A Self-learning intelligent passenger vehicle comfort cooling system control strategy

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A Self-learning intelligent passenger vehicle comfort cooling system control strategy ⁎

Yi Xiea, , Zhaoming Liua, Jiangyan Liub, Kuining Lib, Yangjun Zhangc, Cunxue Wud, Pingzhong Wangd, Xiaobo Wangd a

School of Automotive Engineering, Chongqing University, Chongqing, 400044, China School of Energy and Power Engineering, Chongqing University, Chongqing, 400044, China c State Key Lab of Automotive Safety and Energy, School of Vehicle and Mobility, Tsinghua University, Beijing, 100084, China d Chongqing Chang’an New Energy Vehicle Technology Co,. Ltd, Chongqing, 401120, China b

H I GH L IG H T S

with self-learning of users’ thermal comfort for AC system is built. • AThecontroller self-learning scheme of PMV can predict the thermal habits of passengers. • Thermal of AC system - cabin can describe the cabin temperature evolution. • Effect of model changing external environment are considered by the proposed controller. • The proposed control strategy can keep the passenger comfortable and save energy. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Air conditioning system Intelligent control strategy Self-learning of passengers’ thermal comfort Thermal preference Energy saving

This paper establishes a coupled thermal model of the air conditioning system and cabin for electric vehicles, which considers the effects of solar radiation, vehicle speed, and the external environment on the heat exchanged with the cabin. An intelligent air conditioning system control strategy that can learn passengers’ thermal comfort preferences is proposed. This strategy predicts the preferred predicted mean vote of passengers by learning their thermal comfort preferences, then converts it into a target temperature for the air conditioning system. The performance of the proposed strategy is compared with that of conventional on-off and fuzzy PID controllers. In a simulated hot environment, the proposed control algorithm directly and automatically decreased the cabin temperature to the passengers’ preferred temperature without any manual adjustment. It can also maintain stable passenger PMVs and corresponding temperatures regardless of solar radiation, vehicle speed, and external environmental changes. The proposed strategy can improve the thermal comfort of passengers, compared with the on-off and fuzzy PID controllers; moreover, it consumes less energy. In a simulated driving cycle, its energy consumption was 31.8% less than that of the on-off controller and 10% less than that of the fuzzy PID controller, and its COP was respectively 20.4% and 18.7% more than those of on-off controller and the fuzzy PID controller. Therefore, the proposed strategy can make vehicles, especially electric ones, more efficient.

1. Introduction With the increasingly severe problems in global energy supply and environmental pollution, there are pressing needs for increases in vehicle efficiency and reductions in their emissions [1]. In order to satisfy these needs, automobile subsystems such as their powertrains are gradually becoming governed by intelligent control systems. The heating,

⁎

ventilating and air conditioning (HVAC) system is one of the most important subsystems of a vehicle. It consumes so much energy in providing drivers and passengers with a comfortable cabin environment that the range of the car is reduced by 15–20%[2–3]. For electric vehicles, this negative impact may be even worse. A recent study showed that the usage of HVAC systems causes the vehicle range to fall by 30–40% [4]. Therefore, it is crucial to devise an efficient air

Corresponding authors. E-mail address: [email protected] (Y. Xie).

https://doi.org/10.1016/j.applthermaleng.2019.114646 Received 23 August 2019; Received in revised form 23 October 2019; Accepted 4 November 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Yi Xie, et al., Applied Thermal Engineering, https://doi.org/10.1016/j.applthermaleng.2019.114646

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set-point optimizer for an air conditioning system. This controller uses 9% less energy than an on-off controller. With the development of artificial intelligence, a lot of research has been carried out on driverless cars [21]. As one of the most important auxiliary systems of an automobile, the air conditioning system also needs intelligentization to serve passengers better. Moreover, the energy savings of the air conditioning system are critical in extending the cruising range of electric vehicles. Although intelligent algorithms can make air conditioning systems adjust more rapidly and accurately, they still face various difficulties. For example, how best to satisfy the thermal comfort of passengers and save energy simultaneously. Nowadays, the target temperature of an air conditioning system is set manually. It may be set several times by the driver during driving to adapt to changing external conditions such as the weather and meet thermal comfort requirements. This is because it takes a while for human bodies to feel temperature changes. This method of temperature control may cause unnecessary adjustments and energy wastage. In order to solve the problems mentioned above, we need a control algorithm which can automatically adjust the target temperature to maintain the thermal comfort of passengers and reduce energy wastage by identifying changes in the external environment. In such an algorithm, evaluation of the thermal comfort of the human body is key. Fanger et al. proposed the predicted mean vote (PMV) index to describe the thermal comfort of the human body [22]. Fanger defined PMV = 0 as the most comfortable thermal environment for humans. However, in practice, people have their own preferences. Some like cool environments (PMV < 0) while others prefer warm ones (PMV > 0). Therefore, it is important for HVAC system control algorithms to learn the thermal preferences of passengers. However, this aspect has not been considered in existing research on air conditioning systems. Motivated by the aforementioned research gaps, this paper presents an intelligent control strategy that considers self-learning of the PMV index for electric vehicle air conditioning systems. This algorithm provides a thermally-comfortable environment to passengers and eliminates the need for manual adjustment of cabin temperature to reduce unnecessary energy wastage. Compared with existing HVAC control strategies [8–22], this paper makes four main contributions. First, this paper proposes an HVAC system control strategy based on PMV instead of cabin temperature that aims to provide optimal thermal comfort to passengers, and an adaptive fuzzy-PID algorithm to make the air conditioning system track the temperature confirmed by the PMV and save energy. Second, a self-learning scheme based on historical data of manual temperature adjustment is developed to predict the thermal habits of passengers expressed as PMV values. Third, a coupled thermal model of the air conditioning system and the cabin, based on a practical case, is established and validated by experiments in an environmental chamber. Fourth, the influences of changes in the weather, solar radiation, exterior driving environments, and speed on cabin thermal loads are included in the control system. Moreover, comparisons with two existing HVAC system control methods are made to demonstrate the benefits of the proposed algorithm in providing thermal comfort and increasing energy efficiency.

conditioning system that considers the thermal comfort of passengers while minimizing energy consumption [5]. In electric vehicles, the compressor of the air conditioning system is powered by the battery rather than the internal combustion engine. It can be controlled more precisely by adjusting the motor speed [6–7]. Therefore, the control strategy of the air conditioning system is key to achieving thermal comfort and converting energy for the vehicle’s air conditioning system. Automobile air conditioning system control strategies are evolving along with information technology. The switch control is a widely applied algorithm. It manages the on/off switching of the HVAC system in relation to a set cabin temperature [8]. This rule-based strategy is simple and feasible, especially for internal combustion engine-powered vehicles, but the adjustment effect is poor and the cabin temperature may fluctuate greatly, leading to poor thermal comfort and high energy consumption [9]. PID (proportion integration differentiation) feedback control is another method widely used for the air conditioning systems, due to its high efficiency and simplicity [10]. However, because the air conditioning system is nonlinear and external parameters of vehicles such as speed, solar radiation, and environmental temperature vary drastically, PID control may provide an unsatisfactory outcome. The fuzzy control is one of the language controls and does not need math model of the control system. The control logic can be obtained from the experience and optimized by the operation. Hence, the fuzzy control has strong robust and quick response [11]. However, the fuzzy control cannot ensure the control accuracy, which is the shortcoming compared with the PID control. Therefore, advanced control algorithms have been developed for the air conditioning systems. The improved fuzzy control is the most common in those models. Farzaneh et al. used fuzzy control strategy to establish an air conditioning system controller which has two independent modes [12]. One is targeted for a set cabin temperature and the other is set for the thermal comfort of passengers, which is set as PMV = 0. Although PMV = 0 means that the thermal environment is comfortable, neither hot nor cold for the passengers, it is not suitable for all people. Khayyam et al. proposed a look-ahead fuzzy control algorithm to save energy [13]. Compared with the traditional CEMS (coordinated energy management strategy) system and fuzzy control strategy, this algorithm can reduce energy consumption by 12% and 3%, respectively. Furthermore, Khayyam developed an adaptive intelligent control algorithm for cabin temperature and air quality based on this method [14]. The concentration of CO2 in the air is controlled to ensure good quality air in the cabin. Simulations show that the adaptive controller not only maintains cabin temperature and air quality, it also saved 1% more energy than the traditional fuzzy control strategy. In order to raise the reaction speed of the control system for the vehicle air conditioning system and ensure the control precision and robust, the fuzzy-PID control which is the combination of the fuzzy control and PID control was applied to the air conditioning system [15]. Wang et al. applied the fuzzy-PID control strategy to the air conditioning system and proved that it has higher adaptability, better stability, quicker response, and higher control precision than the PID control and fuzzy control [16]. However, the previous literatures [15–16] does consider the energy saving and thermal comfort of passengers in the fuzzy-PID control strategy of the vehicle air conditioning system. Intelligent control strategies, such as artificial neural network (ANN) control and expert control, also provide novel ideas for HVAC control systems [17]. However, inaccurate models and complicated calculations hinder their application in automobile HVAC systems [18]. In order to surpass these limitations and save more energy, intelligent algorithms combined with control strategies have been widely studied. Ng et al. [19] proposed an adaptive predictive controller for an HVAC system by using an online-trained ANN. This model was constructed using online training with test data and can make a control system accurately predict the dynamic characteristics of the air conditioning system, thereby realizing the precise control of the HVAC system. Huang et al. [20] developed an energy-saving sliding controller with a

2. Thermal modeling of the air condition system and cabin 2.1. Modeling of the air conditioning system In this section, the thermal model for the electric air-conditioning system is established, and this kind of air-conditioning system is widely used not only for the electric vehicle (EV), hybrid EV (HEV) and plug-in hybrid EV (PHEV) but also for the fuel-powered vehicle with 48 V system. The structure of an air conditioning system for the electric vehicle is shown in Fig. 1. It has four main parts: an electric compressor, condenser, expansion valve, and evaporator. In this section, a thermal model of an SUV’s (sports utility vehicle) air conditioning system is established and coupled with a cabin model that considers the 2

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Fig. 1. Schematic diagram of an air conditioning system for the electric vehicle.

Tc,w,i is the wall temperature in each cell. In Eq. (4), Φc,a,i is the heat flux of each cell at the air side of the condenser, ηfc denotes the global finned surface efficiency, kc,a,i is the convection coefficient among the air, flat tubes and fins at the cell surface, Sc,a,i refers to the heat convection area of each cell at the air side, and Tc,a,i is the air temperature in each cell. The wall temperature Tc,w,i can be obtained by solving:

influences of solar radiation, speed, and the car’s interior on cabin temperature. 2.1.1. Electric compressor An electric compressor is the core component of an air conditioning system. It compresses R134a vapor and increases its temperature and pressure to make a refrigeration cycle run continuously. The thermal model of the electric compressor is [16]:

dmcomp = ηv ρr Ncomp Vd hc, o = hc, i

his, o − hc, i + ηis

dTc, w, i Φc, a, i + Φc, r , i = dt mc, i CP, i

(1)

In Eq. (5), mc,i is the mass of the aluminum alloys composing the condenser in each calculation grid, and Cp,i is its specific heat. The total heat fluxes at the refrigerant and air sides of the condenser, Φc,r and Φc,a, are respectively calculated by:

(2)

In Eq. (1), mcomp is the mass flow rate of the refrigerant in the compressor, ηv refers to the volumetric efficiency, ρr denotes the refrigerant density inside the compressor, Ncomp is the compressor speed, and Vd denotes the volumetric displacement of the compressor. In Eq. (2), hc,o and his,o are the enthalpy and isentropic enthalpy of R134a refrigerant at the compressor outlet, respectively, hc,i refers to its enthalpy at the inlet, and ηis denotes the isentropic efficiency of the electric compressor.

∑ Φc,r ,i

(6)

Φc, a =

∑ Φc,a,i

(7)

ṁ v = Cq Av 2ρv ΔP

(8)

where Cq is the flow coefficient of the expansion valve, ρv refers to the density of R134a through the expansion valve, ΔP is the pressure drop of the refrigerant, and Av is the minimum flow area of the valve. 2.1.4. Evaporator The evaporator has almost the same heat transfer process as the condenser. Because the heat transfer process at the air side is related to the cabin air temperature, more attention is given to it and the state of cold air at the evaporator outlet. The heat transfer process in the evaporator is described by the finite element method, as per the condenser. For a cell i, the heat flux is solved by the following equations. For the refrigerant side:

(3)

For the air side:

Φc, a, i = η fc kc, a, i Sc, a, i (Tc, w, i − Tc, a, i )

Φc, r =

2.1.3. Expansion valve The flow in the expansion valve is assumed to have an adiabatic course. Thus, the heat transfer loss of R134a refrigerant is neglected in the thermal modeling, which causes the enthalpy to stay the same from the expansion inlet to its outlet [25]. In this process, the refrigerant mass flow rateṁ v can be calculated by [20]:

2.1.2. Condenser The condenser receives refrigerant gas of high temperature and pressure from the compressor and cools it down to a low-temperature, high-pressure liquid. The condenser is a tube-fin heat exchanger, which makes the hot R134a refrigerant exchange heat with the cool air flowing through the flat tubes and fins. The whole heat transfer process between the refrigerant and air is considered by the thermal model of the condenser. Due to the complex structure of the heat exchanger and the phase change of R134a refrigerant inside the condenser tubes, a finite element method is used to describe the heat transfer process. For a cell i, the heat flux is solved by [23–24]: For the refrigerant side:

Φc, r , i = kc, r , i Sc, r , i (Tc, r , i − Tc, w, i )

(5)

(4)

In Eq. (3), Φc,r,i is the heat flux of each cell at the refrigerant side of the condenser, kc,r,i is heat transfer coefficient between the R134a and the inner wall of the flat tube, and it can be calculated according to Ref. [25], Sc,r,i is the heat convection area of each cell at the refrigerant side, Tc,r,i refers to the refrigerant temperature in each calculation grid, and

Φe, r , i = ke, r ,i Se, r , i (Te, r , i − Te, w, i )

(9)

For the air side:

Φe, a, i = η fe ke, a, i Se, a, i (Te, w, i − Te, a, i ) + ṁ con, i h vap 3

(10)

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In Eq. (9), Φe,r,i is the heat flux of each cell at the refrigerant side of the evaporator, ke,r,i denotes the coefficient of heat transfer between the R134a refrigerant and the inner wall of the flat tube, and it can be calculated according to Ref. [25], Se,r,i is the area of heat convection in each cell at the refrigerant side, Te,r,i refers to the refrigerant temperature in each calculation grid of the evaporator, and Tc,w,i is the wall temperature in each cell. In Eq. (10), Φe,a,i is the heat flux of each cell at the air side of the evaporator, ηfe denotes the global finned surface efficiency of the evaporator, ke,a,i is the convection coefficient among the air, flat tubes and fins at the cell surface, Se,a,i refers to the area of heat convection in each cell at the air side, Te,a,i is the air temperature in each cell, ṁ con, i is the mass flow rate in cell i, and hvap refers to the latent heat of vaporization of water. The wall temperature of the evaporator Te,w,i can be obtained by solving:

dTe, w, i Φe, a, i + Φe, r , i = dt me, i CP, i

2.2. Thermal modeling of the cabin The heat load and its transfer in a vehicle cabin are shown in Fig. 2. The thermal network method is used to establish a thermal model of the cabin. Passengers and cabin components, such as the front and rear windshields, roof, sunroof, side windows, dashboard, and seats, are considered in the model to precisely describe the heat transfer and temperature in the cabin. Moreover, five kinds of heat load acting on the cabin are included in the cabin thermal model. The first is the solar radiation load Qsolar, which is determined by the weather and time of day and measured by a solar power meter. The second is the heat convection between the air and automobile surface Qconv, which is related to the vehicle’s speed. The third, fourth, and fifth thermal loads, respectively, are the body heat of passengers Qp, the heat generated by the mechanical and electronic equipments in the cabin Qd, and the thermal load caused by the ventilation system Qvent. The total heat load of the cabin Qcab can be expressed as [26]:

(11)

Qcab = Qconv + Qsolar + Q vent + QP + Qd

In Eq. (11), me,i is the mass of the aluminum alloy comprising the evaporator in each calculation grid, and Cp,i is its specific heat. The total heat flux at the refrigerant and air sides of the evaporator, Φe,r and Φe,a, are respectively calculated by:

Φe, r =

∑ Φe,r,i

Φe, a =

∑ Φe,a,i

According to energy conservation, the change in cabin temperature Ta is:

dTa Qcab − Q̇ AC = dt Ma Cpa

(12)

(13)

ka Aη fe Cpin ṁ in

Ha, out = Ha, in +

(Te, w − Ta, in )

ka Aη fe Cpin ṁ in

(Ha, s − Ha, in )

(17)

where QAC represents the refrigeration capacity of the air conditioning system into the cabin, Ma denotes the air mass in the cabin, and Cpa represents the specific heat of the air.

The air temperature Ta,out and humidity Ha,out at the outlet of the evaporator are respectively obtained by:

Ta, out = Ta, in +

(16)

3. Validation of the coupled thermal model of the air conditioning system and cabin The cabin temperature was tested in an environmental chamber to verify the simulation precision of the coupled thermal model of the air conditioning system and cabin. A schematic of the test system is shown in Fig. 3 and the test SUV is shown in Fig. 4a. In the experiment, incandescent lights were used to simulate the sun with a radiative power of 1000 W/m2. The temperature in the environmental chamber was controlled by an air-conditioning system and was set to 38 °C to simulate hot summer weather. A blower was used to create wind to simulate vehicle movement. K-type thermocouples were used to measure the cabin temperature and were arranged at the front and back seats, as shown in Fig. 4b and 4c. The experimental cases are presented in Table 1. In the first case, the car maintained a speed of 40 km/h for 1800 s. In the second case, the car was idling. In the third case, the car

(14)

(15)

where Ta,in is the average air temperature at the evaporator inlet, Te,w denotes the wall temperature of the evaporator, ka refers to the convective heat transfer coefficient at the air side, A is the convective heat transfer area, ṁ in and Cpin are the mass flow rate and specific heat of the air at the evaporator entrance, respectively, Ha,in is the air humidity at the inlet, and Ha,s denotes the saturation humidity, which is related to the wall temperature.

Fig. 2. Heat load within a vehicle cabin. 4

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Fig. 3. Schematic of the vehicle test set-up in the environmental chamber.

maintained a speed of 40 km/h for 1800 s then accelerated to 100 km/h and remained at that speed for 1800 s before slowing to a stop for 1800 s. The air-conditioning system was on throughout the process and the compressor speed was maintained at 6000 r/min. Before the tests started, the car was placed under the incandescent lights until the cabin temperature reached 60 °C. In the verification, the speeds of the compressor and the fan, Ncomp and Nfan, the ambient temperature Tambient, the solar radiation power Psolar and the vehicle velocity Vcar were the input parameters for the thermal model of the air conditioning system and cabin. They were exactly the same as the experiment. The cabin temperature was one of the output parameters, and it was compared with the test values to

Table 1 Experimental conditions. Parameter

Case 1

Case 2

Case 3

Vehicle speed (km/h) Test duration (s) Initial cabin temperature (°C)

40 1800 60

0 1800 60

40–100-0 1800–1800–1800 60

valid the prediction precision of the thermal model presented in Section 2. Moreover, the validation was implemented with the process shown in Fig. 5. Like the experiment, the fan speed was assumed to be constant in the simulation, and the air mass flow rate obtained by the experiment

Fig. 4. Experimental facilities: (a) environmental chamber, (b) arrangement of thermocouples in the front seats, and (c) arrangement of thermocouples in the back seats. 5

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Fig. 5. The simulation process for AC-cabin system.

Fig. 6. Comparison between the simulated and experimental cabin temperature curves for cases 1 and 2 (v = vehicle velocity).

reflect the cabin cooling process.

was used for the simulation. A comparison of the simulated and experimentally-observed cabin temperatures is presented in Figs. 6,7. According to these figures, the simulated curves have the same trends as the experimental ones, and the two curves are very similar. At the end of the test, the relative errors between the simulated and observed cabin temperatures in cases 1, 2, and 3 were 8.1%, 9.7%, and 7.4%, respectively, which were considered acceptable. Therefore, the coupled thermal model of the air conditioning system and cabin presented in this paper is precise enough to

4. Intelligent control strategy with self-learning of thermal comfort for air conditioning system In this section, an intelligent control strategy that can self-learn passengers’ thermal habits is proposed for the electric air conditioning system (AC system) established in Section 2. This intelligent strategy uses the PMV index to express the thermal habits of passengers. It

Fig. 7. Comparison between the simulated and experimental cabin temperature curves for case 3. 6

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Fig. 8. Schematic diagram of the intelligent air conditioning system control strategy with self-learning of thermal comfort.

Fig. 9. Input target temperature and predicted temperature.

Fig. 10. Membership functions: (a) membership function of e and (b) membership function of ec.

4.1. Intelligent control strategy with self-learning of thermal comfort

automatically determines the favorite PMV of passengers and adjusts the compressor speed to adjust the cabin temperature accordingly. Moreover, two other popular control strategies, an on-off controller and fuzzy-PID, were also examined in this section to demonstrate the superiority of the proposed intelligent control strategy in terms of passengers’ thermal comfort and energy savings.

The structure of the intelligent control strategy with self-learning of passengers’ thermal comfort (SLPTC strategy) is presented in Fig. 8. There are three parts to this intelligent air conditioning system. The first is a calculator of comfortable cabin temperature, Tcomfort. It includes the components “learner and regulator”, “PMV calculator”, and 7

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Table 2 Fuzzy rules for Kp, Ki, and Kd.

0.42(M − 58.15) M > 58.15 Φ2 = ⎧ ⎨ 0M ≤ 58.15 ⎩

(a) Fuzzy rules for Kp

(22)

Φ4 = 1.4e−3M (34 − Ta)

(23)

Φ5 = 3.96e−8fcl [(Tcl + 273) 4 − (Tr + 273) 4]

(24)

Φ6 = fcl hc (Tcl − Ta)

(25)

Φ3 =

e ec

NB

NS

Z

PS

PB

NB NS Z PS PB

−4 × 104 −4 × 104 −4 × 104 −3 × 104 −2 × 104

−4 × 104 −3 × 104 −2 × 104 −1 × 104 0 × 104

−2 × 104 −1 × 104 0 × 104 1 × 104 2 × 104

0 × 104 1 × 104 2 × 104 3 × 104 4 × 104

2 × 104 3 × 104 4 × 104 4 × 104 4 × 104

where

(b) Fuzzy rules for Ki e ec

NB

NS

Z

PS

PB

NB NS Z PS PB

−5 −5 −4 −3 −2

−4 −3 −2 −1 0

−2 −1 0 1 2

0 1 2 3 4

2 3 4 5 5

hc =

NB

NS

Z

PS

PB

NB NS Z PS PB

10−6 10−5 10−4 10−3 10−2

10−4 10−3 10−2 10−1 1

10−2 10−1 1 10 102

1 10 102 103 104

102 103 104 105 106

“human input”. In the “learner and regulator” component, the comfortable temperature is converted to a PMV value and studied by the controller. When the air conditioning system is activated, the “regulator” component sends the passenger’s preferred PMV to the “PMV calculator”. The PMV preferences are based on past use of the air conditioning system over a certain period. The “PMV calculator” calculates Tcomfort and sends it to the controller. If the passenger finds Tcomfort uncomfortable, the “Human input” function is activated to help him/her reset the temperature. At this time, the reset value of Tcomfort is learned by the “learner and regulator” section. The second part of the intelligent air conditioning system is the controller, where adaptive fuzzy-PID is employed as the control algorithm. After the calculation of the control algorithm, the compressor speed Ncomp is obtained and sent to the air conditioning system. The third part of the intelligent AC system is the executor, consisting of the AC system and cabin. In the third part, the cabin temperature Ta is collected and sent back to the controller as feedback. 4.1.1. The “PMV calculator” and “Tcomfort calculator” components The predicted mean vote proposed by Fanger is used to evaluate the thermal comfort of the passenger [22]. The real-time PMV value can be calculated by:

PMV = Ts (M − ϕ1 −ϕ2 −ϕ3 −ϕ4 −ϕ5 − ϕ6)

(18)

TS = 0.303e−0.036M + 0.028

(19)

Φ1 = 3.05e−3 + 5733 − 6.99M − Pw

(20)

0.25 0.25 > 12.1 V a ⎧ 2.38 |Tcl − Ta | 2.38 |Tcl − Ta | 0.25 ⎨ 12.1 V 2.38 | T − T | > 12.1 V a cl a a ⎩

(26)

1 + 1.29Icl Icl ≥ 0.078 fcl = ⎧ ⎨ ⎩1.05 + 0.645Icl Icl < 0.078

(27)

Tcl = 35.7 − 0.028M − Icl (ϕ5 + ϕ6)

(28)

In Eqs. (18)–(28), M is the metabolic rate of the passengers, and Icl is the thermal resistance of the passenger’s clothes. The PMV model considers the influence of air temperature, mean radiant temperature, wind speed, relative humidity, clothing and metabolic rate on the thermal comfort. Among these factors, M and Icl are the personal factors. According to Refs. [12,27], the passengers are assumed to be at rest, and the metabolic rate is 1 met. For the drivers, because he/she pays attention to the driving, the metabolic rate is 1.5 which is higher than that of the passengers. The simulation is implemented in summer, and people usually wear light clothes. Therefore, Icl is set as 0.7 [27]. For the rest four factors, Pw denotes the partial pressure of the vapor which is affected by the relative humidity in the cabin. In practice, people feel comfortable in a wide range of the relative humidity (20–70%). It has little influence on the thermal comfort, and the cabin temperature is the main influence factor of the thermal comfort. According to Refs. [12,28], the relative humidity is set as 50% in this study. Ta is the temperature near the passenger (cabin temperature in this paper). Tcl refers to the surface temperature of the passenger’s clothes. Tr is the average radiation temperature, and it is assumed the same as the cabin temperature Ta [12,29]. Va is the air velocity near the passenger, and is affected by the fan speed which is regulated by the passengers. hc is the convective heat transfer coefficient between the passenger’s body and the air in the cabin. Based on Eqs. (18–28) and PMVa values predicted by the “learner and regulator” component, the comfortable cabin temperature for passenger Tcomfort can be obtained in the “Tcomfort calculator” by solving:

(c) Fuzzy rules for Kd e ec

(21)

1.7e−5M (5867−Pw

Tcomfort =

PMVa Ts

+ Φ1 + Φ2 + Φ3 + Φ5 − M + 47.6e−3M + fcl hc Tcl (1.4e−3M + fcl hc )

(29)

4.1.2. The “learner and regulator” component People have different thermal habits that cannot be reflected by a uniform PMV standard. In the “learner and regulator” component of the STPLC strategy, a self-learning algorithm (Eq. (30)) is established to predict the PMV preferences of different passengers, PMVa. In the selflearning algorithm, the target temperature is recorded when the difference between the target temperature and the present cabin Fig. 11. Schematic of the on-off controller.

8

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Fig. 12. Description of the WLTC driving cycle.

Fig. 13. Road condition and solar radiation scenarios used in the simulations.

affected by the weather, seasons, and so on. In this research, it is assumed that the car is used for commuting twice per day with the air conditioning system on. In order to maintain timely PMVi values for prediction, a half-month period (15 days) is used to finish the update of all PMVi values. Therefore, N is set as 30 in this paper.

Table 3 Control parameters of the on-off controller. Tset

Thigh

Tlow

Nset

26 °C

27 °C

25 °C

5500 r/min

i

PMVa =

temperature is < 1 °C. This is done to ensure the target temperature is comfortable for the passenger and to avoid the influence of frequent changes in target temperature on the collection of a comfortable temperature. After the target temperature is saved, it is adopted in the calculation of the PMVi for the ith adjustment by solving Eqs. (18–28). Then, Eq. (30) is applied to obtain the average value of PMVi and predict the favorite PMV of the passengers, PMVa. In Eq. (30), n is used to count valid adjustments of cabin temperature and its maximum N is the maximum allowable number of PMVi values used to calculate PMVa. When n < N, all of the PMVi values are used for the prediction of PMVa. However, when n > N, the last N values are selected for the process. This is done to update the PMVa value and better adapt it to the thermal habits of the passengers, because human thermal habits are

∑i = i − n + 1 PMVi n

(30)

i (n < N ) n=⎧ ⎨ ⎩ N (n ≥ N )

(31)

An experiment was carried to verify the prediction precision of the algorithm. A passenger who was unfamiliar with the experimental car (Citroen C5) was required to sit in the car and use the air conditioning system. The experiment was implemented in the summer of 2018 in Chongqing, China. The thermal habit of the subject was measured. In the experiment, the minimum interval in set temperature was 0.5 °C due to limitations in the experimental air conditioning controller used in the car. Moreover, the total number of test points was 300. Fig. 9 shows the target temperature set by the subject and the comfortable 9

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Fig. 14. Age and gender distributions of subjects.

Fig. 15. Solution process of COP and energy consumption.

calculation efficiency [30]. The input variables for the self-adaptive fuzzy-PID controller are the error e between the target cabin temperature Tcomfort and the cabin temperature Ta used as a feedback for the control, and its rate of change ec. Variables e and ec are defined as:

temperature predicted by the proposed algorithm. The manual input temperature varied from 22.5 to 26 °C and the corresponding mean value of the 300 input PMVs was 0.528. This indicates that the subject liked a slightly warm environment. The predicted Tcomfort varied between 23.7 °C and 24.8 °C, which is consistent with the input temperature range. Moreover, the mean value of the 300 predicted PMVa values was 0.53, which is similar to the mean input PMV. The maximum and mean relative errors between the input target temperature and predicted comfortable temperature were 9.2% and 2.3%, respectively, which indicates that the proposed prediction algorithm based on PMVa is precise enough to estimate the thermal preference of the passenger. The reason why the proposed algorithm can accurately predict the thermal preference is that the preference of a specific person remains largely fixed and with minor fluctuations. For example, the input target temperature of the subject in this paper fluctuated near 24.3 °C with an amplitude of 1.8 °C.

ec =

4.1.3. The “manual input” component If the passenger does not want the cabin temperature calculated by the PMVa, the target temperature Tcomfort can be reset using “manual input” component. At this moment, the new temperature is sent to the air conditioning system as the control target. If this temperature satisfies the collection requirement of the target temperature in Section 4.1.2, its corresponding PMV is recorded by the “learner” component and used to predict the PMVa by the “regulator” component

4.2. Two other contrasting control strategies for air conditioning system

e = Tcomfort − Ta

de dt

(32)

(33)

The membership functions of e and ec are set up according to ref. [30–31]. The symmetrical triangular membership functions shown in Fig. 10 are applied to the control variables to increase the calculation efficiency. In the figures, the X coordinates denote e and ec. The value of e varies from −4 to 4, and ec varies from −2 to 2. In the control process, the controller queries the control rules shown in Table 2 according to the fuzzy values related to e and ec. After removing fuzziness, the fuzzy logic system sends the Kp, Ki, and Kd values to the PID controller. This realizes self-adaptation of the PID parameters.

Two other popular control strategies were applied to the air conditioning system in order to demonstrate the superiority of the SLPTC strategy in terms of passenger thermal comfort and energy savings. One is the fuzzy-PID algorithm using the fuzzy logic presented in Section 4.1.4. The other is the on-off controller using the control logic shown in Fig. 11. The compressor speed is controlled by [20]:

4.1.4. The self-adaptive fuzzy-PID controller The self-adaptive fuzzy-PID controller is used in the SLPTC strategy proposed in this paper because of its high control precision and 10

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Fig. 16. Comparison of cabin temperature variations obtained by different control strategies.

Nset Ta > Thigh ⎧ Noutput = unchanged (Nset or 0) Tlow ≤Ta ≤ Thigh ⎨ 0Ta < Tlow ⎩

was directly shone on the car. After this, the car was exposed five more simulated conditions: (1) a mountain road shaded by forest, (2) a flat, exposed road, (3) a tunnel, (4) a road shaded by cloud, and (5) a road exposed to afternoon sun which is weaker than that at noon. The corresponding radiation intensities were 303 W/m2, 1000 W/m2, 0 W/m2, 512 W/m2 and 812 W/m2. The radiation intensity values for the shadowed and afternoon scenarios were measured in corresponding realworld conditions by a TESS 1333 radiation meter on July 17th 2018 in Chongqing, China. The fan speed is set by the passengers. To avoid the influence of fan speed on the controlling process, the mass flow rates of the air through the fan are set as 0.1 kg/s for all of the three strategies. The SLPTC strategy proposed in this paper realizes the automatic control of the preferred temperatures of different individuals by adapting to their comfort PMV indexes. In Fig. 9, the passenger’s comfort PMV value is around 0.5, and the corresponding comfort temperature varies between 24 and 25 °C. Fanger’s study [32] reported that East Asians prefer warm environments (positive PMV). Therefore, the subject’s adjustment data (Fig. 9) was used as input for the selflearning algorithm in the SLPTC strategy and the performance of the proposed controller was tested. Hence, for the proposed strategy, there is no target temperature set by the passenger. When the air conditioner is turned on, the air conditioning system adjusts the target temperature automatically based on the comfortable temperature Tcomfort predicted by the “learner and regulator” component. The control parameters of the on–off strategy are shown in Table 3.The target temperature Tset was set to 26 °C and the upper and lower limits of the control temperatures were 27 °C and 25 °C, respectively. The compressor speed Nset was set to 5500 r/min. In a traditional fuzzy PID air conditioning system controller, the target cabin temperature is set by the driver instead of the control algorithm. In the daily use of the air conditioning system, people like to set a low temperature to obtain a quick fall of the cabin temperature. When they feel cold, they raise the target temperature to achieve the

(34)

where Noutput is the output control signal (compressor speed in this paper), Noutput is the set speed of the electric compressor, and Tlow and Thigh denote the lower and upper limits of the control temperature range, respectively. When the cabin temperature Ta is lower than Tlow, the compressor is turned off and its speed is 0. When Ta is higher than Thigh, the compressor speed stays at Nset. When Ta is between Tlow and Thigh, the compressor speed remains unchanged. The compressor is always kept at its maximum speed in the control process if it is on. 5. Application of the proposed SLPTC strategy and comparison with other popular controllers In this section, the SLPTC strategy established in Section 4 is applied to the air conditioning system built in Section 2 and verified in Section 3. Then, it is compared with the on-off and fuzzy-PID controllers described in Section 4 to prove its superiority in providing thermal comfort and energy savings. 5.1. Boundary conditions and setting of control parameters In order to describe the energy consumption of the air conditioning system in the course of driving, the worldwide harmonized light-duty vehicles test cycles (WLTC driving cycle) was selected and the relevant vehicle speed data are shown in Fig. 12. In the simulation, the WLTC driving cycle was repeated for 5000 s. Variable solar radiation from the sun was added to the environmental conditions to reflect its influence on cabin temperature during driving. Fig. 13 presents the evolution of solar radiation and its corresponding time and environmental effects. The simulation started at noon, when the solar radiation of 1000 W/m2 11

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Fig. 17. Comparison of variations in compressor speed obtained by different control strategies.

thermal comfort. At this time, the cabin is “overcooled” and more energy is used to cool the cabin. If the cabin can directly achieve the comfortable temperature, cabin’s overcooling is avoided automatically and the energy is saved. In order to prove that the SLPTC strategy can do the job and has better performance than the fuzzy-PID controller in the energy conservation, an artificial set temperature for the fuzzy PID was designed in advance to compare its performance with that of the proposed SLPTC strategy. To find a common adjustment in vehicle air conditioning system in summer, thirty people were asked to use the air conditioning system in the experimental environment presented in Section 3 and their target temperature setting habits were recorded. The age and gender distributions of subjects are shown in Fig. 14. Majority of the subjects are male and aged from 20 to 35. Moreover, because the experiment were implemented in summer, subjects wore light clothing. Before the test, subjects were required not to do the vigorous activities. Because the initial cabin temperature was very high in the experiment, 23 subjects set a low cabin temperature in order to make it drop quickly, when they first got into the car. A few minutes later, the subjects raised the set cabin temperature, because the cabin temperature was so low that they felt “cold”. At this moment, the cabin was overcooled, and extra energy was consumed. With this done, the reset target temperature was maintained for a long time (usually until the experiment ended). In the first adjustment of cabin temperature, the set temperature varied between 18.5 and 21 °C. 12 of the 23 subjects set the temperature to around 20 °C (19.5 °C, 20 °C or 20.5 °C), In the second adjustment, 23 subjects selected temperatures between 25 and 27 °C, with 13 selecting 26 °C. Therefore, the first target temperature

Tset_1 was set as 20 °C in the fuzzy PID controller, and the PMV was −1 which means “slightly cold”; the second one Tset_2 was set as 26 °C. 5.2. Definition of energy consumption and COP The energy consumption and coefficient of performance (COP) are applied to the evaluation of the energy saving for the air conditioning system controlled by different strategies, and their solution processes are presented in Fig. 15. The energy consumption Qcomp is defined by

Qcomp =

∫0

t

Pcomp dt

(35)

where t is the operation hours of the air conditioning system, and Pcomp is the power of the electric compressor which is

Pcomp =

Tq∙Ncomp 9550

(36)

In Eq. (36), Tq is the torque of the drive motor for the compressor, and Ncomp is the speed of the compressor. The COP of the air conditioning system is obtained by solving

COP =

Q AC Pcomp

(37)

where QAC is the refrigerating capacity of the air conditioning system. 5.3. Performance of air conditioning system controlled by SLPTC strategy The variations in cabin temperature, compressor speed, and PMV 12

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Fig. 18. Comparison of PMV variation obtained by different control strategies.

Fig. 19. Energy consumption over time of the three types of air conditioning system controller.

are presented in Figs. 16–18, respectively. In the initial stage, the three control strategies instructed the electric compressor to work at high speed, causing the cabin temperature and PMV to decrease quickly. As for the on-off controller, when the cabin temperature Ta reached the target, it fluctuated violently due to frequent starting and stopping of the electric compressor, resulting in continual variation in cabin temperature between Thigh and Tlow. This greatly affected the thermal

comfort of passengers and made them sometimes feels hot and sometimes feels cold. Although the fuzzy PID did not make cabin temperature fluctuate frequently like the on-off controller, it could not always keep the passengers thermally comfortable. Fig. 16 shows that when the cabin temperature approached Tset_1, the subjects suddenly raised the cabin temperature to 26 °C at about 1200 s. At this moment, the PMV has already reached −1, indicating that the subject felt cold and the 13

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Fig. 20. COP of the three types of air conditioning system controllers.

Fig. 21. Comparison of compressor speed variations using the fuzzy PID and SLPTC strategies.

the fuzzy-PID and SLPTC evolve with smaller fluctuations. This is because the compressor frequently starts and stops. As shown in Fig. 21, the SLPTC strategy has a lower compressor speed than the fuzzy PID, resulting in a higher COP for the SLPTC strategy. The average COP for the on-off controller, fuzzy PID, and SLPTC strategy are 1.505, 1.527, and 1.812, respectively, and the proposed strategy respectively improves the COP by 20.4% and 18.7%, compared with the other two control algorithms. According to Fig. 17, the on-off controller causes the compressor to start frequently, which results in more energy wastage than the other two strategies. The working process of the air conditioning system was analyzed to explain the difference in energy consumption between the proposed SLPTC and the traditional fuzzy PID strategies. According to Fig. 21, both the fuzzy PID and SLPTC strategies operate the electric compressor at high speed to make the cabin temperature decrease as rapidly as possible in the initial phase of cabin cooling. Therefore, the energy consumption is similar in this stage. As the cabin temperature approaches the target temperature (from 400 to 200 s), the SLPTC strategy orders the compressor to use a relatively low speed, while the fuzzy PID makes it work at high speed (see Fig. 21). This is because the PMVa set by the SLPTC strategy is 0.5, which has a corresponding temperature of 24–25 °C, while Tset_1 by the fuzzy PID is 20 °C. In the fuzzy PID controller, the target temperature is set manually and the insensitivity of the human body to the mild temperature changes leads

cabin was overcooled. After the cabin temperature was reset, the fuzzy PID still could not maintain stable cabin temperature and PMV, though their fluctuations were small. This was caused by changing vehicle speeds and external environments. The intelligent control strategy with self-learning of passengers’ thermal preferences (SLPTC strategy) overcomes the disadvantages of the control algorithms above. As shown in Figs. 16 and 18, it directly and automatically reaches the preferred PMV and then maintains the PMV at around 0.5. Moreover, it keeps the cabin temperature stable after the temperature corresponding to the target PMV is reached. Therefore, the SLPTC strategy, whose control object is the PMV, can create and maintain a comfortable thermal environment. Fig. 19 presents the variation in the energy consumption of the air conditioning system controlled by different strategies. The on-off control strategy had the highest energy consumption followed by fuzzy PID, while the proposed SLPTC strategy consumed the least energy. At the end of the driving cycle, the energy consumption of the on-off controller, fuzzy PID, and SLPTC strategy were 2.89 kWh, 2.19 kWh, and 1.97 kWh, respectively. Compared with the other two control algorithms, the proposed strategy can reduce energy consumption by 31.8% and 10%, respectively. The COP is another energy consumption standard for the air-conditioning system. Fig. 20 shows the real-time COP of the air-conditioning system controlled by different strategies. The COP fluctuates fiercely for the on-off controller, and the COPs for 14

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to a “cold feeling”, so the adjustment of the target temperature is lagging, which makes the cabin overcooled. However, because the SLPTC maintains the cabin temperature by setting the PMVa automatically, the cabin temperature is always in the comfortable zone rather than tendency of “cold first and then thermal comfort” caused by the fuzzy PID. This makes the compressor work at low speed and avoids cabin overcooling. Therefore, in this phase, the SLPTC strategy has less energy consumption than the fuzzy PID. After the target temperature is reset by the fuzzy PID to 26 °C, although the cabin temperature fluctuation causes the fuzzy PID controller to run the compressor at higher speed than the SLPTC strategy at times 1500 s and 3000 s, both controllers select similar compressor speeds. This causes little change in the difference between the energy consumption curves of the fuzzy PID and SLPTC controllers.

Innovation and Application Project of Chongqing (Grant Nos. cstc2018jszx-cyztzx0130 and cstc2017zdcy-zdyf0139), the National Key R&D Program of China (Grant Nos. 2018YFB0106102 and 2018YFB0106104), and the NSF of China (Grant No. U1864212). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114646. References [1] C. Fiori, K. Ahn, H.A. Rakha, Power-based electric vehicle energy consumption model: Model development and validation[J], Appl. Energy 168 (4) (2016) 257–268, https://doi.org/10.1016/j.apenergy.2016.01.097. [2] P. Liu, D. Li, Issues and factors of train air-conditioning system design and operation [C]//, Proceedings of the Sixth International Conference for Enhanced Building Operations (ICEBO), Shenzhen, China, (2006). [3] M.A. Lambert, B.J. Jones, Automotive adsorption air conditioner powered by exhaust heat. Part 1: conceptual and embodiment design, Proc. Inst. Mech. Eng. Part D: J. Automobile Eng. 220 (7) (2006) 959–972, https://doi.org/10.1243/ 09544070JAUTO222. [4] R. Farrington, J. Rugh, Impact of vehicle air-conditioning on fuel economy, tailpipe emissions, and electric vehicle range, Earth Technologies Forum, 2000 doi: NREL/ CP-540-28960. [5] E. Fleming, S. Wen, L. Shi, A.K.D. Silva, Thermodynamic model of a thermal storage air conditioning system with dynamic behavior, Appl. Energy 112 (12) (2013) 160–169, https://doi.org/10.1016/j.apenergy.2013.05.058. [6] T.H. Lim, Y. Shin, S. Kim, C. Kwon, Predictive control of car refrigeration cycle with an electric compressor[J], Appl. Therm. Eng. 127 (12) (2017) 1223–1232, https:// doi.org/10.1016/j.applthermaleng.2017.08.125. [7] H.Y. Zhang, J.Y. Wang, X. Feng, L. Chang, Y.H. Chen, X.G. Wang, The solutions to electric vehicle air conditioning systems: A review, Renew. Sustain. Energy Rev. 91 (8) (2018) 443–463, https://doi.org/10.1016/j.rser.2018.04.005. [8] J. Liu, H. Zhou, X. Zhou, et al., Automative air conditioning system control - A survey, International Conference on Electronic and Mechanical Engineering and Information Technology, IEEE, 2011 doi: 10.1109/EMEIT.2011.6023817. [9] A. Leva, L. Piroddi, M.D. Felice, et al., Adaptive relay-based control of household freezers with on–off actuators, Control Eng. Pract. 18 (1) (2010) 94–102. [10] W.G. Lv, D.Y. Li, S.Y. Cheng, S.M. Luo, X.W. Zhang, L.H. Zhang, Research on PID control parameters tuning based on election-survey optimization algorithm, International Conference on Computing, IEEE, 2010 doi: 10.1109/CCIE.2010.198. [11] F. Calvino, M.L. Gennusa, G. Rizzo, et al., The control of indoor thermal comfort conditions: introducing a fuzzy adaptive controller, Energy Build. 36 (2) (2004) 97–102. [12] Y. Farzaneh, A.A. Tootoonchi, Controlling automobile thermal comfort using optimized fuzzy controller, Appl. Therm. Eng. 28 (14–15) (2008) 1906–1917, https:// doi.org/10.1016/j.applthermaleng.2007.12.025. 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6. Conclusions and future work This paper establishes a coupled thermal model of a vehicle air conditioning system and cabin, which includes the effects of solar radiation, vehicle speed, and the external environment on the heat exchanged with the cabin. An intelligent control strategy with selflearning of passengers’ thermal comfort preferences (the SLPTC strategy) was proposed and used in an air conditioning system. Based on an extensive study of the SLPTC strategy, four key findings were made. 1. The air conditioning system-cabin thermal model is precise enough to describe the temperature evolution in the cabin. The relative errors in cabin temperature between the simulation and experiment in cases 1, 2, and 3 were 8.1%, 9.7%, and 7.4%, respectively. 2. The prediction algorithm used in the SLPTC strategy is able to accurately estimate the thermal habits of passengers. The maximum and mean relative errors between the input target temperature and predicted comfortable temperature were 9.2% and 2.3%, respectively. 3. Compared with the on-off and fuzzy PID controllers, the SLPTC strategy can directly and automatically decrease the cabin temperature to the preference of passengers without any manual adjustment. It can maintain the preferred PMV and corresponding temperature of passengers regardless of variations in solar radiation, vehicle speed, and the external environment. 4. The proposed algorithm consumes less energy than the on-off and fuzzy PID controllers. Its energy consumption was 31.8% less than that of the on-off controller and 10% less than that of the fuzzy PID controller at the end of the test driving cycle considered in this paper. Moreover, the SLPTC strategy respectively improves the COP by 20.4% and 18.7%, compared with the other two control algorithms. Although the proposed PMV learner and regulator can predict the preferred PMV of passengers, sometimes the predicted PMV is not sufficiently precise to express thermal comfort needs under extreme conditions such as temperatures of over 40 °C. In future work, a deep learning algorithm with an artificial neutral network will be used to improve the precision of prediction of the thermal habits of passengers under various conditions. Moreover, the model’s predictive control will be combined a PMV regulator to reduce the energy consumption of air conditioning systems. For the measurement, the power and energy consumption of the air conditioning system will be added in the experiment to verify the advantage of the SLPTC strategy in the energy saving. Acknowledgments This work was supported by the Fundamental Research Funds for Central Universities (106112017CDJQJ338811), the Technological 15

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inside of vehicles, Energy Procedia 85 (2016) 472–480. [29] M.S. Jang, C.D. Koh, I.S. Moon, Review of thermal comfort design based on PMV/ PPD in cabins of Korean maritime patrol vessels, Build. Environ. 42 (1) (2007) 55–61. [30] G.I. Mann, B.G. Hu, R.G. Gosine, Analysis of direct action fuzzy PID controller structures, IEEE Trans. Syst. Man Cybernet. Part B (Cybernetics) 29 (3) (1999) 371–388, https://doi.org/10.1109/3477.764871. [31] Y.Z. Wang, Q.B. Jin, R.D. Zhang, Improved fuzzy PID controller design using predictive functional control structure, ISA Trans. 71 (11) (2017) 354–363, https:// doi.org/10.1016/j.isatra.2017.09.005. [32] P.O. Fanger, J. Toftum, Extension of the PMV model to non-air-conditioned buildings in warm climates, Energy Build. 34 (6) (2002) 533–536, https://doi.org/ 10.1016/S0378-7788(02)00003-8.

43–52, https://doi.org/10.1080/01457637908939548. [24] C.M.D. Moorthy, S.G. Ravikumaur, K.N. Seetharamu, FEM application in phase change exchangers, Heat Mass Transf. 26 (3) (1991) 137–140, https://doi.org/10. 1007/BF01590112. [25] B.P. Rasmussen, A.G. Alleyne, Dynamic modeling and advanced control of air conditioning and refrigeration systems, Air Conditioning and Refrigeration Center, College of Engineering UIUC, Urbana-Champaign, 2006. [26] J.H. Wu, F. Jiang, H. Song, C.P. Liu, B.W. Lu, Analysis and validation of transient thermal model for automobile cabin, Appl. Therm. Eng. 122 (7) (2017) 91–102, https://doi.org/10.1016/j.applthermaleng.2017.03.084. [27] A. Alahmer, M.A. Omar, A. Mayyas, et al., Effect of relative humidity and temperature control on in-cabin thermal comfort state: Thermodynamic and psychometric analyses, Appl. Therm. Eng. 31 (14) (2015) 2636–2644. [28] M. Simion, L. Socaciu, P. Unguresan, Factors which influence the thermal comfort

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