## 1 Introduction
In a later work, [PERSON] [26] minimized the \(SEC\) of an SWRO system (18 pressure vessels (PVs) each with 6 SWMMs in series) through a non-linear optimization model. A robust model-based control for an RO desalination unit with tubular membranes was proposed by [PERSON] et al. [27]. The three-parameter nonlinear Spiegler-Kedem model was used in this work. The same model was used by [PERSON] et al. [28] in a periodic control work in a tubular RO process. [PERSON] [29] designed a robust PID controller using a multi-objective normal boundary intersection algorithm. A pilot BWRO desalination plant for tap water purification was used. The model of the aforementioned plant was simplified to a single-input single-output (SISO) system, where input was the RO concentrate valve position and output the permeate flow. [PERSON] et al. [30] designed a PID controller for a simulated SWRO system with HFMs using the solution-diffusion model. [PERSON] et al. [31] proposed a cascade control system for a simulated RO system with SWMMs. The models (steady state and dynamic) used had previously been proposed by [PERSON] et al. [32], and were based on solution-diffusion, mass balance and momentum balance. [PERSON] and [PERSON] [33] studied model-based controls in a simulated SWRO system taking into consideration servo and regulatory problems. The model was based on transfer functions and the outputs were \(Q_{\text{p}}\), permeate concentrate (\(C_{\text{p}}\)) and pH\({}_{\text{f}}\) and the inputs \(p_{\text{f}}\) and flux recovery \(R\). A modified PID control with H-infinity loop shaping synthesis for simulated RO systems was proposed by [PERSON] et al. [34]. A transfer function model was obtained for the RO system considering angular pump speed and RO concentrate valve position as inputs and \(Q_{\text{p}}\) and \(C_{\text{p}}\) as outputs. In a later work [35], the same authors carried out a dynamical analysis and control synthesis for RO systems against water hammering. In this case, a dynamical model based on a macroscopic kinetic energy balance and irreversible thermodynamics previously developed by [PERSON] et al. [25] was used. [PERSON] et al. [36] used a transfer function-based model to propose a fractional order controller for a SWRO system. The dynamics of the system were experimentally identified. A control system comprised of two loops, the first using a loop-shaping design method and the second a super-twisting sliding mode control, was proposed by [PERSON] et al. [37]. The RO system model was based on mass and energy balances. An implementation of an expert model predictive controller in a pilot BWRO and SWRO system was carried out by [PERSON] et al. [16]. The expert controller included an identification block with on-line calculation of the parameters of the prediction model. The model for the RO systems was based on transfer functions. [PERSON] et al. [38] proposed a power control strategy for a BWRO desalination plant powered by an isolated hybrid photovoltaic/wind source without battery. A solution-diffusion model was used for the RO process. Experimental work was done to determine performances under different operating conditions in the safe operating window (SOW). Different feedwater concentrations were considered (2, 4 and 6 g L\({}^{-1}\)) and \(R\) was limited to 20%. The proposed control system allowed operation of the BWRO desalination plant for a wide range of power variations. Most of the aforementioned works used process modeling based on transfer functions or more precise models without experimental validation. Under normal conditions, BWRO is more efficient than SWRO desalination due to the difference in the osmotic pressure of the feedwater solutions. This makes the use of RES an attractive option to power BWRO desalination systems. The composition of groundwater, one of the main feedwater sources tends to fluctuate as the result of variations in different factors (temperature, rainfall, agricultural irrigation, etc.) [39; 40].