DESIGN OF OPTIMUM CONTROLLERS FOR HORIZONTAL TANK PROCESS

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1 Volume 118 No , ISSN: (prnted verson); ISSN: (on-lne verson) url: jpam.eu DESIGN OF OPTIMUM CONTROLLERS FOR HORIZONTAL TANK PROCESS 1 E.Gowthaman, V.Aruthra, 3 S.Vjaya Gowr, 4 V.Dnesh Kumar, 5 S.Mohanraj, 6 B.Anand 1 Assstant professor,,3,4,5 UG Students, 6 Professor and Head 1,,3,4,5,6 Department of Electroncs and Instrumentaton Engneerng, Hndusthan College of Engneerng and Technology 1 gowthamee@gmal.com, aruthravenukobal@gmal.com, b_anand_eee@yahoo.co.n Abstract: Horzontal tank level processng plays a crucal role n ol and chemcal levelng at the petroleum and chemcal ndustres. It s necessary to propose the most sutable controller for horzontal tank level control process. It s necessary to propose the most approprate controller for the level control process. The conventonal PID controller shows some nstablty. Thus to preval over ths Zegler-Ncholas based controller and Fuzzy-PID controllers are desgned and compared n LabVIEW platform. Rse tme, settlng tme and dead tme are taken nto consderaton. The result of ths comparatve study proves that Fuzzy PID controller offers better response by mprovng the statc and dynamc characterstcs of level control n the horzontal tank. Keywords: Horzontal Tank, Zegler-Ncholas method, Fuzzy-PID Controller. 1. Introducton Tank level measurement s most mportant parameter n ol or lqud chemcal ndustres. Especally, horzontal tank level. A horzontal tank wth a dameter of 300mm and 480mm long wth a capacty of 33.9 ltres s beng used [7]. Here a controller s used to set the level at the desred value. The nput gven to the tank s lqud and the output of the tank system s the rse or fall n the tank level. As there s a frequent varaton n the level of the horzontal tank t s necessary to montor t. The dead tme and the response tme are beng consdered and studed. Thus n order to mantan the tank level and study the dead tme along wth the response tme Zegler-Ncholas and Fuzzy-PID controllers are compared. E Gowthaman [1] has desgned a fuzzy tuned PID controller for controllng speed of PMDC motor wth 49 fuzzy rules. These rules are framed based on two fuzzy nput such as Error and Change n error and three outputs such as Proportonal gan (K p ), Integral gan (K ) & Dervatve gan (K d ).Dynamcally PID Controller parameters are updated through fuzzy nterference system n platform of LabVIEW. Fgure 1. Horzontal Tank Model E Gowthaman [] has llustrated the performance of hybrd Fuzzy-PID controller of boler drum, fuzzy control theory s desgned for controllng the boler drum level system. Both fuzzy logc and conventonal logc are used n controllng the drum level. Through MATLAB software verfcaton and smulaton are done and the result of drum level system s obtaned. By observng that statc and dynamc characterstcs of fuzzy controller s mproved and also best real-tme control of boler drum level s acheved. E Govnda Kumar [3] explaned the method to overcome the problem of overshoot on controller varables by ntroducng conventonal PID controller wth cascadng of lead-compensator. The developed controller s effectvely used to control the unstable system and also t enhances the control loop performance. E Gowthaman [4] llustrates the closed loop performance of Permanent Magnet Brush Less Drect Current (PMBLDC) usng conventonal PID and 1451

2 Hybrd Fuzzy controller. Both the controllers are observed and ther outcomes are studed and t s declared that Hybrd Fuzzy PID controller gves out better outcome. The entre performance s done usng LABVIEW. S Pooja [5] explaned the method to overcome ssues due to non-lnear behavor of concal tank level. Internal Model Controller (IMC) s desgned and response of the process s obtaned n smulaton and real tme. Varous fault dagnoss methods consdered and better output performance s obtaned n terms of overshoot set pont and settlng tme. Deep Mukherjee [6] descrbes to desgn PID controller for both nteger order and fractonal order wth a tme delay for a typcal nteractng cylndrcal tank system usng MATLAB FOMCON toolbox. Usng Nelder-Mead optmzaton technque wth dfferent performance metrcs ISE, ITSE and IAE. Satean Tunyasrrut [7] explans the controllng the level of horzontal tank usng Fuzzy-PID cascade controller. To develop the cascade controller nterface card module PCI-604E and LABVIEW. The results of the analyss shows that for the water level the tme consumed by cascade controller s less when compared to conventonal controller. Satean Tunyasrrut [8] descrbes a fuzzy logc controller to control the horzontal tank level. A mcrocontroller MCS-51 that uses C language s used for mplementng the controller. By consderng the rse tme and steady state errors ths controller s s found to be effectve. Jayabalan [9] desgned a SMC controller wth PID structure for controllng Frst Order Plus Dead Tme process. Here the error s connected to the proportonal, ntegral and dervatve components. The closed loop responses of SMC wth I-D and SMC wth PID structures are compared. W K Ho [10] Analyses the P-I formulas that optmze load dsturbance response havng gan and phase margns that are lesser than those that optmze for set pont. Fgure. Closed loop system for horzontal tank The block dagram (Fg.) represents the overvew of closed loop system for horzontal tank process. The Fuzzy-PID controller based on IF and THEN rules n accordance to the error and change n error helps to attan optmal response by automatc selecton of controller parameter.. Mathematcal Modelng of Horzontal Tank The contnuty equaton s essental for the equaton of conservaton of mass as follows [8]; dm o o = ρq ρq o dt (1) m = ρv = Mass of water, kg o o Q, Q o =Volume flow rate, nlet and outlet respectvely. ρ = Water densty = 1000 kg/m 3 dv o o = Q Q o () dt When dv = (Dh h )dh and Dh = Rh are substtuted n Eq.() and gven as; o o dh Q Q o = dt (Dh h ) o Where Qo = Cv h and C v = value constant are substtuted n Eq.(3) and gven as; o dh Q C h o = v = f(h,q ) (3) dt (Dh h ) (Dh h ) Taylor seres expanson and Laplace transform are used and we get H 1 K o = = (4) Q s ωs + 1 A(Dh h )( + 1) A 1 Where K = and ω = 1 A(Dh h ) A A = πr = π = 70650mm 6 = m = m 1 K = A(Dh h ) K = = = 81.96m 0.01 ω 1 1 = = = 14.15m A The Transfer Functon s [( ) ( ) ] 145

3 H = (5) Q 14.15s Controller Desgn and Implementaton The frequently used PID controller n an ndustry control systems s based on control loop plot. The dfference between a Process Varable (PV) and Set Pont (SP) s the error value observed n the controller. By adjustng the controller nputs the error can be mnmzed. The Proportonal (P), Integral (I) and Dervatve (D) value s used for the calculaton of PID controller. The output y(t) and the error nput e(t) of the PID controller s represented as, 1 (de(t)) y(t) = K p (e(t) + e(t)dt + T d ) (6) T dt Where, K p =Proportonal gan, T =Integral tme and T d =Dervatve tme. More number of methods are avalable for tunng these parameters (K p, T and T d ). Here, Zegler-Nchols method and modfed PID method are used for closed loop system to manually adjust the controller parameters. These conventonal methods are tme consumng and also t gves out a unstable process. Therefore we have opted for fuzzy based controller that precsely controls the level n horzontal tank wth and wthout nterrupt load. When compared to conventonal controllers Fuzzy controllers can be used to cover wde ranges of operatng condtons and are customzed n natural language terms. The connectvty between the nputs (error and change n error) and outputs (K p, K and K d ) of the fuzzy controllers are demonstrated n fgure 4. Fuzzy s based on self tunng prncple n whch the three parameters K p, K and K d are altered to attan certan control actons even f there nvolves some changes n error for dfferent levels n terms of set pont. Fgure 4. Basc Dagram Fuzzy PID The error and change n error values are beng compared and concluded from the prevous and present set ponts n order to attan a steady state, statc and an undsturbed performance. Fve fuzzy labels (NL, NS, ZE, PS and PL) are structured for fuzzy nput parameters such as error and change n error values whch are mentoned n Table I. Lkewse, for fuzzy output parameters sx fuzzy labels (PVS, PS,PMS,PM,PL,PVL) are consdered and s shown n Table II. As descrbed n the fgure 5(a),(b),(c),(d),(e) trangular membershp functon s used for both the nput and output varables. Table 1. Fuzzy label set for Inputs Fuzzy Label NS NL ZE PS PL Descrpton Negatve Small Negatve Large Zero Postve Small Postve Large Fgure 3. Block dagram of Fuzzy PID controller The PID controller parameters have been mprovsed n the fuzzy PID system and t s gven as, K p =K p + K p (7) K =K + K (8) K d =K d + K d (9) 1453

4 Table. Fuzzy label set for Outputs Fuzzy Label PVS PS PMS PM PML PL PVL Descrpton Postve Very Small Postve Small Postve Medum small Postve Medum Postve Medum Large Postve Large Postve Very Large (d) (a) (e) Fgure 5. MF s for fuzzy controller (a) Error e (b) Change n Error ec (c) Proportonal Gan Kp (d) Intregral Gan K (e) Dervatve Gan Kd (b) Overall twenty fve rules are desgned for fuzzy logc controller. Inputs and outputs are related as shown n (fg.6.) The workng flowchart proposed tank level control s shown n (fg.7.) Few of the rules are lsted below. Rule1. IF Error e s Negatve Large (NL) and Change n Error e c also Negatve Large (NL) THEN Change n proportonal gan K p s Postve Very Large (PVL) and Change n Integral gan K s Postve Medum (PM) and Change n Dervatve gan K d s Postve Very Small (PVS). R. IF e s NS and e c s NL THEN K p s PVL and K s PM and K d s PMS. R3. IF e s ZE and e c s NL THEN K p s PVL and K s PM and K d s PM. R4. IF e s PS and e c s NL THEN K p s PVL and K s PM and K d s PL. R5. IF e s PL and e c s NL THEN K p s PVL and K s PM and K d s PVL (c) 1454

5 A. Conventonal PID Controller Acton on Tank Control Fgure 6. Output varable (K d ) versus the nput varable Error e and Change n Error ec Fgure 8. Block dagram wndow of Conventonal PID controller smulaton The smulaton block dagram (Fg.8.) descrbes the PID controller based on the horzontal tank level control. It consst of the transfer functon of the tank, conventonal PID controller and ther parameter lke proportonal gan K p, ntegral tme τ and dervatve tme τ d. Fgure 7. Flow chart of Closed Loop Horzontal Tank Control. 4. Result and Dscusson The smulaton of PID Controller and fuzzy-pid controller acton on horzontal tank level control are descrbed n ths secton. Conventonal PID controller (exstng approach) parameters are tuned by usng Zegler-Ncholas tunng methodology. The proposed approach (fuzzy tunng) s acheved by tral and error method. (a) 1455

6 (b) Fgure 9. Smulaton result of PID controller Front Panel wndow (a) before settlng pont (b)after settlng pont In conventonal PID controller the set pont 48cm s attaned after seconds. It takes more tme to settle due to overshoot present n the smulaton results Fg.9 (a) & (b). B. Fuzzy-PID Controller Acton on Tank The smulaton block of fuzzy-pid controller based on horzontal tank process s descrbed n fgure10. The smulaton block s desgned usng horzontal tank model parameters. In fuzzy tuned controller membershp functons and rule vewer for nput and output varables are present. Fgure 11. Smulaton results of Fuzzy-PID Controller Performance In Fuzzy-PID controller smulaton results there s no overshoot. Overshoot n conventonal PID controller has been overcome by usng logc rules n fuzzy controller. Also settlng tme s decreased n Fuzzy-PID controller. Here set pont 48cm s settled at 0.69 seconds as shown n (Fg.11.) Table 3. Tentatve Results of PID Controller Based Tank Control Set pont 5 % of 50 % of 75 % of 100 % of Rse tme t r Settlng tme t s Dead Tme t d Table 4. Fuzzy-PID based Tank Control Fgure 10. Fuzzy- PID controller Block Dagram Wndow Set pont Rse tme t r 5 % of % of % of % of Settlng tme t s Dead tme t d

7 C. Performance comparson of PID and Fuzzy PID The desgned Fuzzy-PID controller performance s nvestgated on varous parameters (Rse tme, Settlng tme and Dead Tme) under varous set pont tank level ranges along wth conventonal PID controller performance. Tentatve results are consoldated n Table III & Table IV respectvely. Fgure 14. Dead tme performance of PID and Fuzzy PID Fgure 1. Rse tme performance of PID and Fuzzy PID The comparson of PID and Fuzzy PID controller performance on rsng tme s shown n (fg.1.)the performance of both dgtal controllers are nvestgated for the set pont ranges 1cm, 4cm, 36cm and 48cm of the tank level wth ther rse tme. From the graph, t s clear that, the response of fuzzy-pid controller to tank level settled at 48cm of tank level wth a tme nstance of 0.69 seconds whereas conventonal PID controller obtaned seconds more than that to rse due to mproper selecton of PID controller parameters. The (fg.14.) llustrates the Dead Tme comparson of both conventonal and Fuzzy PID controllers wth varous tank level ranges such as 1cm, 4cm, 36cm and 46cm. The dead tme of Fuzzy- PID controller vares for varous operatng level as 0.76s, 0.479s, 0.788s and 0.545s whereas n conventonal PID controller the dead tme s 0.667s and s constant. 5. Concluson The Conventonal PID and Fuzzy-PID controllers are appled for closed loop horzontal tank level control system. Based on the rse tme, settlng tme and dead tme the performance of the two controllers are verfed. Fuzzy PID s found to be the method that gves the desred response and the outcomes are gven at varous set ponts of the level. The result of the comparatve study between conventonal PID and Fuzzy PID shows that Fuzzy PID gves out better responses n terms of shorter rse tme, settlng tme and dead tme. References Fgure 13. Settlng tme performance of PID and Fuzzy PID. Smlarly, Settlng tme performance of PID and Fuzzy PID controller responses are studed for dfferent tank level ranges. From the above (fg.13.) t s well known that, the settlng tme of Fuzzy PID response s less than conventonal PID controller. [1] E Gowthaman and CD Balaj Self Tuned PID Based Speed Control of PMDC Drve. In: IEEE Internatonal Mult Conference on Automaton, Computng, Control, Communcaton &Compressed Sensng, Kerala, Inda, pp , March 013. [] E Gowthaman and Prasanna Moorthy Performance analyss of hybrd Fuzzy-PID controller acton on boler drum level Onlne Internatonal Conference on Green Engneerng and Technologes, pp.1-6,016. [3] E Govnda Kumar and E Gowthaman Cascade PID-Lead compensator controller for non-overshoot tme response of unstable system 1 st Internatonal conference on Power engneerng, computng and 1457

8 control, PECCON-017, pp ,-4 March 017, VIT Unversty, Chenna. [4] E Gowthaman, V Vnodhn, Mr Yasser Hussan, S K Dhnakaran and T Sabarnathan Speed Control of Permanent Magnet Brushless DC Motor Usng Hybrd Fuzzy Proportonal plus Integral plus Dervatve Controller 1 st Internatonal conference on Power engneerng, computng and control, PECCON- 017, pp ,-4 March 017, VIT Unversty, Chenna. [5] S Pooja and Dr. S.Vjayachtra Real tme performance analyss, fault detecton and control n concal tank system Internatonal conference of Research n Electroncs,vol 04, ISSN ,February 017. [6] Deep Mukherjee, Palash Kumar Kundu, Apurba Ghosh PID controller desgn for an nteractng tank level process wth tme delay usng MATLAB FOMCON toolbox IEEE Internatonal conference on Control, Instrumentaton, Energy and Communcaton, pp.1-5,016. [7] Satean Tunyasrrut and Sant Wangnpparnto control n horzontal tank by Fuzzy-PID cascade controller Internatonal conference of World Academy of Scence, Engneerng and Technology, pp.78-8, 5, 007. [8] Satean Tunyasrrut and Sant Wangnpparnto control n horzontal tank by Fuzzy logc controller Internatonal conference of SICE-ICASE,pp , October 18-1,006. [9] Jayabalan Arunshankar and Elumala Govnda Kumar Control of FOPDT Process usng Sldng Mode Controller wth modfed PI-D Sldng Surface WSEAS TRANSACTIONS on SYSTEM and CONTROL, vol 11,pp.7-31, 016. [10] W K Ho, C C Hang and J H Zhou Performance and gan and phase margns of well known PI tunng formulas IEEE Transactons on control systems technology, vol 3, No,pp.45-48, June [11] S.V.Mankanthan and K.srvdhya "An Androd based secure access control usng ARM and cloud computng", Publshed n: Electroncs and Communcaton Systems (ICECS), 015 nd Internatonal Conference on 6-7 Feb. 015, Publsher:IEEE,DOI: /ECS [1] T.Padmaprya and V.Samnadan, Utlty based Vertcal Handoff Decson Model for LTE-A networks, Internatonal Journal of Computer Scence and Informaton Securty, ISSN , vol.14, no.11, November

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