## Abstract

Fresh water demand is growing drastically in many parts of the world. Desalination of seawater, brackish water, and waste water is one solution to meet the demands of fresh water. Currently, reverse osmosis (RO) desalination process is one of the best methods for the desalination process. In this study, a modified controller design is proposed for RO desalination system based on symbiotic organisms search (SOS) algorithm. A multivariable model of RO desalination plant is considered for experimentation. The RO system considered here is first decoupled using a simplified decoupling process to obtain two non-interacting loops. Then, a proportional-integral-derivative controller with second order derivative (PID-DD) scheme based on SOS algorithm is proposed for each loop to find optimal control parameters of the RO system. To design the PID-DD controller for each loop, integral of squared error (ISE) is considered as fitness function. Four other state-of-the-art optimization algorithms, namely, teacher-learner-based-optimization (TLBO), differential evolution (DE), particle swarm optimization (PSO), and artificial bee colony (ABC), algorithms are also tested for the considered system. To show competitiveness of the proposed SOS-based PID-DD controller, a comparative study based on time domain analysis is performed. Results show the SOS-based PID-DD controller is superior to other PID-DD controllers.

## INTRODUCTION

Desalination is a method by which seawater and brackish water is filtered out in the form of fresh water by using chemical and physical processes so that the unusable water is made available for industrial, irrigation, and drinking purposes (Sobana & Panda 2011). In the last few years, significant developments in the area of desalination technologies have been seen all over the world. At present, many desalination techniques such as multistage-flash distillation (MSF), multiple-effect distillation (MED), evaporation, vapor-compression (VC), and membrane processes are used for water treatment. Among all the desalination methods, the reverse osmosis (RO) water treatment method is accepted worldwide due to its simplicity and high performance with minimal cost requirements (Sobana & Panda 2014).

The RO desalination process, in spite of being simple, is easy to implement and versatile in nature, and thus can be used for treatment of water; but still the technology suffers from the problems of membrane fouling and concentration polarization (Madaeni *et al.* 2015). However, these problems can be solved with advance technology in terms of process and control optimization. Traditionally, a combination of proportional-integral-derivative (PID) controller is incorporated to fulfill the control objectives in many applications. Alatiqi *et al.* (1989) first proposed traditional PID controllers in RO desalination plants. Furthermore, Robertson *et al.* (1996) used a modified Ziegler–Nichols (MZN) method for the tuning of PID controller parameters. Classically, the PID controllers are tuned with conventional techniques such as Ziegler–Nichols, MZN, trial and error method, Cohen and Coon (Bennett 2001), etc. Simple PID controllers with conventional tuning methods do not provide satisfactory results with plant and model uncertainties. A model predictive control (MPC) approach is presented in Abbas (2006) to overcome the limitations of PID controllers in RO desalination units. With the evolution of various optimization techniques, conventional methods of PID controller tuning are being replaced by optimization-based techniques (Åström & Hägglund 2006; Rathore *et al.* 2015a, 2015b; Gupta *et al.* 2016).

A literature survey shows that researchers have used many intelligent optimization techniques for the RO desalination problem. Zilouchian & Jafar (2001) and Kim *et al.* (2008) presented a genetic algorithm (GA)-based controller design for RO desalination plants. In Gambier (2011), a multi-objective optimization-based controller was designed for RO desalination systems. Although the algorithm is found to be superior to conventional methods, it still suffers from proper tuning of algorithm-specific parameters. Fuzzy logic and neural networks have been applied to investigate the RO desalination problem (Madaeni *et al.* 2015). Phuc *et al.* (2016) suggested a modified PID controller based on loop shaping method for desalination plants. However, the problem associated with these controllers is that they increase the complexity, mathematical complications, and computational efforts in the controllers. Therefore, in these techniques, the researchers/engineers need expert knowledge of the complex procedure and its applicability for practical use in RO desalination plants. This makes them less popular among researchers/engineers. Hence, the design procedure for the aforementioned controller needs further investigation (Jiang *et al.* 2016). Moreover, there are no limitations associated with classical PID controllers, which are simple, reliable, and affordable to use (Gambier *et al.* 2009). Therefore, optimization-based controller techniques have proven themselves in terms of better performance, simplicity, and less computation efforts required for the optimal tuning of controller parameters.

Rathore & Singh (2018) proposed a PID controller using teacher-learner-based optimization (TLBO) for RO desalination. The proposed method shows its superiority over other state-of-the-art techniques available in the literature. Recently, Sahib (2015) presented a new controller scheme, which is a combination of PID controller with second order derivative controller (DD). This combination is newly adopted and found to be efficient in a few research problems such as automatic voltage regulator (AVR) (Sahib 2015), automatic generation control (AGC) (Raju *et al.* 2016), etc. However, this control technique is not implemented in RO desalination systems.

In the current work, a new optimization algorithm, i.e., symbiotic organism search (SOS), proposed by Cheng & Prayogo (2014), is applied to design a PID-DD controller for RO desalination plants. The tuning of parameters for PID-DD controllers is achieved by minimizing the integral of square error (ISE) criterion. The RO model proposed by Riverol & Pilipovik (2005) is considered for experimental testing. In this procedure, a simplified decoupling method is first used to transform the multivariable RO model to a single-input single-output (SISO) model. Then, the proposed SOS-based controllers are examined for permeate flux and conductivity variables, respectively. Comparative studies of the proposed controllers with TLBO, DE, PSO, and ABC algorithm-based PID-DD controllers are presented in order to prove its supremacy over others.

The remainder of the paper is organized as follows. The section below introduces the RO seawater desalination process and its model structure. This is followed by a section that gives the modified controller design approach used in this work. Then the basics of the SOS algorithm applied to a RO desalination plant are discussed. Simulation results and comparison follow and the final section concludes the paper and discusses future avenues of research.

## REVERSE OSMOSIS SEAWATER DESALINATION PROCESS

A generalized layout for a RO desalination system is shown in Figure 1. In this model, the RO system is characterized by four main segments, i.e., pre-treatment, high-pressure pump, membrane module, and post-treatment (Gambier *et al.* 2009). In the first segment, i.e., pre-treatment, saline water obtained from the sea or any other source is filtered through a chemical and physical process to remove major impurities present in the water. This process is very important in RO desalination plants in order to enhance the life cycle of the RO membrane. Also, it reduces scaling and fouling. In the next segment, a high-pressure pump is provided to raise the pressure of incoming water from the pre-treatment process. In the subsequent segment, the pressurized water is fed to a membrane assembly module. The membrane assembly module should be strong enough to withstand pressurized feed water. Therefore, the RO membrane assembly module is made up of a composite polyamide-type membrane, which is widely used in many RO desalination plants. After passing through membrane assembly, fresh water accumulates in a storage tank and brine water is discarded by the membrane accumulates at the discharge channel. The fresh water obtained from this process is post-treated in the last segment by adding some inhibitors and adjusting the pH value to the appropriate level (Rathore & Singh 2018).

Figure 1 contains all four segments, manipulated variables, and control variables. Manipulated variables are (pressure) and (pH value) at feed stream, respectively, and control variables are (flux) and (conductivity) at permeate stream, respectively.

### Modeling of RO seawater desalination system

*et al.*(1989) at Doha laboratory. Thereafter, different models of RO system have been developed by many researchers. In the present work, a multi-input multi-output (MIMO) dynamic model proposed by Riverol & Pilipovik (2005) is used for the experiment. There are two control-loops, one is for pressure at the feed stream to control flux and conductivity at the permeate stream and the second is for pH at the feed stream to regulate conductivity at the permeate stream in this model. The algebraic transfer function equations are identified based on this model and can be represented as follows: where (m

^{2}/d) is flux rate and is conductivity at the permeate stream, while (kPa), and are the pressure and pH values at the feed stream. The transfer function values for , , , and are represented as follows: The transfer function Equations (2)–(5) in standardized form can be represented as: where , , , and represent process gain, numerator zero, time constant, and damping ratio, respectively.

The operating range for the linear model parameters of RO system is as listed in Table 1.

System parameters | Range |
---|---|

Feed pressure | 800–1,000 (kPa) |

Feed pH () | 6–7.2 |

Permeate flux-rate | 33,000–15,400 (m^{2}/d) |

Permeate conductivity | 400–500 |

System parameters | Range |
---|---|

Feed pressure | 800–1,000 (kPa) |

Feed pH () | 6–7.2 |

Permeate flux-rate | 33,000–15,400 (m^{2}/d) |

Permeate conductivity | 400–500 |

### Decoupling in RO desalination system

## PROPOSED MODIFIED CONTROLLER SCHEME

The proposed modified controller consists of a PID controller with a DD controller. The second order derivative or double derivative controller provides a better response than PID control structures (Sahib 2015). The control structure of PID-DD is illustrated in Figure 3.

*p*is the order of error function .

## SYMBIOTIC ORGANISMS SEARCH OPTIMIZATION

SOS optimization is a newly developed metaheuristics algorithm based on the natural phenomenon of organisms (Cheng & Prayogo 2014). The SOS algorithm shows the symbiotic relationship within paired organisms present in the ecosystem. Similar to other organisms like honeybee swarms, particle swarm optimization, and genetic algorithms, the SOS optimization algorithm uses the bunch of population and it searches the global best solution for the given problem within the search space. In this algorithm, there are three phases based on the relationships of real-world organisms. The three phases are mutualism, commensalism, and parasitism phases.

Further details of these three phases are given as follows.

### Mutualism phase

### Commensalism phase

### Parasitism phase

In parasitism, only one organism benefits, but the other organism is harmed by the first organism. In this way, plasmodium parasites pass into the human body with the help of Anopheles mosquitoes, where they get food and increase their population and, in return, humans suffer from malaria and may die.

In the SOS algorithm, a parasite vector is created by duplicating organisms in the search space. Further, organisms are modified randomly using a random number to obtain the parasite vector. Organisms are treated as host in the ecosystem for the parasite vector. This parasite vector tries to replace . If the fitness of the parasite vector is better than that of , then the parasite vector will replace .

The steps for the SOS algorithm are given as follows:

*Step 1*: Generate initial population in the ecosystem randomly.

*Step 2*: Determine the fitness value and find their value for each organism.

*Step 3*: Select the randomly such that (*Mutualism phase*)

*Step 4*: Calculate mutual vector and benefit factor () either 1 or 2.

(*Commensalism phase*)

*Step 6*: Repeat step 3 and modify the solution according to Equation (16).

(*Parasitism phase*)

*Step 7*: Repeat step 3 and create parasite vector from .

Calculate the fitness value

**end if**

*Step 7*: Repeat step 2 and proceed for next iteration.

*Step 8*: Stop if termination criterion is met.

## RESULTS AND COMPARISONS

Two case studies are considered in this work to examine the performance of the modified PID controller with different optimizing techniques presented in the literature. The objective function designed in Equation (13) is tested for permeate flux and conductivity parameters, respectively.

### Case study 1

In the first case, the performance of the PID-DD controller with SOS, TLBO, DE, PSO, and ABC optimization algorithms is tested. The PID-DD controller parameters obtained from different algorithms are presented in Table 2 and performance indices are given in Table 3. It is found that the minimum performance index is found with the SOS-based PID-DD (SOS-PID-DD) controller. Time response analysis for flux is plotted in Figure 4 and their values are tabulated in Table 3.

Algorithms | PID-DD parameter values | |||
---|---|---|---|---|

SOS-PID-DD | 800.4356 | 1,248.7717 | 86.9817 | 20.8975 |

TLBO-PID-DD | 468.0110 | 1,475.5126 | 149.9817 | 18.0496 |

DE-PID-DD | 514.8157 | 1,468.0129 | 148.9012 | 39.6841 |

PSO-PID-DD | 428.1203 | 1,388.3628 | 264.3257 | 11.2334 |

ABC-PID-DD | 413.9842 | 1,365.1558 | 246.2006 | 26.9244 |

Algorithms | PID-DD parameter values | |||
---|---|---|---|---|

SOS-PID-DD | 800.4356 | 1,248.7717 | 86.9817 | 20.8975 |

TLBO-PID-DD | 468.0110 | 1,475.5126 | 149.9817 | 18.0496 |

DE-PID-DD | 514.8157 | 1,468.0129 | 148.9012 | 39.6841 |

PSO-PID-DD | 428.1203 | 1,388.3628 | 264.3257 | 11.2334 |

ABC-PID-DD | 413.9842 | 1,365.1558 | 246.2006 | 26.9244 |

Parameters | Controllers | ||||
---|---|---|---|---|---|

SOS-PID-DD | TLBO-PID-DD | DE-PID-DD | PSO-PID-DD | ABC-PID-DD | |

Performance index (ISE) | 1.8762 × 10^{−4} | 2.83469 | 1.86968 | 2.6128 | 2.9022 |

Rise time | 0.39481 | 0.43864 | 0.6801 | 0.5340 | 0.4925 |

Settling time | 2.5084 | 3.8895 | 18.7737 | 9.7542 | 11.1940 |

Overshoot (%) | 3.8913 | 12.5346 | 20.1320 | 22.0740 | 26.7780 |

Peak | 1.0389 | 1.1253 | 1.2013 | 1.2207 | 1.2677 |

Parameters | Controllers | ||||
---|---|---|---|---|---|

SOS-PID-DD | TLBO-PID-DD | DE-PID-DD | PSO-PID-DD | ABC-PID-DD | |

Performance index (ISE) | 1.8762 × 10^{−4} | 2.83469 | 1.86968 | 2.6128 | 2.9022 |

Rise time | 0.39481 | 0.43864 | 0.6801 | 0.5340 | 0.4925 |

Settling time | 2.5084 | 3.8895 | 18.7737 | 9.7542 | 11.1940 |

Overshoot (%) | 3.8913 | 12.5346 | 20.1320 | 22.0740 | 26.7780 |

Peak | 1.0389 | 1.1253 | 1.2013 | 1.2207 | 1.2677 |

### Case study 2

In the second case, to establish the capability of the proposed SOS-PID-DD controller, other controllers based on TLBO, DE, PSO, and ABC optimization algorithms are also designed for loop 2. The PID-DD controller parameter values are presented in Table 4 and performance indices are tabulated in Table 5. It is obvious from simulation results that performance index is minimum for the SOS-PID-DD controller. Time response analysis for conductivity with the PID-DD controller using different algorithms is shown in Figure 5 and their time response specifications are also tabulated in Table 5 for comparison.

Algorithms | PID-DD parameter values | |||
---|---|---|---|---|

SOS-PID-DD | 4.8001 | 20.0607 | 2.0909 | 0.0250 |

TLBO-PID-DD | 2.2136 | 18.0293 | 2.9087 | 0.0341 |

DE-PID-DD | 1.6001 | 16.0607 | 2.02679 | 0.0922 |

PSO-PID-DD | 0.77192 | 8.0531 | 2.0853 | 0.0862 |

ABC-PID-DD | 0.976 | 6.1057 | 2.0473 | 0.0162 |

Algorithms | PID-DD parameter values | |||
---|---|---|---|---|

SOS-PID-DD | 4.8001 | 20.0607 | 2.0909 | 0.0250 |

TLBO-PID-DD | 2.2136 | 18.0293 | 2.9087 | 0.0341 |

DE-PID-DD | 1.6001 | 16.0607 | 2.02679 | 0.0922 |

PSO-PID-DD | 0.77192 | 8.0531 | 2.0853 | 0.0862 |

ABC-PID-DD | 0.976 | 6.1057 | 2.0473 | 0.0162 |

Parameters | Controllers | ||||
---|---|---|---|---|---|

SOS-PID-DD | TLBO-PID-DD | DE-PID-DD | PSO-PID-DD | ABC-PID-DD | |

Performance index (ISE) | 0.0322 | 0.1610 | 0.4050 | 0.4370 | 0.5029 |

Rise time | 0.9807 | 0.9804 | 0.9723 | 0.8552 | 0.9636 |

Settling time | 3.9597 | 10.7761 | 15.1472 | 28.1165 | 15.6693 |

Overshoot (%) | 0.6513 | 1.3364 | 2.2324 | 3.1152 | 2.5406 |

Peak | 1.0065 | 1.0133 | 1.0223 | 1.0312 | 1.0254 |

Parameters | Controllers | ||||
---|---|---|---|---|---|

SOS-PID-DD | TLBO-PID-DD | DE-PID-DD | PSO-PID-DD | ABC-PID-DD | |

Performance index (ISE) | 0.0322 | 0.1610 | 0.4050 | 0.4370 | 0.5029 |

Rise time | 0.9807 | 0.9804 | 0.9723 | 0.8552 | 0.9636 |

Settling time | 3.9597 | 10.7761 | 15.1472 | 28.1165 | 15.6693 |

Overshoot (%) | 0.6513 | 1.3364 | 2.2324 | 3.1152 | 2.5406 |

Peak | 1.0065 | 1.0133 | 1.0223 | 1.0312 | 1.0254 |

## CONCLUSION

In this work, a new optimization approach, i.e., SOS is tested for PID with a second order derivative (DD) controller to examine the performance of permeate flux and conductivity parameters of an RO system. The effect of the SOS algorithm with the PID-DD controller is found to be superior to other methods of optimization in the literature. Hence, it can be concluded that the proposed method is quite satisfactory and can be successfully implemented for RO desalination plants. Future work includes the design and tuning of a modified PID-DD controller for other models proposed for RO desalination plants. Additionally, this work can be extended to design a robust modified PID-DD controller for RO desalination plants.