Water Level Controlling System Using Pid Controller

Transcription

1 Inernaonal Journal o Appled Engneerng esearch ISSN Volume, Number 23 (26) pp Waer Level Conrollng Sysem Usng Pd Conroller Beza Negash Geu Deparmen o Elecrcal, Elecroncs and Communcaons Engneerng (EECE) Amercan Unversy o as Al Khamah, as Al Khamah, UAE. ABSTACT In ceran applcaons such as chemcal and ndusral processes, s mporan o keep he level o waer or any oher lqud n a ank or smlar conaner a a ceran desred level. In hs work, we presen PID based sysem where he level o waer s conrolled by adjusng he rae o he ncomng waer low o he conaner by varyng he speed o a DC moor waer pump ha s llng he conaner. The accuracy o he PID based conrollng s demonsraed usng he MATLAB smulaon soware. Keywords- waer level, low rae, ank, DC moor speed, eedback conrol, proporonal negral dervave (PID). INTODUCTION Waer s an essenal naural resource, whch s val no only o susan le or drnkng purposes bu also used n many ndusral, chemcal, commercal and agrculural processes. The mproper use and managemen o waer aecs he susanably o our envronmen. Among ohers n agrculural areas, waer pumps need o be conrolled n order o supply regulaed waer or he planaons or arm lands. Conrolled waer can be gven by desgnng auomac elecronc conrol sysems as suded n [], [2]. On he oher hand, n chemcal or ndusral processes such as reamen o waer n desalnaon plans, he level o waer n a conaner lke a ank need o be kep a ceran se desred pon. The level o he waer need o be mananed a he desred se pon or he proper unconng o he process and acheve he desred arge or produc. In hs case, a conrollng sysem such as proporonal-negral and dervave (PID) plays a sgncan role n mananng he accurae level by mplemenng he sysem n a eedback conrol sysem. PID s are used n mos praccal conrol sysems rangng rom consumer elecroncs such as cameras o ndusral processes such a chemcal processes [3]-[5]. The PID helps o ge our desred oupu, whch could be velocy n movng objecs, emperaure n parcular envronmen, poson a ceran locaon, lqud level n a conaner and eceera where we wan o acheve a ceran se pon n a shor possble me wh mnmal overshoo and wh lle seady sae error. The perormance o he PID are also deermned by overshoos, rsng me, selng me and seady sae error parameers. In hs work, we assumed a DC moor waer pump llng a ceran waer conaner or ank and he speed o he moor deermnes he rae o waer low o he ank. The DC moors are used exensvely n ndusres due o her varable speed ha sus hem o be used or deren applcaons, her mos demandng speed-orque characerscs and her relably and smplcy n conrollng aspecs [6]. The DC moor s a hghly conrollable elecrcal acuaor and s wdely used or roboc manpulaors, guded vehcles, seel rollng mlls, cung ool, overhead cranes, elecrcal racon and oher applcaons. In comparson o AC drve, DC moor drves are smple and less expensve [6], [7]. In ceran applcaons, he waer, whch could also be any oher lqud n an ndusral or chemcal process need o be careully suppled and kep a a ceran level n he sorage sysem. The nenon o conrollng he level n he sorage s o acheve a perec process conrol and as a resul ncrease ecency and producvy. A PID conrol heory and eedback sysem modellng s appled o desgn he overall sysem. As a resul o mananng he requred waer se level, he sysem no only ncreases process producvy bu also assss owards savng and conservng waer by monorng he level and elmnang overlow n he sorage sysem. SYSTEM MODEL The proposed sysem comprses a DC moor waer pump ha pumps waer o he conaner, he PID and a waer ank or any oher sorage sysem. Consder he dagram n Fg. where he moor pumps waer o he conaner a a rae o q n [m 3 /s] hrough an nle ppe, he conaner wh crossseconal area A[n m 2 ], s lled o waer level, h and waer s leavng he conaner a a rae o q o [m 3 /s] hrough an oule ppe. Usng he balance o he lows no and ou o he ank, he hegh, h s relaed o q n and q o as [8]: q n dh q A () The ou low rom he ank and he hegh can also be relaed assumng lnear ressance o low or smplcy o analyss and s gven as: q h Where [n s/m 2 ] s he low ressance. pump h (2) q n waer A Fgure. Sngle Tank conaner lled o level h. q o 223

2 Inernaonal Journal o Appled Engneerng esearch ISSN Volume, Number 23 (26) pp The overall sysem s a eedback conrol sysem as shown n he block dagram gven n Fg. 2. Frsly, a reerence npu hegh level, h (, s se ha shows he desred level he ank has o be lled. In he orward pah, we have he PID ha conrols he speed o he DC moor. The speed o he moor s drecly relaed o he waer low rae q n supplyng he ank. A he oupu o he overall sysem, we have he waer level, and hs normaon s eedback a he npu and compared wh he reerence desred level. The error sgnal beween he acual oupu and he reerence, e( wll be an npu sgnal o he PID and he speed o he moor [( n rad/s] wll be adjused (eher ncreased or decreased) o conrol he low rae q n unl he requred arge waer level s acheved. The speed normaon o he moor s assumed o be obaned rom speed measuremen devce such as achomeer. The speed wll be ransormed by he speed o hegh ransormaon (STH) block ha relaes he speed o he low rae and hen o he waer level. For smplcy purposes o he sudy, we assume a smple lnear relaonshp beween he speed and he ncomng low rae o he ank gven as: ( K q ( (3) h ( ) e ( PID v ( Moor ( STH Conroller pump Fgure 2. Block dagram o he waer level conrollng sysem MODELING THE MOTO PUMP AND THE PID CONTOLLE The waer pump s a DC moor wh he elecrc equvalen crcu o he armaure and he ree-body dagram o he roor as shown n Fg. 3 [9]. The npu o he moor s a volage source (V) appled o he moor's armaure, he oupu s he roaonal speed o he sha ( =d/. The roor and sha are assumed o be rgd. We urher assume a vscous rcon model, ha s, he rcon orque s proporonal o sha angular velocy. The physcal parameers o he moor are J: momen o nera o he roor [kg.m 2 ], b: moor vscous rcon consan [n N.m.s], K e: elecromove orce consan [n V/rad/sec], K : moor orque consan [n N.m/Amp], : elecrc ressance [n ]. L: elecrc nducance [n H]. Assumng armaure conrolled moor, he orque s proporonal o he armaure curren (T=K and he back em s proporonal o he angular velocy o he sha, e=k e. Usng he above acs and based on Newon s second law and Krchho s volage law, he DC moor equaons relang he moor speed o he physcal parameers o he moor can be wren as: Where d / n J b T K (4) d L e V K e (5) s he angular speed o he moor. V Fgure 3. Equvalen crcu o he DC moor Usng he properes o Laplace ransorm, he above equaons can be expressed n he Laplace or s doman as []: 2 s J ( sb ( K I( (6) sli( I ( V( ske ( (7) The angular speed n he Laplace doman s relaed o he angular poson as (= s( and hence can be subsued n he above equaons. By elmnang he curren I( n (6) and (7) and aer some seps, he moor roaonal speed oupu, (, s relaed o he armaure volage npu, V(, as: ( m( (8) 2 V ( s JL s( J bl) b KKe P The relaon n (8) represens he npu oupu relaons o he moor-pump block shown n Fg. 2. The PID s he oher par o he sysem as shown n Fg.2. The job o he PID s o adjus he oupu, n hs case he waer level a he desred se pon so ha n he deal case here s no error beween he sensed oupu,, and he desred reerence level. In general desgn o he PID, he error e( s relaed o he oupu v( as []: K v( K e( K e( K p d de( (9) Where K p, K and K d are called he proporonal gan, he negral gan and he dervave gan respecvely. The proporonal gan provdes an overall conrol acon proporonal o he error sgnal, he negral gan acon s o reduce seady-sae errors hrough low-requency compensaon by an negraor and he dervave gan mproves ransen response hrough hgh-requency compensaon by a derenaor. By unng he hree parameers o he model, a PID can deal wh specc process requremens. Usng he Laplace doman, he npu-oupu relaon or he s gven as: C armaure crcu V ( e( L e K e K s ( K p skd () + - T b J roor 224

3 Inernaonal Journal o Appled Engneerng esearch ISSN Volume, Number 23 (26) pp OVEALL SYSTEM TANSFE FUNCTION As shown n Fg. 2, he overall sysem response s he combned response o he orward pah and he eedback loop. Here he gan or he eedback loop s assumed uny and n he orward pah we have he PID, he moor pump and he speed o hegh (STH) ransormaon block. The model or he moor pump and he PID s as dscussed n secon III. Le he mpulse response o he STH sysem s, g( ha represens he relaon beween and (. We can nd an expresson or G( he Laplace ransorm o g( by combnng (), (2) and (3). Combnng (), (2) and (3), ( s relaed o as: dh ( K h K A () response o he DC moor combned wh he STH block. The perormance whou s very poor n erms o selng me wh very hgh seady sae error and a nal value 5 % o he requred reerence arge. I shows he requremen o a o oban he desred waer or lqud level. The proporonal reduces he rse me, mproves he seady sae error o some exen bu a rngng and an over shoo sars o appear. A proporonal wh K p= looks beer n erms o reducng he seady sae error compared wh K p=5. For K p=, he selng me s abou 2.95 s, an overshoo o 47%, and seady sae value o.83. The hgh overshoo, selng me and seady sae error necessae he requremen o negral and dervave par o be added n he as no all o he desgn requremens can be me wh a smple proporonal. The relaon n (), n he Laplace doman s gven as: ( K K As (2).4.2 sep response Whou PID Kp= Kp=5 Thereore he ranser uncon G( becomes G( ( K sk A (3) amplude The overall ranser uncon o he orward pah, F(, can be obaned by combnng (8), () and (3) F( C( Pm ( G( (4) e( The overall ranser uncon, G sys(, o he overall sysem ncludng he uny eedback loop s gven as: F( G sys ( (5) h ( F( ) s ESULTS AND DISCUSSIONS MATLAB smulaons were done o sudy he perormance o he sysem and s capably o manan and conrol a desred waer level n he ank. Snce he PID s negraed n MATLAB, s easy o smulae he sysem and observe he resuls or deren values o K p, K and K d parameers o he. An opmum or accepable resul can be obaned by unng he parameers unl he desgn requremens are me. For hs sudy, we assumed he ollowng parameer values or he moor, he ank, and he STH sysem. Moor: -J =. Kg.m 2, b =. N.m.s, K =. N.m/A, K e=. V/rad/s, =, L =.5 H. Tank:- A=.5 m 2, =.5 s/m 2 STH:-K = Furhermore, or a un sep npu reerence waer level or he overall sysem, our desgn crera are o acheve an oupu wh a selng me less han 2 seconds an overshoo less han 5% and a seady-sae error less han %. Fg. 4. shows he sysem response wh and whou proporonal. As seen n he Fgure, he resuls whou he PID (red color) s smply he sep me n seconds Fgure 4. Sep response wh and whou proporonal Fg. 5. shows he sysem response wh he proporonalnegral (PI) wh K p=k =. The addon o he negral par o he proporonal par elmnaes he seady sae error geng a nal value near he requred level compared wh he Fg. 4. However, here s sll a hgh overshoo and he selng me s also geng large Sysem: sys_clp Peak amplude:.49 Overshoo (%): 49.2 A me (second:.64 Sep esponse Tme (second Sysem: sys_clp Selng me (second: 4.64 Kp=, K= Sysem: sys_clp Fnal value: Fgure 5. Sep response wh proporonal-negral (PI) The oher varey o s he proporonal-dervave (PD). Fg. 6 shows he sysem sep response wh he PD wh K p= and K d=5. I reduces he over shoo, mproves he rse me and selng me bu wh a 225

4 Inernaonal Journal o Appled Engneerng esearch ISSN Volume, Number 23 (26) pp sgncan amoun o seady sae error. The nal value s sll no close o he desred level..4.2 Peak amplude:.3 Overshoo (%): 3.24 A me (second:.48 Sep esponse Kp=9, K=5, Kd=2 Fnal value:.4 Sep esponse Selng me (second:.39.2 Sysem: sys_clpd Peak amplude: Overshoo (%): 2.5 A me (second:.23 Kp=, Kd=5.8.6 Sysem: sys_clpd Fnal value: Sysem: sys_clpd Selng me (second: Tme (second Tme (second Fgure 8. Sep response wh proporonal-negral dervave (PID) (K p=9, K =5, K d=2). Fgure 6. Sep response wh proporonal-dervave (PD) Fg. 7 shows he proporonal-negral and dervave (PID) wh K p=2, K =5 and K d=3. In hs case he nal desgn speccaons are me wh overshoo less han 5%, selng me less han 2 seconds and seady sae value o one, whch s he requred waer level speccaons. In hs case, he rse me s also reduced. Thereore, wh he PID, he desred desgn arge s acheved. Furhermore, as shown n Fg. 8, he overshoo can be reduced a he expense o a slgh ncrease n he selng me or he PID wh K p=9, K =5 and K d=2. amplude sep response whou P, Kp= PI, Kp=, K= PD, Kp=, Kd=5 PID, Kp=9, K=5, Kd= me n seconds Peak amplude:.4 Overshoo (%): 4.45 A me (second:.33 Selng me (second:.8 Sep esponse Tme (second Fnal value: Fgure 7. Sep response wh proporonal-negral dervave (PID) (K p=2, K =5, K d=3). Fg. 9 shows all he s ploed n one graph n order o have beer vsualzaon o her perormances and clearly showng he super-perormance o he PID compared wh he ohers. Wh such PID conrolled sysem, he waer level can be conrolled connuously whou he need o manual operaon, whch saves me and manpower rom auomaon. The PID auomacally responds o he sysem so ha he sysem s sablzed near he desred se pon. Fgure 9. Sep response showng he unconrolled sysem, he proporonal, he PI, PD and he PID s n one plo, Table I shows a comparson o he deren s n erms o rse me, selng me, overshoo and seady sae values. From he able, we observe ha a proporonal ends o reduce he rse me and selng me bu never elmnae he seady sae error. There s also a large overshoo. A proporonal-negral (PI) has he eec o elmnang he seady sae error wh he nal value achevng he desred reerence npu bu makes he ransen response worse wh larger overshoo and also large selng me. A proporonal-dervave (PD) has he eec o ncreasng he sably o he sysem by reducng he overshoo, he rse me, he selng me and overall mproves he ransen response. However, here s sll large seady sae error. The proporonal-negral dervave (PID) perorms well n all he parameers and sases he desgn requremens. Thereore, s possble o ulll he desgn requremens and oban opmum perormance wh good accuracy by careully unng and selecng he proper values or K p, K and K d. 226

5 Inernaonal Journal o Appled Engneerng esearch ISSN Volume, Number 23 (26) pp TABLE I. COMPAISON OF THE DIFFEENT CONTOLLES Type o Proporonal (P), K p= PI, K p=, K = PD, K p=, K d=5 PID, K p=2, K =5, K d=3 PID, K p=9, K =5, K d=2 se me ( Perormance parameers Seln g me ( Oversho o (%) Seady sae value CONCLUSIONS Ths paper presens a PID conrolled waer pump sysem n order o manan a desred waer level n a sorage ank ha s used n prvae, chemcal, ndusral or oher relaed applcaons. The speed o he moor and hence he rae o waer low no he ank s conrolled by adjusng he parameers o he PID. A sep reerence waer level s se and he sep response o he overall sysem s nvesgaed n MATLAB envronmen n order o mnmze he overshoo, mprove he selng me (mproved ransen response) and he seady sae error o he sysem. Varous orms o he, P, PI, PD, and PID are suded and he PID acheves super perormance. I s shown ha suable values or K p, K, K d parameers can be ound or he PID by unng o manan he desred waer level or he arge desgn speccaons. The sysem s essenal n hose places where mananng waer or any oher lqud level s crcal or achevng he requred producvy. Such s are powerul n conrollng any smlar processes ha essenally requre close monorng (gh conrol) o he process varables or parameers ha have sgncan mpac on qualy and amoun o producon. EFEENCES [] Beza Negash Geu, Hussan A. Aa, Auomac Conrol o Agrculural Pumps Based on Sol Mosure Sensng, Proceedngs o he IEEE AFICON 25 Conerence, 4-7 Sepember 25, pp [2] Beza N. Geu, Nasser A. Hamad, Hussan A. Aa, emoe Conrollng o an Agrculural Pump Sysem Based on he Dual Tone Mul-Frequency (DTMF) Technque, Journal o Engneerng Scence and Technology (JESTECH), Vol., No. (25), pp [3] Bequee, B. W., Process Conrol: Modellngv Desgn and Smulaon, Prence Hall, 23. [4] Carl Knopse, Gues Edor, PID Conrol, IEEE Conrol Sysem Magazne, February 26. [5] S. Benne, Developmen o he PID, IEEE Conrol Sysem. Magazne, Vol. 3, 993, pp [6] Khan M.., Khan A. A. Umer G. Speed Conrol o DC Moor under Varyng Load Usng PID Conroller, Inernaonal Journal o Engneerng (IJE), Vol. 9, Issue 3, 25, pp [7] Sen P.C.,Prncples o Elecrcal Machnes & Power Elecroncs, John Wley & Sons,996. Elke Laubwald, Coupled Tank Sysems. Avalable a hp:// [8] Arhur G.O. Muambara, Desgn and Analyss o Conrol Sysems, CC Press, 999. [9] Oppenhem A. V., Wllsky A. S., Hamd S., Sgnals and Sysems, 2 nd Ed., Prence-Hall., 997. [] Ang, K.H. and Chong, G.C.Y. and L, Y., PID conrol sysem analyss, desgn, and echnology, IEEE Transacons on Conrol Sysems Technology, 3(4), 25, pp ACKNOWELEDGMENT The auhor apprecaes he suppor and he ncenve provded by he Amercan Unversy o as Al Khamah (AUAK) hrough he naon and connuous encouragemen o he School o Graduae Sudes and esearch o be acve and say nvolved n research. 227