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International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(4): 440-450

Published online December 25, 2024

https://doi.org/10.5391/IJFIS.2024.24.4.440

© The Korean Institute of Intelligent Systems

A Novel Approach to Wastewater Treatment Control: A Self-Organizing Fuzzy Sliding Mode Controller

Varuna Kumara1,2 and Ezhilarasan Ganesan1

1Department of Electrical Engineering, Faculty of Engineering and Technology, JAIN (Deemed to be University), Bengaluru, India
2Department of ECE, Moodlakatte Institute of Technology, Kundapura, India

Correspondence to :
Varuna Kumara (varunakumara@mitkundapura.com)

Received: November 1, 2023; Accepted: December 11, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Wastewater treatment plays a crucial role in protecting the environment and ensuring sustainable use of resources. This paper presents a new methodology for managing wastewater treatment operations by utilizing a self-organizing fuzzy sliding-mode controller (SOFSMC) to enhance the efficiency of treatment procedures. The SOFSMC employs a control strategy that is both adaptive and robust in effectively regulating crucial parameters including dissolved oxygen levels, pH, and flow rates. This is achieved within the challenging and complex framework of wastewater treatment, which is characterized by dynamic and nonlinear dynamics. This study evaluated the performance of an SOFSMC system in relation to traditional control methods, using MATLAB Simulink, which functions as a simulation tool to facilitate meticulous analysis. The results emphasize the potential of SOFSMC as a revolutionary approach for wastewater treatment, providing valuable insights into the system’s effectiveness, flexibility, and adherence to rigorous water quality standards. This approach can improve treatment effectiveness, conserve resources, and protect the environment. This study provides a substantial advancement in the field of wastewater treatment regulation, highlighting its significance in the context of sustainable water management and environmental conservation.

Keywords: Dissolved oxygen, Effluents, Fuzzy logic, Sliding mode controller, Wastewater treatment

Wastewater treatment is of utmost importance because it serves as a crucial component in upholding public health, safeguarding the environment, and promoting sustainable utilization of water resources. This process involves the elimination of both organic and inorganic pollutants from wastewater before it is discharged into the environment or utilized for diverse applications [1]. The implementation of this procedure is crucial in ensuring the preservation of water quality, conservation of ecosystems, and mitigation of the transmission of water-borne illnesses. The origins of wastewater treatment can be traced back to ancient civilizations. Historical societies have acknowledged the importance of segregating human waste from unpolluted water sources to prevent contamination. Notably, the Indus Valley Civilization, one of the earliest urban settlements in the world, exhibited meticulously designed sewage systems dating back to approximately 2500 BCE.

Similarly, ancient Romans devised intricate aqueduct and drainage systems to effectively regulate wastewater disposal. During the mid-20th century, the increasing recognition of environmental concerns and adverse impact of pollution on ecosystems and human well-being led governments to implement rigorous policies regarding wastewater release [2]. The Clean Water Act of the United States, along with analogous legislations implemented globally, has established stringent criteria for wastewater treatment [3]. Consequently, these regulations have spurred the development of advanced technologies and widespread implementation of more comprehensive treatment methodologies.

Efficient control of wastewater treatment is of paramount importance for various crucial factors, including the protection of public health, preservation of the environment, and responsible utilization of water resources. The principal objective of wastewater treatment is the elimination of harmful pollutants from sewage and industrial effluents. Neglecting to address this issue may lead to the proliferation of waterborne illnesses, thereby presenting significant health hazards to local populations. The efficient management of wastewater discharge is crucial for mitigating ecological consequences, thereby safeguarding the well-being of aquatic organisms and preserving ecosystem equilibrium. Wastewater treatment facilities must adapt to dynamic conditions, including fluctuations in influent flow rates, pollutant loads, and meteorological patterns.

Fuzzy logic provides a method for dealing with imprecise and uncertain data and is inspired by the way humans think and make decisions [4]. This mathematical framework permits the representation of nebulous inputs, paving the way for intelligent control systems that make sound judgments in highly uncertain settings. Fuzzy logic is an effective modeling and control tool for wastewater treatment, whereby influent characteristics can vary widely and sensor data can be noisy or uncertain [5]. Because this facilitates the creation of adaptive controllers, maximizing treatment effectiveness is critical.

The ability to steer the system states along a specified sliding surface makes sliding mode control (SMC) a robust control strategy. This method is particularly effective for dealing with nonlinear and uncertain systems because it can be used to steer the system behavior towards a stable trajectory despite external disturbances and unknowns [6]. Nonlinear dynamics is common in wastewater treatment processes, and influent characteristics are known to be highly unpredictable. The ability to maintain stability and desired performance despite disturbances, makes SMC a promising option for controlling wastewater treatment [7]. Self-organizing fuzzy sliding mode controllers (SOFSMCs) are the result of merging fuzzy logic and SMC and combining the flexibility of the former with the stability of the latter. Together, these offer a promising approach for addressing the complex and ever-changing problems of wastewater treatment.

In this study, we built an SOFSMC specifically designed for wastewater treatment processes and then tested it. Our objective was to develop an adaptive control system that can optimize the treatment performance under different conditions by combining the flexibility of SMC with the precision of fuzzy logic to model the inherent uncertainties of wastewater treatment. We hope to make a significant contribution to the field of control systems in critical domains and demonstrate through extensive experimentation and analysis that this novel approach improves the efficiency, reliability, and compliance of wastewater treatment processes.

1.1 Problem Statement

Safe disposal or reuse of polluted water relies on wastewater treatment, which is crucial for ensuring people’s well-being and keeping the environment and water supplies safe and secure. However, wastewater treatment plants (WWTPs) that use conventional control methods often face difficulties in terms of efficiency, adaptability, and robustness. The dynamic and variable nature of influent wastewater can cause suboptimal performance and resource wastage in traditional treatment systems, which is particularly challenging. In addition, strict environmental regulations require highly effective pollutant removal and disinfection, which calls for cutting-edge approaches to pollution management.

This problem statement focuses on the pursuit of a novel and adaptive control strategy to improve wastewater treatment efficiency. Managing the complex and nonlinear dynamics of wastewater treatment plants can be difficult using traditional proportional-integral-derivative (PID) controllers and fixed-parameter control systems. The objective of this study was to test how well an SOFSMC can handle the complexities of wastewater treatment.

1.2 Significance of this Study

The study of controlling wastewater treatment with an SOFSMC is significant in several ways. Its primary function is to provide a novel and flexible solution to difficult problems, which have long plagued wastewater treatment systems. Research on improving the efficiency and dependability of wastewater treatment plants benefits ecosystems, curbs the spread of waterborne diseases, and reduces the pollution in receiving water bodies. Sustainable water resource management has far-reaching implications ranging from maximizing resource utilization to facilitating water reuse through cutting-edge control strategies, especially in this era of growing water scarcity. From a financial standpoint, the proposed controller can make wastewater treatment processes more economically viable by reducing energy consumption, chemical usage, and the need for operational intervention. Additionally, this study contributes to the development of control systems by providing an example of the use of SOFSMC in practical and crucial settings. This research is significant because it can improve wastewater treatment in terms of efficiency, reliability, and sustainability while addressing critical issues of water quality, resource scarcity, and environmental protection that affect people worldwide.

In this literature review, we explore the current body of knowledge and research on methods for controlling wastewater treatment with emphasis on the use of fuzzy logic and SMC strategies. The introductory section establishes the context by thoroughly analyzing previous research, emphasizing the significant findings, progress, and areas that require further investigation within the discipline. In comprehensively examining the existing body of knowledge, our objective was to establish a robust framework for comprehending the importance of SOFSMC in wastewater treatment and its potential advancements in this vital field.

It must be emphasized that the construction of WWTPs does not solve all environmental problems; instead, constant monitoring of treatment plant performance is required to ensure that the intended environmental standards are met [8]. Complex biological, chemical, and physical processes are involved in wastewater treatment, and their nonlinear and time-varying dynamics can directly affect the functioning of the treatment plant [9]. Biochemical oxygen demand (BOD), chemical oxygen demand (COD), levels of suspended and soluble solids, and the pH of the effluent from the treatment plant are all common parameters that are used to evaluate the performance of wastewater treatment plants. In [10], a learning control approach that does not rely on a specific model was proposed. This approach was developed to address the challenges posed by the nonlinearity and environmental uncertainties of WWTPs. Furthermore, a nonlinear-model-based predictive controller (NMPC) was developed to meet the effluent quality regulations of a WWTP while considering economic feasibility [11]. Additional control strategies based on data analysis have also been examined [12]. The development of control strategies based on data analysis can significantly enhance the identification of nonlinearity in WWTPs, thereby improving control performance. However, actual WWTPs frequently encounter significant disturbances linked to uncertainty, resulting in frequent and unpredictable variations in operational procedures, thereby compromising the efficacy of such data-based control methods [13]. In broad terms, the analysis of chattering is advantageous in engineering applications as it can enhance the understanding of its impact on the stability of closed-loop control systems [14].

The SMC is an advanced and diverse control methodology that operates discontinuously and modifies the components of a nonlinear system. The state-investigation control rule is an abstract concept that imposes a consistent temporal constraint. In contrast, the transition can vary from one stable configuration to the next depending on the current state within the state space [15]. In past decades, scholarly literature has primarily concentrated on the introduction of “logic decision” in sliding systems [16], and fuzzy-based sliding mode control (FSMC) has been suggested as a potential alternative for mitigating chattering. The integration of both algorithms effectively addresses two significant issues: the mitigation of chattering attenuation and minimization of rules in dynamic fuzzy controllers. This is achieved by utilizing a singular fuzzy variable known as the sliding surface function, which encompasses all aspects of the dynamic process [17]. The predominant approach involves modifying the primary parameters of the SMC, including robust gain, sliding surface gradient, and switching control, in accordance with the plant characteristics. A primary benefit of these schemes is that they do not require knowledge of the upper bounds of uncertainty and disturbance [18]. In [19], the authors presented adaptive techniques for estimating uncertainties and disturbances using variable structure controllers. However, uncertainties and disturbances inherent to dynamic systems may have bounded characteristics and are not known in terms of their specific parameters in real-world experimental scenarios.

In a previous study [20], a novel SMC technique was proposed for regulating the dissolved oxygen (DO) concentration within a WWTP-integrated nitrogen removal process. The findings from the laboratory-scale reactor experiment demonstrated that the SMC method exhibits a commendable ability to reject disturbances and delivers satisfactory performance across a broad spectrum of operating conditions. Additionally, various strategies have been implemented to mitigate uncertainties and disturbances in WWTPs [21, 22]. To develop an appropriate sliding surface design, SMC strategies require a comprehensive understanding of the nonlinearity exhibited by WWTPs. Thus, the design of SMCs for wastewater treatment plants remains a challenging task [2325]. A novel adaptive FSMC has been proposed for multivariate control in WWTP [26]. The adaptive FSMC employs a fuzzy method to approximate the unknown process, while utilizing the SMC to guarantee the asymptotic stability of the closed-loop system. Simulation results demonstrate that the proposed method exhibits effective disturbance rejection and robustness. However, despite the significant achievements of the aforementioned methods in WWTPs, chattering remains a persistent and significant challenge that has yet to be fully resolved. Based on the review and analysis presented earlier, this paper proposes the use of a SOFSMC to achieve satisfactory and consistent control performance for WWTP.

Fuzzy logic within a control system can incorporate prior knowledge to address uncertainties, absence of adequate models, and disruptions in operational processes. The occurrence of the chattering phenomenon is a significant drawback of SMCs that arises from the use of the sign function during the design process. The proposed SOFSMC approach does not require the inclusion of a robust term to account for inherent uncertainty in the mathematical model of the system. Consequently, it can mitigate the occurrence of the chattering phenomena commonly observed in traditional sliding-mode control systems. The control system model for a WWTP based on self-organizing SMC (SOSMC) is shown in Figure 1 [27]. This model served as the foundational framework for this study.

3.1 Self-organizing SMC

The use of an SOSMC in the context of WWTPs is a novel control approach that integrates the flexible nature of self-organizing systems with the resilience of sliding mode control. The use of this advanced controller holds promise for significantly improving efficiency, reliability, and adherence to regulations in WTTPS procedures. The SMC technique was applied to reduce the effects of uncertainties and nonlinearities. The task of the counting controller is to reject the disturbances caused by varying inflow loads due to environmental conditions. Self-organizing fuzzy neural network (SOFNN) is a hybrid computational model that combines the adaptability of neural networks with the linguistic rule-based approach of fuzzy logic. This sophisticated program can adjust, learn, and make choices despite ambiguities. Its ability to model and process information in a way that closely resembles human reasoning and decision-making, makes it particularly useful for tasks involving pattern recognition, classification, and control.

Notably, no standard SMC methodology has been developed for direct sliding-mode fuzzy controller design. Instead, a fuzzy controller was developed based on theoretical SMC concepts. To attain the desired objective, the fuzzy rule basis is adjusted such that s≤0. If s⋅< 0, the prior alteration of the control signal is preserved, whereas if s⋅> 0, it is reversed. Rules are considered to prevent instances of chattering. The following is an example of a second-order nonlinear dynamic system.

x¨1=f(x)+g(x)u,

where g(x) > 0 and f(x) are two scalar functions of the unknown states of the system; s = + λx, where xR2 expresses the sliding manifold. The time derivative of the sliding surface can be expressed as follows:

s˙=f(x)+g(x)u+λx˙.

When choosing a Lyapunov function, the Lyapunov theory requires that s⋅<0. Accordingly, a fuzzy rule-based system is proposed to determine changes in the control signal Δu.

The control system proposed in this study is illustrated in Figure 2. In this system, the control input u(t) is determined by the fuzzy logic controller (FLC) component, which considers the values of s and at each sampling interval. The proposed algorithm has a self-organizing mechanism that considers dynamic reactions to effectively update the knowledge base of fuzzy rules.

u¯i(k+1)=u¯i(k)+Δu¯i(k),u¯i(k)+ωeiωeciγM×[(1-ς)s(k)+ςΔs(k)]

In this context, the symbol ūi represents the variation in the control input for the i-th rule, whereas Δūi denotes the correction amount associated with each rule. Additionally, ωei and ωeci represent the excitation strength of each fuzzy rule; γ denotes the learning rate; ς signifies the weighting distribution; and M denotes the direct forward system gain, which is commonly assigned a value of 1. In this context, s(k) and Δs(k) represent the sliding surface and the change in the sliding surface over the k-step sampling period, respectively. This methodology facilitates the establishment of a control loop in the absence of initial guidelines. Once the rules are updated using a self-organizing algorithm, the output of the fuzzy inference should be defuzzified.

In an SOFSMC, fuzzy logic is used to dynamically adjust the parameters of the sliding mode controller based on the current state of the system. This allows the controller to adapt to changing conditions and maintain precise control even in the presence of uncertainties and disturbances. To address the chattering phenomenon, a self-organizing mechanism was developed to facilitate the construction of the fuzzy neural network (FNN) structure, thereby establishing a comprehensive assessment of the structural risks associated with FNN.

r(tg)=ρ1(tg)+ρ2(tg).

In this context, the variable “tg” represents the number of sampling intervals at a given time “t”; r(tg) denotes the structural risk value; ρ1(tg) represents the empirical error derived from the tracking error on the “tgth” sampling interval; and ρ2(tg) is the estimation error.

ρ1(tg)=12e(t)Te(t),ρ2(tg)=K(tg)NlogTg-2logK(tg)Tg.

Let Tg represent the ratio of Ttg to t, where T is the period of the control process, and K(tg) denotes the number of fuzzy rules during the tgth sampling interval. Structural risk is said to be low when both empirical risk and structural complexity are small. If the condition r(tg) < α1 holds, the structural risk value is acceptable.

If the self-organizing algorithm under consideration is capable of dynamically determining the appropriate size for a structure in real time, it must strike a balance between minimizing the tracking error and the complexity of the structure. The proposed SOFNN demonstrated the capability to accurately estimate and compensate for uncertain dynamics and disturbances, effectively mitigating the occurrence of chattering in SOSMC.

3.2 Dissolved Oxygen Dynamics

Monitoring and control of DO in WWTPs is of critical importance because it has a direct impact on the success of biological treatments. As aerobic conditions are required for the activity of beneficial microorganisms that break down organic pollutants, DO is a crucial indicator of microbial ecosystem health. By accurately measuring the DO levels, treatment effectiveness can be maximized, leading to the timely degradation of organic matter and decreased energy consumption. Furthermore, protecting environmental quality and meeting strict regulatory standards requires maintaining adequate DO levels to prevent the release of inadequately treated effluents into natural water bodies. DO monitoring and control are essential for reducing water pollution and protecting ecosystem health because they improve the efficiency, cost-effectiveness, and regulatory compliance of wastewater treatment. The amount of oxygen required by an organism to decompose organic matter over a given time is known as BOD. Concentrations of BOD in water that are too high (e.g., 5 mg O2/L) reduce the amount of oxygen in the water, harm ecosystem biodiversity, lower water quality, and pollute the freshwater supplies [29]. BOD measurements require the acquisition of at least two measurements. The first measurement, denoted as DO0 is performed immediately, whereas the second measurement is obtained after incubating the water samples for a few days. The purpose of the incubation is to allow for the subsequent assessment of the remaining quantity of DO, referred to as DO1.

In an activated sludge process, the DO concentration should be sufficiently high to allow microorganisms to obtain the oxygen they need to perform their metabolic processes. However, a high DO concentration can be harmful to sludge quality and lead to excessive energy consumption. A proportional controller can be used to maintain the average DO level at a steady, user-specified value. Pulse width modulation (PWM) is used to modify the aeration rate, which is also known as the oxygen transfer rate:

u(k)=Km(k)(Csat-c^(k)),

where ĉ(k) represents the estimated DO concentration as determined by the Kalman filter. The utilization of this value instead of the measured value is attributed to its reduced noise, leading to improved estimation outcomes. The aeration rate of the proportional controller is calculated as follows:

u(k)=kp·(cref-c^(k).

The reference value for the DO concentration is denoted as cref, whereas the gain of the proportional controller is represented by kp. Figure 3 presents a diagram representing the estimation of DO concentration control.

The simulation setup in MATLAB 2023a Simulink was used to construct a model of the wastewater treatment process. The objective of this study was to evaluate the effectiveness of a SOFSMC in regulating DO levels and other relevant parameters. The equations employed were described in the previous section. The experimental setup comprised a continuous-flow activated sludge reactor, in which the primary variables were configured as follows: influent DO concentration of 4.0 mg/L, biomass concentration of 2,000 mg/L, flow rate of 1,000 L/day, and desired DO setpoint of 6.0 mg/L. The Simulink environment enabled the execution of dynamic simulations, which, in turn, enabled the assessment of the controller’s efficacy in regulating DO levels within specified ranges under fluctuating influent conditions. Figure 4 shows the curves representing the simulated and estimated DO concentrations. The disparity between the set and measured values can be attributed to the use of a closed-loop configuration. This error can be reduced by increasing the value of the proportional gain or by incorporating an integrator into the system.

Two primary options exist for addressing this discrepancy and boosting the controller efficiency. One way to decrease the discrepancy between the target and actual DO levels is to increase the proportional gain of the controller, which accelerates the response to deviations from the setpoint and slows down the time required for the system to stabilize after adjustment. Second, the control loop can be further optimized by including an integrator component. Incorporating this integral action improves the capability of the system to maintain DO concentrations within a specified range over extended periods by systematically correcting long-term cumulative errors.

Monitoring and regulating the pH values and flow rates are crucial aspects of wastewater treatment and directly affect the efficacy and performance of the treatment process. An insight into how these critical parameters respond to the influence of the control system can be obtained from the time-series data that are likely to be included in the simulation result analysis chart, as shown in Figures 5 and 6.

The study results—a pH of 13.40 and a flow rate of 2.87—point to a wastewater treatment system that has been fine-tuned. Achieving a pH of 13.40 indicates that the control system manages and regulates chemical dosing effectively, which keeps the treatment process within the desired pH range. At a rate of 2.87, the influent flow into the treatment system is consistent. To avoid the overuse or underuse of the treatment infrastructure, a constant flow rate should be maintained throughout the treatment process. This indicates that the control strategy effectively performed the task, which led to increased pollutant removal efficiency, decreased operational costs, reduced environmental impact, and enhanced reliability of the treatment process. The optimization yielded the best performance of 0.031 seconds, demonstrating the superiority of the control system and treatment process. This indicates that the system is performing at its optimum level, providing excellent care at a reasonable cost, while also satisfying the most exacting regulatory requirements.

These results demonstrate the value of sophisticated control strategies for improving wastewater treatment and preserving natural resources. Figure 7 shows the observed pH curve with respect to the set value.

In Figure 8, the graph depicting pollutant removal efficiency (%) vs. time (s) provides valuable insights into the dynamic performance of a wastewater treatment process. As time progresses, the pollutant removal efficiency is tracked, showing how effectively the treatment system is cleansing the wastewater. The trends in the graph of Figure 9 reveal crucial information about the treatment’s response to varying influent conditions and its overall stability. Steep initial increases in efficiency may indicate the prompt removal of readily biodegradable pollutants, whereas plateauing or fluctuations might signify the presence of complex or slowly degradable contaminants. The speed with which a controller can respond to deviations from the desired setpoint is a crucial parameter in the dynamics of control systems.

In the graph of response times of Figure 10, the graph saturates once the time reaches 1.85 seconds, indicating that the controller has reached its maximum possible response speed. At this point, the controller quickly responds to disturbances or changes in the setpoint, reducing the overshoot and deviation of the controlled variable while stabilizing it in record time. Saturation is reached in 1.85 seconds, demonstrating the controller’s rapid and effective maintenance of the desired process conditions, which is an essential feature in many control applications.

4.1 Comparative Analysis

An examination of the average control accuracy between the SOFSMC and PID controllers offers significant insights into the effectiveness of these control strategies within the WWTP framework. A study on SOFSMC exhibited a mean control accuracy of 0.23. This value signifies that, on average, the controller effectively regulates crucial parameters (such as DO, pH, and flow rate) within a deviation of 0.23 units from the target setpoint. The PID controller demonstrated a mean control accuracy of 0.194 [30], indicating its ability to sustain control within a deviation of 0.194 units from the desired set point. A comparison of the SOFSMC and PID controllers demonstrated the efficacy of both control strategies in ensuring precise control within the context of wastewater treatment. The marginally higher mean precision of SOFSMC (0.23) can be ascribed to its adaptability and proficiency in managing intricate nonlinear dynamics, rendering it highly suitable for demanding WWTPs.

The use of SOFSMS in wastewater treatment represents a novel and noteworthy advancement in enhancing the effectiveness, dependability, and ecological viability of WWTPs. The research presented in this study highlights the potential of SOFSMC as a viable approach for addressing the intricate difficulties associated with wastewater treatment. A thorough examination and assessment of this novel control strategy yielded compelling findings bolstered by statistical evidence, which demonstrates its versatility, resilience, and precise control capabilities. This novel methodology shows significant promise for augmenting the efficiency of pollutant removal, reducing operational expenditure, and guaranteeing adherence to rigorous environmental regulations. These findings illustrate the importance of employing sophisticated control systems to address pressing concerns related to water quality, resource management, and environmental preservation. The selection of control strategies should be based on the distinct requirements and obstacles encountered by the evaluated WWTP system. The enhanced adaptability and superior performance exhibited by SOFSMC render it a highly appealing choice for systems characterized by dynamic and nonlinear dynamics. Conversely, the PID controller is a well-established and efficient methodology suitable for a broad spectrum of applications.

Fig. 1.

Control system model for WWTP based on SOSMC [27].


Fig. 2.

Proposed control system model.


Fig. 3.

Estimation of DO concentration control.


Fig. 4.

Curves representing simulated and estimated DO concentrations.


Fig. 5.

pH values for different number of tests performed.


Fig. 6.

Flowrate value curve.


Fig. 7.

pH rate values.


Fig. 8.

Pollutant removal efficiency.


Fig. 9.

Controller stability.


Fig. 10.

Response curve of the controller under consideration.


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Varuna Kumara earned his B.E. degree in Electronics and Communication in 2009 and completed his M.Tech degree in 2012 from Srinivas Institute of Technology in Mangalore. Currently a research scholar at JAIN (Deemed to be University) in Bengaluru, India, Varun’s interests lie in the areas of soft computing, image processing, and artificial intelligence & machine learning.. He also holds the esteemed position of Head of the Department of Artificial Intelligence and Machine Learning, at Moodlakatte Institute of Technology in Kundapura.

E-mail: vkumarg.24@gmail.com

Ezhilarasan Ganesan is a professor of Electrical and Electronics Engineering, at the Faculty of Engineering and Technology at Jain University, Bangalore with a specialization in Power Electronics and Industrial Drives. He has a total of 23 years of academic experience and 2 years of industry experience. He holds a B.E. degree in Electrical and Electronics Engineering from Anna University, Chennai, an M.E. degree in Power Electronics and Drives from Anna University, Chennai, and a Ph.D. in Electrical Engineering from SRM Institute of Science and Technology, Kanchipuram. Prof. Ezhilarasan’s research interests lie in the areas of power electronic converters and renewable energy systems.

E-mail: g.ezhilarasan@jainuniversity.ac.in.

Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(4): 440-450

Published online December 25, 2024 https://doi.org/10.5391/IJFIS.2024.24.4.440

Copyright © The Korean Institute of Intelligent Systems.

A Novel Approach to Wastewater Treatment Control: A Self-Organizing Fuzzy Sliding Mode Controller

Varuna Kumara1,2 and Ezhilarasan Ganesan1

1Department of Electrical Engineering, Faculty of Engineering and Technology, JAIN (Deemed to be University), Bengaluru, India
2Department of ECE, Moodlakatte Institute of Technology, Kundapura, India

Correspondence to:Varuna Kumara (varunakumara@mitkundapura.com)

Received: November 1, 2023; Accepted: December 11, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Wastewater treatment plays a crucial role in protecting the environment and ensuring sustainable use of resources. This paper presents a new methodology for managing wastewater treatment operations by utilizing a self-organizing fuzzy sliding-mode controller (SOFSMC) to enhance the efficiency of treatment procedures. The SOFSMC employs a control strategy that is both adaptive and robust in effectively regulating crucial parameters including dissolved oxygen levels, pH, and flow rates. This is achieved within the challenging and complex framework of wastewater treatment, which is characterized by dynamic and nonlinear dynamics. This study evaluated the performance of an SOFSMC system in relation to traditional control methods, using MATLAB Simulink, which functions as a simulation tool to facilitate meticulous analysis. The results emphasize the potential of SOFSMC as a revolutionary approach for wastewater treatment, providing valuable insights into the system’s effectiveness, flexibility, and adherence to rigorous water quality standards. This approach can improve treatment effectiveness, conserve resources, and protect the environment. This study provides a substantial advancement in the field of wastewater treatment regulation, highlighting its significance in the context of sustainable water management and environmental conservation.

Keywords: Dissolved oxygen, Effluents, Fuzzy logic, Sliding mode controller, Wastewater treatment

1. Introduction

Wastewater treatment is of utmost importance because it serves as a crucial component in upholding public health, safeguarding the environment, and promoting sustainable utilization of water resources. This process involves the elimination of both organic and inorganic pollutants from wastewater before it is discharged into the environment or utilized for diverse applications [1]. The implementation of this procedure is crucial in ensuring the preservation of water quality, conservation of ecosystems, and mitigation of the transmission of water-borne illnesses. The origins of wastewater treatment can be traced back to ancient civilizations. Historical societies have acknowledged the importance of segregating human waste from unpolluted water sources to prevent contamination. Notably, the Indus Valley Civilization, one of the earliest urban settlements in the world, exhibited meticulously designed sewage systems dating back to approximately 2500 BCE.

Similarly, ancient Romans devised intricate aqueduct and drainage systems to effectively regulate wastewater disposal. During the mid-20th century, the increasing recognition of environmental concerns and adverse impact of pollution on ecosystems and human well-being led governments to implement rigorous policies regarding wastewater release [2]. The Clean Water Act of the United States, along with analogous legislations implemented globally, has established stringent criteria for wastewater treatment [3]. Consequently, these regulations have spurred the development of advanced technologies and widespread implementation of more comprehensive treatment methodologies.

Efficient control of wastewater treatment is of paramount importance for various crucial factors, including the protection of public health, preservation of the environment, and responsible utilization of water resources. The principal objective of wastewater treatment is the elimination of harmful pollutants from sewage and industrial effluents. Neglecting to address this issue may lead to the proliferation of waterborne illnesses, thereby presenting significant health hazards to local populations. The efficient management of wastewater discharge is crucial for mitigating ecological consequences, thereby safeguarding the well-being of aquatic organisms and preserving ecosystem equilibrium. Wastewater treatment facilities must adapt to dynamic conditions, including fluctuations in influent flow rates, pollutant loads, and meteorological patterns.

Fuzzy logic provides a method for dealing with imprecise and uncertain data and is inspired by the way humans think and make decisions [4]. This mathematical framework permits the representation of nebulous inputs, paving the way for intelligent control systems that make sound judgments in highly uncertain settings. Fuzzy logic is an effective modeling and control tool for wastewater treatment, whereby influent characteristics can vary widely and sensor data can be noisy or uncertain [5]. Because this facilitates the creation of adaptive controllers, maximizing treatment effectiveness is critical.

The ability to steer the system states along a specified sliding surface makes sliding mode control (SMC) a robust control strategy. This method is particularly effective for dealing with nonlinear and uncertain systems because it can be used to steer the system behavior towards a stable trajectory despite external disturbances and unknowns [6]. Nonlinear dynamics is common in wastewater treatment processes, and influent characteristics are known to be highly unpredictable. The ability to maintain stability and desired performance despite disturbances, makes SMC a promising option for controlling wastewater treatment [7]. Self-organizing fuzzy sliding mode controllers (SOFSMCs) are the result of merging fuzzy logic and SMC and combining the flexibility of the former with the stability of the latter. Together, these offer a promising approach for addressing the complex and ever-changing problems of wastewater treatment.

In this study, we built an SOFSMC specifically designed for wastewater treatment processes and then tested it. Our objective was to develop an adaptive control system that can optimize the treatment performance under different conditions by combining the flexibility of SMC with the precision of fuzzy logic to model the inherent uncertainties of wastewater treatment. We hope to make a significant contribution to the field of control systems in critical domains and demonstrate through extensive experimentation and analysis that this novel approach improves the efficiency, reliability, and compliance of wastewater treatment processes.

1.1 Problem Statement

Safe disposal or reuse of polluted water relies on wastewater treatment, which is crucial for ensuring people’s well-being and keeping the environment and water supplies safe and secure. However, wastewater treatment plants (WWTPs) that use conventional control methods often face difficulties in terms of efficiency, adaptability, and robustness. The dynamic and variable nature of influent wastewater can cause suboptimal performance and resource wastage in traditional treatment systems, which is particularly challenging. In addition, strict environmental regulations require highly effective pollutant removal and disinfection, which calls for cutting-edge approaches to pollution management.

This problem statement focuses on the pursuit of a novel and adaptive control strategy to improve wastewater treatment efficiency. Managing the complex and nonlinear dynamics of wastewater treatment plants can be difficult using traditional proportional-integral-derivative (PID) controllers and fixed-parameter control systems. The objective of this study was to test how well an SOFSMC can handle the complexities of wastewater treatment.

1.2 Significance of this Study

The study of controlling wastewater treatment with an SOFSMC is significant in several ways. Its primary function is to provide a novel and flexible solution to difficult problems, which have long plagued wastewater treatment systems. Research on improving the efficiency and dependability of wastewater treatment plants benefits ecosystems, curbs the spread of waterborne diseases, and reduces the pollution in receiving water bodies. Sustainable water resource management has far-reaching implications ranging from maximizing resource utilization to facilitating water reuse through cutting-edge control strategies, especially in this era of growing water scarcity. From a financial standpoint, the proposed controller can make wastewater treatment processes more economically viable by reducing energy consumption, chemical usage, and the need for operational intervention. Additionally, this study contributes to the development of control systems by providing an example of the use of SOFSMC in practical and crucial settings. This research is significant because it can improve wastewater treatment in terms of efficiency, reliability, and sustainability while addressing critical issues of water quality, resource scarcity, and environmental protection that affect people worldwide.

2. Related Works

In this literature review, we explore the current body of knowledge and research on methods for controlling wastewater treatment with emphasis on the use of fuzzy logic and SMC strategies. The introductory section establishes the context by thoroughly analyzing previous research, emphasizing the significant findings, progress, and areas that require further investigation within the discipline. In comprehensively examining the existing body of knowledge, our objective was to establish a robust framework for comprehending the importance of SOFSMC in wastewater treatment and its potential advancements in this vital field.

It must be emphasized that the construction of WWTPs does not solve all environmental problems; instead, constant monitoring of treatment plant performance is required to ensure that the intended environmental standards are met [8]. Complex biological, chemical, and physical processes are involved in wastewater treatment, and their nonlinear and time-varying dynamics can directly affect the functioning of the treatment plant [9]. Biochemical oxygen demand (BOD), chemical oxygen demand (COD), levels of suspended and soluble solids, and the pH of the effluent from the treatment plant are all common parameters that are used to evaluate the performance of wastewater treatment plants. In [10], a learning control approach that does not rely on a specific model was proposed. This approach was developed to address the challenges posed by the nonlinearity and environmental uncertainties of WWTPs. Furthermore, a nonlinear-model-based predictive controller (NMPC) was developed to meet the effluent quality regulations of a WWTP while considering economic feasibility [11]. Additional control strategies based on data analysis have also been examined [12]. The development of control strategies based on data analysis can significantly enhance the identification of nonlinearity in WWTPs, thereby improving control performance. However, actual WWTPs frequently encounter significant disturbances linked to uncertainty, resulting in frequent and unpredictable variations in operational procedures, thereby compromising the efficacy of such data-based control methods [13]. In broad terms, the analysis of chattering is advantageous in engineering applications as it can enhance the understanding of its impact on the stability of closed-loop control systems [14].

The SMC is an advanced and diverse control methodology that operates discontinuously and modifies the components of a nonlinear system. The state-investigation control rule is an abstract concept that imposes a consistent temporal constraint. In contrast, the transition can vary from one stable configuration to the next depending on the current state within the state space [15]. In past decades, scholarly literature has primarily concentrated on the introduction of “logic decision” in sliding systems [16], and fuzzy-based sliding mode control (FSMC) has been suggested as a potential alternative for mitigating chattering. The integration of both algorithms effectively addresses two significant issues: the mitigation of chattering attenuation and minimization of rules in dynamic fuzzy controllers. This is achieved by utilizing a singular fuzzy variable known as the sliding surface function, which encompasses all aspects of the dynamic process [17]. The predominant approach involves modifying the primary parameters of the SMC, including robust gain, sliding surface gradient, and switching control, in accordance with the plant characteristics. A primary benefit of these schemes is that they do not require knowledge of the upper bounds of uncertainty and disturbance [18]. In [19], the authors presented adaptive techniques for estimating uncertainties and disturbances using variable structure controllers. However, uncertainties and disturbances inherent to dynamic systems may have bounded characteristics and are not known in terms of their specific parameters in real-world experimental scenarios.

In a previous study [20], a novel SMC technique was proposed for regulating the dissolved oxygen (DO) concentration within a WWTP-integrated nitrogen removal process. The findings from the laboratory-scale reactor experiment demonstrated that the SMC method exhibits a commendable ability to reject disturbances and delivers satisfactory performance across a broad spectrum of operating conditions. Additionally, various strategies have been implemented to mitigate uncertainties and disturbances in WWTPs [21, 22]. To develop an appropriate sliding surface design, SMC strategies require a comprehensive understanding of the nonlinearity exhibited by WWTPs. Thus, the design of SMCs for wastewater treatment plants remains a challenging task [2325]. A novel adaptive FSMC has been proposed for multivariate control in WWTP [26]. The adaptive FSMC employs a fuzzy method to approximate the unknown process, while utilizing the SMC to guarantee the asymptotic stability of the closed-loop system. Simulation results demonstrate that the proposed method exhibits effective disturbance rejection and robustness. However, despite the significant achievements of the aforementioned methods in WWTPs, chattering remains a persistent and significant challenge that has yet to be fully resolved. Based on the review and analysis presented earlier, this paper proposes the use of a SOFSMC to achieve satisfactory and consistent control performance for WWTP.

3. Methodology

Fuzzy logic within a control system can incorporate prior knowledge to address uncertainties, absence of adequate models, and disruptions in operational processes. The occurrence of the chattering phenomenon is a significant drawback of SMCs that arises from the use of the sign function during the design process. The proposed SOFSMC approach does not require the inclusion of a robust term to account for inherent uncertainty in the mathematical model of the system. Consequently, it can mitigate the occurrence of the chattering phenomena commonly observed in traditional sliding-mode control systems. The control system model for a WWTP based on self-organizing SMC (SOSMC) is shown in Figure 1 [27]. This model served as the foundational framework for this study.

3.1 Self-organizing SMC

The use of an SOSMC in the context of WWTPs is a novel control approach that integrates the flexible nature of self-organizing systems with the resilience of sliding mode control. The use of this advanced controller holds promise for significantly improving efficiency, reliability, and adherence to regulations in WTTPS procedures. The SMC technique was applied to reduce the effects of uncertainties and nonlinearities. The task of the counting controller is to reject the disturbances caused by varying inflow loads due to environmental conditions. Self-organizing fuzzy neural network (SOFNN) is a hybrid computational model that combines the adaptability of neural networks with the linguistic rule-based approach of fuzzy logic. This sophisticated program can adjust, learn, and make choices despite ambiguities. Its ability to model and process information in a way that closely resembles human reasoning and decision-making, makes it particularly useful for tasks involving pattern recognition, classification, and control.

Notably, no standard SMC methodology has been developed for direct sliding-mode fuzzy controller design. Instead, a fuzzy controller was developed based on theoretical SMC concepts. To attain the desired objective, the fuzzy rule basis is adjusted such that s≤0. If s⋅< 0, the prior alteration of the control signal is preserved, whereas if s⋅> 0, it is reversed. Rules are considered to prevent instances of chattering. The following is an example of a second-order nonlinear dynamic system.

x¨1=f(x)+g(x)u,

where g(x) > 0 and f(x) are two scalar functions of the unknown states of the system; s = + λx, where xR2 expresses the sliding manifold. The time derivative of the sliding surface can be expressed as follows:

s˙=f(x)+g(x)u+λx˙.

When choosing a Lyapunov function, the Lyapunov theory requires that s⋅<0. Accordingly, a fuzzy rule-based system is proposed to determine changes in the control signal Δu.

The control system proposed in this study is illustrated in Figure 2. In this system, the control input u(t) is determined by the fuzzy logic controller (FLC) component, which considers the values of s and at each sampling interval. The proposed algorithm has a self-organizing mechanism that considers dynamic reactions to effectively update the knowledge base of fuzzy rules.

u¯i(k+1)=u¯i(k)+Δu¯i(k),u¯i(k)+ωeiωeciγM×[(1-ς)s(k)+ςΔs(k)]

In this context, the symbol ūi represents the variation in the control input for the i-th rule, whereas Δūi denotes the correction amount associated with each rule. Additionally, ωei and ωeci represent the excitation strength of each fuzzy rule; γ denotes the learning rate; ς signifies the weighting distribution; and M denotes the direct forward system gain, which is commonly assigned a value of 1. In this context, s(k) and Δs(k) represent the sliding surface and the change in the sliding surface over the k-step sampling period, respectively. This methodology facilitates the establishment of a control loop in the absence of initial guidelines. Once the rules are updated using a self-organizing algorithm, the output of the fuzzy inference should be defuzzified.

In an SOFSMC, fuzzy logic is used to dynamically adjust the parameters of the sliding mode controller based on the current state of the system. This allows the controller to adapt to changing conditions and maintain precise control even in the presence of uncertainties and disturbances. To address the chattering phenomenon, a self-organizing mechanism was developed to facilitate the construction of the fuzzy neural network (FNN) structure, thereby establishing a comprehensive assessment of the structural risks associated with FNN.

r(tg)=ρ1(tg)+ρ2(tg).

In this context, the variable “tg” represents the number of sampling intervals at a given time “t”; r(tg) denotes the structural risk value; ρ1(tg) represents the empirical error derived from the tracking error on the “tgth” sampling interval; and ρ2(tg) is the estimation error.

ρ1(tg)=12e(t)Te(t),ρ2(tg)=K(tg)NlogTg-2logK(tg)Tg.

Let Tg represent the ratio of Ttg to t, where T is the period of the control process, and K(tg) denotes the number of fuzzy rules during the tgth sampling interval. Structural risk is said to be low when both empirical risk and structural complexity are small. If the condition r(tg) < α1 holds, the structural risk value is acceptable.

If the self-organizing algorithm under consideration is capable of dynamically determining the appropriate size for a structure in real time, it must strike a balance between minimizing the tracking error and the complexity of the structure. The proposed SOFNN demonstrated the capability to accurately estimate and compensate for uncertain dynamics and disturbances, effectively mitigating the occurrence of chattering in SOSMC.

3.2 Dissolved Oxygen Dynamics

Monitoring and control of DO in WWTPs is of critical importance because it has a direct impact on the success of biological treatments. As aerobic conditions are required for the activity of beneficial microorganisms that break down organic pollutants, DO is a crucial indicator of microbial ecosystem health. By accurately measuring the DO levels, treatment effectiveness can be maximized, leading to the timely degradation of organic matter and decreased energy consumption. Furthermore, protecting environmental quality and meeting strict regulatory standards requires maintaining adequate DO levels to prevent the release of inadequately treated effluents into natural water bodies. DO monitoring and control are essential for reducing water pollution and protecting ecosystem health because they improve the efficiency, cost-effectiveness, and regulatory compliance of wastewater treatment. The amount of oxygen required by an organism to decompose organic matter over a given time is known as BOD. Concentrations of BOD in water that are too high (e.g., 5 mg O2/L) reduce the amount of oxygen in the water, harm ecosystem biodiversity, lower water quality, and pollute the freshwater supplies [29]. BOD measurements require the acquisition of at least two measurements. The first measurement, denoted as DO0 is performed immediately, whereas the second measurement is obtained after incubating the water samples for a few days. The purpose of the incubation is to allow for the subsequent assessment of the remaining quantity of DO, referred to as DO1.

In an activated sludge process, the DO concentration should be sufficiently high to allow microorganisms to obtain the oxygen they need to perform their metabolic processes. However, a high DO concentration can be harmful to sludge quality and lead to excessive energy consumption. A proportional controller can be used to maintain the average DO level at a steady, user-specified value. Pulse width modulation (PWM) is used to modify the aeration rate, which is also known as the oxygen transfer rate:

u(k)=Km(k)(Csat-c^(k)),

where ĉ(k) represents the estimated DO concentration as determined by the Kalman filter. The utilization of this value instead of the measured value is attributed to its reduced noise, leading to improved estimation outcomes. The aeration rate of the proportional controller is calculated as follows:

u(k)=kp·(cref-c^(k).

The reference value for the DO concentration is denoted as cref, whereas the gain of the proportional controller is represented by kp. Figure 3 presents a diagram representing the estimation of DO concentration control.

4. Simulation Results and Analysis

The simulation setup in MATLAB 2023a Simulink was used to construct a model of the wastewater treatment process. The objective of this study was to evaluate the effectiveness of a SOFSMC in regulating DO levels and other relevant parameters. The equations employed were described in the previous section. The experimental setup comprised a continuous-flow activated sludge reactor, in which the primary variables were configured as follows: influent DO concentration of 4.0 mg/L, biomass concentration of 2,000 mg/L, flow rate of 1,000 L/day, and desired DO setpoint of 6.0 mg/L. The Simulink environment enabled the execution of dynamic simulations, which, in turn, enabled the assessment of the controller’s efficacy in regulating DO levels within specified ranges under fluctuating influent conditions. Figure 4 shows the curves representing the simulated and estimated DO concentrations. The disparity between the set and measured values can be attributed to the use of a closed-loop configuration. This error can be reduced by increasing the value of the proportional gain or by incorporating an integrator into the system.

Two primary options exist for addressing this discrepancy and boosting the controller efficiency. One way to decrease the discrepancy between the target and actual DO levels is to increase the proportional gain of the controller, which accelerates the response to deviations from the setpoint and slows down the time required for the system to stabilize after adjustment. Second, the control loop can be further optimized by including an integrator component. Incorporating this integral action improves the capability of the system to maintain DO concentrations within a specified range over extended periods by systematically correcting long-term cumulative errors.

Monitoring and regulating the pH values and flow rates are crucial aspects of wastewater treatment and directly affect the efficacy and performance of the treatment process. An insight into how these critical parameters respond to the influence of the control system can be obtained from the time-series data that are likely to be included in the simulation result analysis chart, as shown in Figures 5 and 6.

The study results—a pH of 13.40 and a flow rate of 2.87—point to a wastewater treatment system that has been fine-tuned. Achieving a pH of 13.40 indicates that the control system manages and regulates chemical dosing effectively, which keeps the treatment process within the desired pH range. At a rate of 2.87, the influent flow into the treatment system is consistent. To avoid the overuse or underuse of the treatment infrastructure, a constant flow rate should be maintained throughout the treatment process. This indicates that the control strategy effectively performed the task, which led to increased pollutant removal efficiency, decreased operational costs, reduced environmental impact, and enhanced reliability of the treatment process. The optimization yielded the best performance of 0.031 seconds, demonstrating the superiority of the control system and treatment process. This indicates that the system is performing at its optimum level, providing excellent care at a reasonable cost, while also satisfying the most exacting regulatory requirements.

These results demonstrate the value of sophisticated control strategies for improving wastewater treatment and preserving natural resources. Figure 7 shows the observed pH curve with respect to the set value.

In Figure 8, the graph depicting pollutant removal efficiency (%) vs. time (s) provides valuable insights into the dynamic performance of a wastewater treatment process. As time progresses, the pollutant removal efficiency is tracked, showing how effectively the treatment system is cleansing the wastewater. The trends in the graph of Figure 9 reveal crucial information about the treatment’s response to varying influent conditions and its overall stability. Steep initial increases in efficiency may indicate the prompt removal of readily biodegradable pollutants, whereas plateauing or fluctuations might signify the presence of complex or slowly degradable contaminants. The speed with which a controller can respond to deviations from the desired setpoint is a crucial parameter in the dynamics of control systems.

In the graph of response times of Figure 10, the graph saturates once the time reaches 1.85 seconds, indicating that the controller has reached its maximum possible response speed. At this point, the controller quickly responds to disturbances or changes in the setpoint, reducing the overshoot and deviation of the controlled variable while stabilizing it in record time. Saturation is reached in 1.85 seconds, demonstrating the controller’s rapid and effective maintenance of the desired process conditions, which is an essential feature in many control applications.

4.1 Comparative Analysis

An examination of the average control accuracy between the SOFSMC and PID controllers offers significant insights into the effectiveness of these control strategies within the WWTP framework. A study on SOFSMC exhibited a mean control accuracy of 0.23. This value signifies that, on average, the controller effectively regulates crucial parameters (such as DO, pH, and flow rate) within a deviation of 0.23 units from the target setpoint. The PID controller demonstrated a mean control accuracy of 0.194 [30], indicating its ability to sustain control within a deviation of 0.194 units from the desired set point. A comparison of the SOFSMC and PID controllers demonstrated the efficacy of both control strategies in ensuring precise control within the context of wastewater treatment. The marginally higher mean precision of SOFSMC (0.23) can be ascribed to its adaptability and proficiency in managing intricate nonlinear dynamics, rendering it highly suitable for demanding WWTPs.

5. Conclusion

The use of SOFSMS in wastewater treatment represents a novel and noteworthy advancement in enhancing the effectiveness, dependability, and ecological viability of WWTPs. The research presented in this study highlights the potential of SOFSMC as a viable approach for addressing the intricate difficulties associated with wastewater treatment. A thorough examination and assessment of this novel control strategy yielded compelling findings bolstered by statistical evidence, which demonstrates its versatility, resilience, and precise control capabilities. This novel methodology shows significant promise for augmenting the efficiency of pollutant removal, reducing operational expenditure, and guaranteeing adherence to rigorous environmental regulations. These findings illustrate the importance of employing sophisticated control systems to address pressing concerns related to water quality, resource management, and environmental preservation. The selection of control strategies should be based on the distinct requirements and obstacles encountered by the evaluated WWTP system. The enhanced adaptability and superior performance exhibited by SOFSMC render it a highly appealing choice for systems characterized by dynamic and nonlinear dynamics. Conversely, the PID controller is a well-established and efficient methodology suitable for a broad spectrum of applications.

Conflict of Interest

No potential conflict of interest relevant to this article was reported.

Fig 1.

Figure 1.

Control system model for WWTP based on SOSMC [27].

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 2.

Figure 2.

Proposed control system model.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 3.

Figure 3.

Estimation of DO concentration control.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 4.

Figure 4.

Curves representing simulated and estimated DO concentrations.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 5.

Figure 5.

pH values for different number of tests performed.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 6.

Figure 6.

Flowrate value curve.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 7.

Figure 7.

pH rate values.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 8.

Figure 8.

Pollutant removal efficiency.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 9.

Figure 9.

Controller stability.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

Fig 10.

Figure 10.

Response curve of the controller under consideration.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 440-450https://doi.org/10.5391/IJFIS.2024.24.4.440

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