De-Coupler Design for an Interacting Tanks System

Transcription

1 IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-issn: ,p-ISSN: , Volume 7, Issue 3 (Sep. - Oct. 2013), PP De-Coupler Design for an Interacting Tanks System Mukes Battarai Department Of Cemical Engineering, SADTM Campus, Jaipur National University Abstract: Te dynamic beavior of two interacting system was studied by te introduction of a step cange in inlet flow rate and wit te development of te suitable matematical model of tis interacting system. Tis paper describes ow te effect of te interaction of tis interacting system is eliminated by te design of te suitable de-coupler for te system. Tis paper also includes te analysis of te interacting loops between te controlled variable tat is liquid level and manipulated variable tat is inlet flow rate by te elp of relative gain array. Te result exemplifies tat te gain of eac loop is reduced approximately alf wen te opposite loop is closed and te gain of oter loop canges te sign wen te opposite loop is closed. Tus te decoupling metod illustrate tat it is one of te suitable metod for te reduction of te interaction in te tanks system. Keywords: interacting system, interacting loops, controlled variable, manipulated variable, relative gain array, de-coupler. I. Introduction In most of te cemical industries te control of flow rate and te liquid levels in te tanks are two basic and major problems. Most of te time mixing treatment or te cemical operations are to be taken out in te tanks, but always te level of liquid in tanks must be controlled wit te continuous regulation of flow rate between tanks. Tus we need to design te elements in suc a way tat te control over te variables will become easy. Most industrial process control application involved a number of input and output variables wic are often referred as MIMO system. Te important examples of MIMO system includes eat excangers, cemical reactors and distillation columns. It is more difficult to perform an operations on MIMO system tan in SISO system. It is because of te interaction between te input and output variables. Te term interaction is often referred as Loading. Te process is called as interacting if eac input affects more tan one output or a cange in te output affects te oter outputs, oterwise te process is called non interacting. Wile designing two strongly interacting loops, we ave to introduce te new element called Decoupler in te control system. Te purpose of decoupler is to cancel te interaction effects between two loops and tus render two non interacting control loops. In anoter words, te main aim of te decoupling control system is to eliminate complicated loop interactions so tat a cange in one process variable will not cause corresponding canges in te oter process variables. RGA- Since its proposal by Bristol(1966), te relative gain tecnique as not only become a valuable tool for te selection of manipulated controlled variable pairings, but also used to predict te beavior of control responses. To fully appreciate te concepts of relative gain, te RGA will be constructed for a system represented by p-canonical structure. Te RGA metod indicated ow te input sould be coupled wit te output to form loops wit minimal interaction. A process wit any controlled outputs and N manipulated variables, tere are N! different ways to form te controlled loops. Te RGA provides exactly suc a metodology, wereby we select pairs of input and output variables in order to minimize te amount of interaction among te resulting loops. In tis paper, te dynamic beavior of an interacting two tanks system was studied bot teoretically and experimentally. RGA is used as an interaction measurement and decoupling to design te loops. II. 2.1 Notations and Standards A 1 : Cross sectional area of tank 1, m m 2 A 2 : Cross sectional area of tank 2, m m 2 F : Volumetric flow rate, m 3 /sec : Flow resistance in valve sec/m 2 Teory/Literature Survey 77 Page

2 De-Coupler Design For An Interacting Tanks System R 2 : Flow resistance in valve sec/m 2 τ 1 : Time constant of tank sec τ 2 : Time constant of tank 95 sec µ : Relative gain array 2.2 matematical model Te important assumptions for te derivation of te matematical model for te interacting two tanks system are:- Te flow resistance is linear wit te linear liquid level in te tanks. Te tanks are of equal and uniform cross sectional area. Te density of water remains constant wic means tat it is independent of time. Te interacting two tanks system is sown in te figure below. Fig1:-Interacting tanks system. Applying te material balance in bot of te tanks we get, Accumulation Mass flow in - Mass flow out For 1 st tank For 2 nd tank By using assumptions, ten equations (i) and (ii) become, A 1 d 1 dt F i F 1 (i) A 2 d 2 dt F 1 F 2 (ii) F 1 ( 1 2 ) and F 2 2 R 2 A 1 d 1 dt F 1 iii d 2 A 2 R 2 dt R 2 R 2 R iv 1 1,s 2,s F i,s (V) (1 + R 2 ) R 2,s R 2 1,s 0 (vi) 1 ten steady state equivalents of equations (iii) and (iv) are subtracting equation (v) from (iii) and (vi) from (v) and ten introducing deviation variables we get, were, A 1 d 1 dt F i (vii) A 2 R 2 d 2 dt R 2 2 R (viii) 1 1 1,s 2 2 2,s F i F i F i,s taking te Laplace transform of equations (vii) and (viii) and find τ p2 s + + R 2 1 s τ p1 τ p2 s 2 + τ p1 + τ p2 + A 1 R 2 s + 1 F i and, s (viii) 78 Page

3 2 s 2.3 Loop interaction De-Coupler Design For An Interacting Tanks System R 2 τ p1 τ p2 s 2 + τ p1 + τ p2 + A 1 R 2 s + 1 F i s (ix) Fig2:-Interacting two tanks system Let us consider a two tanks interacting system as sown in figure 2 aving two manipulated variables F i and F 2. Now we need to find te gain of eac manipulated variable on eac of te controlled variable. Te four open loop system is sown in te figure 3 below and given as Fig3:- Scematic of interaction for controlled variable and manipulated variable [ 1 F i 12 ג ] F2 [ 1 F 2 ] Fi (X) [ 2 ] F F2 [ 2 ] i F Fi (xi) 2 were, ij ג is te gain of i t controlled variable relating to te j t manipulated variable. Te RGA provides exactly suc a metodology wereby we select pairs of input and output variables in order to minimize te amount of interaction along te resulting loops. te major advantage of RGA is tat it requires only te steady state process parameters tat is steady state gains. Tus 1 12 ג + i F F 2 (xii) 2 + i F F 2 (xiii) Now we need to introduce feedback system wic connects F 2 wit 2, in order to determine te gain wic connects F i wit i. According to figure 3, we get four closed steady state loops and ence four steady state gains is to be calculated from te four open loop gains. Tus te resulting formulae are:- 12 ג, (xiv) According to te definition, Tus,, µ ij ij ג ij ג (xv) µ 11, µ (xvi) µ 21, µ Page

4 De-Coupler Design For An Interacting Tanks System 2.4 decoupling of interacting loops Fig 4:- block diagram of interacting tanks system wit decoupler. Now our main intention is to reduce or eliminate te interaction between te loops troug te suitable design element wat is called te Decoupler. Decoupling does cange to eac loop wat te oter loops were going to do anyway, tis is one of te important caracteristic of decouplers. In order to reduce tis interaction between two tanks, two decoupler blocks aving transfer functions D 12 (s) and D 21 (s) are installed in te system were decoupler D 12 (s) cancels te effect of manipulated variable F 2 (s) on controlled variable 1 (s) and D 21 9s) cancels te effect of manipulated variable F i (s) on controlled variable 2 (s). Tus we get te design formulae for te decouplers are:- D 12 s G 2 s G 12 s G 1 s G 11 s (xvii) D 21 s G 1 s G 21(s) G 2 s G 22 (s) (xviii) III. Materials And Metods 3.1 experimental work Description of Equipment Interacting two tanks - Te interacting two tanks consists of two vessels arranging cascade aving eac of diameter m, and ence te area m 2 respectively. Small narrow pipe wit valve is connected between te two tanks. Water is supplied troug stainless steel float rotameter aving range LPH wit temperature condition of water at 27 0 C. Te Rotameter as maximum capacity of 100 LPH. Te control system consist of PID controller, control valve and pressure transmitter Experimental procedure Te inlet streams were given to te tanks and te valve in te inlet streams were adjusted to provide a suitable reading on te rotameter. After sometimes te liquid levels in two tanks are in steady state and system was left for stabilization. Ten te following step were performed:- Te inlet flow rate of te tank 1(F i ) was stepped up from 50 LPH to 60 LPH wit constant inlet flow rate of tank 2(F 2 ) at 30 LPH by using te valve and te liquid levels in bot tanks were recorded wit Te inlet flow rate of te tank 2(F 2 ) was stepped up from 30 LPH to 40 LPH wit constant inlet flow rate of tank 1(F i ) at 50 LPH by using te valve and te liquid levels in bot tanks were recorded wit Te inlet flow rate of te tank 1(F i ) was stepped down from 50 LPH to 40 LPH wit constant inlet flow rate of tank 2(F 2 ) at 30 LPH by using te valve and te liquid levels in bot tanks were recorded wit Te inlet flow rate of te tank 2(F 2 ) was stepped down from 30 LPH to 20 LPH wit constant inlet flow rate of tank 1(F i ) at 50 LPH by using te valve and te liquid levels in bot tanks were recorded wit IV. Result And Discussion Relative gain array µ ij is calculated from bot experimental and teoretical final steady state condition wit a step cange in inlet flow rate of te two tanks and are found to be µ teoretical µ experimental Page

5 Te teoretical relative gain µ 11 µ De-Coupler Design For An Interacting Tanks System. It means te gain of eac loop is cut in alf wen te oter closed. Similarly te relative gain µ 12 µ indicates tat te gain loop canges sign wen te 1 oter loop is closed. Obviously last condition was undesirable. it is because of te fact tat te action of te controller depends on te, weter te loop is opened or closed. Now our main intention is to design te decoupler wic is given by te equations (xvii) and (xviii). Tus we get, D D 180s s + 1 Tus we can say tat bot te decouplers are simple gains. Decoupler D 12 (s) as a negative gain because its main intention is to keep te liquid level of tank 1( 1 ), wen te second inlet stream(f 2 ) canges. Similarly, Decoupler D 21 (s) as a positive gain because its main intention is to keep te liquid level of tank 2( 2 ), wen te first inlet stream(f i ) canges. V. Conclusions Tus from te above experiments, te following conclusions can be drawn:- Te decoupler lessen te interaction of two interacting tanks system and te decoupler as same effect as it as before. Since te relative gain is µ 11 µ It means tat wen te loop 1 is closed, te gain of loop is cut into alf. Since te relative gain is µ 12 µ , it means tat te action of controller depends on eiter 1 te loop is open or close and it is undesirable one. Acknowledgement Department of Cemical engineering, Jaipur National University, Jaipur is gratefully acknowledged for te support by providing te process dynamics and control laboratory. References [1] TrielWeiler J.O.," Application of Te Robust Performance Number for Quantification of te Operability of te Quadruple- Tank Process", Brazilian Journal of Cemical Engineering, Vol. 19, Page No [2] Zumberge J., Passino, K.M.," A case study in Intelligent vs. Conventional Control for a process controlexperiment", Journal of control Engineering practice, Vol. 6, No. 9, Page No ,1998. [3] Esce S.K.," Tank Filling Of Liquid Level System", Stevens Institute of Tecnology, 2001, [4] Stepanopoulos G.," Cemical Process Control", An Introduction to Teory and Practice", Prentice-Hall India, Inc.,1984, Page No [5] Couganowr R. Donald," Process Systems Analysis and Control" McGraw-Hill International Editions,Inc Cemical Engineering Series, Page No [6] Luyben L. William," Process Modeling, Simulation, and Control for Cemical Engineers", McGraw-HillInternational Editions1996,page No [7] Edgar T. F. & Rueda L.," Process Dynamic and Control Laboratory Experiments Carried Out OverTe Internet", University of Texas, [8] Ibraim D.," Microcontroller Based Applied Digital Control", Jon Wiley & Son Ltd.,PageNo , [9] Henry J. & Nuttal E.," Cemical Engineering Experimentation over te Internet", AICHE/Labs, [10] Douglas O. J., Desa," Applied Tecnology and instrumentation for Process Control", Taylor & Francis Books Inc., Page No, 71-75, [11] E. P. Gatzke, E. S. Meadows, C. Wang, and F. J. Doyle," Model based control of a four tank system", Computer and Cemical Engineering, Vol. 24, Page No , Page