STUDY OF INTERACTING AND NON-INTERACTING WITH
STUDY OF INTERACTING AND NON-INTERACTING WITHDISTURBANCE AND PID CONTROLLER DESIGNKalyanjee Barman1, Labanya Baruah2, Himadri Deori3, Santu Brahma4B.Tech Final Year Student, Department of Instrumentation Engineering, CIT KokrajharEmail:kalyanbarman22@gmail.com1, hmasantu@gmail.com4Abstract- A multi tank level control systemincludes both the example of interacting andnon-interacting system. The main objective ofthis paper is to determine the mathematicalmodel of interacting and non-interacting tankwith disturbance and also design of PIDcontroller.Basedonprocedureofmathematical modelling for tanks ininteracting and non-interacting mode thispaperisanextensivecomparativeexperimental study liquid level g systems and PID controller.I. INTRODUCTIONThe first stage is in the development of anycontrol and monitoring system is theidentification of the system and mathematicalmodelling of the system. The present work is onthe mathematical model for interacting and noninteracting tank process with disturbances.Disturbance is applied to second tank in each case(interacting and non-interacting tank [2]-[8].two part by the three way valve. The three wayvalve position can be determine by the constant γ.The (1- γ) portion of flow used as a disturbanceto the lower tank and γ portion of flow to theupper tank. By using feedback control systemwe control the liquid level of the lower tank [7][5]-[2].Interacting Tank System: Consider an interactingtank process, with one input and one outputshown in the labview simulation diagram Fig.2.The objective is to control the water level of tank2 i.e. h2 with inlet water flow Qin. Here Q 2assumed as a disturbance variable. The Pumpgenerate water flow, this flow rate can becontrolled by the pneumatic control valve havinggain K [6]-[3]. The output flow of the controlvalve be split in to two part by the three waycontrol valve. The tank 1 flow rate can be Q1 KγQin and tank 2 flow can be Q1 k (1-γ) Qin. Thecontrol objective is to maintain a level in tank2 bythe varying inflow rate of tank1 in presence ofdisturbance flow to tank2 [1].Noninteracting Tank System: In Non-InteractingTank system it consist of two tank as shown inthe labview simulation diagram Fig.1. The pumpsupply the water flow, which is controlled by thepneumatic control valve having valve constant K.The output flow of the valve can be divided in 2,ISSUE-3,201566
INTERNATIONAL JOURNAL OF ADVANCED COMPUTING AND ELECTRONICS TECHNOLOGY (IJACET)Fig.1SystemParameterNon-InteractingTank system(CGS unit)InteractingTanksystem(CGS unit)Cross sectionalarea of tanksA(cm2)78.5 cm278.5 cm2Outlet portcross sectionalarea (a cm2)1 cm21 cm2PneumaticControl valveconstant(Kcm3/sec/bar)3.2(cm3/s/ Bar)3.3(cm3/sec/ Bar)Ball ValveCoefficientβ1 0.6, β2 0.5β1 0.5,β2 0.6Three wayvalvecoefficientγ 0.790.75Pump Flowrate138.89 cm3/s138.89cm3/s(500lph)(500 lph)Total height ofthe Tanks10 cm10 cmTable 1a. Mathematical Modelling of Non interacting TankSystem:Flow through control valve Qin KρgH cm3/secWhere,K Valve Constant (cm3/s/Bar)ρ Density of water (gm/cm3) 1 gm/cm3g acceleration due to gravity (cm/sce2)H Height of the liquid (cm)Using mass balance equation we found thedifferential equations for the systemTank 1AFig.2II. MATHEMATICAL MODELLING OFTHE SYSTEMThe System Specification for both interactingand non-interacting tank is given in the table 1.dh 1 KQ in γ β1 adt2gh 1Tank 2Adh 2 KQ in (1-γ) β1 adt2gh 1 β2a 2gh ,ISSUE-3,201567
INTERNATIONAL JOURNAL OF ADVANCED COMPUTING AND ELECTRONICS TECHNOLOGY (IJACET)The system can be linearized around the operatingpoint, The relation between steady state flow rate andheight can be determine as;//(K Q in ) 2-h1 1 2 a 2 2 g-and h 2 (K Q in ) 2 2 2 a 2 2g-h1 Steady State height of the Tank 1 and/s 0 .2755 s 0 .01736/If Q in 10 lph then we obtain the calculated-h1 0.9048 cm and h 2 2.087 cmThe linearized differential Equations of the system a 2gdh 11 {KQ in γ 1h1 }Adt2 h1 h1 h 2 1a 2 g 2A h1 2g h 1 a K AK(1 - ) A12A 0 2 a 2 g - 2A h 2 b. Mathematical Modelling of interacting TankSystem:Differential equations for the system,Tank 1dh 1 KQ in γ β1 adtFor Tank 22 g (h 1 h 2 )A a 2g a 2gdh 2 {KQ in (1-γ) 1h1 2h 2}dt2 h12 h21ANow the State space representation of the system 1 0 C 0 1 G(s) 02 .00856 s 0 .007251Q in Steady state flow rate. 1 0 h 1 0 1 h 2 Using Matlab Command ‘ss’ and ‘tf’ wedetermine the transfer function of the system,-h 2 Steady state height of the Tank 2- h1 h 2 hh(t ) (t ) 21dh 2 KQ in (1-γ) β1 adtA2 g (h 1 h 2 ) β2a2gh 2The system can be linearized around the operatingpoint, the relation between steady state flow rate andheight can be determine as,//-h1 (K Q in ) 2 1 2 a 2 2 g/(K Q in ) 2 - 2 2 a 2 2gand h 2 (K Q in ) 2 2 2 a 2 2g-h1 Steady State height of the Tank 1- h 2 Steady state height of the Tank 2ui/Q in Steady state flow rate./If Q in 6 lph then we obtain the calculated--G(S) C(sI - A) -1 Bh1 1.003cm and h 2 0.553 cmWhere ,0 0.1779 A ; 0.1779 0.0976 0.0322 B 0.00856 The sensor output equation can be consider as,Y1 h1 and Y2 h2So,Now the linearized differential equation of thesystem,dh 1 {KQ in γ dt 1a 2 g2 (h 1 h 2 )(h 1 h 2 E-2,ISSUE-3,201568
INTERNATIONAL JOURNAL OF ADVANCED COMPUTING AND ELECTRONICS TECHNOLOGY (IJACET)dh 2 {KQ in (1-γ) dt 2 a 2g-2 h2 1a 2 g(h 1 h 2 )} 2 (h 1 h 2 )G(s) 02 .01051 s 0 .008839s 0 .6483 s 0 .04787III. SIMULINK DESIGN OF THE SYSTEM1h 2}Aa. Non-Interacting SystemNow the state space representation of thesystem, h1 h 2 β1 a 2g 2A h 1 h2 β1 a 2g 2A h1 h 2 h1 (t) (t) h2 β a 2g β1 a 2g 2 2A 2A h2 h1 h2 β1 a 2g 2A h1 h2 Fig.3 Non-Interacting Tank Syatem K A K(1 - ) A a. Interacting System:uiG(S) C(sI - A) -1 BWhere , 0.2104 0.2104 ; 0.2104 0.4379 A 0.03153 0.010509B The sensor output equation can be consider as,Y1 h1 and Y2 h2So, 1 h1 0 h 2 Fig.4 Interacting Tank System0 h 1 1 h 2 IV.PID TUNING 1 0 C 0 1 Using Matlab Command ‘ss’ and ‘tf’ wedetermine the transfer function of the system,The basic PID tuning method is Zeigler Nicholsopen loop response. For open loop tuningmethod we open the closed loop feedback. Thenwe apply the step signal in the and from the stepresponse of the system then we determine the Land T UME-2,ISSUE-3,201569
INTERNATIONAL JOURNAL OF ADVANCED COMPUTING AND ELECTRONICS TECHNOLOGY (IJACET)The steady state gain value represented by K.The ‘a’ value can de determine a (K*L)/T.Zeigler-Nichols Tuning Lb. Closed Loop Response of the system:Block Diagram of Closed Non-Interacting TankSystem and step response of the system Shownbelow.L/2Table 2Fig.7 Closed loop Non-Interacting Tank systemwith PID controller.Fig.5V. EXPERIMENTAL RESULTa. Non-Interacting Tank System:Open loop response of the system shown in Fig.6Here,K .4177L 1.132 secT 21.69 secFig.8 Step Response of the Non-Interacting TankA 0.02179system with PID controller.The calculated value forc. Interacting Tank System:PID controller isOpen loop response of the system shown in Fig.9Kp 55; Ti 2.264Td 3416,VOLUME-2,ISSUE-3,201570
INTERNATIONAL JOURNAL OF ADVANCED COMPUTING AND ELECTRONICS TECHNOLOGY (IJACET)Here,K 0.1846, L 0.377 sec, T 13.96 sec andA 0.004985The calculated value for PID controller isKp 200; Ti 0.754Td 0.1885The closed loop block diagram of the system issimilar as the Non-Interacting tank system. Thestep response of the system with PID controller isshown in the figure 7.Engineering Volume 3, Issue 12, December2013.[2] Jayaprakash J, Senthil Rajan T, Harish BabuT. “Analysis of Modelling Methods of QuadrupleTank System”International Journal Of Advanced Research inElectrical, Electronics and InstrumentationEngineering. Vol.3,Issue 8, August 2014.[3] D.Hariharan, S.Vijayachitra “Modelling andReal Time Control of Two Conical Tank Systemsof Non-interacting and Interacting type“International Journal Of Advanced Research inElectrical, Electronics and InstrumentationEngineering” Vol. 2, Issue 11, November 2013.[4] Karl Henrik Johansson “The Quadruple TankProcess: A Multivariable Laboratory ProcesswithanAdjustableZero”IEEETRANSACTIONS ON CONTROL SYSTEMTECHNOLOGY, VOL.8, NO 3, MAY 2000.Fig.10 Step Response of the Non-Interacting Tanksystem with PID controller.[5] S. Saju B.R.Revathi, K.Parkavi Suganya“Modelling and Control of Liquid Level NonLinear Interacting and Non-Interacting System”VI.CONCLUSIONInternational Journal Of Advanced Research inFrom the experiment it is observed the without Electrical, Electronics and Instrumentationused of the PID controller both the system have Engineering. Vol.3, Issue 3, March 2014.large steady state error. The system have moreerror due to the disturbance input in both the [6] L.Thillai Rani, N.Deepa, A.Arulselvisystems. The Interacting tank system have high “Modelling and Intelligent Control of two Tanknonlinearity than the Non-interacting tank system Interacting Level Process” International Journalbecause the flow out of the tank1 depends upon or Recent Technology and Engineering Volumethe height of the tank 2.There are several PID 3, Issue-1,March 2014.controller tuning method the Zeigler Nichols[7] K.Krishnaswamy “Process Control” New Ageopen loop tuning method is simple tuningInternational Publishers, Chapter 2, Page 83-137.method. The system with this PID controllereliminate the steady state error but have peak [8] Y.Christy, D. Dinesh Kumar “Modelling andovershoot. The PID controller increase the rise Design of Controllers for Interacting Two Tanktime of the system and also settling time.Hybrid System” International Journal ofVII. REFERENCESEngineering and Innovative Technology Volume3, Issue 7, January 2014.[1] Prof.D. Angeline Vijula, Anu K, Honey Mol[9] ‘Chemical Process Control’ by GEORGEP, Poorna Priya S. “Mathematical Modelling ofSTEPHANOPOULOS , PHI Publication, 2014,Quadruple Tank System” International Journal ofChapter 18, page 209-302.Engineering Technologyand OLUME-2,ISSUE-3,201571
the mathematical model for interacting and non-interacting tank process with disturbances. Disturbance is applied to second tank in each case (interacting and non-interacting tank [2]-[8]. Noninteracting Tank System: In Non-Interacting Tank system it consist of two tank a
Lecture 25. Bose-Einstein Condensation (Ch. 7 ) 70 years after the Einstein prediction, the BEC in weakly interacting Bose systems has been experimentally demonstrated - by laser coolingof a system of weakly-interacting alkali atoms in a magnetic trap. Nobel 2001 BEC and related phenomena BEC of photons (lasers) BEC in a strongly-interacting system
2. TWO INTERACTING CONICAL TANK PROCESS DESCRIPTION Fig 1: Schematic diagram of two interacting conical tank The proposed system consists of two conical tanks which are in the shape of an inverted cone fabricated from a sheet metal. The height of the process tank is 50cm a
3. If β is small and f 1 is close to one, then the interacting control is favored for that particular disturbance. 4. If β is large, the interacting control is un favorable for that particular disturbance. The Relative Gain for Non-square Multivariable Systems (J.C. Chang and C.C. Yu, CES Vol.45, pp. 1309-1323 1990) Consider a non-square MV .
NDCC Agreement Page 1 of 5 NON-DISCLOSURE, NON-CIRCUMVENTION, NON-COMPETITION AGREEMENT This NON-DISCLOSURE, NON-CIRCUMVENTION and NON-COMPETITION AGREEMENT is effective as DATE between 1. Providing Party: 2. Receiving Party: hereinafter collectively addressed as “the Parties” or individually as a “Party”,
SYSTEM IDENTIFICATION AND MODELING FOR INTERACTING AND NON-INTERACTING TANK SYSTEMS USING INTELLIGENT TECHNIQUES Bhuvaneswari N S1, Praveena R2,Divya R3 Electronics and Instrumentation Engineering Department, Easwari Engineering College, Chennai, Tamilnadu, India. 4. Mathematical Modeling
BEC and Mermin-Wagner theorem (II) This result due to Einstein (1925), which says that there is no BEC at nite temperature for D 2 in the case of non-interacting bosons, was extended to interacting systems by David Mermin and Herbert Wagner in 1966. For the BEC phase transit
from Simulink model and mathematical model. This paper will help the method suitable for research findings concerning on the coupled-tank liquid level control system. 2.MATHEMATICAL MODELING A mathematical model is a description o
Tourism is not limited only to activities in the accommodation and hospitality sector, transportation sector and entertainment sector with visitor attractions, such as, theme parks, amusement parks, sports facilities, museums etc., but tourism and its management are closely connected to all major functions, processes and procedures that are practiced in various areas related to tourism as a .
