Fault-Tolerant Control of a Small Reverse Osmosis Desalination Plant with Feed Water Bypass

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1 21 American onference Marriott Waterfront, Baltimore, MD, USA Jne 3-Jly 2, 21 ThB14.3 Falt-Tolerant of a Small Reverse Osmosis Desalination Plant with Feed Water Bypass A. Gambier, T. Miksch, E. Badreddin Abstract Many applications of Reverse Osmosis (RO) desalination plants reqire falt tolerance, in particlar when hman life depends on the water prity. However, they have been little stdied in the literatre from this point of view, in particlar, when small plants se a feed water bypass to modify the permeate by mixing a little amont of feed water with the permeate. Sch plants have a different system configration and different dynamic behavior from standard plants. The present work is a stdy on Falt-Tolerant (FT) of a small plant with feed water bypass by sing Model Predictive (MP). Very satisfactory reslts show the advantages of sing a falt-tolerant control system in this kind of plants. R I. INTRODUTION EVERSE osmosis is well known as a separation process sed in desalination for removing salt from sea water and brackish water. However, it is also a process, which is extensively sed in the food indstry. It is applied, for instance, for concentrating milk, whey and frit jices. In the wine indstry, it is also applied to remove e.g. acetic acid, alcohol, smoke taint and brettanomyces taint. Reverse osmosis water is sometimes sed in car washes dring the final rinse to prevent water spotting on the vehicle. Moreover, it is tilized to prify fresh water for medical, indstrial and domestic applications. systems for reverse osmosis desalination plants have been stdied in the literatre by sing PID as well as Model Predictive laws (MP) in, for example (bt not only), [1], [5], [7], [14], [26] and [27]. A nonlinear control approach for a high recovery RO system is proposed in [21]. Finally, the necessity of Falt-tolerant (FT) for this class of processes has been stdied in [22] and [1]. Many of the plants, which are presented in the above mentioned literatre, inclde a pre-treatment nit, where the salt concentration of permeate (or also permeate ) is controlled by adjsting the ph vale of the feed water. However, small plants or plants for drink water prification do not inclde ph control and permeate is a non-controlled variable. In order to be able to adjst the permeate, a bypass valve, which allows mixing permeate with a small amont of feed water, was installed for the present work. This Manscript received September 15, 29. A. Gambier is with the Atomation Laboratory, Heidelberg University, B6, No. 26, Mannheim, Germany (corresponding athor, phone: ; fax: ; agambier@ieee.org). T. Miksch is with the Atomation Laboratory, Heidelberg University, B6, No 26, Mannheim, Germany. E. Badreddin is the director of the Atomation Laboratory, Heidelberg University, B6, No 26, Mannheim, Germany. constrction leads to a different system topology, which has first been stdied from the control point of view in [12]. In that work, it is pointed ot that it is necessary to control the permeate in order to obtain better water qality. A mltivariable nconstrained MP is sed as control law. In some medical applications, as for example in srgery rooms and semicondctor indstry, a continos spply of high qality water is essential. Ths, falt-tolerant control systems shold be a standard for this kind of plants bt this topic is still an open problem in the literatre. In the crrent work, a falt-tolerant MP system is proposed for the control of a reverse osmosis desalination plant with feed water bypass, where the water qality (i.e. water as index of salinity) is the most important variable for the falt tolerance. The description of the plant inclding particlarities and strctres is explained in Section 2. Dynamic properties, modeling and the control space are the topics of Section 3. A short introdction to FT and the sed approach are presented in Section 4. Section 6 shows the performed stdies and their reslts. Finally, conclsions are drawn in Section 7. II. PLANT DESRIPTION A. General Description A basic RO system consists in general of a pretreatment stage, a high-pressre pmp, a membrane assembly (RO nit) and a post-treatment nit (see Fig. 1). Salty feed water is first pretreated to avoid membrane foling. Afterward, it passes throgh filter cartridges (a safety device) and is sent throgh the membrane modles (permeators) by a high-pressre pmp. Becase of the high pressre, pre water permeates throgh the membranes and the salty water becomes concentrated (retentate or brine). The water prodct flows directly from the permeators into the post treatment nit, and the retentate (at high pressre) is discharged, sally, after passing throgh an energy recovery system (see [9] and [34] for a review of membrane processes). Feed water L hemical additives RO Unit LP PUMP Filter retentate ph Pre-treatment Unit HP pmp Membrane Assembly Fig. 1. Schematic diagram of a standard RO plant and its control loops Pretreatment is important in RO plants becase sspended particles mst be removed in order to maintain the membrane srfaces continosly clean. Ths, pretreatment consists of fine P hemical additives F F ph fresh water Post-treatment Unit /1/$ AA 3611

2 filtration and the addition of chemicals to inhibit precipitation and the growth of microorganisms. The ph vale of the feed water is also adjsted in this nit. The high-pressre pmp spplies the pressre that is needed to allow water to pass throgh the membrane in order to reject salts. The pressre range is from 15 to bars for drink and brackish water and from 54 to 8 bars for seawater. The membrane assembly consists of a pressre vessel and several membrane nits sch that feed water is pressrized against the membrane. The membrane mst be able to resist the entire pressre drop across it. The semi-permeable membranes vary in their ability to pass fresh water and reject the passage of salts. Finally, the post-treatment consists of stabilizing the water and preparing it for distribtion. This post-treatment might consist of removing gases sch as hydrogen slfide, adding minerals and adjsting the ph vale. Two valves are sed for the control of permeate and its, which are carried ot by maniplating the of retentate and the chemicals at the pretreatment nit, respectively, as it is shown in Fig. 2. Valve 1 Valve 2 ph inlet RO Plant Fig. 2. I/O representation of the standard RO plant Notice that changes in the retentate also affect the permeate. However, changes in the ph of feed water do not modify the permeate. This leads to a trianglar system as given in Fig. 3. G v1 (s) G v2 (s) Inlet ph Fig. 3. Block diagram of a RO standard plant G * 11(s) G * 21(s) G * 22(s) B. Plants with feed water bypass In the case of small plants, pre-treatment nits are very simple and normally ph control of feed water is not implemented. can be changed by sing a bypass pipeline, which permits to mix a small amont of feed water with the prodct, if the qality reqirements for the prodct this allows. This is the case for example of the laboratory plant of Fig. 4, which is presented and described in [11]. The I/O strctre for this kind of plants is given in Fig. 5. Notice that in this case, changes in the bypass affect the permeate and therefore the system is not trianglar. Moreover, the retentate flow varies in the same amont as the bypass flow changes. The I/O representation is given in Fig. 6. arbon Filter Unit Valve 2 (Bypass) Filter ondctivity Sensors Valve 1 () HP Pmp Fig. 4. Reverse osmosis desalination plant with feed water bypass Valve 1 Valve 2 Bypass Fig. 5. I/O description for RO plant with bypass G v1 (s) G v2 (s) Bypass RO Plant G * 11(s) G * 12(s) G * 21(s) G * 22(s) Fig. 6. Block diagram of a RO plant with feed water bypass G bp (s) III. PLANT DESRIPTION AND DYNAMI LINEAR MODEL A. Steady-state plant characteristics The plant nder consideration has a capacity in nominal operation of abot 2 l/h (i.e.. m 3 /h) for a feed water of l/h. The concentrate is also 2 l/h, i.e. % retentate and % permeate. The bypass is abot.2 l/h for the nominal operation. The range for permeate is given by 21 l/h < q p < 433 l/h for a valve opening varying between 1% > p > 1%. Notice that this valve may not be completely closed in order that the plant is able to works. The maximm water prity is obtained by a completely closed bypass valve and a valve in the retentate stream closed p to 9% (1% valve opening). In this case, the is 391 S/cm (i.e. 26 ppm). The maximm vale for the (462 S/cm) is obtained for both valves opened p to 1%. Ths, the range for the is 391 < p < 462 S/cm. 3612

3 The normal operation point is % valve opening for both valves. Under these conditions, the permeate is 2 l/h and the permeate 4 S/cm (283ppm). Notice that in order to pt the set point, for example, at 2 l/h it is necessary to open the retentate valve p to 6% (Fig. 7, a). Once the valve is fixed to this vale it is not possible to modify this by sing the bypass valve. On the contrary, modifying the bypass valve, the can be adjsted to another reference vale (Fig. 7, b). q p Set point plane Set point plane ( ) (b) Fig. 7. Steady-state otpt description for the inpt ranges B. Dynamic behavior of the plant The open-loop step response of the plant is shown if Fig. 8, where one observes that a step change in the retentate valve prodces a permanent change in the permeate flow rate and in its. On the other hand, a step change in the bypass valve prodces a permanent change in the permeate bt only a transitory distrbance in the permeate. y 1 : Flow Rate in m 3 /h t [s] 1 y 2 : in S/cm t [s] 1 1 : valve opening in % t [s] t [s] 1 Fig. 8. Open loop behavior of the RO plant with feed water bypass. Dynamic model of the plant For the controller design, a model-based predictive control approach is sed. Therefore, a time-discrete state-space linear model, whose general eqations are given by xˆ( k 1) Axˆ( k) B( k) E v ( k) and (1) y( k) xˆ ( k) D( k) Fe ( k), (2) p is obtained offline from sampled-data for a sampling time of.15 s and the operating point mentioned above. The corresponding estimated model (inclding the dynamic of the valves) is smmarized in Table I. TABLE I STATE -SPAE LINEAR MODEL A e e e e Q v = E E T diag (1) B D R v = F F T Stochastic processes are assmed to be independent and Gassian with mean vale eqal to zero. ovariance matrix of otpt vector process is noted R v. ovariance matrix of states vector process Q v is sed as design parameter for the Kalman estimator ([6]). A diagonal matrix with all elements eqal to 1 leads to satisfactory reslts. Notice that it cold be possible to redce the model from order nine to order seven with an infinity norm error bond of 3e-4. However, the obtained model does not lead to satisfactory reslts in particlar for the design of the Kalman estimator. The semi-permeable membranes vary in their ability to pass fresh water and reject the passage of salts. This ability decreases with the time becase of scaling and foling. Therefore, membranes have to be washed when the permeability factor decay nder a limit vale. If the permeability factor after cleaning does not reach a minimm working vale, membranes are replaced. It is important to remark here that some athors point ot that reverse osmosis plants have a strong nonlinear behavior becase of foling. This statement cold not be confirmed experimentally at least for the small plant. Foling is a very slow process that is normally interrpted once a week by membrane washing. Ths, it is possible to observe that the plant has a qite linear behavior changing slowly its parameter in the corse of a week bt withot affecting significantly the control. IV. FAULT-TOLERANT ONTROL SYSTEMS A. Overview and definitions There are several definitions and classifications of FT systems (FTS). In the following, the definitions given in [2] are adopted, where a FTS is a control system that can work stably with an acceptable degree of performance even 3613

4 thogh in the presence of component falts. FTS shold detect and accommodate falts avoiding the occrrence of failres, i.e. irrecoverable damages at the system level. Falt tolerance can be reached by means of different mechanisms. For example, it is possible to obtain a limited falt tolerance by sing a robst control system design. This approach is sometimes named Passive Falt-Tolerant System (PFTS). ontrarily, Active Falt-Tolerant Systems (AFTS) reqire a new controller either by sing adaptive control or switching control. Adaptive control leads to the falts accommodation, whereas switching control makes possible a reconfigration of the control system. Notice that reconfigration can take place at different levels depending on the severity of the falt and on the available system infrastrctre. The simplest case of reconfigration is given by controller switching. However, there cold be other kind of reconfigrations if some redndancy is available: changes on the control system topology by sing fnctional redndancy (redesign of the control system by sing other actators or/and other sensors) or plant reconfigration if physical redndancy (i.e. standby backp of sensible components) is foreseen in the plant. AFTS need a priori knowledge of the expected falts or a mechanism for the detection and isolation of nanticipated falts, namely a FDI scheme. A simplified classification of FTS is smmarized in Fig. 9. Passive Falt Tolerant Systems (PFTS) Robst Fig. 9. lassification of FTS Falt Tolerant Systems (FTS) ler Redesign Active Falt Tolerant Systems (AFTS) Falt Accommodation ler Reconfigration system Reconfigration Plant Reconfigration Reconfigration B. laws for FTS The above mentioned mechanisms for providing falt tolerance have different degrees of complexity. PFTS is the simplest case, followed by falt accommodation and finally the system reconfigration in its different stages. Hence, the design of FT systems shold be ndertaken inclding this seqence, i.e. first the controller shold be robst, then it has to provide facilities for a falt accommodation and if all these mechanisms are insfficient in order to solve the problem a reconfigration shold be attempted. Some control laws have been modified as well as developed to manage falt accommodation: For example in [2], the Dynamic Safety Margin (DSF) is proposed to provide falt accommodation for controllers that cannot manage constraints as for example PID (Proportional, Integral and Derivative) control, LQ (Linear Qadratic) optimal control and nconstrained MP (Model Predictive ); another approach for LQ controllers can be fond in [29]; falt tolerance based on designing controllers by sing Eigenstrctre Assignment (EA) has been proposed in [15]. A different approach, the Psedo Inverse Method (PIM), is proposed in [3]. It tries to obtain a controller for the falty closed loop system by minimizing the distance to the nominal control system. The constrained MP has also been stdied for falt-tolerant behavior. It was first proposed in [19] and later implemented in []. A real-time stdy of falt-tolerant MP is presented in [23]. Reslts of a comparison between LQ, PIM and MP from a real-time point of view are presented in [24], where it is shown that MP has several advantages regarding the other ones. The MP law shows some robstness, which can be sed for PFT. If the inherent robstness of MP is not sfficient for the reqirements, it is also possible to apply the robst MP algorithm proposed in [16]. This algorithm provides robst properties withot a significant increase of the comptational brden. Moreover, MP provides satisfactory facilities for falt accommodation by adjsting constraints, since the controller is continosly redesigned online. The MP control law is well known and details of it can be fond in the specialized literatre (e.g. [17]). In the following, only the main idea is given for the sake of completeness. The MP control is obtained by the nmerical optimization of the performance index kn1 kn S Q R ik ik J e( k N) e( i) ( i) (1) sbject to the constraints y( k) x( k), x( k 1) Ax( k) B( k), i for 1,,, min i i i L m max i for 1,, and min i i i L m max x x x for i 1, L, n. imin i imax N and N are the prediction horizon and the control horizon, 2 respectively. The term v( ) denotes T M v () Mv () and variable e( ) is the control error defined by e() r() y (). (3) Matrices Q = Q T mm and S = S T mm are positive semi definite and R=R T ll is positive definite. Variables y m, l and x n are the otpt vector, the inpt vector and state vector, respectively. (i) is defined as first difference (i) (i 1). Model matrices A, B and are of adeqate dimension. is a slack variable sed to relax the constraints and a weighting factor. The falt-tolerant MP approach, which is implemented in this work, is obtained by changing on-line the constraints according to the falt case. It is detailed described in [23].. The FDI nit For this stdy no FDI nit has been implemented becase it is assmed that all falts are known. Ths, a FDI nit consists (2) 3614

5 here only of a signal, which annonces the falt after a delay in order to emlate the elapsed time between the falt occrrence and its detection. A more sophisticate FDI will be implemented in the ftre by sing the FDI toolbox described in [33]. V. STUDIES AND RESULTS For the stdies, the plant is set to a permeate of 2 l/h and a valve openings of %. and the are the controlled variables. Then, the reference signal for the permeate is changed first to 3 l/h and afterward to 3 l/h. The is set at the operating point of 4 S/cm. This is assmed to be an index for the water qality, which in most applications of sch small plants is a very important property and normally also the reason for sing this kind of eqipments. Therefore, this variable is considered of highest priority in the falt-tolerant control system. This means that in case of falts, the permeate can freely change within a defined range in order to maintain the as close as possible to its set point. The is normally controlled by Valve 2. However, the can be modified by both control signals as it is apparent from Fig. 7. This provides some redndancy that can be sed for obtaining falt tolerance. The performed stdies are smmarized in TABLE II. TABLE II STUDIES OF FAULT-TOLERANE FOR THE WATER ONDUTIVITY Description min,1 max,1 min,2 max,2 Nominal 1 1 ase 1 Valve 2 limited to -% 1 ase 2 Valve 2 stck at 1% 1 ase 3 Valve 1 stck at 3% The design parameters for the MP are given in Table III. The sampling time and the prediction horizon are optimally chosen according to [12]. TABLE III DESIGN PARAMETERS FOR THE MP PARAMETERS NUMERIAL VALUES R diag(1.,.1) Q 1 (Q = T Q 1) diag(1,.1) S 1 (S = T S 1) Q 1 T.15 s Horizons N = 14 N = 14 The delay of the FDI to find the falt has been assmed to be 5s and the adaption of the falt-tolerant MP for accommodating falts has been spposed to take 1s. Reslts are presented in Fig. 1, Fig. 11 and Fig. 12, respectively. For all figres, reslts for nominal MP are presented with solid red lines and reslts for the falt-tolerant MP are shown with dashed black lines. The first falt case is presented in Fig. 1. It consists of limiting the range of valve two between and %. After the falt, the nominal MP tries the contine maintaining the otpts at the set points bt the cannot be controlled any more. The falttolerant MP abandon the set-point control of the (bt maintained it in a pre-defined band) in order to improve the control, since this is the most important variable. y 1 : in m 3 /h y 2 : ondctivity in S/cm : valve opening in % 1 Reference signals Standard MP FT system Fig. 1. system behavior for ase 1 ( 2 % for t 18 s) In the second falt case, Valve 2 goes to an opening of 1% and it stays permanently at this vale. The standard MP shows a similar behavior as the first case. The falttolerant MP recovers the falt retrning the to its set point at the expense of an acceptable steady-state error. This is shown in Fig. 11. y 1 : in m 3 /h y 2 : ondctivity in S/cm : valve opening in % 1 Reference signals Standard MP FT system Fig. 11. system behavior for ase 2 ( 2 = 1 % for t 18 s) Finally, ase 3 (Valve 1 is maintained fix at 3%) is the most difficlt becase it is not possible control the only with Valve 2. The standard MP introdces a major deviation from the set point for the, whereas the falt-tolerant MP recover the falt withot steady-state error. Notice that the concrring natre of the two otpts in the falt case, i.e. prodcing as mch water as possible bt keeping the right range of salinity, is a mlti-objective optimization problem. This will be ndertaken in a ftre work. VI. ONLUSIONS In this contribtion, the control problem of a small-sized reverse osmosis desalination plant with feed water bypass is stdied. In order to garantee an acceptable water qality along 3615

6 y 1 : in m 3 /h y 2 : ondctivity in S/cm : valve opening in % Reference signals Standard MP FT system Fig. 12. system behavior for ase 3 ( 1 = 3 % for t 18 s) the complete operation time even in case of falts, a falttolerant MP based on adjsting its constraints is proposed. In this first stdy only actators constraints are considered. Obtained reslts are very satisfactory and this motivates the extension of the work in order to inclde other falts, additional falt-tolerant mechanisms, which introdce, for example, mltiobjective optimization. Finally, the approach has to be combined with a robst falt-detection approach. AKNOWLEDGMENT This work has been spported by the Eropean ommission by means of the project Open-Gain nder contract No REFERENES [1] Abbas, A., Model-predictive control of a reverse osmosis desalination nit. Desalination, 194, , 26. [2] Abdel-Geliel, M., E. Badreddin and A. Gambier. Application of dynamic safety margin in robst falt detection and falt tolerant control. 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