharge rates are summarized in Table 3. Numerical simulations in STAR-CCM+ validated this model, showing good agreement with experimental data, confirming the accuracy of the heat generation model for the EV battery pack.
| Discharge Rate (C) | Heat Generation Power per Cell (W) | Heat Generation Rate per Cell (W/m³) |
|---|---|---|
| 0.5 | 1.85 | 4772.81 |
| 1.0 | 5.96 | 15376.20 |
| 1.5 | 12.43 | 32068.15 |
| 2.0 | 21.23 | 54758.37 |
Given the nonlinear and time-varying nature of the EV battery pack thermal system, traditional PID control often fails to provide optimal performance. To overcome this, I designed a fuzzy PID controller that adjusts PID parameters online based on the temperature error and its rate of change. The input variables are the temperature error e (difference between actual and target temperature) and the error change rate ec. These are fuzzified into fuzzy sets {NB, NM, NS, ZO, PS, PM, PB} with triangular membership functions. The fuzzy domains are set as e ∈ [-12, 12], ec ∈ [-6, 6], and output adjustments Δkp ∈ [-0.3, 0.3], Δki ∈ [-6, 6], Δkd ∈ [-3, 3]. The fuzzy rules for adjusting kp, ki, and kd are formulated based on expert knowledge and system behavior, as shown in Table 4.
| E | EC | ||||||
|---|---|---|---|---|---|---|---|
| NB | NM | NS | ZO | PS | PM | PB | |
| NB | PB/NB/PS | PB/NB/PS | PM/NB/ZO | PM/NM/ZO | PS/NM/ZO | PS/ZO/PB | ZO/ZO/PB |
| NM | PB/NB/NS | PB/NB/NS | PM/NM/NS | PM/NM/NS | PS/NS/ZO | ZO/ZO/NS | ZO/ZO/PM |
| NS | PM/NM/NB | PM/NM/NB | PM/NS/NM | PS/NS/NS | ZO/ZO/ZO | NS/PS/PS | NM/PS/PM |
| ZO | PM/NM/NB | PS/NS/NM | PS/NS/NM | ZO/ZO/NS | NS/PS/ZO | NM/PS/PS | NM/PM/PM |
| PS | PS/NS/NB | PS/NS/NM | ZO/ZO/NS | NS/PS/NS | NS/PS/ZO | NM/PM/PS | NM/PM/PS |
| PM | ZO/ZO/NM | ZO/ZO/NS | NS/PS/NS | NM/PM/NS | NM/PM/ZO | NM/PB/PS | NB/PB/PS |
| PB | ZO/ZO/PS | NS/ZO/ZO | NS/PS/ZO | NM/PM/ZO | NM/PB/ZO | NB/PB/PB | NB/PB/PB |
The fuzzy outputs are defuzzified using the centroid method to obtain Δkp, Δki, and Δkd, which are then used to update the PID parameters:
$$ k_p = k_{p0} + \Delta k_p $$
$$ k_i = k_{i0} + \Delta k_i $$
$$ k_d = k_{d0} + \Delta k_d $$
where kp0, ki0, kd0 are initial PID values (set as 1.5, 0.01, and 0.5 via trial-and-error). The controller output adjusts the pump speed (0–5000 rpm) to regulate coolant flow, thereby controlling the temperature of the EV battery pack.
To evaluate the system, I developed a co-simulation model using AMESim and Simulink. AMESim modeled the liquid cooling system with components like pumps, cold plates, and the EV battery pack thermal dynamics, while Simulink implemented the fuzzy PID controller. This approach leveraged AMESim’s multi-domain simulation capabilities and Simulink’s algorithmic flexibility. The simulation scenarios included constant current discharge and realistic flight conditions to assess performance.
In the constant current scenario, the EV battery pack started at 40°C with a target of 30°C, coolant at 20°C, and a discharge rate of 1.5C. The fuzzy PID controller demonstrated significantly faster response compared to traditional PID. As shown in simulation results, the fuzzy PID reduced the battery pack temperature to near 30°C in about 1300 seconds, whereas traditional PID required approximately 3300 seconds—a 45.83% improvement in response time. Moreover, the fuzzy PID maintained a smaller temperature deviation, with the final temperature at 30.0°C versus 30.52°C for traditional PID. The pump speed under fuzzy PID surged initially to 5000 rpm for rapid cooling, then adjusted smoothly as the temperature approached the target, whereas traditional PID showed a sluggish pump speed rise, peaking around 500 rpm. To test robustness, I introduced coolant temperature step changes (to 35°C at 600–720 s and 10°C at 1320–1440 s). The fuzzy PID controller exhibited smaller temperature fluctuations and quicker recovery, highlighting its adaptability for the EV battery pack.
For the flight condition, I analyzed a typical profile for a small two-seat electric aircraft, including phases like ground preparation, taxiing, takeoff, climb, cruise, descent, and landing. The power demands and energy reserves are listed in Table 5. The discharge current I for each phase was calculated using:
$$ I = \frac{P}{U} $$
where P is power and U is the total battery pack voltage (216 V). Substituting into the heat generation formula yielded time-varying heat rates, as plotted over the flight duration. This profile was input into the AMESim model for co-simulation with the fuzzy PID controller.
| Flight Phase | Time (s) | Power Demand (kW) | Energy Reserve (kWh) |
|---|---|---|---|
| Ground Preparation | 120 | 5 | 0.17 |
| Ground Taxiing | 15 | 21 | 0.09 |
| Takeoff Run | 6 | 24 | 0.04 |
| Climb | 394 | 15 | 1.64 |
| Cruise | 3000 | 5 | 4.17 |
| Descent | 665 | 2 | 0.37 |
| Landing Run | 10 | 9 | 0.25 |
| Total | 4210 | – | 6.73 |
| With 20% Margin | – | – | 8.41 |
The simulation results under flight conditions further affirmed the superiority of the fuzzy PID controller for the EV battery pack. With traditional PID, the battery pack temperature took about 3500 seconds to stabilize at 32.98°C, still 2.98°C above the 30°C target. In contrast, fuzzy PID achieved stabilization at 29.9°C within approximately 1200 seconds, reducing the response time by 65.70% and maintaining a mere 0.1°C deviation. The pump speed with fuzzy PID responded promptly, reaching 5000 rpm early to counteract high heat generation, then modulating efficiently. Traditional PID, however, showed delayed and limited pump speed adjustments, inadequate for the dynamic thermal demands of the EV battery pack during flight.
In summary, this study demonstrates that a fuzzy PID-based control strategy significantly enhances the thermal management of EV battery packs for electric aircraft. The key findings are: First, the fuzzy PID controller provides faster response times—45.83% improvement in constant current conditions and 65.70% in flight conditions—ensuring the EV battery pack temperature rapidly converges to the target. Second, the algorithm exhibits strong adaptability to nonlinear and time-varying thermal dynamics, with pump speed adjustments that are both rapid and precise, avoiding over-cooling or insufficient cooling. Third, the robustness of fuzzy PID is evident in handling disturbances like coolant temperature variations, making it suitable for real-world aviation environments. These advantages underscore the potential of fuzzy PID control in optimizing the performance and safety of EV battery packs, contributing to the advancement of electric aircraft technology. Future work could explore integration with other cooling methods or advanced machine learning techniques for even greater efficiency.