optimal model based control for reverse osmosis ...

Journal of Advanced Research in Dynamical and Control Systems

Vol. 9. Sp– 18 / 2017

OPTIMAL MODEL BASED CONTROL FOR REVERSE OSMOSIS DESALINATION PROCESS 1

*Lakshmanaprabu S.K , 2Shankar K, 3Sabura Banu U

1 *Research Scholar, 2Assistant Professor, 3Professor Department of Electronics and Instrumentation Engineering 1,3 BS Abdur Rahman Crescent Institute of science and Technology, Chennai, India 2 School of Computing, Kalasalingam Academy of Research and Education, Krishnankoil, India. [email protected] 1,3

ABSTRACT In this paper, multiloop Internal model controller based PID (IMC-PID) controller is designed for simulation of reverse osmosis (RO) desalination process. The main aim of this work is to control the permeate flow rate and PH level of reverse osmosis by manipulating the feed pump pressure and recycle ratio. The process interaction is analyzed by Relative Gain Array (RGA) method and proper variable is chosen and paired for satisfactory control performance. The higher order model is reduced into First Order plus Dead Time (FOPDT) system. In proposed method IMC based PID controller was designed by choosing proper filter constant and controller performances were shown. Simulation studies show the feasibility of computational analysis of the interacting process. Keywords: Desalination; multiloop control; IMC based PID control.

I. INTRODUCTION The Requirement of producing fresh water can be fulfilled by automating the desalination plants. Many methods have been used for desalination, but reverse osmosis is limelight techniques because of low energy requirement and modular design and low water production cost[1].The reverse osmosis process is more sensitive to change in load input as well as the operating conditions. So it is necessary to maintain the operating condition and fluid flow of process in control limit [2][3]. The productivity of reverse osmosis can be improved by proper controlling techniques. Many control techniques have been implemented in reverse osmosis process, but multi loop control scheme is preferable for industrial process for easy implementation and failure tolerance[4][5].The multi loop SISO controllers is tuned by Zeigler-Nichols settings, the biggest-log-modulus tuning method and sequential loop closing method. The centralized control like constrained model predictive control (CMPC) and Dynamic Matrix control (DMC) (Gambieret al. (2007)) also designed for Reverse osmosis process[6][7][8]. JARDCS

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The Internal Model Control (IMC) is only applicable for open loop stable process, but the use of feedback controller make unstable process into stable process. So the best part of IMC [9][10] and feedback algorithm combined to design IMC based PID. Initially IMC controller is designed by considering Pade’s approximated dead time. Process model decide the PID parameter values, the controller performance is based on tunable filter time constant. In this paper, IMC a model based controller for controlling the permeate flow rate and pH level of the reverse osmosis desalination system. Internal Model Control (IMC) has the combined advantage of both open and closed systems.IMC performances are compared

with

conventional controller based on integral square error (ISE) and integral absolute error (IAE) for set point and load disturbances.

II. PROCESS DESCRIPTION The desalination system consists of equalization tank and reverse osmosis membrane and collection tank. The input sea water is filtered by input filters and it is pumped to the membrane section for purification. The manipulated input for the process is pump pressure change on feed water and reverse ratio. Many types of molecules and ions are removed from the sea water. The final output of fresh water is stored in product tank.

Figure 1: Schematic diagram of Reverse osmosis process

A. Mathematical model The mathematical model for RO system is developed by mass balance equation. The Multi Input Multi Output model was developed by sobana and panda [2] [3]. The transfer function model is developed by proper selection of operating points. The transfer function for feed tank, brine tank, permeate tank also modelled and the higher order process is converted into reduced order transfer function model. Here, two input two output is consider for controller design. The inputs for the system are pump pressure and ratio of flow rates of seawater feed to that of brine stream. The output of the process are permeate flow rate and permeate pH. JARDCS

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 1.4944e 0.55 s  Fp   0.71615 s  1  pH     0.114411e 0.55 s p   7s  1 

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0.092857e 0.3666 s   1.1875s  1   P    0.1781e 0.15 s   RFB   2.5s  1 

III. INTERACTION ANALYSIS The challenging task of MIMO is to understand the effect of each manipulated variable on output. The control engineer must know the exact process interaction between inputs and outputs before designing controller. This analysis is called as interaction analysis or control loop selection. One method for designing and analyzing a MIMO control scheme for a process in steady state is with a Relative Gain Array (RGA). The RGA provides a quantitative approach to the analysis of the interactions between the controls and the output, and thus provides a method of pairing manipulated and controlled variables to generate a control scheme. This simple measure of interaction matrix named as relative gain array matrix describes the impact of each manipulated variable on the controlled output.

 K 11 Gain matrix of plant is G (0)    K 21

K 12   1.494  K 22   0.114

 11 Relative Gain array R G A       21

11 

0.928   0.178 

12   22 

k11k22  1.6 k11k22  k12 k21  1 .6 RGA       1 .6

 1 .6  1 .6 

The column in RGA matrix for inputs and row in RGA matrix for outputs. For example, first row second column matrix elements give the impact of second input on first output. Similarly 2nd row 2nd column element describes the impact of 2nd input on 2nd output. From this matrix, process engineer can easily compare the relative gain of each input output pairs and he can select the best pairing for control loop design. RGA is a normalized form of the gain matrix. RGA has been widely used for the multi-loop structure design, such as a ratio of an openloop gain to a closed-loop gain. Variable pairing is done by selecting the positive values of relative gain close to value 1.

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IV. IMC-PID CONTROLLER DESIGN IMC controller rearranged and converted into standard feedback control structure. PID controller is designed by using IMC procedure, because most industries still using PID controllers. IMC fails to control unstable process, so PID must be use to control Unstable process. The main advantage of feedback structure is it can change unstable process into stable process. The Internal model control uses the model transfer function for control design. The inverse of process will act as very good controller; this fundamental concept is used in IMC with filter. The controller can be tuned by adjusting the filter values. IMC controller rearranged and converted into standard feedback control structure. PID controller is designed by using IMC procedure, because most industries still using PID controllers. IMC fails to control unstable process, so PID must be use to control Unstable process. The main advantage of feedback structure is it can change unstable process into stable process.

Figure 2: Multiloop IMC based PID control scheme

A two-input, two-output (TITO) multi-delay process is one of the most commonly encountered multivariable processes in the process industry. A large number of previous studies focused on designing multi-loop control system of TITO processes. For a 2×2 system, the general stable square transfer function matrix is represented as Standard feedback IMC controller is Gs 

q(s) ~ 1  g p (s )q( s)

Figure 3: standard feedback representation for IMC control

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A. IMC-based PID design for FOPDT Approximated FOPDT process g p (s )=

K p e -θ S

(8)

τp +1

Pade’ approximation for dead time e -θ s =

(9)

-0 . 5 θ + 1 0 .5 θ + 1

PID Parameter is calculated by K

c

=

( τ p + 0 .5 θ )

τ I = τ p + 0 .5 θ τ

D

=

(10)

(λ + 0 .5 θ )

τ pθ 2τ

p

(11) (12)

+θ

Table 1: IMC based PID controller for different filter constant

First Order Plus Dead Time System Transfer Function G 11 (s)=

G

22

1.4944 e -0.55s 0.71615 s+1

(s)=

0 .1 7 8 1 -0 .1 5 s e 2 .5 s + 1

PID (𝛌=0.6)

PID (𝛌=0.8)

PID (𝛌=1.2)

Kp=0.779 Ki=0.786 Kd=0.155 Kp=21.43 Ki=8.3 Kd=1.5

Kp=0.634 Ki=0.639 Kd=0.126 Kp=16.53 Ki=6.42 Kd=1.20

Kp=0.462 Ki=0.991 Kd=0.199 Kp=11.35 Ki=4.406 Kd=0.826

V. RESULT AND ANALYSIS The closed loop servo and regulatory response of RO desalination process with multiloop controller is shown in figure 4 and 5. The closed loop RO desalination system with multiloop IMC-PID controller is simulated for the set point change in flow rate (80 m3/h) and pH (7.0). Fig.4 shows how the output flow rate and pH values track the set points using multiloop IMC-PID control. The controller 1 manipulates the change of pressure ΔP in pump to settle the output in set point. During this time the interaction effect due to second input affects the flow rate, but the IMC based PID will consider that effect as disturbance and compensate the interaction effect by compensating the change of pressure ΔP in input. The pH set point tracking is shown in Figure.5. The output pH values maintained at 7, the set point changes applied to flow rate. The change in set point of flow rate also affects the pH level, at 50th sec flow rate is changed from 80 m3/hr to 60 m3/hr, this decreases the pH level by 6.4 because of JARDCS

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the change in pressure in input pump. During this time controller 2 manipulates the reflux ratio to make change in pH level to 7. Similarly, at 100th sec flow rate is changed from 60 m3/hr to 90 m3/hr, the pH level of process is maintained by loop2 controller. The both multi loop controller tunable parameter is lambda 1 and lamda2. The tunable parameter 1 ,  2

changed by trial and error method. For each  1 ,  2 values the performances indices like

ITAE, ISE,IAE is calculated. The performances of controller for various filter values are tabulated. The optimal range of filter parameter for multiloop IMC based PID controller is concluded and tabulated.

Figure 4: Servo response of multiloop IMC-PID controller

Figure 5: Servo and regulatory response of multiloop IMC-PID controller

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Table 2: Closed loop performance (IAE, ISE,ITAE) of desalination process using IMC-PI for different filter values.

PID PID PID (𝛌=0.6) (𝛌=0.8) (𝛌=1.2) IAE 85.87 69.9 102.49 LOOP1 ISE 4910.1 4426.4 4912.8 ITAE 67.52 42.3 145.5 IAE 5.8 4.989 6.93 LOOP2 ISE 19.94 17.19 24.55 ITAE 7.91 5.52 9.458

VI. CONCLUSION This paper has shown that dynamic behaviour of multivariable RO desalination system. The two input and two output transfer function model was developed for RO desalination process. The gain matrix was computed to measure the interaction of process at steady state. The control loop is selected based on the impact of input on the outputs. The diagonal elements of the decentralized controllers are tuned using IMC based PID tuning procedure. The IMC PID control parameter tuned depends upon the selection of the tuning parameter  , which is done by trial and error method. The closed loop simulation studies are carried out to obtain the output responses and the corresponding ITAE, IAE and ISE values. The qualitative and quantitative comparison of the closed loop simulation studies conducted by adjusting filter values.IMC based PID controller is tuned based on closed loop time constant (𝛌). Proper Selection of

will increase the robustness. The optimum values for filter values lies in-

between 0.6 to 0.8. The performance of the controllers can be increased by proper selection of filter constant using soft computing techniques.

REFERENCE 1. A. Abbas, “Model predictive control of a reverse osmosis desalination unit” , Desalination 194 (1-3) (2006) 268–280. 2. S. Sobana, Rames C. Panda, “Identification, modeling and control of continuous reverse osmosis desalination system: a review”, Separation Science and Technology 46 (4) (2011)551–560.

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3. S. Sobana, R.C. Panda, “Development of a transient model for the desalination of sea/brackish water through reverse osmosis”, Desalination and Water Treat. 51 (2013)2755–2767. 4. Ali A, Majhi S, “PID controller tuning for integrating process”, ISATransaction, Vol.49, pp. 70-78, 2010. 5. K.J. Astrom, K.H.johansson, Q GWang, “Design of decoupled PI controllers for twoby-two system”, IEEE proceedings: control Theory and Applications, Vol.149, pp.74-78, 2002. 6. J.Z. Assef, J.C. Watters, P.B. Desphande, I.M. Alatiqi, Advanced control of a reverse osmosis desalination unit, Proc. International Desalination Association (IDA) World Congress, Abu Dhabi, V, 1995, pp. 174–188. 7. J.Z. Assef, J.C. Watters, P.B. Deshpande, I.M. Alatiqi, Advanced control of a reverse osmosis desalination unit, J. Process Control 7 (4) (1997) 283–289. 8. A.C. Burden, P.B. Deshpande, J.C. Watters, Advanced process control of a B-9 Permasep permeator desalination pilot plant, Desalination 133 (2001) 271–283. 9. Awais, M.M., 2005. Application of internal model control methods to industrial combustion. Applied Soft Computing 5 (2), 223–233. 10. Mudi RK, Dey C, Performance improvement of PI controller through set point Weighting, ISA Transaction 2011;50:220-30.

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