FAULT-TOLERANT SUPERVISORY CONTROL OF A REVERSE OSMOSIS DESALINATION PLANT POWERED BY RENEWABLE ENERGIES

Transcription

1 FAULT-TOLERANT SUPERVISORY ONTROL OF A REVERSE OSMOSIS DESALINATION PLANT POWERED BY RENEWABLE ENERGIES A. Gambier, T. Miksch, E. Badreddin Atomation Laboratory, Heidelberg University gambier@ni-heidelberg.de, {tobias.misch, badreddin}@ziti.ni-heidelberg.de ABSTRAT Many applications of Reverse Osmosis desalination plants (RO plants) reqire a falt tolerant system, in particlar when hman life depends on the availability of the plant for prodcing fresh water. However, they have been little stdied in the literatre from this point of view, in particlar, when the plant is powered by renewable energies. In this case, the availability of the power spply is limited and depending on weather conditions. Therefore, the plant has to be able to work at different operating point and hence, falt tolerance becomes essential. The present work reports a stdy, in the framework of the Eropean project Open Gain, on Falt-Tolerant ontrol (FT) of a RO plant powered by renewable energies. The approach is based on optimized PID control loops in the lowest control level and a Model Predictive ontrol (MP) as spervisory controller. The MP provides falt tolerance by sing a prioritized lexicographic algorithm. Keywords: falt tolerant control, reverse osmosis desalination 1. INTRODUTION Reverse osmosis desalination plants se sensible components, which are also prone to parameter changes becase membranes are sensitive to temperatre of feed water, foling, scaling and pressre variations. RO plants are normally controlled by sing PID control laws, which are tned bt not optimized. Althogh sch plants are difficlt to control and control is a very important aspect for the safety and economical plant operation, this sbject is not mch researched and only some contribtions can be fond in the literatre. For example, the first mlti-loop control system for a RO plant was proposed in Alatiqi, Ghabris, and Ebrahim (1989). It incldes one pressre controller and two ph controllers. For desalination plants in general and RO in particlar, only few contribtions regarding model based control have been reported. A simplified dynamic model for an indstrial plant is reported in Al-Bastaki and Abbas (1999). In Alatiqi, Ettoney, and El-Dessoky (1999), an overview abot process control of desalination plants is given and Assef et al. (1995) presents some advanced control techniqes for RO plants. DM (Dynamic Matrix ontrol) is compared with standard PID control in Robertson et al. (1996). Decopled control is proposed in Riverol and Pilipovik (25). Some ideas of sing hybrid control in desalination plants are proposed in Gambier and Bareddin (22) and the simltaneos design of two PI controllers for a RO plant by sing mltiobjective optimization is the sbject of Gambier, Wellenrether, and Badreddin (26). A nonlinear control approach for a high recovery RO system is proposed in McFall, et al. (28). FT (Falt Tolerant ontrol) approaches are presented in McFall et al. (27) with simlation reslts and in Gambier,. Blümlein and Badreddin (29) for a realtime application. Dynamic models for the control of RO plants are reviewed in Soltanieh and Gill (1981) and in Gambier, Krasnik and Badreddin (27). Finally, different configrations for the control system are analyzed in Gambier, Wellenrether, and Badreddin (29), and a laboratory plant for experimenting with the real-time control of a RO process is described in Gambier, Miksch, and Badreddin (29). Until now, no work has proposed a falt tolerant control system, which is optimized in order to operate with renewable energies. In the present stdy, a spervisory control system based on a falt tolerant MP, which optimize the set points according to the available energy is presented. The low level control is implemented by sing parameter optimized PID controllers. In Section 2, the RO process is described from the control viewpoint. Section 3 is devoted to introdce the problem of falt-tolerant control. In Section 4, the proposed approach is described. Simlation reslts are shown and analyzed is Section 5. Finally, conclsions are drawn in Section PROESS DESRIPTION 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 Figre 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 Page 129

2 passing throgh an energy recovery system (see Bros (2) and Wilf et al. (27) for a review of membrane processes). 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 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. Feed water L hemical additives P RO Unit LP PUMP Filter retentate ph Pre-treatment Unit HP pmp Membrane Assembly hemical additives F F ph fresh water Post-treatment Unit Figre 1: Schematic Diagram of a RO Plant and Its ontrol Loops 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 flow rate and its condctivity, which are carried ot by maniplating the flow rate of retentate and the chemicals at the pretreatment nit, respectively, as it is shown in Figre 2. ontrol signal 1 ontrol signal 2 Valve 1 Valve 2 Retentate flow rate ph inlet RO Plant Permeate flow rate Permeate condctivity Energy consmption Figre 2: I/O Representation of the RO Plant Notice that changes in the retentate flow rate also affect the permeate condctivity. However, changes in the ph of feed water do not modify the permeate flow rate. This leads to a trianglar system as given in Figre FAULT-TOLERANT ONTROL 3.1. Overview and Definitions There are several definitions and classifications of FT systems (FTS). In the following, the definitions given in Mahmod, Jiang, and Zhang (23) are adopted, where a FTS is a control system that can work stably with an acceptable degree of performance even 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. ontrol signal 1 ontrol signal 2 G v1 (s) G v2 (s) Retentate flow rate Inlet ph G 11(s) G 21(s) G 22(s) Permeate flow rate Figre 3: Block Diagram of a RO plant Permeate condctivity 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 ontrol System (PFTS). ontrarily, Active Falt-Tolerant ontrol 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 most simply 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 Figre 4. Passive Falt Tolerant ontrol Systems (PFTS) Robst ontrol Falt Tolerant ontrol Systems (FTS) ontroller Redesign Active Falt Tolerant ontrol Systems (AFTS) Falt Accommodation ontroller Reconfigration ontrol system Reconfigration Plant Reconfigration Figre 4: lassification of FTS Reconfigration ontrol 3.2. ontrol Laws for FTS The above mentioned mechanisms for providing falt tolerance have different degree of complexity. PFTS is the simplest case, followed by falt accommodation and finally the system reconfigration in its different stages. Page 13

3 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 Abdel-Geliel, Badreddin and Gambier (26), 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 ontrol); another approach for LQ controllers can be fond in Staroswiecki (26); falt tolerance based on controllers designed by sing Eigenstrctre Assignment (EA) has been proposed in Jiang (1994). A different approach, the Psedo Inverse Method (PIM), is proposed in Staroswiecki (25). 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 Maciejowski (1997) and later implemented in Ocampo- Martinez (27). A real-time stdy of MP is presented in Miksch, Gambier and Badreddin (28a). Reslts of a comparison between LQ, PIM and MP from a real-time point of view are presented in Miksch, Gambier and Badreddin (28b), where it is shown that MP has several advantages regarding the other ones. 4. FT APPROAH FOR THE RO PROESS The proposed approach incldes a low level control system based on parameter optimized PID controllers and a MP, which provides spervisory control and falt tolerance Lowest ontrol Loops Standard control systems of RO plants are normally based on PID controllers. A method for the join optimazation of two copled control loops of a RO plant has been proposed in Gambier, Wellenrether, and Badreddin (27). Later the athors investigate in Gambier, Wellenrether, and Badreddin (29) other control system topologies. They fond that a better topology for sch kind of systems is sch one as given in Figre 5. Therefore, this is the control system sed in the crrent approach for the lowest control loops. 3 e 1 e 2 2 G c1 (z) G c2 (z) K G 11 (z) G 21 (z) G 22 (z) Figre 5: ontrol system topology for the low level control system q p p The transfer fnction for the first control loop is given by A11 r1 e1 ( z), (1) A 11 and the transfer fnction of the second control loop is in this case A21A22 A11r2 A11Q11T1 r1 e2 ( z). (2) A A A Polynomials A ij and B ij are denominator and nominator of the transfer fnction G ij (z), where the variable z has been eliminated for simplicity in the notation. onstants r 1 and r 2 are the amplitde of the set points. Transfer fnctions for the control signals are: A Qr AQr z ( ) PA QB A A21 A11A22 and (3) Q ( A A A r A Q T r ) z ( ). (4) where A11 P11A11 Q11B11, T B A B A K A P A Q B and PID controllers are obtained taking Qij ( z) i( z) ej( z). (5) P ( z) ij 2 P ( z) z( z 1) and Q ( z) q z q z q, (6) ij ij ij, ij,1 ij,2 respectively. Moreover, parameters have to satisfy the constraints 1 q ij, 1 1 qij, q ij,2 in order to show PID behavior. (7) The parameter optimization is carried ot following Gambier, Wellenrether, and Badreddin (29) by sing an Mlti-objective Optimization method (MOO). This is not presented here in order to save space Improving the Lowest Level ontroller Design A particlar control problem with RO plants consists in that plant parameters change fast becase of foling and membrane cleaning has to be carried ot often (e.g. once a week). Ths, process parameters obtained after cleaning are very different from the parameters obtained one week later before cleaning. Therefore, the control performance deteriorates fast in the corse of the week, when the controller was adjsted by sing parametric optimization. Hence, a robst control approach shold be sed. The method given in Gambier (29) extended the parameter optimization of PID controllers by sing MOO when Page 131

4 the parameter ncertainties are given in the form of intervals polynomials. Ths, it is possible to design robst control loops in the lowest level satisfying the first level of falt tolerance. An additional problem is given by the fact that MOO optimization reqires a predefined parameter space in which the controller parameters shold be searched. This problem has been solved by Bajcinca and Hlin (24). The toolbox presented in that work allows obtaining all stabilizing PID controllers in the parameter space for a given plant. This is sed here in order to initialize the MOO algorithm Spervisory ontrol Loop The spervisory control is implemented according to Figre 6 by sing model predictive control. The MP has two main fnctions. On the one hand, it provides the optimal set points for the low level control loops, sch that the system works at the optimal operating point according to the energy availability. On the other hand, the MP is responsible for providing falt tolerance. Prediction of Available Energy MP Spervisor FDI 3 e 1 2 e 2 G c1 (z) G c2 (z) 1 K 21 2 G 11 (z) G 21 (z) G 22 (z) G E (z) Figre 6: FT-MP as Spervisory ontroller The MP design for falt tolerance follows the work of Miksch, Gambier, and Badreddin (21). It is based on the lexicographic mlti-objective optimization of an l 1 norm by sing a linear program. onstraints are given in the way of prioritized objectives, whose priorities are defined in order to satisfy the definition of performance regions as given in the example of Figre 7. q p Region of nacceptable performance Region of degraded performance Region of reqired performance p Figre 7: Example of performance regions for the otpts ( p, q p ) q p p E c onstraints are adjsted according to the information spplied by a FDI nit (Falt Detection and Identification). However, the FDI block of Figre 6 is for the crrent work only simple logic that gives as otpt the corresponding vale for, according to a predefined known falt. A general FDI nit has still to be implemented. The spervisor implements a logic that bilds the constraints set depending on {, 1,, n }and the falt parameters, i.e. (, θ). (8) For example, if the valve opening of valve 1 is limited now ntil a maximm vale of 7%, the FDI nit yields and () =.7. Ths, the spervisor will deliver at the otpt () =.7 (this is the new constraint for 1 ) Predictor for the Available Energy An experimental model of the energy consmption and a prediction of the available energy from the PV and wind sbsystems are sed to determine the set points for the PID controllers. The predictor of the available energy is carried ot according a simple charging model for the lead-acid battery pack. This model is obtained from Hang et al. (21) as a linear pertrbed model. Model parameters are experimentally obtained for satisfy a real laboratory system. 5. STUDIES AND RESULTS The control system proposed in this work is being implemented at the present time. Some reslts of the low level control system can be fond in Gambier, Wellenrether, and Badreddin (29). Some reslts abot sing the MP as a falt tolerant controller are presented in the following. For the stdies, the plant is set to a permeate flow rate of 2 l/h and a valve openings of %. Permeate flow rate and the condctivity are the controlled variables. Then, the reference signal for the permeate flow rate is changed first to 3 l/h and afterward to 3 l/h. The condctivity is set at the operating point of 4 S/cm. This condctivity is assmed to be an index for the water qality, which in most applications of sch 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 falttolerant control system. This means that in case of falts, the permeate flow rate can freely change within a defined range in order to maintain the condctivity as close as possible to its set point. The condctivity is normally controlled by Valve 2. However, the condctivity can be modified by both control signals. This provides some redndancy that can be sed for obtaining falt tolerance. The performed stdies are smmarized in Table 1. Table 1: Stdies of Falt-tolerance for the Water ondctivity Description mi ma mi ma n,1 x,1 n,2 x,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% Page 132

5 The design parameters for the MP are given in Table 2. The sampling time and the prediction horizon are optimally chosen according to Gambier and Badreddin (29). Table 2: 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 Figre 8, 9 and 1, 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 Figre 8. 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 condctivity cannot be controlled any more. The falt-tolerant MP abandon the set-point control of the flow rate (bt maintained it in a predefined band) in order to improve the condctivity control, since this is the most important variable. y 1: Permeate flow rate in m 3 /h y 2: ondctivity in S/cm : Retentate valve opening in % 2: Bypass valve opening in % 1 Reference signals Standard MP FT system Figre 8: ontrol 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 condctivity to its set point at the expense of an acceptable steady-state error. This is shown in Figre 9. Finally, ase 3 (Valve 1 is maintained fix at 3%) is the most difficlt becase it is not possible control the flow rate only with Valve 2 (Figre 1). The standard MP introdces a major deviation from the set point for the condctivity, 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. y 1 : Permeate flow rate in m 3 /h y 2: ondctivity in S/cm : Retentate valve opening in % 2: Bypass valve opening in % 1 Reference signals Standard MP FT system Figre 9: ontrol system behavior for ase 2 ( 2 = 1 % for t 18 s) y 1: Permeate flow rate in m 3 /h y 2: ondctivity in S/cm : Retentate valve opening in % : Bypass valve opening in % Reference signals Standard MP FT system Figre 1: ontrol system behavior for ase 3 ( 1 = 3 % for t 18 s) 6. ONLUSIONS AND FUTURE WORK In this contribtion, the control problem of a reverse osmosis desalination plant is stdied. In order to garantee an acceptable water qality along the complete operation time even in case of falts, a falt-tolerant MP based on adjsting its constraints in the spervisory level 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. Moreover, the whole control system of Figre 6 has still to be implemented since it has only been tested partially. Finally, the approach has to be combined with a robst falt-detection approach. AKNOWLEDGMENTS This work has been spported by the Eropean ommission by means of the project Open-Gain (contract No. 335). REFERENES Abbas, A., Model-predictive control of a reverse osmosis desalination nit. Desalination, 194, , 26. Abdel-Geliel, M., E. Badreddin and A. Gambier. Application of dynamic safety margin in robst falt detection and Page 133

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