## Abstract

This paper describes a novel hybrid technique with fractional order PID controller (FOPID) for simultaneously controlling the humidity of indoor air temperature and the direct expansion (DX) air conditioning (A/C) system. The proposed hybrid system is a joint performance of the butterfly optimization algorithm (BOA) and adaptive network fuzzy inference system (ANFIS), hence forth it is called BOANFIS Technique (BOANFIST). The purpose of the proposed system is to disconnect the temperature and humidity control circuits. The proposed control is modeled and replicated on MATLAB platform and is assessed using existing systems. The statistical performance of the proposed and existing systems of mean, median and standard deviation is also evaluated. It reduces computational time up to 1.01 s and also reduces energy consumption to around 16.42 KWh/day. Furthermore, the simulation outcomes suggest that the proposed technique may efficiently and accurately obtain the optimal global solutions of the proposed technique compared to existing systems.

## 1 Introduction

In buildings, it is significant to control indoor humidity at a suitable level, because it directly affects building owners' thermal comfort, indoor air quality (IAQ), with operational ability to build air conditioning installations [1]. Several humidity control techniques, heat pipe technology and outside air pre-conditioning [2] have been formulated for huge central A/C systems not appropriate for DX A/C systems [3]. Despite that, a large amount of DX A/C systems are presently fitted through single speed compressor as well as fans, which rely on cycling on and off to keep only the interior temperature of the dry lamp. This outcome is uncontrolled balance indoor humidity, which leads to thermal discomfort, poor IAQ with less energy efficiency for residents [4].

The variable frequency inverters are generally enabled the distribution fan in a DX A/C system, creating a novel method to concurrently control RH and indoor air temperature using DX A/C systems [5]. Nevertheless, complex dynamic heat with mass transfer properties that occur on variable-speed DX air conditioning systems make it very hard for enlarging a control system for instantaneous control of indoor air humidity and temperature [6–8]. For instance, due to great cross-coupling among two feedback loops, which is due to the variation of the compressor that produces the temperature control, and because the variation of speed of supply fan produces a humidity control, DX air conditioning systems variable speed drives that have conventional PID feedback controller is insufficient [9–12].

Whereas the DX A/C system is an inside evaporator, heat and mass shift among air and refrigerant could be appraised using an elaborate physical model, hence it is necessary for decoupling two coupled control loops [13–20]. However, the heat and mass shift of DX evaporator affects a huge number of factors consisting of heat and fluid flow geometry, flow turbulence, and so on. [21]. If physical model is produced for DX cooling with dehumidification coil, hence, it is practically not possible to take all of these elements [22]. Based on the assumption of Lewis unit number, the mass shift coefficient is appraised as heat transfer coefficient. However, many reported studies suggest that the Lewis number deviates as being one. Furthermore, the improvement of a controller based on physical models is necessary [23–25]. To overwhelm the issues, the novel system for DX A/C system is essential. The proposed approach optimally controls air temperature as well as humidity through better accuracy and less computation time.

The rest of paper is declared as follow: Section 2 describes the literature review of the current work, Section 3 explains the system modeling and design, Section 4 clarifies proposed optimization. Section 5 describes result and discussion. Finally, section 6 finishes the manuscript.

## 2 Recent research work

Numerous investigation works can be found in the literature that relied on optimal PID controller design for DX A/C system with dissimilar systems and aspects. Some of the work is reviewed.

Xia et al. [26] have established hunting results on the poor operational safety and performance of DX A/C system; when it is variable speed (VS) operated to dissimilar sensible and latent cooling capabilities. The obtainable dynamic design was more formulated by involving equations to estimate temperature sensor dynamics and wind side motion parameters. Sholahudin et al. [27] have illustrated the determination of dynamic effectiveness for DX A/C system that was advanced by Bayesian artificial neural network (ANN). Input and output data sets were created via changing the compressor speed at different signal amplifiers by a dedicated AC simulator and containing dynamic cooling load with ambient temperature. Energy dissipation that refers to potential losses at work in system and selected as ambient temperature output variables for thermal comfort. The key specification of the ANN design, which contains the number of neurons and latency lines, were optimized to improve the prediction accuracy.

For enhancing the DX A/C system designed air flow rate of 20,000 m^{3}/h, design concept of split front evaporator by modernized suction head and suffocation on capillaries was adopted and the design explained by Tang et al. [28]. DX A/C system design was experimented and verified on a trial basis. The front split decreased the cooling pressure drop at evaporator suction head and suffocation design restricted the maximal flow rate in every branch circuit, helping to improve the cooling flow distribution of system.

Xie et al. [29] have executed the occupant behavior (OB), which was identified as an important factor influencing the energy consumption of a building's occupants. Air conditioning application and aggression simulation technique; It integrate OB design with Energy Plus (E+) modified distributed air conditioning system. Initially, we created an observation system, which utilizes motion sensors with thermostats for measuring the utilization and usefulness of air conditioning in a hotel building.

Yan et al. [30] have illustrated short to medium size buildings; DX A/C systems were highlighted applications. Multi-variable Controller (MVC) was established for DX Variable Speed (VS) air conditioning systems. Yan et al. [31] have executed the primary A/C uses offering occupants acceptable levels of interior thermal comfort and six parameters. Despite that many A/C systems only control air temperature. Any time five non-temperature parameters differ remarkably, a resident may feel hot and uncomfortable. For solving the problem, a full thermal comfort index must be utilized to regulate A/C systems; a fuzzy logic controller was obtained. However, the fuzzy logic control method was complex and then the previously installed fuzzy logic driver was interpreted for its actual use.

Chen et al. [32] have introduced the conventional on-off control single evaporator DX A/C system; it must operate under various seasonal cooling load conditions. Therefore, it would be difficult to try to maintain a different indoor temperature environment the entire time if not complex and costly ancillary activities provide different dehumidification capabilities.

### 2.1 Background of the research work

A review of the current research work displays that the operation and control of an air conditioning system is always a challenging and difficult task. A TEV features and the non-linearity of evaporator superheat. Hunting also causes a lack of safety and operational efficiency of the DX A/C system. Various approaches such as Markov Chain method, Artificial Neural Network (ANN), Monte-Carlostochastic Model and Fuzzy Logic Controller (FLC) are used in air condition system stability. The ANN approach is utilized for dynamic performance recognition in DX AC system and the drawbacks of ANN hardware are dependence, inexplicable characteristics of appropriate network structure and complexity of displaying the trouble. Therefore, the outcomes are perceived dependent on the assumption; hence it may not be extensively accepted. However, studies on the investigation of temperature sensor dynamics with air side operating features cannot be recognized. To overcome these challenges, optimal DX system control is required. A/C using advanced hybrid technology. In the literature, numerous works are presented to solve this problem and the presented papers do not provide efficient outcomes. These problems have inspired the present investigation work.

## 3 Direct expansion air conditioning (DX-A/C) system

Figure 1 illustrates the schematic diagram of the DX A/C system. It consists of two portions, i.e., DX refrigeration and air distribution subsystem. The DX refrigeration plant comprises of electronic expansion valve (EEV), changeable speed compressor, DX condenser and evaporator. The DX plant thermodynamic cycle contains the processes of isenthalpic expansion, isentropic compression, rejection and condensation of isobaric heat, and processes of evaporation and absorption of isobaric heat [33]. The evaporator DX was located in the air supply pipe to act as an air cooling coil. Moreover, EEV incorporates a pulse generator, a step motor and a throttle needle valve that is utilized for preserving the superheat degree of refrigerant in evaporator outlet. Besides, condenser cooling air is utilized by condenser air duct for conduction that carries unwanted heat as condenser to the outside of the laboratory. Cooling air temperature input into the condenser is utilized by electric heater that is controlled via solid state relay (SSR). Furthermore, the air distribution subsystem integrated an air distribution duct network by changeable speed centrifugal supply fan; returns air dampers with conditioned space [34].

### 3.1 Dynamic model of DX A/C system

Depending on energy and mass conservation, the DX A/C system dynamic model is exposed. The following assumptions are taken for the DX A/C mathematical modeling system [35].

25% fresh air is permitted to enter the system and it mixes with 75% re-circulated air in the evaporator.

Inside the heat exchangers, adequate air mixing takes places in which air is conditioned.

DX evaporator air side may be separated into two areas, i.e., dry and wet-cooling region; in region of dry-cooling, the air temperature is diminished and the dehumidification occurs mainly in the wet-cooling area.

In air ducts, the thermal losses are neglected.

Air conditioning in the room is extracted using a fan; up to 75% of air is re-circulated and remaining air is blown out of the system through a fan.

_{2}in conditioning room [37]. Sensible heat load

_{2}in the room,

DX-A/C system dynamic model is established by evaluation technique for model parameter recognition with satisfactory accuracy.

## 4 Control strategy

The FOPID controller parameter may be tuned by the BOANFIS system, which manages the indoor humidity and air temperature. The proposed control strategy schematic diagram is portrayed in Fig. 2.

Schematic diagram of control strategy

Citation: International Review of Applied Sciences and Engineering 14, 3; 10.1556/1848.2023.00524

Schematic diagram of control strategy

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Schematic diagram of control strategy

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### 4.1 Proposed BOANFIST to control indoor air temperature and humidity

The proposed hybrid system is known as the BOANFIS Technique because it combines the Butterfly Optimization Algorithm (BOA) and the ANFIS; hence it is called (BOANFIST). A butterfly can produce the fragrance by several intensities that are interrelated by their fitness [40]. While a butterfly is capable to smell the fragrance of other butterfly, it would travel on a global search. Five layers are shown on ANFIS. Every layer has certain nodes on node function; (a) Fuzzification method; (b) Fuzzy of last piece; (c) Normalization functions membership; (d) Fuzzy rules of resultant piece; (e) Network exit. For deciding the parameters of fuzzy inference system on ANFIS structure of Sugeno hybrid training algorithm is used. For creating as well as organizing the parameter units of membership functions in fuzzy inference system, the algorithm combines least squares methods as well as the BP gradient descent algorithm [41].

#### 4.1.1 Step by step method of hybrid BOANFIS method

The indoor air dry-bulb temperature

Initiation*Step 1:*

Initialize state, disturbance and control vector

Random generation*Step 2:*

Fitness Function*Step 3:*

New Position Updation with ANFIS*Step 4:*

Estimation of Membership Function*Step 5:*

Estimation of Firing Strength*Step 6:*

Normalization*Step 7:*

De-Fuzzification*Step 8:*

Tuning the FOPID Parameters*Step 9:*

In this manner, for a Sugeno fuzzy inference system, an adaptive network is nearly equal. The structure of ANFIS is shown in Fig. 3.

Termination*Step 10:*

The aforementioned process is completed when optimal results are attained using the goal function. In addition to the initialization phase, the preceding steps are repeated iteratively until a final base is met. Figure 4 depicts the established algorithm's flow chart.

Structure of the ANFIS

Citation: International Review of Applied Sciences and Engineering 14, 3; 10.1556/1848.2023.00524

Structure of the ANFIS

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Structure of the ANFIS

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Flowchart of the proposed hybrid BOANFIS algorithm

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Flowchart of the proposed hybrid BOANFIS algorithm

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Flowchart of the proposed hybrid BOANFIS algorithm

Citation: International Review of Applied Sciences and Engineering 14, 3; 10.1556/1848.2023.00524

## 5 Result and discussion

A novel BOANFIST hybrid technique is proposed in this paper for concurrent control of indoor air temperature and humidity on DXA/C system with FOPID. To achieve the desired responses, FOPID controller gain is rotated through the ANFIS approach and RDF weight matrices are predictable with the help of the BOA method. The proposed BOANFIST technique guarantees the system stability under large disturbances with the reduction of the overshoot and the computation. The BOANFIST model is performed on MATLAB/Simulink platform. The results obtained are linked with some of the current methods, such as BOA, GOA and CS. The simulation parameters are shown in Table 1.

Simulation parameters

Parameters | Ratings |

1.005 kJ kg^{−1} | |

1.2 kg/m^{2} | |

0.04 m^{3} | |

0.16 m^{3} | |

2,450 kJ kg^{−1} | |

77 m^{3} | |

1.812 × 10^{6} Pa | |

0.0934 kW m^{−2} °C^{−1} | |

0.0457 kW m^{−2} °C^{−1} | |

4.14 m^{2} | |

17.65 m^{2} | |

0.486 × 106 Pa |

To achieve the enhanced performance of the proposed hybrid system, control parameters are carefully adjusted in simulation. The adjustment parameter is set to 0.5 and sampling interval 2 s. The pressure value of the condensation and evaporation is considered as 1.812 × 106 Pa and 0.486 × 106 Pa. Furthermore, the water vaporization latent heat value is taken as 2,450 kJ/kg and the coefficient of the heat transfer value is 0.0934 kW m^{−2} °C^{−1} and 0.0457 kW m^{−2} °C^{−1}. These values provide better control performance and lead to a very easy atmosphere for indoors depending on the proposed system. It consists of numerous ways of restrictions on this DX A/C system. The matrices are taken as 23, 23, 23, 15, 12.44/1,000, 13.5/1,000 and 0.001. It is considered as 0.0415, 0.309 and 0.7. The output performance of the proposed hybrid BOANFIS method is illustrated in Fig. 4. At time 0–50 s, the system efficiency is slowly maximized. From this, the indoor humidity and air temperature can achieve their set points after working with the DX A/C system. The Bode diagram of the proposed system is displayed in Fig. 5.

Bode plot

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Bode plot

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Bode plot

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The error of the proposed BOANFIST approach is demonstrated in Fig. 6. The proposed system error is gradually decreased at 0–50 s. After 250 s, the proposed system error is preserved at constant value. The overall performance analysis of the BOANFIST technique is expressed in Fig. 7. It indicates that the output of the proposed system is enhanced via the BOANFIST approach. Furthermore, the error of the system is gradually reduced. The convergence curve for the proposed hybrid BOANFIST method is shown in Fig. 8.

Error of proposed system

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Error of proposed system

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Error of proposed system

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Performance of proposed system

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Performance of proposed system

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Performance of proposed system

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Convergence curve for proposed system

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Convergence curve for proposed system

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Convergence curve for proposed system

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The proposed system accomplishes 1.69 convergence values. Besides, the overall performance analysis of the conventional CS system is displayed in Fig. 9. Overall performance analysis of conventional BOA system is demonstrated in Fig. 10. Furthermore, overall performance analysis of conventional GOA technique is displayed in Fig. 11. Overall comparison of proposed output performance to existing system is demonstrated in Fig. 12. The proposed system enhanced the output performance in less time when contrasted to the existing BOA, CS and GOA approaches. The overall error comparison of BOANFIST system with existing system is demonstrated in Fig. 13. Figure 14 portrays convergence comparison of the BOANFIST and existing system. The convergence of BOANFIST system results 1.69. The value of the convergence curve of BOA, CS and GOA system implies 1.75, 1.85 and 1.787. Likened to existing ones, the value of the BOANFIST hybrid method is less.

Performance of CS system

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Performance of CS system

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Performance of CS system

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Performance of BOA system

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Performance of BOA system

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Performance of BOA system

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Performance analysis of GOA system

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Performance analysis of GOA system

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Performance analysis of GOA system

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Comparison of output performance with existing system

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Comparison of output performance with existing system

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Comparison of output performance with existing system

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Comparison of BOANFIST error with existing system

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Comparison of BOANFIST error with existing system

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Comparison of BOANFIST error with existing system

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Convergence comparison of BOANFIST and existing systems

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Convergence comparison of BOANFIST and existing systems

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Convergence comparison of BOANFIST and existing systems

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Comparison of BOANFIST and existing systems

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Comparison of BOANFIST and existing systems

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Comparison of BOANFIST and existing systems

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Accuracy comparison of BOANFIST with existing techniques

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Accuracy comparison of BOANFIST with existing techniques

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Accuracy comparison of BOANFIST with existing techniques

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Recall and precision comparison of BOANFIST and existing methods

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Recall and precision comparison of BOANFIST and existing methods

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Recall and precision comparison of BOANFIST and existing methods

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Specificity comparison of BOANFIST with existing methods

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Specificity comparison of BOANFIST with existing methods

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Specificity comparison of BOANFIST with existing methods

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Statistic measures of BOANFIST and existing systems

Technique | Mean | Median | S.D |

BOANFIST | 1.5420 | 1.5043 | 0.0509 |

BOA | 1.5930 | 1.5502 | 0.0588 |

GOA | 1.6467 | 1.6095 | 0.0617 |

CS | 1.7096 | 1.6628 | 0.0635 |

Error comparison of BOANFIST and existing methods for 50 number of trials

Method | RMSE | IAE | ITAE | ISE |

BOA | 0.0191 | 0.06327 | 0.001549 | 0.003392 |

GOA | 0.0211 | 0.02633 | 0.0003478 | 0.0002656 |

CS | 0.0134 | 0.03827 | 0.00129 | 0.00378 |

Proposed BOANFIST | 0.01102 | 0.0214 | 0.000278 | 0.0002156 |

Error comparison of BOANFIST and existing methods for 100 number of trials

Method | RMSE | IAE | ITAE | ISE |

BOA | 0.0234 | 0.0801 | 0.00278 | 0.00523 |

GOA | 0.0366 | 0.0462 | 0.000427 | 0.000298 |

CS | 0.0344 | 0.0428 | 0.00202 | 0.00393 |

Proposed BOANFIST | 0.01981 | 0.0231 | 0.000328 | 0.000267 |

Performance comparison of BOANFIST and existing approaches

Method | Computational time (s) | Energy consumption (kWh/day) | Precision (%) | Recall (%) | Accuracy (%) | Specificity (%) |

BOA | 1.1 | 18.05 | 98 | 97.8 | 95.37 | 99.09 |

GOA | 1.2 | 19.25 | 79 | 82 | 93.61 | 97.68 |

CS | 1.23 | 21.82 | 90 | 92 | 91.78 | 90.34 |

Proposed BOANFIST | 1.01 | 16.42 | 95 | 94 | 99.69 | 93.36 |

## 6 Conclusion

A hybrid BOANFIST system is proposed in this paper for the DX-A/C system control of the indoor air temperature and humidity with FOPID controller. The suggested hybrid technique is a joint execution of ANFIS as well as BOA. The FOPID controller parameters are adjusted via the ANFIS approach and the weight matrices were predictable by the help of BOA method. The proposed BOANFIST method guarantees the system stability under large disturbances. At this point, the proposed model was executed at MATLAB/Simulink working stage. As a result, the proposed hybrid BOANFIST system effectively controls the temperature and indoor air with minimal computation reducing the complexity of the algorithm.

## Data availability

Data sharing does not relate to this article, as no novel data was created or investigated under this study.

## Funding information

This research did not receive any particular grant from funding agencies in the public, commercial, or non-profit sectors.

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