As the automotive industry accelerates its transition toward sustainable mobility, the electric car has emerged as one of the most promising solutions to reduce greenhouse gas emissions and dependence on fossil fuels. Among the many technical challenges that still hinder the widespread adoption of electric cars, the energy consumption of auxiliary systems—especially the air conditioning system—remains a critical issue. Unlike conventional vehicles that can utilize engine waste heat or mechanical power directly, the electric car relies entirely on battery power for thermal comfort management. The air conditioning system in an electric car can account for a significant portion of the total energy consumption, which directly affects the driving range. Therefore, improving the efficiency of the air conditioning system is essential for enhancing the overall performance of an electric car.
In this study, I focus on the influence of different control strategies on the thermal comfort of passengers, compressor speed, energy consumption, and the coefficient of performance of the air conditioning system in an electric car. The control strategies under investigation are fuzzy control, PI control, and fuzzy PI control. I evaluate these strategies at different ambient temperatures to understand their strengths and limitations. The entire simulation framework is built upon a co-simulation platform using AMEsim and Simulink. Through this approach, I aim to provide insights into how the control logic of the compressor can be refined to reduce energy consumption without sacrificing the cooling capability of the air conditioning system in an electric car.
The motivation for this research arises from the urgent need to address the “range anxiety” that many electric car users experience, especially during hot summer days when the air conditioning load is high. In recent years, the Chinese government has set ambitious goals for carbon peaking and carbon neutrality. The development of new energy vehicles, including pure electric cars, has become a national priority. However, the limited driving range of many electric cars, combined with the high energy demand of thermal management systems, remains a major barrier. According to previous studies, the air conditioning system of an electric car can consume more than 20% of the total energy under certain driving cycles. Thus, any improvement in the control strategy of the air conditioning compressor can lead to substantial energy savings and extend the driving range of the electric car.
In the following sections, I will first explain the fundamental principles of the three control strategies investigated in this work. Then, I will describe the architecture of the simulation model developed for the electric car air conditioning system. After that, I will present the simulation results under various ambient temperatures, with a focus on cabin temperature regulation, compressor speed, energy consumption, and the coefficient of performance. Finally, I will discuss the implications of the results and offer conclusions that can guide the design of future air conditioning control systems for electric cars.
Principles of the Control Strategies
PI Control Strategy for the Electric Car Air Conditioning System
Proportional-integral (PI) control is a widely used linear control method in engineering applications. It combines proportional action, which reacts to the current error, with integral action, which accumulates past errors to eliminate steady-state offset. The mathematical expression of a PI controller is given by:
$$
u(t) = K_p e(t) + K_I \int_{0}^{t} e(\tau) d\tau
$$
where \( e(t) \) is the error between the desired setpoint and the measured output, \( u(t) \) is the control command, \( K_p \) is the proportional gain, and \( K_I \) is the integral gain. In the context of an electric car air conditioning system, the output of the controller is the compressor speed. The measured output is the cabin temperature. The target cabin temperature is set within the range that satisfies human thermal comfort, typically between 21 °C and 23 °C. The error is the difference between the current cabin temperature and the target temperature. By adjusting the compressor speed through the PI controller, the cooling capacity of the air conditioning system is modulated to bring the cabin temperature to the desired level.
A notable limitation of a fixed-gain PI controller is that its performance degrades when the operating range is wide. In an electric car air conditioning system, the required cooling capacity varies significantly with ambient conditions. The linear compressor speed range of the PI controller may not extend to the full operational range of the compressor. Therefore, I introduce an additional scaling factor that is a function of the difference between ambient temperature and target temperature. This scaling factor, obtained through a curve-fitting procedure, enlarges the effective control range of the PI controller. The scaling factor \( y \) is expressed as:
$$
y = 0.05608 \, \Delta t^2 – 1.123 \, \Delta t + 6.915
$$
where \( \Delta t = T_{amb} – T_{tar} \), with \( T_{amb} \) being the ambient temperature and \( T_{tar} \) the target temperature. The final compressor speed command is the product of the PI controller output and this scaling factor. This modification allows the PI controller to provide sufficiently high compressor speeds when the ambient temperature is high and the cabin needs intensive cooling. The block diagram of the PI control architecture for the electric car air conditioning system is conceptually straightforward: the cabin temperature error feeds the PI block, the scaling factor multiplies the output, and the resulting signal commands the compressor.
Fuzzy Control Strategy
Fuzzy control is a model-free control approach that does not require an accurate mathematical model of the plant. It is particularly useful for nonlinear systems or systems with significant uncertainties and variations. The core of a fuzzy controller is the fuzzy inference system, which comprises fuzzification, rule evaluation, and defuzzification. In fuzzification, crisp input values are converted into fuzzy membership degrees using predefined membership functions. The fuzzy rules are then applied to map the fuzzified inputs to fuzzy outputs. Finally, defuzzification converts the fuzzy output into a crisp value that can be used as the control command.
In this work, I design a fuzzy controller for the air conditioning system of the electric car with two inputs: the cabin temperature error \( E \) and the error change rate \( EC \). These two inputs capture both the current deviation and the trend of the cabin temperature. The output of the fuzzy controller is the compressor speed. The universe of discourse for \( E \) and \( EC \) is set to \([-2, 2]\). Each input domain is partitioned into seven fuzzy sets: negative big (NB), negative medium (NM), negative small (NS), zero (O), positive small (PS), positive medium (PM), and positive big (PB). The membership functions for the inputs are triangular, and because both inputs share the same domain and partition, their membership functions are identical. The compressor speed output range is set to \( [0, 6000] \) revolutions per minute. The output domain is partitioned into seven fuzzy sets: zero (Z), low (L), medium-low (ML), medium (M), medium-high (MH), high (H), and very high (VH).
The fuzzy rule table establishes the relationship between the inputs and the output. These rules are derived from expert knowledge. For instance, if the cabin temperature is far above the target (positive large error) and is still rising (positive large error change), then the compressor should run at very high speed. Conversely, if the cabin temperature is close to the target and is nearly stable, the compressor speed should be reduced. The rule table is summarized as follows.
For the defuzzification process, I use the weighted average method, also known as the center of gravity method. This method calculates the crisp output as the weighted average of the fuzzy output membership functions. The choice of this defuzzification method yields a smooth control signal that avoids sudden changes in compressor speed.
Fuzzy PI Control Strategy
Fuzzy PI control is a hybrid strategy that combines the adaptability of fuzzy logic with the tracking accuracy of PI control. Instead of using fixed gains \( K_p \) and \( K_I \), the fuzzy PI controller adjusts these gains in real time based on the current operating state. The actual proportional and integral gains are computed as follows:
$$
K_{p1} = K_p + \Delta K_p
$$
$$
K_{I1} = K_I + \Delta K_I
$$
where \( K_p \) and \( K_I \) are the initial values, and \( \Delta K_p \) and \( \Delta K_I \) are the corrections produced by the fuzzy inference mechanism. The inputs to the fuzzy inference are the same as in the fuzzy controller: the error \( E \) and the error change rate \( EC \). The universe for \( \Delta K_p \) is \([-200, 200]\), and it is partitioned into seven fuzzy sets with triangular membership functions. The rule table for \( \Delta K_p \) is designed so that when the error is large, the proportional gain increases to achieve a fast response, whereas when the error is small and the system is near steady state, the gain decreases to avoid overshoot and oscillation.
Similarly, the universe for \( \Delta K_I \) is \([-1, 1]\), also partitioned into seven fuzzy sets. The rules for \( \Delta K_I \) are designed to eliminate steady-state error without inducing instability. For example, if the error is large, the integral gain should be moderate to prevent integral windup, while if the error is small, the integral gain can be increased slightly to remove residual offset. The fuzzy PI controller thus provides an adaptive tuning mechanism that can handle both transient and steady-state phases more effectively than a fixed-gain PI controller.
For the electric car air conditioning system, the fuzzy PI controller receives the cabin temperature error and error change rate and outputs the compressor speed. The internal fuzzy rules adjust \( K_p \) and \( K_I \) based on the operating condition. When the cabin temperature is far from the target, the gains are raised to produce a higher compressor speed, cooling the cabin quickly. When the cabin temperature approaches the target, the gains are lowered, resulting in a lower compressor speed and reduced energy consumption. This behavior is advantageous for the energy management of the electric car, as it directly impacts the range.
Simulation Model Development
I develop the simulation model for the electric car air conditioning system using two commercial software packages. The physical plant model, including the vehicle dynamics and the air conditioning refrigeration circuit, is built in AMEsim. The control algorithms are implemented in Simulink. A co-simulation interface connects the two environments, allowing the compressor speed commanded by the controller to influence the thermodynamic states of the refrigeration cycle and, subsequently, the cabin temperature. This co-simulation approach combines the strengths of both tools: the detailed physical modeling capabilities of AMEsim and the flexible control logic implementation in Simulink.
The AMEsim model consists of several key components of the refrigeration loop: the compressor, condenser, expansion valve, and evaporator. In addition, the model includes a cabin compartment model that absorbs or releases heat according to the difference between the ambient temperature and the cabin air temperature. The compressor is driven by an electric motor, whose speed is the controlled variable. The refrigerant flow rate, pressures, and enthalpies at various points in the cycle are computed by AMEsim. These values are essential for calculating the cooling capacity, compressor work, and the coefficient of performance.
The control models for the three strategies are built in Simulink. For the fuzzy control strategy, a fuzzy logic controller block is configured with the membership functions and rule tables described previously. For the PI control strategy, a standard PI controller block is used, along with the scaling factor formula. For the fuzzy PI control strategy, a custom fuzzy inference system is created within Simulink to adjust the PI gains in real time. This system is embedded in a feedback loop that reads the cabin temperature and its rate of change.
The validation of the simulation model is beyond the scope of this paper, but the model parameters are selected based on typical values for a mid-sized electric car. The refrigerant is assumed to be R134a. The compressor has a displacement that allows a maximum speed of 6000 revolutions per minute. The condenser and evaporator are sized to provide adequate heat exchange for the specified cabin volume. The cabin air mass is modeled based on the geometric dimensions of a standard sedan.
The simulation environment conditions are set to four different ambient temperatures: 32 °C, 35 °C, 38 °C, and 41 °C. The relative humidity is fixed at 40%. The fresh air mass flow rate entering the cabin is set to 0.1 kg/s. The ambient pressure is 1.013 bar. The initial cabin temperature is assumed to be higher than the ambient temperature due to solar heating and thermal soak. Through a simplified relation, \( T_{cab} = 1.6 \, T_{amb} \). Thus, the initial cabin temperatures are as shown in the following table.
| Ambient Temperature (°C) | Initial Cabin Temperature (°C) |
|————————–|——————————-|
| 32 | 51.2 |
| 35 | 56.0 |
| 38 | 60.8 |
| 41 | 65.6 |
The target cabin temperature is set to between 21 °C and 23 °C. If the final cabin temperature under a particular control strategy lies within this range, the strategy is considered capable of meeting the thermal comfort requirement.
Energy Consumption and COP Calculation
The energy consumption of the air conditioning system in an electric car is primarily the work done by the compressor. The compressor work per unit mass of refrigerant is the difference in enthalpy between the discharge state and the suction state. The total power consumed by the compressor can be expressed as:
$$
W = q \cdot (h_2 – h_1)
$$
where \( q \) is the refrigerant mass flow rate, \( h_1 \) is the enthalpy at the compressor inlet, and \( h_2 \) is the enthalpy at the compressor outlet. In the refrigeration cycle, the cooling capacity delivered to the cabin is:
$$
Q_{cool} = q \cdot (h_1 – h_4)
$$
where \( h_4 \) is the enthalpy at the evaporator inlet. The coefficient of performance is defined as the ratio of the cooling capacity to the compressor work:
$$
COP = \frac{h_1 – h_4}{h_2 – h_1}
$$
This expression assumes that the expansion process is isenthalpic and that the evaporator and condenser pressures are known. The enthalpy values are obtained from the AMEsim simulation results, which provide the thermodynamic state at all four key points of the cycle.
In addition to the instantaneous coefficient of performance, I calculate the cumulative energy consumption over a simulation period. The simulation duration is set to 200 seconds, which is sufficient for the cabin temperature to reach a stable value under most conditions. The energy consumption is computed by integrating the instantaneous compressor power over time. This energy value is compared across the different control strategies.
Simulation Structure
The co-simulation model is structured as follows. The AMEsim model outputs the cabin temperature and the thermodynamic states of the refrigerant. These signals are sent to Simulink through the interface. In Simulink, the control strategy computes the compressor speed command. The command is then sent back to AMEsim, where it adjusts the compressor speed in the physical model. The simulation runs with a fixed time step, and all results are recorded for offline analysis. Each control strategy is simulated under all four ambient temperatures, yielding a total of twelve simulation cases. The initial cabin temperature is set according to the ambient condition, and the control system is activated at the start of the simulation.
Simulation Results and Discussion
Cabin Temperature Response
The primary objective of the air conditioning system in an electric car is to provide a thermally comfortable cabin environment. Therefore, I first examine the cabin temperature response under the three control strategies. The temperature profiles over time for the four ambient temperatures are summarized in the following discussion.
As representative examples, let us consider the cases of 32 °C and 41 °C. At 32 °C ambient, all three strategies eventually bring the cabin temperature into the target range. The fuzzy control strategy produces a cabin temperature of 21.24 °C, the PI control achieves 22.02 °C, and the fuzzy PI control reaches 22.27 °C. The difference between these values is small, but the transient behavior may differ. At 41 °C ambient, the fuzzy control strategy is unable to cool the cabin sufficiently; the final temperature is 23.43 °C, which is slightly above the upper limit of 23 °C. In contrast, both PI and fuzzy PI control manage to keep the final cabin temperature within the target range, with final values of 22.98 °C and 22.98 °C respectively.
| Ambient Temperature (°C) | Fuzzy Control (°C) | PI Control (°C) | Fuzzy PI Control (°C) |
|————————–|——————–|—————–|————————|
| 32 | 21.24 | 22.02 | 22.27 |
| 35 | 21.81 | 22.10 | 22.41 |
| 38 | 22.12 | 21.85 | 22.30 |
| 41 | 23.43 | 22.98 | 22.98 |
From the table, it is evident that the fuzzy control strategy demonstrates some instability at higher ambient temperatures. This is likely due to the limited ability of the static rule base to adapt to the extreme cooling demand. The fuzzy controller does not have an integral action, so it cannot eliminate the steady-state error when the cooling load is high and the compressor speed saturates. Although the fuzzy controller can adjust the compressor speed in a nonlinear manner, its output is bounded by the maximum speed and the rules may not produce a sufficient command to overcome the heat load at 41 °C.
On the other hand, the PI control strategy, with its integral term, can eliminate the steady-state error and therefore achieve the target temperature even under high loads. The scaling factor introduced in the PI control extends its speed range, enabling it to produce the necessary compressor speed. The fuzzy PI controller inherits the integral action of the PI controller and adds adaptive gain tuning. As a result, it also achieves the target temperatures across all ambient conditions. The settling times of the PI and fuzzy PI controllers are similar, which indicates that the fuzzy gain adjustment does not significantly slow down the response. Rather, it helps in fine-tuning the response near the setpoint.
The transient behavior of the fuzzy controller shows more oscillation when the ambient temperature is high. For example, at 38 °C, there is a noticeable fluctuation in the cabin temperature before it reaches a near-steady value. This oscillation is undesirable because it can affect the thermal comfort of the occupants. The PI and fuzzy PI controllers produce smooth temperature trajectories without significant oscillations, confirming their superior stability.
Compressor Speed
The compressor speed is directly related to the energy consumption of the air conditioning system. In an electric car, a lower compressor speed generally translates into lower electrical power consumption and therefore a longer driving range. However, the compressor speed must be high enough to provide adequate cooling capacity. The average compressor speeds after reaching steady state for the different control strategies are compared in the following discussion.
In general, the fuzzy control strategy exhibits a higher compressor speed than the other two strategies when the ambient temperature is low (32 °C and 35 °C). This might seem counterintuitive, because a higher compressor speed would produce more cooling, potentially overshooting the target. However, the fuzzy controller tends to be less efficient in modulating the speed near the setpoint, leading to oscillatory behavior and an average speed that is higher than necessary. As a result, the energy consumption is higher and the coefficient of performance is lower for the fuzzy controller at moderate temperatures.
At high ambient temperatures, the fuzzy controller may actually have a lower average compressor speed than the PI controllers, but this comes at the cost of not achieving the target temperature. The compressor speed saturation or the rule base limitations prevent the fuzzy controller from applying a sufficiently high speed to overcome the large heat load, even if the maximum speed is not reached. This confirms that the fuzzy control strategy, as designed in this study, is not suitable for extreme cooling conditions.
The PI and fuzzy PI controllers produce compressor speeds that are more closely aligned with the actual cooling demand. The fuzzy PI controller tends to command a slightly lower compressor speed than the PI controller. This is because the fuzzy adjustment mechanism reduces the proportional and integral gains when the error becomes small, which reduces the propensity for overshoot and results in a lower steady-state compressor speed. The following table summarizes the approximate compressor speeds (in rev/min) at the end of the simulation (steady state) for each strategy and ambient temperature.
| Ambient Temperature (°C) | Fuzzy Control (rev/min) | PI Control (rev/min) | Fuzzy PI Control (rev/min) |
|————————–|————————–|———————-|—————————-|
| 32 | 3100 | 2200 | 2100 |
| 35 | 4000 | 3200 | 3100 |
| 38 | 4800 | 4300 | 4200 |
| 41 | 4900 | 5600 | 5600 |
Note that these values are approximate and extracted from the simulation data for illustration. At 41 °C, the PI and fuzzy PI controllers both command a compressor speed near 5600 rev/min, which is necessary to meet the high cooling load. The fuzzy controller’s speed is slightly lower, but insufficient to reach the target temperature.
Energy Consumption
Energy consumption is a critical metric for the electric car because it directly affects the driving range. The total energy consumed by the air conditioning compressor during the 200-second simulation is calculated by integrating the compressor power over time. The results are expressed in kilowatt-hours (kW·h). The following table shows the cumulative energy consumption for the three control strategies at four ambient temperatures.
| Ambient Temperature (°C) | Fuzzy Control (kW·h) | PI Control (kW·h) | Fuzzy PI Control (kW·h) |
|————————–|———————-|——————-|————————-|
| 32 | 1.15 | 0.72 | 0.68 |
| 35 | 1.98 | 1.47 | 1.40 |
| 38 | 2.45 | 2.61 | 2.47 |
| 41 | 2.90 | 4.70 | 4.70 |
These numbers reveal several important insights. At ambient temperatures of 32 °C and 35 °C, the fuzzy control consumes significantly more energy than both PI controllers. This is due to the higher average compressor speed and the oscillatory behavior, which wastes energy. The fuzzy PI control consumes slightly less energy than the PI control, confirming that adaptive gain tuning can reduce unnecessary compressor activity.
At 38 °C, the energy consumption of the fuzzy control becomes slightly lower than that of the PI controllers, but the fuzzy control still fails to provide stable cabin temperature. Therefore, comparing energy consumption without considering thermal comfort is misleading. The fuzzy controller may use less energy because it does not fully cool the cabin, but this is not acceptable.
At 41 °C, the energy consumption of the PI and fuzzy PI controllers is identical, both at 4.70 kW·h. This occurs because the control system has reached the maximum compressor speed and operates at the limit of its cooling capacity. Both controllers command the compressor at high speed, and the difference between their gains becomes negligible when the error is consistently large. In this extreme condition, the primary objective is to cool the cabin as much as possible, and energy optimization takes a back seat. Thus, the energy consumption of the two strategies converges.
The energy savings achieved by the fuzzy PI controller compared with the PI controller are 0.04 kW·h at 32 °C, 0.07 kW·h at 35 °C, and 0.14 kW·h at 38 °C. At 41 °C, there is no savings because of the saturation condition. Over a longer period, these small savings can accumulate and contribute to a noticeable extension of the driving range of an electric car. Moreover, when the ambient temperature is moderate (e.g., 32 °C to 38 °C), the fuzzy PI controller’s ability to reduce the compressor speed while still maintaining thermal comfort is particularly valuable.
Coefficient of Performance
The coefficient of performance of the air conditioning system is a measure of how efficiently the compressor work is converted into cooling capacity. A higher COP indicates that the system transfers more heat per unit of work. In an electric car, a higher COP means that for the same amount of cooling, less electrical energy is taken from the battery, leading to a longer range. The COP values obtained from the simulations are shown in the following table.
| Ambient Temperature (°C) | Fuzzy Control | PI Control | Fuzzy PI Control |
|————————–|—————|————|——————|
| 32 | 1.80 | 2.20 | 2.30 |
| 35 | 1.55 | 1.80 | 1.85 |
| 38 | 1.50 | 1.40 | 1.45 |
| 41 | 1.35 | 1.20 | 1.20 |
At moderate ambient temperatures, the fuzzy PI control achieves the highest COP among the three strategies. For example, at 32 °C, the COP is 2.30, which is 0.1 higher than that of the PI control. This improvement is a direct consequence of the lower compressor speed and reduced energy consumption. The fuzzy control has the lowest COP at 32 °C because it operates inefficiently with high speed oscillations.
At higher ambient temperatures, the COP decreases for all strategies due to the increased temperature lift across the compressor. The difference between the PI and fuzzy PI controls diminishes, and at 41 °C, they have the same COP. The fuzzy control at 38 °C has a slightly higher COP than the PI controllers, but this is negated by its failure to provide adequate cooling. It is important to remember that the COP is defined only when the system is operating under a given thermal load; if the cabin temperature is not maintained, the comparison becomes less meaningful.
The results demonstrate that the fuzzy PI control strategy offers the best compromise between energy efficiency and thermal comfort. By adaptively adjusting the controller gains, it avoids unnecessary high compressor speeds and thus achieves a higher COP. This is particularly beneficial for the electric car, where every percentage point of efficiency improvement can translate into miles of additional range.
Discussion of the Results
The simulation results indicate that the control strategy has a profound impact on the performance of the air conditioning system in an electric car. The fuzzy control strategy, despite its ability to handle nonlinearities, fails to meet the cooling demand at high ambient temperatures. This is a fundamental shortcoming of fuzzy controllers without integral action: they cannot eliminate steady-state errors in systems with constant disturbances. The cabin heat load acts as a disturbance that the fuzzy controller cannot fully compensate for when the error is small but persistent.
The PI controller, on the other hand, can eliminate steady-state errors through the integral action. The introduction of a scaling factor allows the PI controller to operate over a wider range of compressor speeds, making it suitable for the electric car air conditioning system. The PI controller performs well in all tested ambient temperatures and provides stable cabin temperatures within the target range.
The fuzzy PI controller builds on the strengths of both approaches. It retains the integral action of the PI controller and adds fuzzy logic to adjust the gains. This adaptive tuning leads to a better transient response and a slightly lower steady-state error compared with the fixed-gain PI controller. More importantly, the fuzzy PI controller reduces the energy consumption because the gain reduction near the setpoint lowers the compressor speed. The COP is correspondingly higher.
One might wonder why the fuzzy PI controller achieves a higher cabin temperature than the PI controller in some cases (e.g., 22.27 °C vs. 22.02 °C at 32 °C). This is not a disadvantage; both temperatures are within the comfort range. A slightly higher cabin temperature at moderate ambient conditions can be beneficial because it reduces the cooling load and energy consumption. The fuzzy PI controller effectively allows the cabin temperature to float a little higher when the load is low, which is an intelligent energy-saving behavior.
In contrast, the fuzzy controller at moderate ambient temperatures overshoots and oscillates, resulting in a lower average cabin temperature but at the expense of excessive energy use. This suggests that the rule base of the fuzzy controller is not optimally tuned for the electric car application. A more sophisticated fuzzy rule base, perhaps with additional inputs such as ambient temperature or solar load, might improve its performance. However, this would increase the complexity of the controller.
Overall, from the perspective of the electric car, the fuzzy PI control strategy emerges as the preferred choice because it offers lower energy consumption and higher COP while maintaining good thermal comfort. The energy savings, although seemingly small in absolute terms over a 200-second simulation, would be significant over a full day of driving, especially in hot climates.
| Criteria | Fuzzy Control | PI Control | Fuzzy PI Control |
|---|---|---|---|
| Thermal comfort at high ambient temperature | Insufficient | Adequate | Adequate |
| Stability of cabin temperature | Oscillatory | Stable | Stable |
| Energy consumption | High at moderate temperatures | Moderate | Lowest |
| COP | Low at moderate temperatures | Moderate | Highest |
| Complexity | Medium | Low | Medium |
| Suitability for electric car | Limited | Good | Excellent |
The above summary underscores that the fuzzy PI strategy combines the best features of both fuzzy and PI control. It can adapt to changing conditions and optimize energy consumption without compromising the cabin thermal environment. Since the compressor is the primary energy consumer in the air conditioning system of an electric car, any reduction in its average speed can have a direct impact on the vehicle range.
Mathematical Formulation of the Control Commands
To provide a more rigorous understanding of the control strategies, I present the mathematical formulation that defines the compressor speed command in each case.
For the PI controller, the compressor speed \( n_{PI} \) is computed as:
$$
n_{PI} = y \cdot \left( K_p e + K_I \int_{0}^{t} e \, dt \right)
$$
where the error \( e = T_{target} – T_{cab} \). The scaling factor \( y \) is a quadratic function of the temperature difference \( \Delta t = T_{amb} – T_{target} \), as given earlier.
For the fuzzy controller, the compressor speed \( n_{Fuzzy} \) is a nonlinear function of the error and its derivative:
$$
n_{Fuzzy} = F_{Fuzzy}(e, \dot{e})
$$
where \( F_{Fuzzy} \) represents the fuzzy inference process involving fuzzification, rule evaluation, and defuzzification.
For the fuzzy PI controller, the compressor speed is computed similarly to the PI controller but with varying gains:
$$
n_{FPI} = y \cdot \left( (K_p + \Delta K_p) e + (K_I + \Delta K_I) \int_{0}^{t} e \, dt \right)
$$
where:
$$
\Delta K_p = F_{\Delta K_p}(e, \dot{e})
$$
$$
\Delta K_I = F_{\Delta K_I}(e, \dot{e})
$$
The functions \( F_{\Delta K_p} \) and \( F_{\Delta K_I} \) are fuzzy logic mappings based on the rule tables given earlier. These functions ensure that the gains are increased when a large error indicates insufficient cooling and decreased when the error is small to prevent overshoot.
The design process of the fuzzy PI controller involves prioritizing the tuning of the baseline gains \( K_p \) and \( K_I \), followed by the design of the fuzzy rule tables for \( \Delta K_p \) and \( \Delta K_I \). The rules follow intuitive logic: if the error is large and positive (cabin too hot), then \( \Delta K_p \) should be positive to increase the proportional gain and quickly raise the compressor speed. Conversely, if the error is small and positive, a smaller \( \Delta K_p \) or even a negative value may help avoid overshoot. Similar logic applies to the integral gain.
For the electric car, the use of the scaling factor \( y \) is justified because the standard PI control range (0-1200 rev/min) is insufficient for cooling a hot cabin during summer. The scaling factor translates the error magnitude into a multiplier that can extend the speed up to 6000 rev/min. The quadratic relation was obtained through a curve fitting of the desired speed at various ambient temperatures for a baseline PI controller. This heuristic approach works well in practice, as demonstrated by the simulation results.
Implications for Electric Car Range
The energy consumption of the air conditioning system directly impacts the driving range of an electric car. To quantify this effect, let us assume an electric car with a battery capacity of 60 kW·h and an average driving efficiency of 6 km per kW·h. If the air conditioning controller can reduce energy consumption by 0.1 kW·h over a 200-second period, it might seem small. However, during a typical one-hour drive in summer, the savings would scale. For instance, if the average compressor power is reduced by 0.5 kW, then in one hour the energy saved is 0.5 kW·h. This translates into an additional driving range of about 3 km. Over a full day of driving in hot weather, the cumulative savings could be substantial.
The fuzzy PI controller achieves its energy savings by minimizing the compressor speed while still meeting the cooling demand. In contrast, the fuzzy controller tends to overshoot and waste energy, which could reduce the range of the electric car. The PI controller, while functional, is not as efficient as the fuzzy PI controller in the moderate temperature range.
Furthermore, the coefficient of performance affects the energy consumption in a more fundamental way. A higher COP indicates that the refrigeration cycle is operating more efficiently. The fuzzy PI controller’s ability to maintain a high COP under part-load conditions is valuable for the electric car. Part-load operation is common in real driving scenarios because after the cabin is cooled, the compressor only needs to maintain the temperature, which requires less power. The adaptive gains of the fuzzy PI controller help in achieving a smooth transition from high-load cooling to low-load maintenance.
Conclusion
In this paper, I have investigated the influence of three control strategies—fuzzy control, PI control, and fuzzy PI control—on the cabin temperature, compressor speed, energy consumption, and coefficient of performance of the air conditioning system in an electric car. Through a co-simulation of AMEsim and Simulink, I have analyzed the performance of these strategies under ambient temperatures of 32 °C, 35 °C, 38 °C, and 41 °C.
The main findings are as follows:
1. The fuzzy control strategy is not able to meet the cooling requirement of the cabin at high ambient temperatures. At 41 °C, the cabin temperature exceeds the upper limit of the comfort range, indicating a steady-state error that cannot be eliminated by the fuzzy controller. Moreover, at moderate temperatures, the fuzzy control produces noticeable temperature fluctuations and uses excessive energy.
2. The PI control strategy, with the addition of a scaling factor, can effectively regulate the cabin temperature within the target range across all tested ambient temperatures. It provides stable and accurate control, but its fixed gains do not perfectly optimize energy consumption.
3. The fuzzy PI control strategy outperforms both the fuzzy and PI controllers. It achieves stable cabin temperatures within the target range, while consuming less energy and achieving a higher coefficient of performance than the PI controller. The adaptive gain adjustment allows the fuzzy PI controller to reduce the compressor speed near the setpoint, which lowers the energy consumption without sacrificing comfort.
4. At extreme ambient temperature (41 °C), the air conditioning system operates at its capacity limit, and the PI and fuzzy PI controllers exhibit similar energy consumption because the compressor saturates. This indicates that under max cooling load, the potential for control optimization is limited by the hardware capacity.
The results highlight the importance of selecting an appropriate control strategy for the air conditioning system in an electric car. The fuzzy PI controller, by intelligently adjusting the controller gains, offers an attractive balance between thermal comfort and energy efficiency. This is particularly relevant for extending the driving range of electric cars in hot climates.
Future work could involve validating the simulation results with experimental tests on a real electric car air conditioning system. In addition, the fuzzy PI controller could be further optimized by considering other input variables, such as solar radiation and vehicle speed, to improve its adaptability. The impact of different refrigerants on the COP could also be investigated. Nevertheless, the current study provides a solid basis for the design of energy-efficient air conditioning control systems for electric cars.
Through this research, I hope to contribute to the ongoing effort to reduce the energy consumption of auxiliary systems in electric cars, thereby accelerating the adoption of clean and sustainable transportation. The electric car is not just a vehicle; it is a platform for integrating advanced control technologies that can make mobility more efficient and environmentally friendly.