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 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