PID Control of Reverse Osmosis Based Desalination Process
Introduction
One of the most widespread problems upsetting people throughout the world is insufficient access to clean water. Right now, the solution is desalination. The desalination processes can be classified according to the separation methods as: thermal based or membrane based methods. The most common membrane based method is the reverse osmosis (RO) where the feed water is passed through semi-permeable membranes under high pressure to remove the salt particles. The very high feed pressures required to achieve a desired permeate production rate makes the cost of energy of a typical seawater RO desalination system approaching to 45% of the total permeate production cost. Different attempts have been made to reduce the energy needed by RO desalination system such as increasing membrane permeability, use of energy recovery devices, and use of an efficient and accurate control system [3].
Several contributions can be found in the literature on the design and implementation of controllers for RO systems. For instance, in [4] authors used open loop step response data from RO plant to construct a MIMO model. Best pairing of input/output control structure were formulated using system relative gain array and controllability tests. SISO PID controllers were tuned using Zeigler-Nichols settings. The RO plant was simulated in closed-loop with BLT (Biggest-log modulus) tuning criteria. However, the robust characteristics of the controller and the controller performance in presence of measurement-noise or in real time are not very well understood from these theoretical results. Moreover, controller tuned by Ziegler Nichols method produces a good but not optimum system response. Classical Dynamic Matrix Control (DMC) algorithm uses a step response model to calculate the values of the manipulated variables that give the smallest sum of squares error between the set points and the predicted values of the controlled variables. Abbas [5] used constrained and unconstrained DMC algorithms to control a simulated RO model developed by Alatiqi et al. in [3]. He showed that the DMC algorithms produce faster response and more robust characteristics than conventional PI control when applied to Alatiqi model.
In this work, a rigorous mathematical model for the DuPont's B10 Hollow Fibre module presented in [3] has been fitted. Then, a first order transfer function has been built to provide linear approximation of the rigorous mathematical model. Finally, a PID controller has been designed for the linear transfer function and used to control the rigorous model. Optimal PID design based on the minimization of the integral of the squared error (ISE) performance index was used to tune the controller.
Section snippets
Modeling of RO process
Models that adequately describe the performance of RO membranes are very important since these are needed in the design of RO processes. In this work, a steady state model of RO process that takes into account concentration polarization (CP) has been developed for the DuPont's B10 Hollow Fibre module presented in [3], based on Kimura-Sourirajan model which describe transport phenomena through the membrane [6]. According to Marcovecchio [7], this model is the most used for this propose because
System identification
Identification was carried out using MATLAB's identification tool box where a sum of sinusoids input signal shown in Figure 2 (left) were generated and fed to the rigorous model. Then, a linear transfer function was fitted to approximate the response of the rigorous model shown in Figure 2 (right) to the sinusoidal input.
The best transfer function to fit the process in the least square sense was found to be:
Figure 2 shows the response of the process transfer
Controller Design and Response
The PID controller is usually used to improve the dynamic response as well as to reduce or eliminate the steady state error. The derivative controller adds a finite zero to the open loop plant transfer function and improves the transient response. The integral controller adds a pole at the origin, thus increasing system type by one and reducing the steady state error due to a step function to zero. Minimizing integral of squared error (ISE) is commonly referred to as a good performance index in
Conclusion
Developing an optimization-based PID controller for a rigorous model (representing the real plant) of a hollow fiber RO process has been addressed in this work. Such controller was built based on linear approximation of the dynamics of the rigorous nonlinear mathematical model. Linear regression was used to estimate the linear approximate model. The PID design was based on minimizing integral of square error performance index. Simulation showed that the process was able to track step change of