Design and implementation of facility intelligent carbon dioxide incubator control system based on POA optimized fuzzy PID

To solve the problem that traditional carbon dioxide incubators are difficult to accurately control the required carbon dioxide environment to the detriment of experimental cultivation, and given the difficulties of time lag, nonlinearity, time-varying, and poor adaptive ability of the incubator control system, this study designs a set of intelligent carbon dioxide incubator control system suitable for laboratory cultivation. The system is based on the POA (Pelican optimization algorithm) to optimize the fuzzy PID (Proportional Integral Derivative) control to regulate the opening degree of the solenoid valve to accurately control the carbon dioxide concentration in the incubator to the set range. In this study, the simulation and comparison tests of POA-based optimized fuzzy PID control, PID control, and fuzzy PID control are carried out by MATLAB/Simulink, and it is found that the overshooting amount of the system is reduced by 11.6%, the regulating time is shortened by 69.3 s, and the steady state error is reduced by 0.1% compared with that of the traditional fuzzy PID control. It can be obtained through practical tests that the accuracy, response, and stability of the optimized fuzzy PID control of the pelican algorithm are better than those of the fuzzy PID control method, and it has better robustness. Therefore, the carbon dioxide incubator control system has high practical application value.


Introduction
A carbon dioxide incubator is a device that can be used to cultivate plant and animal cells, tissues, organs, bacteria, fungi, and other types of biological samples, and it is characterized by the ability to control the carbon dioxide concentration, humidity, temperature and other parameters in the culture environment [1] to provide the most suitable culture environment.Carbon dioxide incubators can also provide a high concentration of carbon dioxide to meet the needs of cell division, differentiation, and reproduction of various biological samples [2].Precise control of carbon dioxide concentration is critical to the accuracy and reliability of many biological experiments.Unstable or inappropriate carbon dioxide concentration may affect the growth, metabolism, signaling, and other important processes of organisms, which ultimately affects the interpretation of experimental results and the reliability of data [4].Hence, ensuring accurate control of carbon dioxide levels within the incubator is a critical concern that requires attention during experimental cultivation.
The time lag, nonlinearity, time-varying, and poor adaptive ability of the CO 2 incubator control system adversely affect the precise regulation of CO 2 in the incubator, so it is crucial to develop an efficient CO 2 control strategy for the incubator [3].Currently, carbon dioxide control is mainly controlled by PID and fuzzy PID control strategies.Wang et al. [5] explored an effective control logic system for automotive air conditioning utilizing PID control.They created a dynamic simulation model for transcritical CO 2 air conditioning to enhance the control system's stability.However, it's worth noting that their approach is currently limited to the simulation phase.Qi et al. [6] developed a costeffective and integrated greenhouse carbon dioxide measurement and control system using fuzzy PID control, which offers practicality and efficiency.Shuai and Lin [7] devised a carbon dioxide control system that combines BP neural networks with fuzzy control.This innovative approach addresses challenges seen in existing control methods, eliminating the necessity for extensive data inputs.However, it's worth noting that their approach remains in the simulation phase.
In summary, PID control and fuzzy PID control can solve the system time lag, nonlinearity, timevarying, and other issues.Carbon dioxide has a certain degree of regulation to a certain extent, but some of the research is still in the simulation stage, and the use of group intelligence algorithm optimization fuzzy PID control research is relatively small.
To enhance control precision and system adaptability, this study presents a novel intelligent carbon dioxide incubator control system.This system leverages a fuzzy PID controller optimized by the POA.The POA emulates pelican behaviors and hunting strategies, enabling continuous iterations to determine the optimal fuzzy PID parameters.This iterative process seeks the global optimal solution, ultimately facilitating precise control of carbon dioxide concentrations within the incubator, ensuring they remain within the specified range.

System architecture and design
The carbon dioxide control system for the incubator is depicted in Figure 1, comprising four distinct modules: the detection module, execution module, environment module, and control module.

Carbon dioxide concentration C modeling and analysis
The carbon dioxide concentration model adopted in this study is the classical first-order hysteresis model.This model accounts for the relationship between the inflow of carbon dioxide into the tank and the flow rate, which is determined by the opening of the solenoid valve, denoted as F(t).This opening is established according to the principles of mass conservation once the system attains equilibrium.

𝑞 𝐶 𝐹 𝑡 𝑞 𝐶 𝑞 𝐶 𝑡
V -Volume of the incubator, L; C -Carbon dioxide concentration into the incubator, %; C -Carbon dioxide concentration in the air entering the incubator, %;C t -Carbon dioxide concentration in and out of the incubator, %; q -Flow rate of carbon dioxide into the incubator, L/min; q -Flow rate of air into the incubator, L/min; q -Flow rate of carbon dioxide out of the incubator, L/min; t -Lag time, s; t-System working time, s Figure 2 illustrates the dynamic model of the carbon dioxide control system.The control process adheres to the principle of mass conservation, ensuring that the total mass of carbon dioxide entering the incubator and the mass of carbon dioxide exiting the incubator are combined.Also, it equals the total amount of carbon dioxide within the incubator.This equilibrium is achieved through the adjustment of the solenoid valve's opening degree.

C(t)
Dynamic model of the CO 2 control system.Because of the minimal concentration of carbon dioxide in the air, its influence on this control system is negligible, resulting in: Equation ( 2) is obtained by taking the Laplace transform: From Equation (3), the control response is characterized as a first-order linear system.Through the actual test,  =5%,  =3.74 L/min,  =150L,  =2.90 L/min, and  =0.57s.Bringing the measured data into Equation (3), the transfer function of the system can be derived as: .  . (4)

Pelican optimization algorithm
The Pelican Optimization Algorithm is a population-based optimization technique that draws inspiration from the hunting behaviors of pelicans.It mimics the two main phases of pelican hunting: surveying prey and exploiting it.Through iterative updates, the algorithm converges towards the best solution [7].

Initialization.
The initialization expression for the pelican population is as follows: x , -Location of the j th dimension of the i th pelican; N -Pelican populations; m -Dimension of the solution problem; rand -Random numbers in the range of [0,1]; u 、l -The solution problem's j dimension has upper and lower bounds.
In the Pelican Optimization Algorithm, the pelican population can be represented using the following matrix: -Population matrix of pelicans;  -Location of the i th pelican Within the Pelican Optimization Algorithm, the objective function of a specific problem is employed to compute the objective function value for each pelican.These individual objective function values are subsequently organized into a vector, collectively forming the objective function values for the entire population of pelicans.
F -Vector of objective functions for pelican populations; F -The objective function's value for the i th pelican.

Approaching prey (survey phase).
In the initial stage, the Pelican Optimization Algorithm focuses on locating its prey and subsequently navigating towards a predefined area.By emulating the pelican's approach to its target, this algorithm effectively scans the search space.This approach leverages the algorithm's ability to explore diverse regions within the search space.Within the POA algorithm, the prey's location is generated randomly within the search space.This randomization enhances the algorithm's exploration capacity, making it adept at solving diverse search problems.Its mathematical expression is shown below: x , -Considering the j th dimension of the i th pelican's position after the first-stage update.;I -Random integers of 1 or 2; p -The position of the j th dimension of the prey's location.;F -The objective function value of the prey.
In the POA algorithm, a new position for a pelican is chosen only when it leads to an improvement in the objective function value at that particular position.This updating mechanism, commonly known as an "effective update," guarantees that the algorithm stays within or moves towards optimal or higherperforming regions, avoiding transitions to suboptimal areas.Its mathematical expression is shown below: X --The updated position of the i th pelican.;F --The objective function value calculated using the new position of the i th pelican after the first-stage update

Horizontal flight (development phase).
During the second stage of the POA algorithm, as the pelicans reach the water's surface, they employ a strategy involving the spreading of their wings, lifting the fish, and subsequently storing the captured prey in a throat pocket.This surface-based flying tactic employed by pelicans enables them to capture more fish within a designated attack area.By modeling this specific behavioral process, the POA algorithm enhances its capacity to converge toward more favorable positions within the prey area.Consequently, this improvement bolsters the algorithm's ability to perform local search and exploit nearby regions.From a mathematical perspective, the algorithm examines positions in proximity to the pelican to facilitate convergence toward better positions.The mathematical expression is shown below: ICAMIM-2023 Journal of Physics: Conference Series 2720 (2024) 012036 x , -Considering the j th dimension of the i th pelican's position after the second-stage update; R -Random integers of 0 or 2; t -Current number of iterations; T -The highest or maximum number of iterations allowed or specified.

Fuzzy PID controller design
The fuzzy PID controller comprises two main components: the fuzzy controller [9] and the PID controller [10].The block diagram representing this configuration is depicted in Figure 3.This controller takes the system error  and the rate of change of the error  as the inputs of the controller, which are fuzzified and defuzzified to obtain the correction quantities ∆ , ∆ , and ∆ , which are used as the three parameters of the PID controller.Where  ,  , and  are the corrected proportional, integral, and differential coefficients, and  ,  , and  are the proportional, integral, and differential parameters before correction, respectively.
The fuzzy PID controller is given by The error  , the rate of change of error  and the corrections ∆ , ∆ , ∆ of the carbon dioxide concentration collected by the carbon dioxide sensor from the set value are transformed into the fuzzy linguistic variables E, ∆E/∆t, and  ,  and  through the blurring process, respectively.The quantization domains of the corresponding fuzzy linguistic variables are all defined as [-3,3], and the fuzzy subsets used in this system are defined as follows: {NB (negative big), NM (negative medium), NS (negative small), Z (zero), PS (positive small), PM (positive medium), and PB (positive big)}.Fuzzification of these subsets is accomplished through triangular membership functions, and the system utilizes the Mamdani inference mechanism with the center of gravity defuzzification.Detailed fuzzy rules can be found in Table 1.

POA-optimized fuzzy PID control
Through the POA optimization algorithm to optimize the quantization factors  ,  and the proportional factors ,  ,  of the fuzzy PID, the optimization is searched within the range of meeting the set requirements to find the optimal proportional factor and quantization factor, so that the system regulation does not only rely on the experience of the experts, but also has the ability of selfadjustment [8].The system's control characteristics and self-adaptive capabilities are enhanced through the schematic block diagram illustrated in Figure 4.

Analysis of test results
A Simulink simulation diagram has been developed within MATLAB/Simulink [11] to evaluate the control performance of the carbon dioxide incubator control system using the fuzzy PID controller optimized by the Pelican Optimization Algorithm, as illustrated in Figure 5. Furthermore, a dedicated incubator device has been designed for experimental purposes, and its physical configuration is presented in Figure 6.Carbon dioxide incubator control system test set.A comparative analysis has been conducted to assess the suitability of the Pelican algorithm for optimizing fuzzy PID control.This analysis includes a comparison with both traditional PID control and conventional fuzzy PID control through simulations.The results of these simulations are illustrated in Figure 7, and a detailed comparison is provided in Table 2.The comparison presented in Figure 7 and Table 2 demonstrates the significant precision achieved by traditional PID control, fuzzy PID control, and Pelican algorithm-optimized fuzzy PID control.Among these control methods, it is evident that the Pelican algorithm-optimized fuzzy PID control stands out with the highest level of accuracy, boasting an impressively low steady-state error of just 0.002%.The data analysis underscores the benefits of the Pelican algorithm optimized fuzzy PID control: it reduces rise time by 8.6 s and 6.2 s, curbs overshooting by 20.5% and 11.6%, and trims regulation time by 68.1 s and 69.3 s.The optimized fuzzy PID control using the Pelican algorithm has demonstrated remarkable improvements in system performance.It substantially reduces overshooting, shortens both rise and regulation times, and enhances control accuracy, achieving an impressive steady-state error of just 0.002%.This performance surpasses that of both traditional PID control and fuzzy PID control.In contrast to the other methods, the Pelican algorithm optimized fuzzy PID control considerably diminishes overshooting, trims response times, and bolsters stability and interference resistance.This marks a substantial enhancement in system performance.In conclusion, the Pelican algorithm's optimized fuzzy PID control emerges as highly suitable for the carbon dioxide concentration control system.It effectively meets performance and precision demands, ensuring accurate carbon dioxide concentration management.

Conclusion
(1) To address the challenges posed by nonlinearity, time-varying behavior, and delays in controlling carbon dioxide concentration within a carbon dioxide incubator used for experimental cultivation, we developed a mathematical model for the carbon dioxide concentration control system.Subsequently, we optimized this system using the Pelican algorithm to implement precise regulation of carbon dioxide concentration.
(2) We conducted simulations and comparisons involving the Pelican algorithm-optimized fuzzy PID control, fuzzy PID control, and PID control.The analysis outcomes demonstrate significant performance improvements achieved by the fuzzy PID control when optimized with the Pelican algorithm.When contrasted with traditional PID control, it demonstrates a 20.5% reduction in overshooting, a 68.1 s decrease in regulation time, a 0.16% improvement in steady-state error, and precise carbon dioxide concentration regulation within the target range.This not only enhances the steady-state accuracy of the system but also renders it highly suitable for incubator carbon dioxide control systems.

Figure 3 .
Figure 3. Block diagram of Fuzzy PID control principle.The equation for PID is          (11) u t -Controller output; e t -The deviation quantity is the difference between the given quantity and the output quantity; K -Constant of proportionality; T -Integration time constant, i.e., parameter K ; T -Differential time constant, i.e. parameter K The PID three-parameter correction equation is   ∆   ∆   ∆

Figure 4 .
Figure 4. Schematic structure of optimized fuzzy PID controller with pelican algorithm.To ensure response time, overshoot, and stability in the control system, the fitness function is established using the Absolute Error Integral performance index (ITAE):  |  | (14)

Figure 5 .
Figure 5.Control model diagram of carbon dioxide incubator based on POA Fuzzy PID.

Figure 6 .
Figure 6.Carbon dioxide incubator control system test set.A comparative analysis has been conducted to assess the suitability of the Pelican algorithm for optimizing fuzzy PID control.This analysis includes a comparison with both traditional PID control and conventional fuzzy PID control through simulations.The results of these simulations are illustrated in Figure7, and a detailed comparison is provided in Table2.

Figure 7 .
Figure 7.Comparison of control model simulation curve results.

Table 1 .
Table of fuzzy rules.

Table 2 .
Comparison of simulation results of control model for CO 2 concentration.