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Article

Intelligent Control System for Multivariable Regulation in Aquaculture: Application to Mugil incilis

by
Andrés Valle González
,
Carlos Robles-Algarín
* and
Adriana Rodríguez Forero
*
Facultad de Ingeniería, Universidad del Magdalena, Santa Marta 470003, Colombia
*
Authors to whom correspondence should be addressed.
Technologies 2025, 13(7), 279; https://doi.org/10.3390/technologies13070279
Submission received: 5 June 2025 / Revised: 27 June 2025 / Accepted: 30 June 2025 / Published: 2 July 2025

Abstract

Aquaculture has emerged as a sustainable alternative to meet the growing demand for aquatic products while preserving natural ecosystems. This study presents the design, simulation, and experimental validation of an intelligent multivariable control system for aquaculture tanks aimed at cultivating Mugil incilis, a native species of the Colombian Caribbean. The system integrates three control strategies: a classical Proportional-Integral-Derivative (PID) controller, a fuzzy logic–based PID controller, and a neural network predictive controller. All strategies were evaluated in simulation using a third-order transfer function model identified from real pond data. The fuzzy PID controller reduced the mean squared error (MSE) by 66.5% compared to the classical PID and showed faster settling times and lower overshoot. The neural predictive controller, although anticipatory, exhibited high computational cost and instability. Only the fuzzy PID controller was implemented and validated experimentally, demonstrating robust, accurate, and stable regulation of potential hydrogen (pH), dissolved oxygen, and salinity under dynamic environmental conditions. The system operated in real time on embedded hardware powered by a solar kit, confirming its suitability for rural or off-grid aquaculture contexts. This approach provides a viable and scalable solution for advancing intelligent, sustainable aquaculture practices, particularly for sensitive native species in tropical regions.

Graphical Abstract

1. Introduction

Intelligent aquaculture has emerged as a key technological strategy to ensure food security and address the challenges posed by the degradation of aquatic ecosystems. The increasing pressure on natural resources has led to the development of sustainable aquaculture systems, supported by digital and automated solutions that optimize production processes without compromising environmental health. In this context, maintaining the stability and accuracy of critical parameters, such as temperature, dissolved oxygen (DO), hydrogen potential (pH), and salinity, is essential for the success of cultivation practices [1,2]. However, these variables exhibit nonlinear behavior and are highly sensitive to external disturbances, which limits the effectiveness of conventional control strategies such as the classical Proportional-Integral-Derivative (PID) controller [3,4].
The rapid industrialization and the significant role of aquaculture in Colombia—growing from approximately 1000 tons in the 1960s to around 180,000 tons annually today—have driven research aimed at accelerating the technological transformation of the sector. Despite this growth, most farming operations in the country still rely on traditional, labor-intensive practices, with limited technological integration and a high level of operational risk [5,6]. Poor water quality remains one of the main factors affecting fish health and farm profitability, as it leads to oxygen depletion, stress, disease, and, in extreme cases, mass mortality. In most cases, control is still conducted manually during working hours, using handheld measurement devices to monitor temperature, salinity, pH, and dissolved oxygen. This limits the response time to environmental fluctuations, undermining both productivity and sustainability.
Recent advances in artificial intelligence (AI) and embedded systems offer promising solutions. Automated monitoring systems can continuously analyze environmental variables, transmit data to the cloud, and support decision-making by generating real-time corrective actions. These systems help reduce water and energy consumption, improve feed efficiency, and create more stable and predictable environments for aquatic species [7,8].
In response to these limitations, multiple advanced technological approaches have emerged, integrating artificial intelligence techniques, embedded electronics, and sensor networks. Zhang et al. [9] proposed an optimized fuzzy PID controller to regulate oxygen supply in live fish transportation systems, achieving substantial improvements over classical methods. In the context of urban aquaponics, Kok et al. [10] developed an automated system based on PID controllers, although limited to a small number of variables. Wibisono and Jayadi [11] incorporated IoT (Internet of Things) sensors with fuzzy logic to control temperature, pH, and dissolved oxygen in catfish farming systems, though with a more reactive than proactive approach. In more recent studies, Qomaruddin et al. [12] developed an intelligent system for vannamei shrimp cultivation that adaptively adjusts pumps and aerators, while Abdullah et al. [13] combined neural networks and fuzzy logic to predict water quality parameters with data transmission via GPRS. These proposals highlight the potential of distributed intelligent systems to transform aquaculture management, particularly when focused on continuous monitoring, autonomous decision-making, and real-time adaptation.
Relevant advances have also been reported in the incorporation of predictive models and intelligent algorithms for water quality management. Trach et al. [14] employed artificial neural networks combined with fuzzy logic to predict ammonium toxicity in aquatic environments, enabling the identification of risk conditions before they affected the species. Aldair [15] explored predictive controllers based on neural networks in interconnected systems, highlighting their anticipatory capabilities under complex dynamics, although limited to simulated environments. Ahmed et al. [16] proposed a hybrid approach that combines machine learning with fuzzy inference systems to model and predict water quality parameters, demonstrating the value of integrated solutions in highly uncertain settings. In line with these efforts, Nagothu et al. [17] demonstrated an autonomous aquaculture maintenance system based on fuzzy logic and IoT, capable of maintaining optimal levels of dissolved oxygen and salinity in experimental trials. Zhou et al. [18] introduced an enhanced PID controller using radial basis function (RBF) neural networks and evolutionary algorithms, which successfully eliminated overshoot and improved adaptability to nonlinearities typical of recirculating aquaculture systems. Finally, Shin [19] developed a mobile remote-control application for smart fish farms using MQTT communication and a multi-node architecture, highlighting the growing interest in mobile, integrated, and scalable solutions within the context of digital aquaculture.
Nevertheless, significant challenges remain to be addressed. Many of the reviewed studies focus on the control of a single critical variable, without considering the need for simultaneous multivariable regulation, which is essential for maintaining ecosystem stability in intensive cultivation systems. Moreover, most of these investigations are limited to simulated environments or commonly studied species, overlooking regionally important species such as Mugil incilis, whose physiology is highly sensitive to environmental fluctuations [20,21]. This native Caribbean species holds substantial ecological and nutritional value in food security but faces cultivation constraints due to the lack of adapted technological solutions, among other factors. In addition, few developments have been experimentally validated under real-world conditions, where uncontrolled external disturbances present a considerable challenge for any automation strategy.
The main contribution of this study is the design and real-world validation of a multivariable intelligent control system that simultaneously regulates pH, dissolved oxygen, and salinity under dynamic aquaculture conditions. Implemented on a low-cost Raspberry Pi platform and tested with Mugil incilis—a native and environmentally sensitive species—the system integrates industrial-grade sensors and actuators in a compact, autonomous architecture. Unlike prior studies that focus on simulations or single-variable control, this prototype offers a computationally efficient, adaptive, and field-validated solution aligned with the sustainability and digital transformation goals of tropical aquaculture systems.
The intelligent nature of the proposed system is reflected in its ability to autonomously adapt control gains using fuzzy logic, enabling real-time responses to environmental variations. Additionally, neural predictive capabilities were explored to enhance anticipatory behavior. These features go beyond fixed-rule automation, providing the system with learning-inspired mechanisms for decision-making under uncertainty.
Given these characteristics, the fuzzy PID controller was chosen over classical and neural-based alternatives due to its superior balance between accuracy, adaptability, and computational feasibility. Unlike the classical PID, the fuzzy-enhanced model dynamically adjusts its gains to better handle nonlinear and time-varying conditions, while avoiding the high processing demands of neural predictive controllers. This makes it particularly suitable for embedded implementation in aquaculture environments characterized by limited hardware resources and high environmental variability.
This paper is structured as follows: Section 2 describes the identification of the system’s dynamic model based on experimental data, followed by the design of three control strategies—classical PID, fuzzy PID, and a neural predictive controller based on an RBF neural network. This section also includes the definition of performance metrics, the results of the comparative simulations, and a detailed description of the implemented experimental architecture, including sensors, embedded units, and actuators. Section 3 presents the results obtained during the experimental validation of the fuzzy PID controller in a real-world environment. Section 4 discusses the observed performance, comparing it with previous studies and the simulation outcomes. Finally, Section 5 presents the study’s conclusions and outlines future research directions aimed at strengthening intelligent aquaculture in tropical contexts.

2. Materials and Methods

2.1. System Identification

The dynamic modeling of the aquaculture system was a fundamental step in the design of the control strategies. In this work, an empirical approach was adopted based on experimental data collected directly from a Mugil incilis culture tank located at the facilities of the GIDTA Research Group (Research and Technological Development Group in Aquaculture) of the University of Magdalena. A total of 500 records per variable were obtained using a time-window sampling strategy distributed over two weeks of operation, with a sampling frequency of 5 min. This method allowed the capture of daily variability in pond conditions. Data acquisition was performed using an integrated system with industrial-grade sensors for pH, dissolved oxygen (DO), electrical conductivity (EC), and temperature, all connected to an embedded platform.
After organizing and cleaning the dataset, an exploratory analysis was conducted using box-and-whisker plots for the pH, temperature, dissolved oxygen (DO), and electrical conductivity (EC) variables (Figure 1). These plots enabled visualization of the dispersion, symmetry, and presence of outliers in each case. The variables pH, temperature, and DO exhibited distributions that were relatively concentrated around their medians, suggesting stable behavior during the sampling period. In contrast, the electrical conductivity variable showed greater dispersion, with a wide interquartile range and the presence of extreme values, indicating higher variability and possible environmental disturbances. These differences in scale and behavior motivated the application of min–max normalization in order to ensure comparability between variables and to avoid bias during the dynamic model identification stage. Normalization was performed using Equation (1):
x n o r m = x x m i n x m a x x m i n
where x represents the original value, and xmin and xmax are the minimum and maximum observed values for the variable, respectively.
Subsequently, Q–Q (quantile–quantile) plots were used as a preliminary validation tool to verify whether the monitored variables exhibited approximately normal distributions. This condition is favorable for applying system identification techniques based on linear models, such as transfer function fitting using least squares. Figure 2 shows that the empirical quantiles of the pH, DO, and EC variables align reasonably well with the theoretical quantiles of a normal distribution. Although the temperature variable displays slight deviation at the extremes, it was not considered sufficient to compromise the validity of the model. Therefore, the identification process proceeded without applying additional statistical transformations to the dataset.
Once the data were preprocessed, a correlation matrix was constructed (Figure 3) to analyze the linear relationships among the monitored variables. This matrix revealed strong correlations between dissolved oxygen and both pH (r = 0.71) and electrical conductivity (r = 0.76), which supported their selection as input variables for the dynamic model. Consequently, a structure was proposed with two inputs (pH and conductivity) and one output (DO), in order to represent the combined influence of these parameters on a key variable for fish health.
Temperature was monitored due to its biological relevance for the species Mugil incilis, but it was not included in the system identification process or in the controller design. This decision was supported by its low correlation with the other system variables (correlation coefficients below r = 0.4), suggesting a weaker influence on the dynamics of dissolved oxygen within the evaluated operating range. Moreover, thermal regulation was not within the scope of this study, so the modeling and control efforts focused on the variables with the greatest dynamic impact on the system.
Once the variables were defined, the identification process of the pond model was carried out. In many studies of aquatic systems, first- or second-order models are commonly used due to their simplicity and ease of implementation. However, in this case, the identification process conducted using MATLAB’s System Identification Toolbox (version R2024b), based on the constructed dataset, produced two transfer functions: a second-order model for the pH/DO relationship and a third-order model for the conductivity/DO relationship.
A comparative analysis of both transfer functions revealed that their step responses exhibited similar dynamic behaviors, with moderate differences in settling time and overshoot. The correlation coefficient between the two outputs (R2 = 0.82) indicated a strong linear relationship, suggesting that both models follow similar trends in response to the same input. Nevertheless, the transfer function based on conductivity and dissolved oxygen was selected, as it not only demonstrated solid dynamic performance but also presented a third-order structure. This higher level of complexity allows for a more accurate representation of the system’s internal dynamics, including delays and interactions between variables, making it more suitable for the design and evaluation of advanced control strategies such as those proposed in this work. Moreover, this model better reflects the multivariable nature of the physical system and the gas exchange and chemical response processes occurring in the aquatic environment.
The final model features three zeros and three poles and was obtained after five iterations, converging toward a local minimum. The quality of the fit was evaluated using a mean squared error (MSE) of 0.01949 and a final prediction error (FPE) of 0.02029, both of which support the validity of the model (see Equation (2)).
5.436 s 3 + 0.8484 s 2 + 0.0327 s + 0.0003434 s 3 + 0.08078 s 2 + 0.02119 s + 0.0002891
The transfer function in Equation (2) has three real zeros located at z1 = −0.1041, z2 = −0.0342, and z3 = −0.0177, and three poles at p1 = −0.0332 + 0.1383j, p2 = −0.0332−0.1383j, and p3 = −0.0143. All poles are located in the left-half plane, confirming the internal stability of the system. Additionally, all zeros are also located in the left-half plane, which ensures that the system is minimum phase (i.e., inversely stable). These properties are favorable for control applications as they guarantee well-behaved responses in both direct and inverse configurations.
In summary, the third-order transfer function presented in Equation (2) was obtained through a structured system identification process. Experimental input–output data were collected under real aquaculture operating conditions, and various model structures—first to fourth order—were evaluated using MATLAB’s System Identification Toolbox. The parameters were estimated by minimizing the prediction error through least-squares fitting. The selected model provided the best trade-off between complexity and accuracy, achieving a normalized root mean square error (NRMSE) of 92.3% and capturing the dominant dynamics of the system with stable and physically consistent coefficients. These features validated its suitability for control strategy design.

2.2. Controller Design

Based on the identified dynamic model of the aquaculture system, three control strategies were designed and implemented to evaluate their comparative performance in regulating critical environmental variables: dissolved oxygen, pH, and electrical conductivity. Each controller was initially tuned in a simulated environment, after which the best-performing strategy was selected for real-world implementation. The selected strategies were a classical PID controller, a self-tuning fuzzy PID controller, and a predictive controller based on a radial basis function (RBF) neural network.

2.2.1. PID Controller

The classical PID controller was included as a baseline reference due to its widespread adoption in industrial systems [22]. Its control law is given by Equation (3),
u t = K p e t + K i 0 t e t d t + K d d e ( t ) d t
where:
  • e(t) is the error between the reference value and the measured variable.
  • u(t) is the control signal.
  • Kp, Ki, and Kd are the proportional, integral, and derivative gains, respectively.
The parameters of the classical PID controller were tuned using MATLAB’s PID Tuner tool (version R2024b), which automatically adjusts the gains to achieve a balance between speed, stability, and robustness through frequency-domain optimization. This approach enables efficient configurations without relying on traditional empirical methods.

2.2.2. Fuzzy PID Controller

The fuzzy PID controller was designed as an adaptive strategy to address the nonlinear nature of the aquaculture system [23]. This approach integrates a classical PID controller with a Mamdani-type fuzzy inference system that adjusts the Kp, Ki, and Kd gains in real time based on the system’s dynamic behavior. The input variables were defined as the error e(t) and the error change Δe(t), both modeled using seven triangular membership functions associated with the following linguistic labels: NG (Negative Large), NM (Negative Medium), NP (Negative Small), Z (Zero), PP (Positive Small), PM (Positive Medium), and PG (Positive Large), as shown in Figure 4. The defined universes of discourse were e(t) ∈ [−100, 100], Δe(t) ∈ [−4, 4], and output u ∈ [−3, 3].
Although the plant model is fixed and its dynamics remain unchanged, the fuzzy characterization was applied over the system’s closed-loop response. In particular, the fuzzy inference system interprets the real-time error and its rate of change, adjusting the PID gains accordingly. This means that the linguistic labels (NG, NM, NP, Z, PP, PM, PG) do not characterize the open-loop plant directly, but rather the closed-loop behavior resulting from the interaction between the controller and the process.
Recent advances in fuzzy control systems have demonstrated the versatility of these methods across various nonlinear domains. For instance, Chang et al. [24] developed a quantized fuzzy feedback controller for lateral dynamics in electric vehicles, showing that fuzzy logic can enhance control precision in highly dynamic, real-time environments with quantization constraints. Similarly, Nagy et al. [25] proposed a Takagi–Sugeno (TS) fuzzy observer-based controller for discrete-time nonlinear systems, integrating fuzzy inference with observer design to improve robustness against disturbances and unmodeled dynamics. While these approaches provide valuable insights into the theoretical and practical advantages of fuzzy control, they typically involve complex tuning and higher computational demands. In contrast, the fuzzy PID controller implemented in this study was designed to offer a balance between adaptability and simplicity, enabling real-time control in resource-constrained embedded systems such as those found in aquaculture applications.
The inference system generates a ΔK value that is applied directly to the PID gains. In this case, a single fuzzy rule matrix was used, and its output was applied in parallel to Kp, Ki, and Kd, which reduces system complexity and facilitates embedded implementation. The knowledge base of the system was expressed in a 7 × 7 rule matrix, based on the combination of linguistic labels for e(t) and Δe(t). This matrix, shared across all three PID parameters, is presented in Table 1.
Figure 5 shows the functional scheme implemented in Simulink. The fuzzy system generates the adjustment signal ΔK, which is directly applied to the blocks representing the PID gains. In parallel, a classical PID controller using the same transfer function was integrated to compare performance under identical conditions. This architecture enabled a controlled evaluation of the advantages of the fuzzy approach over the traditional one.

2.2.3. RBF Neural Controller

Aquatic systems exhibit highly nonlinear behavior, with multiple interdependent variables that respond to internal and environmental factors over varying time scales. To address this complexity, a predictive controller based on a radial basis function (RBF) neural network was implemented, aiming to anticipate the future behavior of the system and proactively adjust the control actions.
The RBF neural network used in this study is based on the architecture proposed by Moody and Darken, consisting of three layers: an input layer, a hidden layer with Gaussian activation functions, and a linear output layer. Mathematically, the model output is represented as [26],
y ^ k = i = 1 N w i ϕ i x + b
where:
  • y ^ k is the estimated output of the network.
  • wi are the connection weights.
  • ϕi(x) is the Gaussian radial basis function.
  • b is a bias term, and N is the number of neurons in the hidden layer.
Each ϕi(x) is defined as follows:
ϕ i x = e x c i 2 2 σ i 2
where ci is the center of the i-th neuron and σi is its width. This structure enables the modeling of complex nonlinear relationships and is particularly suitable for systems with dynamic variations and time delays. Prior to training, data preprocessing included min–max normalization, correlation analysis to select the most relevant variables (pH, DO, salinity, and temperature), and splitting of the dataset into training (70%), validation (15%), and test (15%) subsets. These steps allowed the network to be trained using representative samples of the pond’s behavior, avoiding overfitting and enhancing generalization capability.
The RBF neural network was trained using simulation data generated from the system’s dynamic model. Figure 6 shows the functional scheme of the predictive neural controller implemented in Simulink. The central block represents a predictive control system that uses an internal neural network model to anticipate the system’s future response to a given reference. The optimization component compares the prediction to the reference and generates the required control signal.
The controller operates on the identified dynamic transfer function of the system. The output signal is compared against the simulated real plant, and the resulting error is amplified by a gain block to generate the final correction. This architecture allows for anticipatory behavior, adjusting the system before a significant error occurs.

2.3. Performance Metrics for Control System Evaluation

To assess the performance of the designed controllers, three widely used quantitative metrics in the analysis of dynamic systems were selected: settling time (Ts), percentage overshoot (%OS), and mean squared error (MSE) [27,28]. These metrics allow the evaluation of key aspects such as system speed, stability, and accuracy in response to a reference signal or disturbance.
The settling time is defined as the time required for the system response to remain within a specified tolerance band around the desired final value, without exceeding it again (see Equation (6)).
T s = t i m e   a t   w h i c h   y ( t ) y r e f < ε   f o r   a l l   t > T s
where:
  • y(t): system output.
  • yref: reference value.
  • ε: 2% tolerance margin.
The overshoot measures how much the output exceeds the reference value during the transient phase, expressed as a percentage of the reference. This indicator allows for evaluation of the aggressiveness of the controller in response to changes,
% O S = y m a x y r e f y r e f × 100
where:
  • ymax: maximum value reached by the response.
  • yref: reference value.
The mean squared error (MSE) quantifies the average squared difference between the system output and the reference over time, penalizing larger deviations. It is useful for comparing the overall accuracy between strategies,
M S E = 1 N i = 1 N y t i y r e f t i 2
where:
  • N: total number of samples.
  • ti: the i-th sampling instant.
  • y(ti): system output at ti.
  • yref(ti): reference value at ti.
As an indicator of relative computational load during simulation, the average execution time per step was included, as reported by MATLAB/Simulink using the Simulink Profiler tool. This value represents the time required by the system to execute a complete iteration of the control algorithm.

2.4. Comparative Analysis of Controllers and Selection for Implementation

To select the most suitable control strategy for physical implementation, a comparative evaluation was conducted in the MATLAB/Simulink simulation environment. Each controller was applied to the same identified dynamic model of the system, under identical initial conditions, and evaluated using three quantitative metrics: settling time (Ts), percentage overshoot (%OS), and mean squared error (MSE). In addition, the average execution time per simulation step was measured as an indicator of the relative computational load of each approach, using the Simulink Profiler tool.
As shown in Figure 7, the fuzzy PID controller exhibited the most well-damped and precise transient response, achieving fast convergence to the setpoint without significant overshoot. Although all control strategies ensured closed-loop stability, the fuzzy controller provided superior relative stability, understood as reduced oscillations and faster error attenuation. In contrast, the classical PID controller displayed sluggish behavior and a prolonged settling time, while the RBF neural controller—despite its anticipatory capabilities—produced excessive overshoot and sustained oscillations before reaching steady-state. These results further support the selection of the fuzzy controller for real-world implementation.
To ensure a fair comparison, each controller was tested using its best-performing configuration based on preliminary tuning trials. For the classical PID and the RBF-based neural controller, the parameters were manually adjusted through iterative testing to minimize overshoot and reduce settling time. In contrast, the fuzzy controller leveraged its inherent adaptive mechanism to modulate the PID gains in real time, resulting in a more flexible response. While the fuzzy approach offers more degrees of freedom due to its rule-based structure, care was taken to select optimized configurations for all controllers under the same plant conditions.
In addition, the data presented in Table 2 support the observations from the comparative plot of the three controllers. The RBF neural controller exhibited the greatest anticipatory capability but delivered the poorest performance in terms of accumulated error (MSE = 0.645), along with a high overshoot (30%) and the longest settling time (180 s). Its high computational load (1280 ms per cycle) rendered it unsuitable for execution on the selected embedded platform (Raspberry Pi 4), compromising real-time stability.
The classical PID controller, although efficient in terms of resource usage (7 ms per cycle), exhibited a slow response (120 s) and a moderate MSE (0.543), highlighting its limited ability to adapt to disturbances.
In contrast, the fuzzy PID controller achieved the best balance between performance, robustness, and computational feasibility. It yielded the lowest MSE (0.182), a fast settling time (49 s), and a reduced overshoot (9%). Its architecture, based on fuzzy logic, enabled stable and efficient implementation—even with a moderate processing load—establishing it as the most suitable option for multivariable control in aquaculture within the context of this study.

2.5. Experimental Implementation of the Intelligent Control System

The fuzzy PID controller was experimentally implemented in a fishpond containing Mugil incilis specimens, integrating industrial sensors, embedded processing, and a remote monitoring interface. Figure 8 shows the general hardware layout used, designed with a focus on modularity, robustness, and autonomous operation in aquaculture environments. The system is composed of the following:
  • An ESP-32 data acquisition module, featuring Wi-Fi connectivity to transmit measurements to the central processing unit.
  • A Raspberry Pi 4, which serves as the main control and processing unit. It is equipped with a Whitebox T3 shield, enabling efficient sensor connection via the I2C protocol.
  • A set of Atlas Scientific sensors to measure pH, dissolved oxygen, electrical conductivity, and temperature, all equipped with BNC connectors for enhanced robustness in humid environments. Salinity was estimated indirectly by electrical conductivity measurements. This relationship is considered valid in brackish water aquaculture applications, where electrical conductivity is a commonly used proxy variable to represent variations in salinity concentration.
  • An Atlas Scientific peristaltic pump responsible for adjusting pH and salinity levels in response to the control signal generated by the fuzzy system.
  • An autonomous solar kit, composed of a 300 W panel, a 12 V/55 Ah battery, and a 500 W inverter, ensuring continuous operation even in remote areas without access to the electrical grid.
Figure 8 also illustrates the functional architecture of the intelligent control system, highlighting the flow of data and control signals across all components. The pH, dissolved oxygen, conductivity, and temperature sensors are connected to the Raspberry Pi through the Whitebox T3 shield using BNC and I2C interfaces. The embedded control algorithm, implemented in Python (version 3.11) on the Raspberry Pi 4 (Raspberry Pi Foundation, Cambridge, United Kingdom), processes these inputs in real time and adjusts the actuation commands sent to the peristaltic pump. An ESP32 module is used to monitor alarm conditions and transmit alerts to a central server via Wi-Fi, enabling remote supervision. The system operates independently thanks to a solar-based power subsystem. This layered configuration ensures robust, real-time, and autonomous control of critical environmental parameters in the aquaculture pond.
To facilitate system replication and provide a consolidated technical overview, Table 3 summarizes the main characteristics of the components used, including sensors, actuators, and processing elements.
The computing module was integrated into a custom-designed 3D-printed chassis, specifically made to house the Raspberry Pi, the shield, and peripheral connections, as illustrated in Figure 9. This semi-sealed design protects the electronics against splashes and environmental moisture, ensuring durability in outdoor conditions. Additionally, to guarantee uninterrupted system operation even during power outages or in remote environments, an autonomous solar power solution was incorporated. This subsystem supplies energy to the Raspberry Pi, sensors, and actuators through a charge regulator, a deep-cycle battery, and a voltage inverter.
The system was programmed in Python on the Raspberry Pi using the scikit-fuzzy library, where the rules, membership functions, and universes of discourse were defined for the three controlled variables: pH, dissolved oxygen, and salinity. Data acquisition was performed via the AtlasI2C library, enabling efficient communication with the Atlas Scientific sensors over the I2C bus.
Every minute, the system executes a monitoring-control cycle that performs the following functions:
  • Reads the values from all sensors.
  • Calculates the control signal through the fuzzy system.
  • Adjusts the speed of the peristaltic pump according to the control output.
This architecture allows for continuous maintenance of the physicochemical parameters within their optimal ranges. Prior to field validation, a rigorous calibration process was carried out for all sensors using standard solutions provided by the manufacturer. Sensors were rinsed, immersed in reference solutions, and adjusted using the recommended software. Once their accuracy was verified, a functional test was performed with pond samples, and the system responses were recorded.
System initialization was completed by installing the module in a protected environment, connecting sensors and actuators according to the physical layout (see Figure 10), and running the automatic control cycle.

2.6. Experimental Scheme for System Validation

The experimental validation of the control system was carried out in a cultivation tank inhabited by Mugil incilis specimens, where the embedded system equipped with the previously selected fuzzy PID controller was installed. The sensors were calibrated following established protocols using standard solutions, and initial reference values were set for each variable: pH 7.5, dissolved oxygen 8.0 mg/L, and salinity 22%. The first 110 recorded data points corresponded to a system stabilization stage under initial conditions.
Starting from data point 111, abrupt changes were introduced in the setpoints to evaluate the controller’s adaptation capability:
  • pH increased to 8.3.
  • DO reduced to 6.6 mg/L.
  • Salinity increased to 31%.
The system executed a monitoring and control cycle every 60 s, and data were logged throughout the test for subsequent performance evaluation using settling time and mean squared error as reference metrics.

3. Experimental Results

3.1. Controller Performance in Real Conditions

Figure 11 shows the evolution of pH after the setpoint change from 7.5 to 8.3. The system exhibited an overdamped response, reaching the new reference without overshoot or oscillation, and stabilizing in less than 25 s. Figure 12 presents the behavior of dissolved oxygen following the change to 6.6 mg/L. Again, the system responded smoothly with a gradual adjustment, indicating precise gain adaptation by the fuzzy logic controller. Figure 13 displays the response of electrical conductivity (used as a proxy for salinity), which adjusted from 22% to 31%. While the response was stable and without oscillations, it showed slightly longer convergence time, likely due to higher variability in ionic content and environmental disturbances.
These results confirm the fuzzy PID controller’s ability to regulate multiple nonlinear variables simultaneously, maintaining system stability and control precision under real operating conditions. The recorded behavior confirms that the fuzzy PID controller successfully maintained the water conditions within the target values in an adequate time frame, without overshoot or instability. Its adaptation capability to setpoint changes was consistent, even under real operating conditions with live fish in the pond and the presence of uncontrolled environmental disturbances. These experimental results validate the feasibility of the proposed approach and reinforce its applicability for multivariable control systems in intelligent aquaculture, especially in contexts with technical constraints and high natural variability.

3.2. Overall System Performance

To complement the visual analysis presented in the previous subsection, two key performance metrics were calculated to quantitatively assess the controller’s behavior: the mean squared error (MSE) and the 2% settling time (Ts) for each regulated variable. These indicators allow for direct comparison of control accuracy and response speed.
Table 4 summarizes the performance results. The fuzzy PID controller maintained low errors and fast settling times across all variables. The pH variable showed the best performance, with the lowest MSE (0.105) and the fastest settling time (20 s), consistent with its overdamped and smooth response. Dissolved oxygen also performed well, with a moderate MSE (0.258) and stabilization within 25 s. Conductivity presented the highest MSE (0.364) and the longest settling time (28 s), likely due to greater susceptibility to environmental variability, including ionic fluctuations and water agitation.
In all cases, the controller produced stable and controlled responses, free of overshoot and oscillations. These results reaffirm the robustness, adaptability, and computational efficiency of the proposed fuzzy PID strategy, supporting its suitability for real-time embedded applications in dynamic aquaculture environments.

3.3. Temperature Monitoring During Experimental Validation

In addition to the active regulation of pH, dissolved oxygen, and salinity, continuous monitoring of water temperature was carried out due to its biological relevance for Mugil incilis. Although no thermal control strategy was implemented, the data recorded during the experiment (Figure 14) indicate that water temperature remained stable within a range of 25 °C to 29 °C, without abrupt variations. This passive thermal stability served as an important validation factor, confirming that the controller’s performance was not significantly influenced by external temperature disturbances. As such, the experimental results reflect the system’s actual behavior under naturally stable thermal conditions.

4. Discussion

The results clearly contrast the performance of the three evaluated controllers: classical PID, fuzzy logic PID, and RBF neural predictive PID. The classical PID controller, although simple to implement and with low computational load, showed limited performance against the nonlinear dynamics of the system. Its inability to adapt to disturbances or abrupt changes resulted in prolonged settling times and persistent tracking errors, with an MSE of 0.543 in simulation.
In comparison, the fuzzy PID controller achieved substantial improvement in all evaluated metrics. The fuzzy logic allowed dynamic adjustment of the PID gains according to system conditions, resulting in a faster response, lower overshoot, and higher precision. In simulation, it reduced the MSE by 66.5% compared to the classical PID and by 71.8% compared to the RBF neural controller. This superiority was also evident in the experimental validation, where the variables pH, dissolved oxygen, and conductivity stabilized in less than 30 s without significant oscillations. The experimental MSE values were low (0.105, 0.258, and 0.364), validating the robustness of the system under real conditions.
On the other hand, the predictive controller based on RBF neural networks demonstrated an interesting anticipatory capability against dynamic signals, but its behavior presented significant limitations: high overshoot, prolonged oscillations, and a settling time much longer than that of the other controllers. Additionally, its architectural complexity implied a high computational cost, measured as the average execution time per step (1280 ms), which restricts its implementation on embedded platforms like the Raspberry Pi 4. These conditions considerably limit its applicability in real-time control systems with constrained resources.
This finding is consistent with previous works by Ahmed et al. [16] and Aldair [15], who also identified that neural predictive models are effective in simulations but require higher-capacity platforms to be viable in physical implementations. Similarly, studies such as those by Wibisono and Jayadi [11], and Kok et al. [10], proposed simpler control schemes focused on a single variable or reactive logic, whereas this study achieved real-time multivariable regulation with low computational load and robust performance.
Overall, the balance between accuracy, adaptability, and efficiency achieved by the fuzzy PID controller positions it as a viable solution for embedded systems applied to aquaculture, especially in technically constrained contexts, such as those found in various areas of the Caribbean region of Colombia.
To further contextualize the contribution of this work, Table 5 presents a comparative summary of recent studies that apply intelligent control or predictive systems in aquaculture environments. While many of these approaches have successfully implemented machine learning, fuzzy logic, or hybrid optimization models, they are typically focused on isolated parameters (e.g., ammonia or temperature), simulated scenarios, or purely predictive analytics. In contrast, the system proposed in this study integrates real-time, multivariable control of pH, dissolved oxygen, and salinity, validated under real conditions with Mugil incilis. Furthermore, it emphasizes operational efficiency and environmental sustainability, with practical outcomes including reduced water use, lower labor demands, and improved decision-making capacity. This comparison underscores the scientific and applied relevance of our approach in moving from prediction to real-time intelligent regulation.
To synthesize the main findings and highlight their practical relevance, the following remarks summarize the key insights obtained from this study:
  • Robust multivariable control: The fuzzy PID controller maintained stable pH, DO, and salinity levels under dynamic conditions, confirming its effectiveness for real-time regulation in aquaculture.
  • Validation with native species: Successful tests with Mugil incilis demonstrated the system’s adaptability to environmentally sensitive species in real-world scenarios.
  • Practical and scalable solution: The low-cost, embedded implementation makes the system replicable for small- and medium-scale aquaculture in tropical regions.
  • Future potential: Incorporating predictive modules and additional water quality parameters (e.g., turbidity, ammonium) could enhance system resilience and decision-making support.

5. Conclusions

This study presented the design, simulation, and experimental validation of an intelligent control system for regulating key water quality parameters in aquaculture ponds dedicated to the cultivation of Mugil incilis. Three control strategies were compared—classical PID, fuzzy PID, and neural predictive controller—based on both simulation and real-world performance. Among them, the fuzzy PID controller demonstrated the best balance between accuracy, adaptability, and computational efficiency.
The fuzzy PID controller successfully maintained pH, dissolved oxygen, and salinity within optimal ranges, with settling times under 30 s and without overshoot or instability. Its low computational load allowed real-time operation on embedded hardware, making it well-suited for rural or off-grid aquaculture systems.
The proposed system can be replicated in other aquaculture contexts by adjusting the control rules and sensor calibration according to the species’ physiological ranges and local water characteristics. Because the architecture is modular and based on low-cost, open-source hardware, it can be adapted to other tropical or temperate environments with similar resource constraints. Additionally, the fuzzy logic framework allows for flexible tuning without requiring large datasets or complex model training.
In summary, this work demonstrates a practical and scalable solution for multivariable environmental control in aquaculture, offering a path toward more sustainable and autonomous fish farming systems. Looking ahead, this type of system could support precision aquaculture practices in remote or resource-limited areas, facilitate real-time decision-making through mobile integration, and contribute to climate-resilient fish production strategies.
Future research will focus on integrating additional sensors (e.g., ammonium, nitrites, turbidity), exploring hybrid AI approaches, and evaluating the impact of control accuracy on fish growth and health indicators. Long-term implementation studies in commercial settings will also be pursued to validate operational benefits and scalability.

Author Contributions

Conceptualization, A.R.F.; Data curation, A.V.G.; Formal analysis, C.R.-A.; Investigation, A.V.G.; Methodology, A.V.G. and C.R.-A.; Software, A.V.G.; Supervision, C.R.-A. and A.R.F.; Validation, C.R.-A. and A.R.F.; Visualization, A.V.G.; Writing—original draft, C.R.-A.; Writing—review and editing, C.R.-A. and A.R.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fondo General de Regalías of Colombia, as part of the project titled Fortalecimiento de las capacidades institucionales para la investigación del cultivo y reproducción inducida de la lisa (Mugil incilis) como una alternativa para su conservación en el Caribe colombiano—Magdalena, under code BPIN 2021000100084. Collaborating institutions in this project include the Universidad del Magdalena and the Instituto Nacional de Formación Técnica Profesional Humberto Velásquez García (INFOTEP).

Institutional Review Board Statement

Not applicable

Informed Consent Statement

Not applicable

Data Availability Statement

The original data presented in this study, corresponding to the experimental dataset used for system identification of the aquaculture plant, are openly available in https://n9.cl/u74bxl (accessed on 4 June 2025).

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
PIDProportional-Integral-Derivative
RBFRadial Basis Function
IoTInternet of Things
pHHydrogen Potential
DO
EC
Dissolved Oxygen
Electrical Conductivity
MSEMean Squared Error
I2CInter-Integrated Circuit
MQTTMessage Queuing Telemetry Transport
AIArtificial Intelligence
PWMPulse Width Modulation
ESPEspressif Systems Platform (e.g., ESP-32 microcontroller)
EZOEmbedded Zero Offset (Atlas Scientific sensor interface family)

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Figure 1. Box-and-whisker plots of the physicochemical parameters.
Figure 1. Box-and-whisker plots of the physicochemical parameters.
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Figure 2. Q–Q plots of the physicochemical parameters.
Figure 2. Q–Q plots of the physicochemical parameters.
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Figure 3. Correlation matrix of the physicochemical parameter dataset.
Figure 3. Correlation matrix of the physicochemical parameter dataset.
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Figure 4. Membership functions for the inputs and output of the fuzzy PID controller.
Figure 4. Membership functions for the inputs and output of the fuzzy PID controller.
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Figure 5. Simulink diagram of the fuzzy PID controller compared with the classical PID controller.
Figure 5. Simulink diagram of the fuzzy PID controller compared with the classical PID controller.
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Figure 6. Architecture of the RBF neural network used in the predictive controller.
Figure 6. Architecture of the RBF neural network used in the predictive controller.
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Figure 7. Step response comparison of the three controllers evaluated in simulation.
Figure 7. Step response comparison of the three controllers evaluated in simulation.
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Figure 8. General schematic of the intelligent control system implemented in the aquaculture setup.
Figure 8. General schematic of the intelligent control system implemented in the aquaculture setup.
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Figure 9. Custom 3D-printed chassis showing internal embedded circuits and protective housing.
Figure 9. Custom 3D-printed chassis showing internal embedded circuits and protective housing.
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Figure 10. Implemented system in a test fish tank, including the control unit, sensors, peristaltic pumps, and solar components (inverter, battery, and charge controller).
Figure 10. Implemented system in a test fish tank, including the control unit, sensors, peristaltic pumps, and solar components (inverter, battery, and charge controller).
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Figure 11. pH response to setpoint change during experimental validation.
Figure 11. pH response to setpoint change during experimental validation.
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Figure 12. Dissolved oxygen response to the new setpoint.
Figure 12. Dissolved oxygen response to the new setpoint.
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Figure 13. Electrical conductivity response to the new setpoint (used as a proxy for salinity).
Figure 13. Electrical conductivity response to the new setpoint (used as a proxy for salinity).
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Figure 14. Water temperature profile during the experimental validation (passive monitoring).
Figure 14. Water temperature profile during the experimental validation (passive monitoring).
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Table 1. Fuzzy rule matrix of the fuzzy PID controller.
Table 1. Fuzzy rule matrix of the fuzzy PID controller.
Δe(t)/e(t)NGNMNPZPPPMPG
NGNGNGNGNGNMNPZ
NMNGNGNGNMNPZPP
NPNGNGNMNPZPPPM
ZNGNMNPZPPPMPG
PPNMNPZPPPMPGPG
PMNPZPPPMPGPGPG
PGZPPPMPGPGPGPG
Table 2. Comparison of controller performance in simulation based on dynamic metrics and computational load.
Table 2. Comparison of controller performance in simulation based on dynamic metrics and computational load.
ControllerTs (s)%OSMSEAverage Execution Time per Step (ms)Adaptive
Classical PID120240.5437No
Fuzzy PID4990.182780Yes
RBF Neural180300.6451280Yes
Table 3. Technical specifications of the hardware implemented in the intelligent control system.
Table 3. Technical specifications of the hardware implemented in the intelligent control system.
ComponentModel/ManufacturerRangeAccuracyInterface
pH SensorAtlas Scientific EZO-pH0–14±0.002 pHI2C (with converter)
DO SensorAtlas Scientific EZO-DO0–20 mg/L±0.05 mg/LI2C
Conductivity SensorAtlas Scientific EZO-EC0–100,000 µS/cm±2%I2C
Temperature SensorDS18B20 or included in EZO−10 to 85 °C±0.5 °C1-Wire/I2C
Peristaltic PumpAtlas Scientific EZO-PMPVariable speedProportional controlPWM/digital
Data Acquisition ModuleESP-32Wi-Fi, UART
Control UnitRaspberry Pi 4GPIO, I2C, Python
Electronic InterfaceWhitebox T3 (EZO carrier)Up to 8 EZO modulesI2C
Table 4. Performance metrics of the fuzzy PID controller during experimental validation.
Table 4. Performance metrics of the fuzzy PID controller during experimental validation.
Controlled VariableMSETs (s)Observations
pH0.10520Overdamped response
Dissolved Oxygen0.25825Gradual adjustment with controlled slope and no overshoot
Conductivity0.36428Smooth transition, without delays, overshoot, or abrupt signal changes
Table 5. Comparative summary of recent intelligent aquaculture systems and their key contributions.
Table 5. Comparative summary of recent intelligent aquaculture systems and their key contributions.
ApproachKey ContributionReference
This studyReal-time multivariable control of pH, DO, and salinity using a fuzzy-enhanced PID controller. Experimental validation with Mugil incilis in a real pond. Reduces labor and water use, improves decision-making through continuous data.This work
Fuzzy neural network + genetic algorithm for DO predictionImproved accuracy and stability in dissolved oxygen forecasting within aquaponic water (including pH, conductivity, temperature variables considered).[29]
Dual-input fuzzy logic controller for ammonia nitrogen removalClosed-loop fuzzy controller on Raspberry Pi with RS485 and solenoid valves; >95% energy and water savings through real-time NH3 control.[30]
Ensemble learning model integrated with ROS (WaQuPs) for water quality predictionCombines multiple machine learning models into an ensemble optimized for accuracy in water quality prediction. Integrates with Robot Operating System (ROS) for real-time processing, applicable to aquaculture environments[31]
Decision tree regression with AdaBoost for water temperature forecastingApplies ensemble learning for accurate, automatic water temperature prediction in aquaponic systems, reducing manual monitoring needs[32]
Fuzzy logic–based water quality monitoring and maintenanceAn IoT-enabled, autonomous fuzzy logic controller maintaining key water parameters in experimental aquaculture trials; demonstrates practical precision control[17]
DE-GWO-SVR hybrid optimization for DO predictionHybrid differential evolution (DE) and gray wolf optimizer (GWO) enhanced SVR model for accurate DO prediction in perch aquaculture; robust against nonlinear and noisy data (R2 = 0.94).[33]
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MDPI and ACS Style

Valle González, A.; Robles-Algarín, C.; Rodríguez Forero, A. Intelligent Control System for Multivariable Regulation in Aquaculture: Application to Mugil incilis. Technologies 2025, 13, 279. https://doi.org/10.3390/technologies13070279

AMA Style

Valle González A, Robles-Algarín C, Rodríguez Forero A. Intelligent Control System for Multivariable Regulation in Aquaculture: Application to Mugil incilis. Technologies. 2025; 13(7):279. https://doi.org/10.3390/technologies13070279

Chicago/Turabian Style

Valle González, Andrés, Carlos Robles-Algarín, and Adriana Rodríguez Forero. 2025. "Intelligent Control System for Multivariable Regulation in Aquaculture: Application to Mugil incilis" Technologies 13, no. 7: 279. https://doi.org/10.3390/technologies13070279

APA Style

Valle González, A., Robles-Algarín, C., & Rodríguez Forero, A. (2025). Intelligent Control System for Multivariable Regulation in Aquaculture: Application to Mugil incilis. Technologies, 13(7), 279. https://doi.org/10.3390/technologies13070279

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