Dissolved oxygen control strategies for water treatment: a review Open Access

Since the start of the 21st century, more and more attention has been paid to environmental concerns and sustainable development than ever before due to climate change, scarcity of resources such as drinking water and pollution. Among all these issues, the issues of water and aquatic environments are particularly severe (Iratni & Chang 2019). Research activities for water treatment have subsequently increased in recent years, especially research interest in dissolved oxygen (DO) control for energy saving and efficiency improvement (Amand et al. 2013). Dissolved oxygen refers to the molecular oxygen dissolved in water. It is an important water quality parameter, whose concentration will affect many reactions or processes that need to take place in water. In particular, DO plays a crucial role in wastewater treatment and aquaculture.

Wastewater treatment plants (WWTP) play a vital role in wastewater treatment, improving the water quality of urban discharged water bodies, conserving water sources, and reducing chemical oxygen demand (COD) and ammonia nitrogen emissions, since good water resources and environment are extremely important to ensure global sustainable development (Behera et al. 2015). However, it is still difficult to control and operate the WWTP to achieve satisfied effluent requirements under the lowest energy consumption, because of the extensive uncertainties and nonlinearities existing in it (Mulas et al. 2015). As a critical variable, appropriate DO concentration can stimulate microorganisms to degrade organic matter. Hence, in the WWTP, DO control is one of the topics of most concern, when it comes to providing proper DO to maintain the biomass activities in the aerated process (Huang et al. 2020). DO control has become a part of wastewater treatment process, the effects of which will not only relate to the power energy consumption but also influence the effluent water quality, since a low effluent quality can cause significant ecosystem problems in receiving water bodies (Kozák 2014). DO control strategies span from modifications and developments of conventional control to advanced control and intelligent control (Amand et al. 2013). The proportional-integral-derivative (PID) DO control strategy has been the most commonly used in WWTP to realize the effective adjustment of the DO and achieve good DO set-point tracking (Man et al. 2018). As an advanced control strategy, model predictive control (MPC) has been gradually applied in the WWTP, having broad application prospects (Bu et al. 2016; Han et al. 2016; Sadeghassadi et al. 2018). Recently, artificial intelligence with high-performance algorithms has drawn great interest from researchers and has been used by some of them to balance the relationship between the effluent quality and operation cost (Qiao et al. 2019; Han et al. 2020).

Modern aquaculture has the features of high density, intensification and industrialization, developing with reduction in natural aquatic resources and increase in human consumption demand for aquatic product (Jiang et al. 2012). DO is a key water quality factor in modern aquaculture, low levels of which can cause production problems linked to slow growth or death of fish, while high levels of which can cause increase of power costs of aeration systems (Sacasqui et al. 2017). Reasonable prediction and control of DO is essential for aquaculture development due to its characteristics of nonlinear, large time delays, and instability (Ferreira et al. 2021; Roy et al. 2021). Only when the prediction and control of DO is realized accurately, the expected production and aeration costs can be balanced (Li et al. 2021b). The proposals of various prediction and control models, such as neural networks, fuzzy control and MPC, provide new approaches for the prediction and control of DO in aquaculture.

As far as we know, although interesting reviews on various mainstream control methods and applications have been published, there is still a lack of comprehensive reviews on DO control strategies in the community. This review covers various DO control strategies for wastewater treatment processes and aquaculture, emphasizing strategies, algorithms and models for DO control. The remainder of the paper is organized as follows. Section 2 introduces the fundamental concepts and principles of the mainstream control methods for DO control as well as their categorization with the goal of providing a common narrative framework of the analyzed literature. Section 3 systematically and comprehensively investigates and analyzes various DO control strategies in the wastewater treatment domain which is the main application area of DO control, through specific categorization. To provide a broader view to the readers, section 4 covers DO prediction and control strategies for aquaculture. Section 5 provides a critical discussion on the various DO control strategies and their challenges and limitations. The paper ends in section 6 with a brief but refined conclusion.

Conventional control methods are the most widely used control methods in practical industrial and agricultural applications. They can be categorized as two types: classical control and modern control. In past years, both researchers and engineers have utilized those conventional control methods to control the DO concentration in different scenarios (Khan et al. 2018; Revollar et al. 2018; Angani et al. 2019). This section reviews some key branches of conventional control methods of DO concentration.

Classical control methods are the most widely used control methods in actual industrial and agricultural production practice. Both the earliest on/off control and the subsequent PID control belong to classical control. Particularly, PID control is widely welcomed by engineers and technical experts, because of its simple structure, strong robustness and adaptability, as well as its ability to meet the needs of most practical applications (Shah & Agashe 2016).

PID control, namely proportional-integral-derivative control, is a feedback control and has three terms (P, I, D) whose functionality covers the ability to deal with transient and steady-state responses, and thus offers the simplest but most efficient solutions to extensive real-world control problems (Åström & Hägglund 1995). In the past 50 years, PID control has been gradually more and more popular in industries and agricultures for process control strategies, because of its simplicity, flexibility, easy operation, and good performance including low percentage overshoot and small settling time (Åström & Hägglund 2001). Therefore, PID control is regarded as an effective strategy for DO control. In DO control practice, experts and engineers usually choose different types of PID controllers, including the P, PI, PD and PID controllers, according to the different requirements of the actual system.

Model predictive control was initially proposed in the petrochemical industry, aiming to solve problems which are difficult for classical PID control to deal with (Havlena & Barva 2000). As a model-based advanced control strategy, it consists of model prediction, rolling optimization and feedback correction. Theoretically, this method has the advantage of handling time-varying or nontime-varying, linear or nonlinear, time-delay or no-time-delay constrained optimal control problems. Therefore, it obtains more and more extensive applications in various control fields, especially in process control field (Ding et al. 2018; Zhang et al. 2022).

MPC is the generally agreed collective term of a class of control algorithms aimed at solving control problems by using optimization methods (Lee 2011). The mainstream MPC algorithms include model algorithmic control (MAC) and dynamic matrix control (DMC) based on the nonparametric model, as well as generalized predictive control (GPC) based on the parametric model. GPC and DMC as the most popular used algorithms are briefly described and compared in Table 1.

Intelligent control is a control mode or a control system that can effectively overcome the high complexity and uncertainty of the controlled object and environment, and achieve the desired goal. The initial idea of intelligent control was first proposed by professor Fu jingsun in the 1960s, in order to achieve the modernization and automation of control systems (Kahraman et al. 2020). After that, artificial intelligence has gradually entered into the framework of control systems. In recent years, the combination of control theory and intelligent computer technologies, which mainly contains fuzzy logic and neural network, has been closer and deeper (Szuster & Hendzel 2018). This section aims to describe two of the most widely used intelligent control methods, namely, fuzzy control and neural network control.

Fuzzy control, also called fuzzy logic control, is a computer digital control technique. It is based on the knowledge of fuzzy computing that contains fuzzy set theory, fuzzy linguistic variables and fuzzy inference system, and it imitates the way of thinking of human brain, identifies and judges the fuzzy phenomenon, and controls the controlled object accurately (Nguyen et al. 2019). The concept of fuzzy control theory was firstly proposed by Professor L. A. Zadeh in 1965 and by Professor E. H. Mamdani, who developed the world's first fuzzy controller, and achieved success in control of laboratory steam engine a few years later (Zadeh 1973; Mamdani & Assilian 1999). Since then, fuzzy control has gained popularity and acceptance through its successful application in more and more industries and fields, although it has received lasting controversy in academic circles because of its lack of requirement of an accurate mathematical model.

The key features in fuzzy control are mainly the design and implementation of a fuzzy controller. A typical fuzzy controller usually contains four parts: fuzzification, knowledge database, fuzzy inference, defuzzification (Chiu 1998). Firstly, the precise input values are mapped to the fuzzy set of input universe according to the membership function in the knowledge base; then, fuzzy reasoning, as the core of fuzzy controller, is carried out, based on a series of control rules expressed by fuzzy language variables in the knowledge base; finally, because the result of fuzzy inference is still fuzzy and cannot be directly used as a control output, it is necessary to perform a defuzzification operation to obtain the entity of control output to act on the controlled object.

Through the input and output data of the controlled object, neural network control uses neural network learning algorithms to continuously acquire the knowledge of the controlled object, so as to realize the prediction and estimation of the system model, so as to generate control signals and make the output as close as possible to the desired trajectory (Hunt et al. 1992). As a highly complex nonlinear dynamic learning system, the neural network is particularly suitable for processing inaccurate and fuzzy information processing problems that need to consider many factors and conditions at the same time such as the identification and prediction of nonlinear systems (Sherstinsky 2020). Hence, the neural network system has increasingly been applied to solve nonlinear problems in industry and agriculture, and has achieved extraordinary achievements.

The main characteristics of the neural network system and their good effects are shown in Table 2. Representative neural network models include error back propagation (BP) neural network, Hopfield neural network, radial basis neural network, etc. The application of these models mainly lies in the identification and modeling of nonlinear systems, as well as the prediction of nonlinear processes. DO control is a type of process control, which also involves some nonlinear and hysteresis problems, hence neural networks may make some contributions in predicting and controlling the DO concentration (He et al. 2021).

Since the several control methods mentioned above have not only their own advantages but also some inherent limitations when used individually, hybrid control methods developed gradually by combining two or more control methods together. In general, hybrid control methods could always get better results by benefiting from the qualities of integrated methods.

There are several main fusion methods. The combination of intelligent control methods and classical controllers forms a type of typical hybrid control methods, including fuzzy PID and neural network PID control methods. The intelligent control methods act as supervisory controllers while PID controllers act as regulatory controllers to send execution signals to actuators (Dasen et al. 2019). Furthermore, intelligent control methods are also combined with MPC method to perform better than simply adopting one single control method (Li et al. 2020). Lastly, different intelligent control methods are integrated mutually to complement each other as well, such as the fusion of fuzzy logic and neural networks (Siddique 2014). Overall, more and more hybrid control methods are gradually being used in the control of DO concentration and have been proven to be effective control methods.

Depending on the control strategies classified in the previous section, conventional, intelligent and hybrid approaches to control DO concentration are possible. Throughout this section, we categorize and narrate and discuss various control strategies proposed in the literature.

For DO control in WWTP, conventional control methods appear earliest, last for the longest time and have the most stable effects. As described in section 2, conventional control can be divided into classical control and advanced control, and two typical methods are PID control and MPC, respectively. In this section, these two typical control strategies of DO concentration in WWTP are reviewed. Moreover, when it comes to conventional control strategies integrated with other control methods, they will be reviewed in section 3.3.

Due to its simple and convenient operation, the PID controller is the most widely used controller in WWTP. Turmel introduced an auto-tuned PID controller that was different from the manually tuned PID. The new PID controller showed proper performance and shorter response time for DO concentration to reach the set value (Turmel et al. 1997). The research was the first in scientific literature concerning DO control in wastewater treatment process. One development direction of the PID controller is to improve its automatic tuning methods, since the traditional PID control could not tune its own parameters online. In this case, research efforts were dedicated to designing new tuning methods for better performance (Liu & Yu 2017; Butkus et al. 2021). Kim designed a new automatic tuning method for the PID controller – a new online process identification method, which showed better performance than previous tuning methods and successful application of DO control (Kim et al. 2009), while Wahab proposed a novel tuning method along with three other existing methods and optimized parameters of multivariable PID controllers, improving the closed-loop performance of WWTP and saving energy (Wahab et al. 2009). In addition, PID DO control associated with an external loop for ammonia control is a simple but efficient approach. The earlier successful implementation was accessed in the WWTP of Galindo-Bilbao (Ayesa et al. 2006).

Another main development direction of PID controller is to adopt intelligent algorithms to auto-tune PID controller parameters. Through fuzzy reasoning (Liu & Yu 2017; Zhang et al. 2019), the parameters of PID controller can be self-tuned online, causing more accurate DO control performance and faster response speed than traditional PID control. Du chose to utilize a radial basis function neural network (RBFNN) algorithm as the adaptive PID algorithm to adjust parameters online, with the simulation result of good tracking, anti-disturbance and strong robustness (Du et al. 2018). In addition, a novel PID control improvement strategy (Du et al. 2020) deserves to be mentioned, which proved that it could decrease the updating number of the control input and save energy as a dynamic event-triggered PID control strategy.

Model predictive control is a type of control method developed in practical application due to its prediction advantages, it has been proved to be suitable for wastewater treatment applications. The first attempt to apply MPC in real wastewater treatment plants was provided in (O'Brien et al. 2011), which provided more benefits than the traditional PID control. The MPC system showed the capabilities to provide prediction in dealing with dynamic process conditions, eliminate disturbance for smoother operation of WWTP, and reduce aeration costs in comparison with the PID control system in a wastewater treatment plant in Lancaster, UK. Santin also applied MPC to improve DO tracking capabilities in WWTP, and they integrated these with other advanced control strategies for other proposed objectives (Santin et al. 2016).

The application of specific algorithms of MPC in WWTP often have the effects of reducing power usage, increasing plant efficiency and reducing carbon footprint. Mulas implemented a DMC algorithm, a representative algorithm of MPC, to optimize the control effects of the activated sludge process in a full-scale municipal wastewater treatment plant (Mulas et al. 2015). By comparing the DMC performances with the current control strategy in the plant, the simulation result demonstrated the effectiveness and potentiality of DMC. Sadeghassadi presented a GPC technique and its constraint term to realize improved control of DO concentration in the presence of dynamic input disturbance, with the simulation result showing quick DO set-point change tracking capability and good adaptability to the system uncertainties and disturbances (Sadeghassadi et al. 2016).

Other novel and unique algorithms of MPC have also been tried to improve DO concentration control in WWTP. Zeng and Liu adopted a computationally efficient economic MPC algorithm (EMPC) and compared its performance with PI and MPC schemes (Zeng & Liu 2015). Simulation results showed outstanding effects of optimization of the effluent quality and operating cost. Model-free predictive control has already been shown to be improved by the introduction of polynomial regression vectors containing the control input and measurement output and it was then extended to the nonlinear systems of WWTP and tested its effectiveness through numerical simulation. The application of MPC schemes for DO control in WWTP in the recent 10 years are shown in Table 3.

MPC approaches combined with other advanced control strategies to realize improved control of DO concentration have been an ongoing trend and will be reviewed in section 3.3.

As described in section 2, the predominant intelligent control methods are introduced, namely fuzzy control and neural network control. This section will review intelligent control strategies for DO concentration control in WWTP from these two aspects separately. As for those hybrid methods integrating two or more control methods, they will be reviewed in section 3.3.

For DO control in the WWTP, although DO concentration is positively correlated with the air flow rate, the relationship between them is not completely linear. Hence, it is difficult to establish an accurate mathematical model, however, fuzzy control theory instead shows powerful control capabilities for uncertain systems like this.

Fuzzy logic controllers are designed to achieve more stable and precise DO control (Traore et al. 2005; Piotrowski 2020), to compensate for the difficulty of parameter adjustment of traditional PID controllers caused by the high nonlinearity of DO change processes. In comparison with classical PID control methods, these two articles both proved fuzzy logic to be a robust and effective DO control tool, which could highly improve control action performances, such as a smooth characteristic of blower speed and a smaller overshoot, as an alternative control algorithm of PID methods.

Based on the basic fuzzy controllers (BFC), various improvement measures have been put forward in the past years. Coelho Belchior described an adaptive fuzzy controller (AFC) developed for tracking the DO reference trajectory in the bioreactors in the WWTPs and another supervisory fuzzy controller developed for working in parallel with the AFC (Coelho Belchior et al. 2012). At the same time, when this data-driven controller was designed, the global stability of its closed-loop system was also guaranteed by the Lyapunov synthesis approach. When compared with the PI controller and the BFC in the simulation experiment based on the BSM n.1, the results showed that the AFC could achieve accurate DO control without a precise mathematical model of the system under control and prior knowledge of the plant. Bahita and Belarbi demonstrated another type of AFC for DO concentration in a bioreactor in the WWTP (Bahita & Belarbi 2015). In order to control the DO concentration levels in the activated sludge process, the paper designed a Takagi Sugeno fuzzy inference system (TS-FIS) to approximate the feedback linearization law as an approximator of the ideal control law based on a fuzzy Mamdani approximator (FMA), observing better tracking performance compared to those of a classical PI controller.

Other novel and specific fuzzy control strategies are proposed as well. Qiao developed a self-organizing fuzzy control (SOFC) method, motivated by the characteristics of WWTP and the application difficulties of fuzzy logic controllers (FLC) (Qiao et al. 2016). The main feature of the proposed controller was that it could automatically extract fuzzy rules, thereby not requiring the accurate plant model of WWTP. This controller was demonstrated by simulation results based on BSM1, showing that it could improve the accuracy and adaption ability of DO control with flexible fuzzy rules compared with PID, model predictive control (MPC) and BFC. For the DO control of a Sequencing Batch Reactor (SBR) in the WWTP, a supervisory heuristic fuzzy control system was proposed by (Piotrowski 2020), which could calculate the set point of dissolved oxygen and adapt parameters of the lower controller, showing outstanding control ability of DO concentration in the simulation tests. In addition, Boiocchi applied the fuzzy logic module to regulate the DO set point of the PI control loop and still used PID to control the DO concentration, achieving low N₂O emissions and low effluent NH₄⁺ concentration (Boiocchi et al. 2017). The application of fuzzy control schemes for DO control in WWTP in recent 10 years are shown in Table 4.

An artificial neural network (ANN) has outstanding nonlinear adaptive information processing ability because of its special features of self-learning and of high-speed search for optimal solution. Therefore, it also contributes to the intelligent control and prediction tracking of dissolved oxygen in the process of wastewater treatment, especially when wastewater treatment systems do not have sufficient expertise knowledge to build up advanced fuzzy control systems of DO concentration.

The first neural network assisted intelligent controller successfully applied in a specific wastewater treatment plant was described by Chang et al. (2001). The paper developed a genetic algorithms (GA)-based neural network for the assistance of intelligent controller design and verified the applicability of such a controller in an industrial wastewater treatment plant (WWTP) in Taiwan, showing the ability of capturing the uncertainties in the wastewater treatment process and providing immediate guidance and control message while integrating on-line process data. Ruan also utilized GA to design intelligent control system (Ruan et al. 2017). The author integrated the global search ability of GA and the local detail superiority of wavelet transform to extract complex interrelationships between various operation variables, with the results showing that it could overcome the pure delayed behavior of the water quality parameters and achieve reasonable forecasting and control performances with optimal DO.

Due to the strong self-learning ability of ANNs, adaptive controllers based on different types of neural networks have been gradually popular in various fields. This trend has emerged in the application of the WWTPs as well. Han and Qiao proposed an adaptive controller based on a dynamic structure neural network (ACDSNN) for DO control in the activated sludge wastewater treatment process, which could adapt to the variation of the operating character of the WWTP and maintain the control accuracy (Han & Qiao 2011). The numerical simulation demonstrated that the proposed ACDSNN could have superior performance with the help of its adaptive strategy, especially when the required DO concentration was changed in the control. It used a feedforward neural network (FNN) controller to automatically determine the online NN structure, showing better control accuracy for nonlinear and time-varying problems than PID and MPC controllers.

On the basis of the work of (Lin & Luo 2014), Lin and Luo presented a neural nonlinear adaptive control technique, which adopted RBFNN to approximate all uncertain dynamics of the wastewater treatment, so that the DO concentration control problem existing in such uncertain processes could be solved (Lin & Luo 2015). The stability of the closed-loop system was proved by the Lyapunov method, while the presented adaptive NN controller was simulated to achieve satisfied control performance. Adaptive neural network controllers still come with some defects, such as slow convergence, local minima, huge time consumption and low efficiency. To try to solve such problems, Cao and Yang discussed an adaptive controller based on a novel online sequential extreme learning machine (OS-ELM) technique (Cao & Yang 2020). In contrast with other extensive comparison case studies (Holenda et al. 2008; Han et al. 2012; Han et al. 2016), it was proved that the proposed algorithm not only required no human experience or offline training phase, but also had fast training speed and guaranteed the performance of the system through its online learning mechanism.

For DO control in the WWTP, neural networks have drawn great interest of researchers in the last decade, due to their characteristics of self-organization, self-learning and nonlinear dynamic processing. The application of NN schemes for DO control in WWTP in the decade are shown in Table 5.

The conventional control methods are simple and convenient to operate and stable in performance, but it cannot adapt to the environment variability in the wastewater treatment process. When the original control environment changes, the control results will be disturbed with lower control accuracy. Intelligent control methods, which are more flexible than traditional control methods, have been applied in DO control of wastewater treatment process, but these control methods have more or less limitations and flaws when used individually. For such reasons, many researchers have begun to try to apply the hybrid control methods combined with different control methods to realize the improved control of DO concentration in the wastewater treatment process in recent years. In this section, research articles about hybrid control methods for DO concentration in the WWTP are focused on.

Neural networks integrated with other control methods constitute the mainstream of hybrid control methods. In general, neural networks are combined with fuzzy logic control methods (Zhang & Qiao 2020), MPC methods (ex. (Han et al. 2012; Han & Qiao 2014; Sadeghassadi et al. 2018)), traditional PID control methods (Du et al. 2018), or hybrid control methods (Han et al. 2019).

As a typical FNN, radial basis function (RBF) neural network has been integrated with other control strategies to improve DO control performance in the WWTP because of its powerful nonlinear fitting ability and simple learning rules. Han and Qiao optimized the structure of a fuzzy neural network (FNN) controller based on the RBFNN, using a novel growing and pruning (GP) approach (Han & Qiao 2010). This proposed GP-FNN approach was proved to be capable of automatically determining the parameters and structure of the FNN, and could be a potential tool to control dynamic systems like DO treatment process, in comparison with other algorithms commonly used in the literature (Akratos et al. 2008; Ekman 2008).

Using merits of the RBFNN, several studies reported the joint advantages of it and MPC in DO concentration control in the WWTP. First, a self-organizing RBFNN MPC (SORBF-MPC) was studied (Han et al. 2012). It introduced a variable structure RBF for addressing the MPC of the DO concentration in the WWTP. On the basis of this study, a nonlinear MPC (SORBF-NMPC) system based on the self-organizing RBFNN was designed (Han & Qiao 2014), providing satisfactory tracking and disturbance rejection performance. In further study, Qiao developed a self-organizing recurrent RBFNN based nonlinear MPC scheme (SR-RBF-NMPC) (Qiao et al. 2016). Comparisons with SORBF-NMPC schemes and other existing methods demonstrated its ability to achieve better control performance for DO concentration.

Furthermore, Du combined the benefits of RBFNN and PID control methods to develop an adaptive PID (RBF-PID) algorithm based on RBFNN to adaptively adjust PID parameters for better control of DO concentration in activated sludge processing (Du et al. 2018). Man proposed a developed back propagation neural network (BP)-PID control strategy and a fuzzy-PID control strategy, and compared these two strategies with conventional PID methods, showing better control performance (Man et al. 2018).

Several studies reported adaptive predictive control of DO concentration in the wastewater treatment process based on neural networks integrating with MPC methods. (Han et al. 2018) proposed a data-based predictive control (DPC) strategy using a self-organizing fuzzy neural network to identify the real-time states of WWTP and an adaptive second-order Levenberg-Marquardt algorithm to derive the control law of DPC for DO concentration control in WWTP. For realizing the optimal variable set-point tracking control of the DO concentration in a biological WWTP, (Sadeghassadi et al. 2018) designed a constrained nonlinear neural-network MPC methods to track the DO set point derived by multi-objective function. According to simulations with BSM1, this work achieved improvement in effluent quality and reduction in energy consumption in comparison with a fixed set-point PI controller. The adaptive fuzzy neural network-based model predictive control (AFNN-MPC) demonstrated that it could be a superior and efficient solution to control DO concentration (Han et al. 2019).

Both neural networks and fuzzy logic control methods belong to intelligent control methods. They may be combined together to be mutually beneficial. Fu developed a T-S fuzzy NN based DO concentration control system, using the error BP to adjust the learning rate online (Fu et al. 2015). The digital simulation proved that it had better effect and more stability, compared to simple T-S fuzzy controller, BP network controller and PID controller. The author forecasted that the method of self-organization fuzzy neural network might be researched, which was reflected in the work of (Zhang & Qiao 2020). This study presented a multi-variable direct self-organizing fuzzy neural network control (M-DSNNC) system comprised of a fuzzy neural network controller and a compensation controller. A merit of this work is that it does not need an exact plant model so that there is no need to waste time to establish the accurate mathematics model of WWTP. Besides this, a self-organizing mode allows the system to adapt the uncertainty environment.

Other hybrid control methods integrate fuzzy logic control methods with model predictive control methods or PID control methods. The fuzzy C-means cluster algorithm linked with least squares is an effective way to partition the required fuzzy space of input variables and establish fuzzy predictive model of DO concentration (Yang et al. 2014; Li et al. 2020). For both studies, digital simulations proved significant performance benefits and steady output. In addition, Santin presented a two-level hierarchical control structure, hoping to maintain control accuracy of DO concentration as well as reduce operational costs (Santin et al. 2015). The author chose MPC as a controller of the lower level and chose a fuzzy controller for the higher level, and met expectations. Liu adopted a self-adaptive fuzzy PID controller to accomplish DO concentration control and carried out the digital simulation (Liu & Yu 2017). Subsequently, Dasen proved its effectiveness and practicality in the actual sewage treatment central control system (Dasen et al. 2019).

Nowadays, DO control is combined with ammonia control, to not only save aeration energy but also achieve good effluent quality and low N₂O emissions and nitrogen removal (Bertanza et al. 2020; Zhang et al. 2021; Polizzi et al. 2022). Bertanza adopted fuzzy logic to calculate the DO set point which was based on effluent ammonia concentration (Bertanza et al. 2020). Simulation results, according to the BSM2 protocol, showed that the effluent quality could be improved by 7–8% and the aeration energy requirement could be reduced up to 13%. Subsequently, the system was installed in a full-scale WWTP and proved a reduction of the specific power consumption of 40–50% with respect to the previously installed PID controller (fixed DO set point). Sheik designed a two-level hierarchical supervisory control framework to alter the DO in the seventh reactor to control ammonia, achieving significant removal in ammonia and better effluent quality (Sheik et al. 2021). MPC and fuzzy logic are designed in the supervisory layer to alter the DO7 set point based on the ammonia composition. Polizzi proved that lowering the DO set point of the oxidation unit could result in energy saving according to plant managing decisions, based on the titrimeter long-term operation and historical data modeling (Polizzi et al. 2022). The applications of hybrid control schemes for DO control in WWTP in the recent 10 years are shown in Table 6.

The DO control strategies mentioned above explore from a theoretical point of view how to reduce the aeration energy consumption and operating costs of WWTPs, as well as how to achieve better effluent quality, more effective nitrogen removal and reduction of N₂O emissions. In practice, there are many real limitations and difficulties that prevent the full-scale implementation of these strategies. The obstacles may lie in lack of hardware conditions and support, inaccurate data acquisition and processing and unappropriated description of the transport phenomena in reactors, for example, such as the lack of flexibility in the actuators (air supply systems, pumps) and fault detection and correction of sensors. It is urgent and necessary to solve these limitations and obstacles.

Dissolved oxygen is an essential water quality factor for animals to survive and breathe in water, and suitable DO concentration is a critical element to ensure the healthy growth of fish in aquaculture. Industrial aquaculture develops gradually because of its good characteristics of high economic benefits and friendly environment. As industrial aquaculture, which is the collection of instrument, biological engineering and water treatment technology, is different from traditional natural aquaculture, the abnormal changes of some survival factors such as DO concentration will lead to the large-scale death of cultured organisms (Liu et al. 2014a). Therefore, it is of great importance to realize intelligent monitoring and control systems for industrial aquaculture, especially to realize the prediction, intelligent monitoring and control of DO and other water quality parameters. This section will give a comprehensive elaboration on researches about prediction and control methods of DO concentration in aquaculture from over the recent 10 years.

The prediction of DO concentration in aquaculture water under different aquaculture modes can provide an important theoretical basis for scientific management of aquaculture water quality, and it is also a crucial step before realizing accurate control of DO concentration. Many scholars have proposed a variety of methods for DO prediction, such as support vector machine (SVM) (Wei et al. 2011) and neural network models (Chen et al. 2020). This section reviews all kinds of methods applied for prediction of DO concentration in aquaculture water (Table 7).

SVM is a kind of generalized linear classifier which classifies data by supervised learning. When it is used to solve regression problems, it is called support vector regression (SVR). In the early stage, Liu et al. used SVR for much DO prediction work in aquaculture water, proposing several hybrid models based on SVR, such as real-value GA support vector regression (RGA–SVR), LSSVR model combining with improved particle swarm optimization (IPSO) algorithm (IPSO-LSSVR), and LSSVR with wavelet analysis (WA) and an optimal improved Cauchy particle swarm optimization (CPSO) algorithm (WA-CPSO-LSSVR), and obtaining relatively precise and reliable prediction results (Liu et al. 2013a, 2013b, 2014b, 2014c). Other researchers have also used SVM to predict DO concentration in aquaculture water. Yu proposed a least squares support vector machine (LSSVM) with an optimal IPSO and RBFNN data fusion method (RBFNN-IPSO-LSSVM) for DO prediction in outdoor crab ponds and validated its effectiveness and accuracy (Yu et al. 2016). Huan designed a combined forecasting model (EEMD-LSSVM) based on ensemble empirical mode decomposition (EEMD) and LSSVM to achieve multi-step prediction in order to forecast DO concentration for 24 hours into the future, and the root mean square error of this model achieved 0.0261 (Huan et al. 2018).

Neural network models are the most widespread prediction models. Various specific models have gotten their application for DO prediction in aquaculture, such as back propagation neural network (BPNN) RBFNN, fuzzy neural network (FNN), extreme learning machine (ELM), and recurrent neural network (RNN), etc. Chen utilized BPNN optimized by particle swarm optimization (PSO-BPNN) to realize three-dimensional short-term prediction of DO concentration, and the average error of the model tested only 0.0705 (mg/L) (Chen et al. 2018a). After that, he tried another model called subtractive clustering (SC)-K-means-RBF model for three-dimensional short-term prediction of DO concentration (Chen et al. 2018a), validating the effectiveness of the model. When talking about FNN, it was combined with primary component analysis (PCA) and GA, respectively, achieving stable and accurate DO prediction results (Peng et al. 2017; Ren et al. 2018).

As a specific FNN, ELM has been widely used by researchers for predicting DO concentration in aquaculture water. Huan used ELM to realize DO prediction, combining with K-means clustering (Huan et al. 2017). Cao proposed a hybrid model based on EEMD and regularized ELM (RELM) for DO prediction, and had satisfactory performance and high precision (Cao et al. 2019). Shi provided clustering-based softplus ELM (CSELM) to predict DO change from time series data at first (Shi et al. 2019), and on this basis, he then proposed a new hybrid method based on PSO and improved softplus ELM with partial least square (ELS) method, providing an accurate predictive model for DO tracking (Shi et al. 2020). Furthermore, Kuang proposed a hybrid model composed of K-means, improved genetic algorithm (IGA), and ELM, namely (KIG-ELM), in order to predict DO change through analyzing DO content, getting significant prediction results (Kuang et al. 2020).

Moreover, RNN plays an important role in DO prediction as well. In long-term DO prediction, Liu studied and validated the effectiveness of attention-based RNN, and achieved comparable performance with the state-of-the-art methods (Liu et al. 2019). After that, long short-term memory network (LSTM), which is a time recurrent neural network, was adopted to predict DO in the aquaculture pond (Huan et al. 2020). As a special class of LSTM neural network, gated recurrent unit (GRU) neural network was integrated with K-means or gradient boost regression tree (GBRT) to realize DO prediction of aquaculture water over different time intervals or three-dimensional prediction in different spaces in the pond, respectively (Cao et al. 2020, 2021).

In modern fishery, the use of sensors and wireless sensor networks (WSN) makes it easy to obtain various parameters data of aquaculture, causing the possibility of DO prediction. Stable and precise prediction of DO in aquaculture water is essential for its intelligent management and control. The realization of accurate prediction and control of DO concentration may timely avoid the financial loss caused by inappropriate DO concentration and reduce energy consumption.

DO concentration control in industrial aquaculture used to be timing control or manual control, which could neither meet the production needs of modern aquaculture nor keep up with the trend of scientific and technological progress. Many researchers have realized such dilemmas and made a lot of effort to achieve improvement and breakthrough of DO concentration control. Throughout this section, relevant literatures are reviewed.

Peng and Zhou designed an intelligent control and diagnosis system for aquaculture ponds, which realized the automatic adjustment of DO and other related parameters and deserved to be an early successful attempt of intelligent system applied in aquaculture, even though the control system cost a lot because it was established with complete sets of Siemens equipment (Peng & Zhou 2011). At the same time, an intelligent monitoring system for industrialized aquaculture was designed, using the algorithm of fuzzy control combined with neural network to process data and output closed-loop control signal (Shi et al. 2011). Through the test, the DO error was controlled within ±0.3 mg/L.

The WSN is an effective approach to establish monitoring and control systems for aquaculture, since it has more compact structures, higher accuracies, easier layouts and lower costs than traditional wired sensor network. An early example was shown in (Chang & Zhang 2013), which realized closed-loop automatic monitoring and control system of water quality factors for aquaculture. As for DO control, fuzzy PID algorithm was designed to process sensor data and output control signals to control the air flow rate to ensure the steady DO concentration (Shi et al. 2018), based on the work of Jiang who proposed a normalized fuzzy control system to improve the large fluctuation and long stable time of conventional PID control (Jiang et al. 2012). In order to make up for the deficiency of PID control of DO concentration, a MPC algorithm called DMC algorithm was proposed to achieve predictive control of DO concentration in Cynoglossus semilaevis industrial aquaculture (Liu et al. 2014a). Experimental tests showed that the DMC model could better solve DO nonlinear prediction problems and DO optimal control problems, in comparison with conventional PID control. Chen adopted fuzzy PID control combined with the gray prediction model to design the control mode, whose control target was DO concentration in recirculating aquaculture, and got excellent control precision and performance (Chen et al. 2019).

Sacasqui introduced an adaptive predictive control of DO concentration in whiteleg shrimp aquaculture (Sacasqui et al. 2017), the designed nonlinear controller was established on the NEPSAC control strategy (Chevalier et al. 2014), and managed to predict and control the DO behavior several hours in advance.

Prediction of DO concentration in aquaculture is related to the realization of intelligent DO monitoring and control. Several studies reported various DO prediction methods. The methods adopted to predict DO content in aquaculture was mainly based on neural networks combined with other algorithms, such as fuzzy neural networks prediction model (Ren et al. 2018), the subtractive clustering (SC)-K-means-radial basis function (RBF) model (Chen et al. 2018a), ensemble empirical mode EEMD-LSSVM model (Huan et al. 2018), attention-based recurrent neural networks (RNN) model (Liu et al. 2019), and a hybrid model based on the multiple-factor analysis and the multi-scale feature extraction (Cao et al. 2019). These works pave the way for achieving more intelligent predictive DO control systems for fish growth in aquaculture.

The work of Ferreira et al. (2021) and Roy et al. (2021) showed the design process of the monitoring and control system for smart fish farming, respectively, demonstrating great significance to the development of efficient and intelligent fishery. Even though establishing such intelligent monitoring and control systems may require huge initial investment, it is still extremely worth developing and extending smart aquaculture across the regions. At the same time, it will be the trend and breakthrough point of future researches to embed advanced intelligent control algorithms in the control systems for aquaculture to realize the intelligent optimal control of DO concentration in water. The applications of control schemes for DO control in aquaculture from the last 10 years are shown in Table 8.

DO control plays an important role in the municipal wastewater treatment plants and in modern aquaculture. For both WWTPs and modern industrialized aquaculture plants, aeration energy consumption accounts for the largest proportion of the total plant energy consumption (Lazic et al. 2012; Cruz et al. 2019). Improving aeration control technologies and strategies to reduce aeration energy consumption has become a research direction for many scholars. This review has reviewed and categorized various DO control strategies and technologies in WWTP and in aquaculture. For further analysis, a comprehensive discussion has been made on the different types of DO control strategies.

Many advanced and intelligent automatic control strategies have been researched to improve DO control performance and reduce energy consumption and operating costs in WWTP. Popular advanced control strategies, such as MPC methods intelligent control methods and hybrid control methods, have their unique merits and flaws.

MPC is one of the advanced control technologies widely approved after PID, which adopts the rolling optimization strategy, has strong anti-interference ability and good dynamic performance. This method has been successfully implemented in a WWTP located in Lancaster, UK (O'Brien et al. 2011). However, there are still some difficulties in the application of MPC to improve DO control in the wastewater treatment industry. First, though linear predictive control technology is relatively mature, nonlinear predictive control technology is still immature due to the high cost of modeling the nonlinear model. As the DO control is a kind of process control which includes uncertain nonlinearities and time-delayed components, it is difficult to obtain a highly accurate model, which makes the application of predictive control in the WWTP limited. Then, MPC theory disconnects with its practical applications, providing little guidance on practical applications. Moreover, predictive control algorithms involve a huge number of calculations and require computing equipment with excellent performance. These also hinder its application in DO control of the WWTP.

Fuzzy control does not need to establish an accurate mathematical model of the controlled object in the design, and is combined with PID control to achieve more effective DO control (Piotrowski 2020; Piotrowski & Ujazdowski 2020; Wu et al. 2022). Neural networks can map arbitrarily complex nonlinear relationships with simple learning rules, due to their strong nonlinear fitting and self-learning abilities. Therefore, neural networks have been used in an attempt to construct optimistic algorithms and models, combined with other control methods, in order to achieve optimal DO control (Zhang & Qiao 2020; Ansari et al. 2021; He et al. 2021). The drawbacks are that it requires a lot of data for training, which generally requires high hardware configuration, and it is difficult to understand its internal mechanism and to choose meta parameters and network topologies.

Hybrid control strategies have been gradually studied and tried in DO control, to improve control performance and achieve the goal of reducing aeration energy consumption and operating costs, good effluent quality and low N₂O emissions of WWTP (Zhang & Qiao 2020; Li et al. 2021a; Zhang et al. 2022). The majority of those literatures just provides simulation and experimental results, which demonstrates that sophisticated hybrid control strategies are still in the stage of simulation experimentation and are not able to be transformed into full-scale engineering implementation. There is still a certain gap between the experimental stage and practical usage.

In the practical application of WWTPs, PID control is by far the most widely used and approved DO control strategy, because the performance of PID control can basically meet the requirements of aeration control, it is easy to debug, and the cost is low. However, the control performance of PID control is limited. The traditional PID parameters are not adaptive, which makes it difficult not only for the controller to quickly track the trajectory of the DO concentration setting, which is varied in time according to higher exigencies such as a good effluent quality, but also for the actual DO concentration to quickly reach and maintain at the desired level. When intelligent control and other advanced control strategies are attempted in aeration control, the accuracy of DO control is improved, and the aeration energy consumption is significantly reduced, as reviewed above. However, even though these complicated control methods may be proved to be successful under experimental conditions, most of them cannot be put into practice for various reasons. The main reasons are as follows: (1). Complicated control approaches do not always demonstrate a very significant improvement in the simulation results, when comparing with more classical and simple control approaches which are properly designed and tuned. In control, more complex controllers do not mean better control effects, especially when considering robustness and the risk of equipment failure. (2). High-performance computers or edge hardware with sufficient computing power are required. (3). The control strategies can only be realized by upgrading the equipment, which will cause large equipment replacement and transformation costs in the short term. (4). The difference of on-site environments makes the control strategies unable to be applied directly. In summary, engineering is the integration of advancement, reliability and economy of technology, so the actual infrastructure and environment cannot be effectively combined with these control strategies, making these control strategies unable to be fully implemented.

The development of DO control in aquaculture is relatively slower than that of WWTPs. It will be a worthwhile but tentative process to adopt the successful advanced control strategies applied in the WWTPs to improve DO control in aquaculture, combined with their own characteristics. In addition, it is significant to find ways to connect DO prediction methods with its control methods, which has not been created yet, to realize intelligent management and control of aquaculture.

More than 20 years into the 21st century, DO control strategies for wastewater treatment processes and aquaculture have changed. Various advanced control strategies including model-based predictive control, intelligent control and hybrid control have been proposed in an effort to save aeration energy, improve control efficiency and nitrogen removal, as well as increase the effluent quality in WWTP and the health index of cultured fish in aquaculture. However, the main efforts have been focused on method development using simulation models so far, only a few advanced control models have gotten successful implementation, while PID controllers are still the most widely used and effective control method in engineering practice. The challenges and limitations for a broader implementation of all these control strategies may lie in the lack of hardware conditions and suitable facility environments. How to solve the challenges and make these controllers achieve broader implementation will be a research focus and will help to reinforce the benefits of improved process control.

Not applicable.

All authors contributed equally to the paper.

This article does not contain any studies with animals performed by any of the authors.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

Research and creation of key technologies of digital fishery intelligent equipment (Grant no. 2021TZXD006) and 2021 modern agricultural industrial technological systematic shrimp and crab intelligent farming (Grant no. CARS-48).