Modelling and Controller of Liquid Level system using PID controller Deign Gloria Jose 1, Shalu George K. 2

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1 Modellng and Controller of Lqud Level system usng PID controller Degn Glora Jose 1, Salu George K. 2 1PG student, Dept. of EEE, MBCET, Trvandrum, Kerala 2 Assstant Professor, Dept. of EEE, MBCET, Trvandrum, Kerala *** Abstract Te control of lqud level n tanks s one of te basc problem n te process ndustres. Te tess 2. MODELLING OF LIQUID LEVEL SYSTEM work deals wt desgn of PID controller for te Lqud Level System. System dentfcaton of LLS s done and modeled Te dagram of plant (te Lqud Level system) under consderaton s sown n te fg 1. Te plant level troug Emprcal Zegler-Ncols Tunng metod. A process controller VLPA-101-CE s truly versatle and transfer functon s obtaned wt frst order system plus gly relable standard computer based level delay. Te system s controlled by PID controller and tuned by usng Zegler-Ncols tunng metod. Te PID controller process Controller. It s a self contaned process and control equpment. Te VLPA- 101-CE as mnature s mplemented n MATLAB and ten smulated n Smulnk pump, level sensor for sensng and personal to test te output of te system wt respect to nput. Te computer for controllng. output s obtaned wt less steady state error. Key Words- PID controller: Zegler-Ncols tunng: modelng of lqud level system. 1. INTRODUCTION Development of Lqud Level System as become an unavodable part n many ndustres due to te wde use of bolers n nuclear power plants and oter lqud based producton tecnques.. In process control, level control s a common metod. Hence te level control system must be properly controlled by te sutable controller. Table 1 lqud level system specfcatons Pump Process tank Reservor tank Model Tullu 80 Materal Acrylc Materal Mld Steel Speed 6500RPM 2 Capacty 7 Capacty lters lters PID controller s one of te most easest and smplest controller tat always been used n ndustral. Tere are several metods to obtan te parameters for PID controllers suc as tral and error metod, Coen-Coon (C-C) metod and Zegler- Ncols (Z-N). Te values of te parameters n te controller determne te performance of system. In ts paper Zegler-Ncols (Z-N) tunng metod s used. Fg 1: Te Lqud Level System VLPA-101-CE To analyze te systems nvolvng flud flow, t essental to dvde flow regmes nto turbulent flow and lamnar flow, accordng to te value of magntude of Reynolds number. If te Reynolds number s greater tan or about 3000 to 4000, ten t s turbulent flow. And f te flow s lamnar ten te Reynolds number s less tan or about And wen Reynolds number s between 2000 and 3000 s called as transtonal flow. In lamnar flow, flud flow manly occurs n streamlnes wt no turbulence. Systems nvolvng turbulent flow are represented by nonlnear dfferental equatons, wle systems nvolvng lamnar flow are represented n lnear dfferental equatons. (Te flow of lquds n Industral processes s often troug ppes and tanks. Suc flow s often turbulent and not lamnar.) In order to dentfy te beavor of a process, a matematcal descrpton of te process as to be 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certfed Journal Page 2222

2 developed. But usually, te matematcal model of most of te pyscal processes s nonlnear n nature. On te oter and, most of te analyss lke n smulaton and desgn of te controllers, assumes tat te process s lnear n nature. In order to buld ts gap, te lnearzaton of te nonlnear model s needed. Ts lnearzaton s always done wt respect to a partcular operatng pont of te system. Ts secton llustrates te nonlnear matematcal beavor of a process and te lnearzaton of te model. Consder a specfc example of a smple process descrbed n Fg CAPACITANCE OF LIQUID-LEVEL SYSTEMS Te capactance of a tank s defned to be te cange n quantty of stored lqud necessary to cause a unty cange n te potental (ead). Te potental (ead) s te quantty tat ncludes te energy level of te system. Capactance (C) s notng but s cross sectonal area (A) of te tank. Fg 2: Example of a pyscal process Rate of cange of flud volume n tank = flow n flow out dv q Snce volume s (area x egt) (4) From te above fgure t s understood tat q s te nflow rate and qo s te outflow rate (n m3/sec) of te tank, and s te egt of te lqud level of te tank at any tme nstant. And also assume tat te cross sectonal area of te tank be A. In steady state condton, bot q and qo are same, and te egt of te lqud level of te tank wll be constant. d( A ) q A q (5) (6) 2.1 RESISTANCE OF LIQUID LEVEL SYSTEM Te resstance for lqud flow n suc a ppe or restrcton s defned as te cange n te level dfference to a unt cange n flow rate; tat s, cange n level dfference( m) Resstance 3 cange n flow rate( m / s) dh R dq (1) (2) And cross sectonal area can be replaced by capactance C q Were te resstance R may be wrtten as R dh dq q 0 Ten rearrangng te equaton (8) we get q 0 R (7) (8) (9) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certfed Journal Page 2223

3 Substtute equaton (9) n equaton (7), we get C q (10) After smplfyng above equaton te equaton (10) becomes (11) Takng Laplace transform consderng ntal condtons to zero R RC Rq RCsH ( s) H( s) RQ ( s) (12) processes te process reacton curve s an S-saped curve. Te procedure to obtan te reacton curve of a plant n an open loop experment as follows: 1) Wen te plant s n open loop condton, take te plant manually to a normal operatng condton. 2) Say te plant output settles at y(t) = y 0 for a constant plant nput u(t) = u 0. 3) At an ntal tme t 0, apply a step cange to te plant nput from u 0 to u (ts sould be n te range of 10 to 20% of full scale). 4) Record te plant output untl t settles to te new operatng pont. 5) Tus te curve obtaned s called process reacton curve. Wc s sown n fgure 3.8, m.s.t. stands for maxmum slope tangent. Te transfer functon can be obtaned as H ( s) ( ) R Q s ( RCs 1) (13) C=cross sectonal area of te tank =πr 2 cm 2 =35πcm 2 Radus of te tank s 6cm. In te mddle of te process tank conssts of a tube wt radus 1cm. 3. SYSTEM IDENTIFICATION Te determnaton of te dynamc beavour of a process by experment s called process dentfcaton. Te metod used n modellng of lqud level system s te system dentfcaton s Emprcal metod n wc te expermental nputoutput data s used. In ts secton, te transfer functon model usng process reacton curve metod s dscussed for wc te nput and output data are generated from te real tme system response. Open-loop dentfcaton s wdely used n te ndustry. In open loop step testng, a step cange n nput s appled to te process wc wll produce a correspondng response. It s called process reacton curve. In te cemcal ndustry, for many Fg 3 Plant Step Response 6) Were te process gan value K can be calculated as y and y 0 are outputs u and u 0 are nputs y K u o 0 y u (14) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certfed Journal Page 2224

4 In wc y 0 and u 0 are set ponts. 3.1 EMPIRICAL ZIEGLER AND NICHOLS METHOD A very useful emprcal tunng formula was proposed by Zegler and Ncols n early Te tunng formula s obtaned wen te plant model s gven by a frst-order transfer functon model wt a pure tme-delay. In real-tme process control systems, a large varety of plants can be modeled approxmately. If te system model cannot be pyscally derved, experments can be made to extract te parameters for te approxmate model. Many ndustral processes sow step responses wt pure a perodc beavour accordng to Fgure 3.9. Ts S-sape curve s caracterstc of many gorder systems and suc plant transfer functons may be approxmated by te matematcal model can be expressed as G K ( Ts 1) (15) Fg: 4. Sketces of te responses of a frst order plus delay model Te transfer functon model usng process reacton curve metod s sown ere: H ( s) 1 e Q ( s) (5s 1) Ls ( s) e s (16) Ts contans a 1 st order delay element and a dead tme K = process gan T = process tme constant, L = dead tme of te process 3.2 TANGENT METHOD 1. Obtan te step response expermentally. 2. Draw a tangent at te nflecton pont. 3. Fnd gan value as rato of steady - state cange n output y to ampltude of nput step A. 4. Dead tme L= from tme of step nput to te ntersecton of te tangent lne wt te tme axs. 5. T+L= tme nterval between te step nput and te ntersecton of te tangent lne wt te fnal steadystate output level. K = 1, L = 1 and T = 5 and L a K T 4. EMPIRICAL ZIEGLER-NICHOLS TUNING FORMULA For nstance, f te step response of te plant model can be measured troug an experment, te output sgnal can be recorded as sketced n Fg.3, from wc te parameters of K, L and T can be extracted. Te S-saped reacton curve can be caracterzed by two constants, delay tme L and tme constant T, wc are determned by drawng a tangent lne at te nflecton pont of te curve and fndng te ntersectons of te tangent lne wt te tme axs and te steady-state level lne. Usng te parameters L and T, we can set te values of K P, K and K d accordng to te formula sown n te table below. 6. Te output sgnal can be recorded as sketced n Fg.3.10, from wc te parameters of K, L and T can be extracted 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certfed Journal Page 2225

5 controller type Table 2: Zegler Ncols tunng formula From step response From frequency K p T T d K p T T d P 1\a 0.5K c PI 0.9\a 3L 0.4K c 0.8T c PID 1.2\a 2L L\2 0.6K c 0.5T c 0.12T c 5. TUNING OF PID CONTROLLER PARAMETERS Smulaton of lqud level system usng te controller PID Fg 5: Smulaton of sngle tank usng pd controller Table:3: PID Parameters from Emprcal Zegler- Ncols tunng formula K p K K d CONCLUSION Te control of lqud level n tanks s one of te basc problem n te process ndustres. To aceve ts, PID controller for te plant s smulated and mplemented. Te work manly ncludes te desgn and modelng of lqud level system. System dentfcaton of LLS s done and modeled troug Emprcal Zegler-Ncols Tunng metod. A transfer functon s obtaned wt frst order system plus delay. Ten te PID controller s desgned by usng Zegler-Ncols tunng metod. REFERENCES [1] Tatsuo Nakagawa, Akko Hyodo, and Kenj Kogo Contactless Lqud-Level Measurement Wt Frequency Modulated Mllmeter Wave Troug Opaque Contaner IEEE sensors journal, vol. 13, no. 3, marc [2] Book, Dr. A. Azz. Bazoune Capter 7 Flud Systems and Termal Systems. ME 413 Systems Dynamcs & Control. [3] Pd Controller Desgn From "Lnear Feedback Control" by Dngyu Xue, YangQuan Cen, and Derek P. Aterton. constant and output s obtaned as Fg 6: Smulaton result of sngle tank usng PID control Smulaton results sows tat controller can mantan a level at a gven value and be able to accept new set pont values dynamcally. And t sgnfcantly reduce te oversoot and steady state error. 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certfed Journal Page 2226