Development of a fuzzy logic based software for automation of a ...

Development of a fuzzy logic based software for automation of a single pool irrigation canalDevelopment of a fuzzy logic based software for automation of a single pool irrigation canalDr. R. Gopakumar 1 , Reena Nair 1, Vinuraj R. 2 , Sony Davis 3 , Bijeesh V. 4 , Junil Jacob 5Government Engineering College, Sreekrishnapuram, Palakkad, Kerala – 678 633, India.E-mail: gopak02@yahoo.co.inAbstract— A fuzzy logic based software for automation of asingle pool irrigation canal is presented. Purpose of thesoftware is to control downstream discharge and water level ofthe canal, by adjusting discharge release from the upstreamend and upstream gate settings. The software is developed on afuzzy control algorithm proposed by the first author during hisdoctoral research work and published in literature. Details ofthe algorithm are given. The algorithm was originallydeveloped using fuzzy logic tool box of MATLAB, which isproprietary software not available freely and hence cannot beadopted for general use. Present study describes developmentof a canal automation software based on this algorithm usingopen source tools, which are freely available. The software istransparent and intuitive, which can be easily applied by fieldengineers. The effort required in tuning the fuzzy model hasbeen reduced by including an optimization technique. Also, anew procedure has been introduced for fuzzy inference basedon the Mamdani Implication method. The software is tested byapplying it to water level control problem in a canal with asingle pool, as reported in literature, and satisfactory resultsare obtained.Keywords- Irrigation canals; canal automation software;open source tools; Fuzzy systemsI. INTRODUCTIONIrrigation is the largest user of water, which comes morethan 80 % of world water consumption. Hence it is essentialthat irrigation canals are to be operated to their maximumefficiency by minimizing wastage of water and maximizingflexibility in operations. Also, many irrigation canals areunder dilapidated conditions and their rehabilitation can beeconomically achieved by operating them effectively (andnot by rebuilding them as originally designed, which will behighly expensive). Effective operation of the canals inaccordance with these principles can be achieved throughcanal automation, which means application of automaticdevises or logic to assist in the operation of the canal [1]. Inthe present context, canal automation implies developmentand application of a fuzzy logic based software to control thedownstream discharge and water level of a single pool canal(Fig. 1). Here the term “pool” implies the stretch of the canalbetween two check gates. The canal is under known steadyflow condition initially with water level at the downstreamReservoirUpstream gateCanal bedPoolofftakeReservoirFigure 1. Schematic diagram of the single-pool canalend at its specified target value. Perturbations in the systemare due to changes in the discharges through the offtake,which is located at the downstream end of the pool (Fig. 1).Under the effect of these perturbations, the water level at thedownstream end starts deviating from its target value.Purpose of the fuzzy control software is to determine theinflow discharges and the gate settings at the upstream end,at every regulation time step, so that stable control at thedownstream end is achieved in a minimum of time.Different types of canal automation algorithms have beenproposed in the past as described in [2]. Some of them aredeveloped on control systems theory. Examples are classical(e.g., Proportional plus Integral, PI), predictive (e.g., ModelPredictive Control, MPC) and optimal (e.g., LinearQuadratic Regulator, LQR) controllers. Difficultiesassociated with application of these controllers have beendiscussed in literature. Tuning of PI controller, to determinethe controller parameters, is a tedious task [3]. Also, bothLQR and MPC assume that the system can be described bylinear differential equations, where as the underlyingunsteady flow equations are non-linear. The optimizationinvolved in MPC is a difficult task and consume significantamount of computing power [4]. Also, for LQR controllers,the relationship between the measured water levels and thecontrol actions is mathematically complex and hence thecontroller appears as a “black box” [5]. Such “black box”type controllers are less likely to be accepted by the canaloperators than ones that are intuitive [6].There is another class of canal automation algorithms,which make use of inversion of the following dynamic waveequations (Saint-Venant equations) [7], as the designtechnique:Continuity equation∂A∂Q+ = 0∂t∂x(1)International Journal of Computer & communication Technology Volume-2 Issue-VIII, 201138

Development of a fuzzy logic based software for automation of a single pool irrigation canalMomentum equation∂Q+∂t2⎡Q⎤ ∂h⎢ ⎥ + gA − gAS0x ⎣ A ⎦ ∂x∂∂+ gAS f= 0where A is flow cross sectional area, h is flow depth, Q isdischarge, S 0 is bed slope, S f is friction slope, g isacceleration due to gravity, t is time variable and x is spacevariable. Gate Stroking [8] and CLIS [9] are examples forthe algorithms coming under this class.The Gate Stroking is a feed forward control algorithm,suitable for scheduled offtake discharge changes, where theofftake discharge changes are known a priori. It is based onthe method of characteristics, which is more complex. Theinherent difficulties and impracticality of Gate Stroking havebeen demonstrated in literature [10, 11]. Finite differencealternatives for the Gate Stroking method were also proposed[12, 13]. These algorithms involve inversion of thegoverning equations (1) and (2) in both time and space. Butthe information from initial conditions and transientboundary conditions degrades with time due to friction andhence backward computation in time can cause instability[14]. However, the problem of instability is not applied toinverse computations in space and a feed back controlalgorithm of this type, suitable for unscheduled offtakedischarge changes, was reported later [15]. CLIS [9] is amodified version of this algorithm, made suitable forscheduled flow changes also. For all these algorithms, therecovery time, which is the time period in which thecontrolled variables are expected to attain their target values,is taken as the upstream wave traveling time, which is muchmore than the physically correct downstream wave travelingtime. Additionally, CLIS makes use of linearized version ofthe Saint-Venant equations for the inverse modeling whereas the underlying system dynamics are nonlinear.Reference [16] describes development of a fuzzy logicbased dynamic wave model inversion algorithm for canalregulation, which was capable of overcoming theaforementioned drawbacks of existing algorithms. Tuning ofthe algorithm was easy and computations were easy toimplement. No linearizations of the governing equationswere involved and the recovery time was rightly taken as thedownstream wave traveling time. The fuzzy controlalgorithm was transparent and intuitive and can be expectedto be more acceptable for canal operators as compared to“black box” type controllers. However, the algorithm wasdeveloped using the fuzzy logic tool box of MATLAB,which is proprietary software not available freely and hencecannot be adopted for general use. Present study describesdevelopment of a canal automation software based on thisalgorithm, for a single pool canal, where in freely availablecomponents are used.II.THEORETICAL ASPECTS(2)functions and fuzzy rules can be found in literature [18, 19].Fuzzy rule based models are suitable for nonlinear inputoutputmapping [18]. In fuzzy rule based modeling, a giveninput data undergoes the processes of fuzzification,application of fuzzy operators, implication, aggregation anddefuzzification, before finally forming into output from themodel [20]. Various steps involved in the design of fuzzylogic controllers have been discussed in literature [18].As mentioned previously, present study describesdevelopment of a canal automation software based on thefuzzy control algorithm proposed in [16]. The fuzzyalgorithm involves replacing (2) by a fuzzy rule based modelwhile retaining (1) in its complete form. The fuzzy rulebased model has been developed on fuzzification of a newmathematical model for dynamic wave velocity, obtained as:t( Discontinuity in gradient of Q )t( Discontinuity in gradient of A)t( ΔQ)( ΔA)tmm( Vw)m= = (3)twhere, ( V ) t w m is the wave velocity at point m along thecanal, at time t.Discontinuity in gradient of a flow parameter (Q or A), atpoint m and at time t, has been determined as the differencebetween its gradient corresponding to the final steadycondition (which the flow will attain under the effect of theperturbation) and its gradient corresponding to the conditionat time t, both gradients being evaluated at point m. Thefuzzy rule based model is developed on fuzzification of (3).While computing the dynamic wave velocity (V w ) at anynode (i,j+1) in the computational domain (Fig. 2), thecorresponding values of ∆A and ∆Q are determinedapproximately by adopting the following discretization:ΔAΔQj + 1i=j + 1i=F.S F.S j+1 j+1[ Ai+1- Ai] -[ Ai+ 1- Ai](4)F.S F.S j+1 j+1[ Q - Q ] -[ Q - Q ](5)i+1ii+1In (4) and (5), the notations with superscript “F.S”indicate the values of the flow parameters corresponding tothe final steady state.Equation (1) has been discretized at the node (i,j), in thex-t computational domain (Fig. 2), using the Vasiliev scheme[21], which is an unconditionally stable implicit finitedifference scheme, as follows:j+1 j 1 j+1 j+[ A − A ] + [ Q − Q ] 01 1i ii+1 i-1=Δt2Δxwhere i = node number in the x – direction and j = nodenumber in the t – direction.imm(6)The concept of fuzzy logic was first introduced by Zadeh[17]. Details of fuzzy sets, fuzzy numbers, membershipInternational Journal of Computer & communication Technology Volume-2 Issue-VIII, 201139

Development of a fuzzy logic based software for automation of a single pool irrigation canalTime ( t )1i-1,,j+1i,,j+1i,,jΔti+1,,j+12 N-1Distance (x)Figure 2. Computational domain for the fuzzy control algorithm:N = number of nodes in the x – direction, i = node number in the x –direction, j = node number in the t – direction.Here, it is assumed that the control is achieved by rapidmovement of check gates, which will result in the formationof gravity waves. If the wave velocity (V w ) corresponding toa certain inflow discharge is assumed to remain constantover the entire pool under consideration then a set of crisprules can be written, based on (3) and applicable everywherein the pool, as IF ∆Q is low THEN ∆A is low, IF ∆Q ismedium THEN ∆A is medium, IF ∆Q is high THEN ∆A ishigh etc. where “low”, “medium”, “high” etc. arequantitative variables and ∆Q and ∆A indicate crispnumerical values. If the above assumption on V w holds goodonly approximately then the rules become fuzzy, “low”,“medium”, “high” etc. become linguistic variables and ∆Qand ∆A indicate fuzzy subsets. The fuzzy rule based model isdeveloped on this principle. A major advantage of the abovefuzzy formulation is that it is developed on fuzzification of amathematical model (3) relating the input and outputvariables. Hence the rules linking these variables can beaccurately specified. Such a fuzzy model works in the bestway and also the results are significantly better than the casewhere the model is developed using sample data [22]. Theerror, associated with the assumption on V w remainingapproximately constant in a pool, reduces as the waveamplitude reduces because as the amplitude reduces thewave resembles more closely a linear gravity wave whichpropagates downstream with minimum distortion,attenuation and change in velocity [23, 24, 25]. Hence it canbe expected that the algorithmic error will be a minimum andconsequently stable control at the downstream end will beachieved early in those cases where the final steady profileconform to uniform flow. Such a case is very difficult tocontrol by other existing algorithms [26]. Software in thepresent context has been developed for this particular case.III. DEVELOPMENT OF THE SOFTWAREThe software consists of three modules; the first one fortuning, the second one for fuzzy inference and the third onefor computing the required inflow rate, at the upstream end,ΔxNusing the first and second modules. The Graphical UserInterface of the software is developed using ‘Qt’ and thecomputational modules are developed using 'C' language.For the applications specified in the algorithm, only one toone correspondence is used. Therefore the fuzzy libraries andtool boxes given in [27, 28, 29] are not required as they aredesigned for a wide variety of applications.A. TuningTuning of the fuzzy control algorithm involvesdetermination of the membership function parameters (core,support and boundary) of each fuzzy subset and constructionof the fuzzy rule base. It is done by considering a fictitiouscase where the flow corresponding to maximum designdischarge in the canal is uniform at the upstream end. For abase flow corresponding to the maximum design dischargeand for various inflow discharges, respective values of ∆Qand ∆A are obtained by solving (3) along with the basicequation for gravity wave velocity [30] given below, whichhas been derived from momentum equation:VgA1= V2 +(A1Y1− A2Y ) (7)A (A − A )w 22 1 2In (7), the subscript 1 indicates the upstream end fromwhere the wave is produced and the subscript 2 indicates aneighboring section where the effect of the wave has not yetreached, V is flow velocity and Y is depth of centroid ofthe section below the free surface. The solution procedure isas follows. For a certain inflow discharge, ∆Q = Q 1 – Q 2 is aknown value. Also, as flow is uniform at the upstream end,∆A can be replaced by A 1 -A 2 in (3). Thus in (3) and (7) theonly unknowns are A 1 and Y 1 . But Y1is a function of A 1 . Sofor a trial value of A 1 corresponding value of Y 1 isdetermined and applied in (7) to determine V w . Same valueof V w should be obtained when the above value of A 1 is usedin (3). If not, the above procedure is repeated with other trialvalues of A 1 until V w obtained from the two equations areequal. An optimization technique has been adopted to reducethe number of trials required in tuning. It involves comparingthe difference between V w values, resulting from (3) and (7),during successive trials and the computation will proceed inthat direction where the above difference will keep reducing.This is continued until the difference lies within somepermitted tolerance. Once the correct value of A 1 is obtained,the value of ∆A= A 1 -A 2 is calculated. Thus values of ∆Q and∆A are obtained for the specified inflow discharge. Thisprocedure is repeated for other inflow discharges also andrespective values of ∆Q and ∆A are determined. Thesevalues are stored in two arrays. Each value in the input array(∆Q) has a corresponding value in the output array (∆A)also, both having degree of membership equal to one (corevalues of the fuzzy sets). Then by adopting the method ofpartitioning [18], a set of triangular membership functionsand fuzzy rules are derived relating ∆Q and ∆A.International Journal of Computer & communication Technology Volume-2 Issue-VIII, 201140

Development of a fuzzy logic based software for automation of a single pool irrigation canalB. Fuzzy InferenceThe software introduces a new procedure to compute theoutput (∆A) for a given input (∆Q), based on the MamdaniImplication method of inference [31] and the CentroidMethod of defuzzification [18], as described below.Suppose x n is the given input data (∆Q), with m 1 and m 2as the corresponding degrees of membership in theneighboring membership functions shown in Fig. 3. Sincethese membership functions have been developed bymethod of partitioning, they will form isosceles triangles.µ(x i )Figure 3. Fuzzification of input dataThe value of x 2 nearest to x n is found from the array of∆Q. The values x 1 , x 3 and x 4 are also obtained from the samearray. Then the values of m 1 and m 2 are computed asfollows:tanθ = 1/ (x 2 - x 1 ). m 1 = (x 3 -x n ) tanθ. m 2 = (x n -x 2 ) tanθThere is one to one correspondence between the inputand output fuzzy sets stored in the two arrays. Hence m 1 andm 2 can be easily mapped to the corresponding outputmembership functions, as shown in Fig. 4.µ(y i )1m 1m 21m 1m 2x 1(a 1, b 1 )θ(a 2, b 2 )x 2 x 3 x 4x nθ 1 θ 2Figure 4. Computing the output membership function by implication.The values of a 2 , a 3 , a 4 and a 5 shall be obtained as follows:Calculation of a 2tan θ 1 = 1/(y 2 – a 1 ). Suppose o 1 = a 2 – a 1.Then, tan θ 1 = b 2 /o1. But b 2 = m 1.Therefore, o 1 = m 1 /tan θ 1. Hence, a 2 = a 1 + o 1 .Calculation of a 3tan θ 2 = 1/(y 3 – y 2 ). Suppose o 2 = y 3 – a 3.Then, tan θ 2 = b 3 /o 2. . But b 3 = m 1Therefore, o 2 = m 1 /tan θ 2. Hence, a 3 = y 3 – o 2 .Calculation of a 4Suppose o 3 = y 3 – a 4 . Then, tan θ 2 = b 4 /o 3.θ(a 3, b 3 )(a 4, b 4 )(a 5, b 5 )y 2y 3 (a 6, b 6 )θΔQΔABut b 4 = m 2Therefore, o 3 = m 2 /tan θ 2. Hence, a 4 = y 3 – o 3Calculation of a 5 is similar to that of a 4The above calculations are for the case when m 1 > m 2 .Calculations for the case where m 1 < m 2 is similar.For the resulting polygon with coordinates as shown inthe Fig. 5, the x-coordinate of the centroid , ΔA, which isthe required output, is calculated using following equations[32].6P 1 i i+1 i+1 ii=1= / 2∑ ( a b ) − ( a b )(8)6∑ΔA= 1/(6P ) ( a + a(9)i=1ii+ 1 ) × ( aibi+1 − ai+1bi)This module performs only mathematical calculations.The computational cost is independent of any characteristicsof the canal and hence the time and space complexity isconstant.C. Steps in Computation1. Recovery time (Δt) is obtained as the downstreamwave traveling time.2. The canal reach is discretized into (N-1) subreachesusing N nodes, as shown in Fig. 2; node 1being at the upstream end and node N at thedownstream end.3. Computation starts at the last node N, assumingthat Q and h at this node will be equal to theirtarget values at the end of the time step (Δt).4. Q and h at the nodes N-1, N-2 …,2, 1 are obtainedsuccessively, by application of (6) and the fuzzyrule based model. Note that A is a function of hdepending on geometry of the canal.5. The upstream gate is adjusted to release thedischarge computed at node 1 for the recovery timeperiod (Δt).6. If the flow depth (h) at node N at the end of Δtdeviate from its target value then repeat the abovesteps for the next Δt.7. Otherwise stop.The computation module performs a set of operations foreach node in the pool. Hence the time complexity is linearwith the number of nodes in the pool. But the number ofnodes is not a parameter that takes very high values.Therefore the computational time of this module will notvary much with the number of nodes.IV. SOFTWARE TESTINGThe software is tested by comparing its outputs with thatobtained using MATLAB fuzzy logic tool box [16]. Thesoftware has been applied to water level control problem in afictitious canal with a single pool [15]. Schematic diagram ofthe canal is shown in Fig. 5. The canal length (L) is 5000 m,bottom width 5.0 m and side slope 1.0. Its bottom slope isInternational Journal of Computer & communication Technology Volume-2 Issue-VIII, 201141

Development of a fuzzy logic based software for automation of a single pool irrigation canal0.0003. Width of upstream and downstream rectangulargates is 5.0 m with discharge coefficient 0.75. There is aconstant head reservoir at upstream end and another one atdownstream end. Their respective water levels are 6.3 m and2.8 m. Also bottom elevation of the pool at the upstream endis 1.5 m and at the downstream end is 0.0 m. An offtakecanal is provided just upstream of the downstream gate.Target water depth at downstream end of the canal is 3.46 m,which corresponds to normal depth at a peak flow rate of 40m 3 /s.Figure 5. Schematic diagram of the single-pool canal used for testingthe canal automation software.For a base flow corresponding to the peak flow rate of 40m 3 /s, and for various inflow discharges ranging from 35 m 3 /sto 45 m 3 /s, corresponding values of ∆Q and ∆A are obtainedand membership functions are developed by following theprocedure explained under the section “Tuning”. They areshown in Fig. 6. In the figure “L” implies “low” values and“H” implies “high” values. Higher the coefficient of “L” and“H” higher will be their gradation towards “low” and “high”values respectively. The fuzzy rules, connecting theantecedent ∆Q and the consequent ∆A, are derived in theform IF ∆Q is “a” THEN ∆A is “a” where “a” take values inascending order from 9L to 9H (Fig. 6). Hence a total ofeighteen rules are included in the fuzzy rule base.(a)Membership degreeMembership degree10.59L 8L 7L 6L 5L 4L 3L 2L L H 2H 3H 4H 5H 6H 7H 8H 9H0-5 -4 -3 -2 -1 0 1 2 3 4 5∆Q (m 3 /s)(b)10.56.3 m1.5 mFlowBed slope = 0.0003Offtake5000 m3.46 m2.8 m0.0 m9L 8L 7L 6L 5L 4L 3L 2L L H 2H 3H 4H 5H 6H 7H 8H 9H0-0.803 -0.6037 -0.4044 -0.2051 -0.0058 0.1935 0.3928 0.5921 0.7914∆A (m 2 )Figure 6. Membership functions of the fuzzy model for the single-poolcanal: (a) input membership functions, (b) output membership functions.Initially the flow is steady in the canal with a dischargeof 20 m 3 /s. There is no flow in the offtake canal and theentire flow is diverted to the downstream reservoir. Flow inthe offtake canal is then increased from 0 to 20 m 3 /s in 2minutes. With such a disturbance, the response of the systemis studied. The computational nodes are placed at a distanceinterval (Δx) of 100 m each. The recovery time (Δt) is takenas downstream wave traveling time of 797 s [15]. At everyrecovery time step, the upstream gate opening is adjusted, inaccordance with the gate equation given in [15] so as tomaintain the constant gate discharge output from the fuzzycontrol algorithm.The simulation results include variation of the upstreamgate opening with time (Fig. 7), development of watersurface profile along the canal with time (Fig. 8), variation ofthe discharge with time at both upstream and downstreamends (Fig. 9) and variation of the change in water level withtime at both these locations (Fig. 10). These results arecomparable to those obtained using MATLAB fuzzy logictool box [16] and hence it can be concluded that the softwareis giving accurate outputs.Gate opening (m)Water surface elevation (m)4.543.532.521.510.500 20 40 60 80 100 120 140Time (minutes)Figure 7. Variation of the upstream gate opening of the single-poolcanal with time during control14131211109Target profile4105 s2511 sCanal bed120 s80 1000 2000 3000 4000 5000Distance (m)Figure 8. Development of water surface profiles with time in thesingle-pool canal during controlInternational Journal of Computer & communication Technology Volume-2 Issue-VIII, 201142

Development of a fuzzy logic based software for automation of a single pool irrigation canalDischarge (m 3 /s)70605040302010Upstream endDownstream endACKNOWLEDGMENTThe funding provided by CERD (Centre for EngineeringResearch and Development), Kerala, in carrying out thisresearch is gratefully acknowledged.REFERENCES[1] A.J. Clemmens. “Editorial”, Journal of Irrigation and DrainageEngineering, ASCE, vol. 124(1), 1998, pp. 1-2.Change in water level (m)00 20 40 60 80 100 120 140Time (minutes)Figure 9. Variation of discharge with time, at upstream anddownstream ends of the single-pool canal during control1.41.210.80.60.40.20-0.2-0.4-0.6Upstream endDownstream end0 20 40 60 80 100 120 140Time (minutes)Figure 10. Variation of change in water level with time, at upstream anddownstream ends of the single-pool canal during controlV. CONCLUSIONSA software for automation of a single-pool canal, basedon a fuzzy control algorithm, is presented in this study. Thefuzzy algorithm was originally developed using MATLABfuzzy logic tool box, which is not freely available. Thus theoriginal work was unsuitable for common field applications.This problem has been overcome in the present study usingfree and open source packages. Additionally, existing canalcontrol software are based on either control systems theoryor dynamic wave model inversion, both require strongtheoretical background for application. This difficulty doesnot arise for the present software. It is transparent andintuitive and can be easily applied by field engineers.Number of trials required for tuning the fuzzy model hasbeen effectively reduced by including an optimizationtechnique. Also, a new procedure has been introduced forfuzzy inference based on the Mamdani Implication method.The technical details of computation are abstracted from theend user and therefore the software is extremely userfriendly. As the front end was designed using Qt and thecomputational modules uses 'C' language, only a minimumnumber of freely available packages are required to installthe software. The software has been tested by applying it to acanal control problem reported in literature. The resultsobtained are comparable to those obtained using MATLABfuzzy logic tool box, which proves that the software is givingaccurate outputs.[2] P-O. Malaterre, D.C. Rogers and J. Schuurmans.“Classification of canal control algorithms”, Journal of Irrigationand Drainage Engineering, ASCE, vol. 124(1), 1998, pp. 3-10.[3] B.T. Wahlin and A.J. Clemmens. “Performance of historicdownstream canal control algorithms on ASCE Test Canal 1”,Journal of Irrigation and Drainage Engineering, ASCE, vol.128(6), 2002, pp. 365-375.[4] B.T. Wahlin. “Performance of model predictive control onASCE Test Canal 1”, Journal of Irrigation and DrainageEngineering, ASCE, vol. 130(3), 2004, pp. 227-238.[5] A.J. Clemmens and J. Schuurmans. “Simple optimaldownstream feedback canal controllers: theory”, Journal ofIrrigation and Drainage Engineering, ASCE, vol. 130(1), 2004,pp. 26-34.[6] V.M. Ruiz-Carmona, A.J. Clemmens and J. Schuurmans.“Canal control algorithm formulations”, Journal of Irrigation andDrainage Engineering, ASCE, vol. 124(1), 1998, pp. 31-39.[7] V.T. Chow, D.R. Maidment and L.W.Mays. AppliedHydrology, McGraw-Hill International Editions. 1988.[8] E.B. Wylie. “Control of transient free-surface flow”, Journal ofHydraulic Division, ASCE, vol. 95(HY1), 1969, pp. 347-361.[9] F. Liu, J. Feyen, P-O. Malaterre, J-P Baume and P. Kosuth.“Development and evaluation of canal automation algorithmCLIS”, Journal of Irrigation and Drainage Engineering, ASCE,vol. 124(1), 1998, pp. 40-46.[10] E. Bautista, T.S. Strelkoff, and A.J. Clemmens. “Generalcharacteristics of solutions to the open-channel flow, feed forwardcontrol problem”, Journal of Irrigation and Drainage Engineering,ASCE, vol. 129(2), 2003, pp. 129-137.[11] E. Bautista and A.J. Clemmens. “Volume compensationmethod for routing irrigation canal demand changes”, Journal ofIrrigation and Drainage Engineering, ASCE, vol. 131(6), 2005, pp.494-503.[12] G.Chevereau. Contribution a l’étude de la régulation dans lessystèmes hydrauliques a surface libre, Ph.D. thesis, Institut NationalPolytechnique de Grenoble, Grenoble, France. 1991.[13] F. Liu, J. Feyen and J. Berlamont. “Computation method forregulating unsteady flow in open channels”, Journal of Irrigationand Drainage Engineering, ASCE, vol. 118(10), 1992, pp. 674-689.International Journal of Computer & communication Technology Volume-2 Issue-VIII, 201143

Development of a fuzzy logic based software for automation of a single pool irrigation canal[14] J.A. Cunge, F.M. Holly Jr and A.Verwey. Practical Aspects ofComputational River Hydraulics, London: Pitman. 1980.[15] F. Liu, J. Feyen and J. Berlamont. “Downstream controlalgorithm for Irrigation canals”, Journal of Irrigation and DrainageEngineering, ASCE, vol. 120(3), 1994, pp. 468-483.[16] R. Gopakumar and P.P Mujumdar. “A fuzzy logic baseddynamic wave model inversion algorithm for canal regulation”,Hydrological Processes, Vol. 23, No. 12, 2009. pp. 1739-1752.[17] L.A. Zadeh. “Fuzzy Sets”, Information and Control, 8, 1965,338-353.[18] T.J. Ross. Fuzzy Logic with Engineering Applications,McGraw-Hill International Editions. 1995[19] H.J. Zimmermann. Fuzzy Set Theory and Its Applications,Kluwer Academic Publishers. 1991.[20] MATLAB. Fuzzy Logic Tool Box, The Math Works. 1995.[21] J.A. Liggett and J.A Cunge. “Numerical methods of solution ofthe unsteady flow equations”, Unsteady flow in open channels, KMahmood and V Yevjevich eds. Volume 1. Water ResourcesPublications. 1975.[22] S.O. Russell and P.F. Campbell. “Reservoir operating ruleswith fuzzy programming”, Journal of Water Resources Planningand Management, ASCE, vol. 122(3), 1996, pp.165-170.[23] M.G. Ferrick. “Simple wave and monoclinal wave models:River flow surge applications and implications”, Water ResourcesResearch, vol. 41(W11402), 2005, pp. 1-19.[24] V.M. Ponce and D.B. Simons. “Shallow wave propagation inopen channel flow”, Journal of Hydraulic Division, ASCE, vol.103(HY12), 1977, pp. 1461-1476.[25] C.W-S. Tsai and B.C. Yen. “Linear analysis of shallow waterwave propagation in open channels”, Journal of EngineeringMechanics, ASCE, vol. 127(5), 2001, pp. 459-472.[26] A.J. Clemmens, T.F. Kacerek, B. Grawitz, W. Schuurmans..Test cases for canal control algorithms. Journal of Irrigation andDrainage Engineering, ASCE, 124(1), 1998, pp. 23-30.[27] FISLAB: the Fuzzy Inference tool-box for SCILAB. Ann.Univ. Tibiscus Comp. Sci. Series V, 2007, pp. 105-114[28] Fuzzy Lite – A fuzzy logic library written in C++.http://code.google.com/p/fuzzy-lite, accessed on 02/02/2011[29] E.L. Posselt , L.F.D.R.E Silva, R. Frozza and R. Fredimolz.“Qualitative Study of Software for Fuzzy Systems Simulation andDevelopment”, Proceedings of the 11th WSEAS (World Scientificand Engineering Academy and Society ) international conferenceon neural networks, evolutionary computing and Fuzzy systems,Stevens Point, Wisconsin, USA. 2010[30] M.H. Chaudhry. Open-Channel Flow, Englewood Cliffs, N.J:Prentice-Hall. 1993.[31] E.H. Mamdani and S. Assilian. “An experiment in linguisticsynthesis with a fuzzy logic controller”, International Journal ofMan-Machine Studies, vol. 7(1), 1975, pp.1-13.[32] http://en.wikipedia.org/wiki/centroid, accessed on 30/5/2011International Journal of Computer & communication Technology Volume-2 Issue-VIII, 201144