Control of a Nonlinear Spherical Tank Process Using GA Tuned PID Controller

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1 ISSN (Online) : ISSN (Print) : International Journal of Innovative Reearch in Science, Engineering and Technology Volume 3, Special Iue 3, March International Conference on Innovation in Engineering and Technology (ICIET 4) On t & nd March Organized by K.L.N. College of Engineering, Madurai, Tamil Nadu, India Control of a Nonlinear Spherical Tank Proce Uing GA Tuned PID Controller D.Pradeepkannan, Dr.S.Sathiyamoorthy Department of Electronic and Intrumentation, K. L. N. College of Engineering, Pottapalayam, India Department of Electronic and Intrumentation, J.J. College of Engineering and Technology, Tiruchirrappalli,India. ABSTRACT Conventional PID controller i a implet well known controller ued in almot all proce Indutrie for controlling the proce parameter at deired et value. The tuning of thee controller i done by a claical Zeigler Nichol (ZN) tuning. The dynamic of a pherical tank proce i nonlinear in nature and it exhibit non linear behavior and time delay between the input and output. The ZN tuned PID controller parameter doe not cope with all operating point a it exhibit different non linear characteritic at variou operating point. Thi paper aim at real time implementation of enhanced PID controller performance for a nonlinear pherical tank proce. The idea i to keep the ZN tuned PID value a the bae value o a to fine tune thee parameter uing a Genetic Algorithm approach to obtain the optimal et of tuning value which can cope up with all operating point. The mathematical model i developed by applying the governing ma balance equation and ubtituting the arbitrary contant. The ytem identification of the non linear proce i done by black box modeling and found to be (FOPDT) Firt order plu dead time model. The controller performance of the ZN tuned PID controller i fine tuned uing GA baed PID controller in term of time domain pecification a well a performance indice. Better enhanced controller performance wa obtained for a GA tuned PID controller than that of ZN tuned PID controller at all operating point. All the imulation are carried out in Mat lab environment and the real time implementation i done on a ingle pherical tank etup in LabVIEW Environment. KEYWORDS PID controller; ZN tuning; Genetic Algorithm; Non linear pherical tank proce. I. INTRODUCTION Proportional Integral Derivative Controller ha been uing in Indutrial control application for a long time. The reaon for their wide popularity lie in the implicity of deign and good performance which include low percent over hoot and mall ettling time for low proce Atrom.K.J and Hagglund.T,(995).According to the urvey in 989, 90 percentage of proce indutrie ue the conventional PID controller [3].The wide pread ue of the PID controller in the Indutry i due to their implicity and eae of retuning online [4].The PID controller i o named becaue it output um of three term, proportional, integral and derivative term. Each of thee term i dependent on the error value e between the input and the output. t u(t ) K c[e(t ) e(t )dt Copyright to IJIRSET i 0 d de(t ) dt () e(t) i the error ignal, u(t) i the controller output, Kc i the controller gain, τi and τd are integral gain and derivative gain. Proportional term peed up the repone a the cloed loop time contant decreae with the proportional term but doe not change the order of the ytem a the output i jut proportional to the input. The proportional term minimize but doe not eliminate the offet.integral term eliminate the offet a it increae the type and order of the ytem by one. Thi term alo increae the ytem repone peed but at the cot of utained ocillation. Derivative term primarily reduce the ocillatory repone of the ytem. It neither change the type and order of the ytem nor affect the offet. Determining optimum value of Proportional contant k p, i, d i termed a tuning. Any change in thee parameter caue change in the type, order and repone of the ytem. Thu they play a vital role in obtaining a

2 Analyi of Front End Swi Rectifier in Drive Sytem During Voltage Sag good controller performance characteritic. There have been a variou type of tuning technique applied for PID controller. One of the oldet i that Zeigler Nichol technique. Thee technique may be of Optimization technique or claical technique. Claical technique make certain aumption about the plant and the deired output and try to obtain analytically, or graphically ome feature of the proce that i then ued to decide the controller etting. Thee technique are computationally very fat and imple to implement, and are good a a firt iteration. But due to the aumption made, the controller etting uually do not cope up with non linear behavior of the proce and are unable to give deired repone at all operating point which then require further fine tuning. One of the mot ucceful and oldet claical technique i Zeigler Nichol method. It wa put forward by John Ziegler and Nathaniel Nichol in 94 and i till a imple, fairly effective PID tuning method. He propoed two method, one i open loop tep repone method and the econd i cloed loop frequency repone method. The Ziegler and Nichol firt PID tuning method i the technique made baed on certain controller aumption. Hence, there i alway a requirement of further tuning; becaue the controller etting derived are rather aggreive and thu reult in exceive overhoot and ocillatory repone. Alo the controller parameter are rather difficult to etimate in noiy environment. The econd method i baed on knowledge of the repone to pecific frequencie. The idea i that the controller etting can be baed on the mot critical frequency point for tability. Thi method i baed on experimentally determining the point of marginal tability. Thi frequency can be found by increaing the proportional gain of the controller, until the proce become marginally table. Thee two parameter define one point in the Nyquit plot. The gain i called ultimate gain Ku and the time period Tp. A the proce exhibit non linear behavior at variou operating point, thi paper aim at fine tuning of the controller etting can be done by computational technique uch a genetic algorithm. Thi paper i organized a follow. The ection decribe about literature review of Genetic Algorithm for PID tuning. Section 3 explain about the mathematical modeling of the non-linear pherical tank proce. Section 4 decribe the Experimental et up and it real time implementation of conventional PID controller and GA tuned PID controller. Section 5 decribe the Reult obtained for ervo operation at variou operating point of the tank for both ZN PID controller and GA tuned PID controller. Finally the concluion i given in ection 6. to be repreented in a way that i analogou to gene o that the procee that bring about a change in the gene can be ued. Uually thi i done by repreenting the olution in a binary format. GA i very popular in PID tuning and ha gained wide application in control ytem Kumar.S.M.G, Jain.R and Anantharaman.N.(008).Sadaivarao.M.Vand Chidambaram,(006) ue GA for improving performance of a PID controller ued in bioreactor and compared the performance with Ziegler Nichol, Skogetad modification Skogetad.S.(003) found that GA outperformed both in term of overhoot, diturbance rejection, gain margin and phae margin. GA ha been ued in poition and peed control of a DC motor NeenuThoma P. Poongodi(009). SharifianM.B.B.Rahnavard.RandDelavari.H(0). GA ha been ued for PID of revere omoi Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won- YongChoe and Hoon Heo,(008) and cacade control ytem tuning in Sadaivarao.M.V and Chidambaram,(006). Lot of work ha been done in uing GA along with other computational technique. In Kim et al. ue bacteria forage along with GA for PID controller tuning of AVR ytem. GA wa ued with Neural Network Dolezel, PetrMare,(009) and with fuzzy logic for developing elf tuning method. III. MATHEMATICAL MODELLING A pherical tank ytem, hown in figure i eentially a ytem with non linear dynamic. The pherical tank ytem ha a maximum height of 0.5meter and the maximum radiu of 0.5 meter. The level of the tank at any intant i meaured by the combination of orifice and Differential preure tranmitter whoe output i (4-0)mA. Thi output i compared with the deired et point value of level which will be configured a (4-0)mA. The error ignal i amplified baed on the controller pecification. The controller output i ued to vary the inflow rate q (t) of the pherical tank o a to maintain the et point at deired level of the tank. An Electro pneumatic converter i ued to convert the controller output of (4-0)mA in to a pneumatic ignal of (3-5) pi o that the final control element will be able to throttle the inflow rate. II. GENETIC ALGORITHM. Genetic algorithm (GA) i a earch algorithm that explore the earch pace in a manner analogou to evolution in nature Salami.M and Cain.G(995). It ue probabilitic rule to earch for and change the potential olution in the earch pace, uing a cot function to analyze the fitne of olution. GA require the olution Figure. Schematic diagram of Spherical Tank proce Copyright to IJIRSET 58

3 Analyi of Front End Swi Rectifier in Drive Sytem During Voltage Sag let, q (t) - inlet flow rate to the tank in m 3 /ec q (t) - outlet flow rate of the tank in m 3 /ec H - Height of the pherical tank in meter. R - Radiu of tank in meter (0.5 meter). x o - Thickne of pipe in meter(0.04 meter). Uing law of conervation of ma the non-linear plant equation i obtained for the pherical tank, dh () q ( t ) q ( t ) A( h ) dt Where, A r urface Radiu on the urface of the fluid varie according to the level (height) of fluid in the tank. Let thi radiu be known a r urface. r rh h, A ( rh h ) (3) urface 0 And q (t ) a g( h x ), where a ( x ) (4) 0 Subtituting (3) and (4) in equation () and linearizing the non linearity in pherical tank give rie to a tranfer function of a gh( ) Q ( ) ( rh h )SH( ) h xo (5) Rearranging, H( ) Q( ) a g ( rh h )S h x 0 (6) The experimental et up of the ingle pherical tank ytem i hown in figure. The pherical tank i made up of SS36 material which ha high corroion reitance property and ha a maximum height and radiu of 0.5 meter. Water from the reervoir tank of ize 50mm x 450mm x 450mm i pumped through a Kirlokar make 0.5 HP pump having a dicharge of 500 litre per hour that flow through a Teleline make rotameter having a range (40-440)LPH to the pherical tank. The level of the tank at any intant i meaured by the Roe mount Differential preure tranmitter having a meaurement range of (0-400)mm of water column correpond to the output range of (4-0)mA. Thi output i compared with the deired et value of level which will be caled in the control law a (4-0)mA. The error ignal i alo in the range of (4-0)mA which i then amplified baed on the controller pecification. Thi output i ued to vary the inflow rate q (t) of the pherical tank with the ue of an ABB make Electro pneumatic converter which convert the output of (4-0)mA in to a pneumatic ignal of (3-5) pi o that the Equal percentage control valve will be able to throttle the inflow rate. The controller parameter are determined for both ZN tuned PID Controller a well a GA tuned PID controller. The value of k p, k i, k d for ZN tuned PID are found to be 0.33, 0.036, repectively. An USB 6009 NI Data acquiition card i ue to communicate the data from the tranmitter to the PID controller block of LabVIEW program both for ZN and GA tuned control algorithm to perform it operation for a given tep change in inflow rate q i, and the correponding teady tate repone i obtained a follow. Applying the teady tate condition value, the linearized plant tranfer function i given by, Y( S ) (7) U( S ) S IV. EXPERIMENTAL SET UP OF SINGLE SPHERICAL TANK PROCESS Time in /T econd. Fig. 3. Repone of ZN tuned PID controller for a et point of 0cm of water column. It i evident from the repone that the ZN tuned PID controller output could track the et point at an operating point of 0cm of water column with a ettling time of 3.5econd and with minimal overhoot where the ampling rate T i 3ample per econd. Fig.. Experimental et up for ingle pherical tank ytem. Copyright to IJIRSET 58

4 Analyi of Front End Swi Rectifier in Drive Sytem During Voltage Sag Time in /T econd. Fig. 4. Repone of ZN tuned PID controller for a et point of cm of water column. It i evident from the repone that the ZN tuned PID controller output could track the et point at a different operating point of cm of water column with a ettling time of 8.econd and with minimal overhoot where the ampling rate T i 3ample per econd. Fig. 5. General Flow chart of Genetic Algorithm B. Tuning of GA-Baed PID Controller A. GA baed PID controller Genetic Algorithm can naturally be applied to the optimal-tuning of PID controller a a mathematical Genetic algorithm (GA) are an evolutionary optimization mean for optimization. The role of the PID controller in approach, which are an alternative to traditional a ytem i to drive the output repone to track the et optimization method. GA i one of the mot appropriate point within minimum ettling time. Obviouly, the method for complex non-linear model where location of parameter etting of the PID controller hould be fine the global optimum i a difficult tak. GA follow the tuned o a to meet the requirement. Optimization of concept of olution evolution by tochatically PID controller firtly need deign the optimization goal, developing generation of olution population uing a and then encode the parameter to be earched. Genetic given fitne. Genetic algorithm are a probabilitic operator i running until the top condition i atified. earch approach, which are founded on the idea of The decoded value of the lat chromoome are the evolutionary procee. The GA procedure i baed on the optimized PID controller parameter. Darwinian principle of urvival of the fittet. An initial population i created containing a predefined number of individual, each repreented by a genetic tring. Each individual ha an aociated fitne meaure. The concept that the fittet bet individual in a population will produce a fitter offpring i then implemented in order to reproduce the next population. Selected individual are choen for reproduction at each generation, with an appropriate mutation factor to randomly modify the gene of an individual, in order to develop the new population. The reult i another et of individual baed on the original ubject leading to ubequent population with better fitne and thoe with lower fitne will naturally get dicarded from the population. (Goldberg 989; Fig. 6. Schematic diagram of GA baed PID tuning a proce Lewin 994, 996).For mot application of genetic algorithm to optimization problem, the real coding Initially a chromoome i randomly generated. The technique i ued to repreent a olution to a given chromoome are candidate olution to the problem. The problem. In real coding implementation, each chromoome i encoded a a vector of real number, of fitne value of all chromoome are evaluated by the ame length a the olution vector. According to calculating the objective function (ISE) in decoded form. Hence, baed on the fitne of each individual, a group of control objective, three parameter K p, K i and K d of a the bet chromoome i elected through the election PID controller are required to be deigned in thi proce. The Genetic operator, croover and mutation, reearch. For a given problem with three deciion variable, thi paper adopt a real-valued vector [x, x, are applied to thi urviving population in order to x3] a a chromoome to repreent a olution to the improve the next generation olution. The proce problem. Copyright to IJIRSET 583

5 Analyi of Front End Swi Rectifier in Drive Sytem During Voltage Sag continue until the population converge to the global maximum or another topping criterion i reached. The GA optimization tool in matlab i ued to fine tune the PID parameter o a to obtain the deired performance characteritic. The following figure 7 how the Optimization wizard for GA tuned PID controller. The fitne function yntax i developed a a function and aved with a file name Sphh. Then the other parameter uch a lower bound, upper bound, number of variable, Initial population, Initial range, number of iteration, Mutation factor, Cro over factor and election function are given to the wizard. On running the program, it determine an optimal et of tuned parameter for PID controller a k p =6.997, I= 6.44ec and d =.998ec. Time in /T econd. Fig. 9. Repone of GA tuned PID controller for a et point of 4cm of water column. Fig. 7. Optimization wizard for GA tuned PID controller Time in /Tecond. Fig. 0. Repone of GA tuned PID controller for a et point of 3cm of water column. It i evident from the repone that the GA tuned PID controller output could track the et point at a different operating point of 4cm of water column with a ettling time of 4.53econd and with mooth repone and no overhoot where the ampling rate T i 3ample per econd. V. RESULTS AND DISCUSSION Time in /T econd. Fig. 8. Repone of GA tuned PID controller for a et point of 4cm of water column. It i evident from the repone that the GA tuned PID controller output could track the et point at a different operating point of 4cm of water column with a ettling time of 7.3econd and with mooth repone and no overhoot where the ampling rate T i 3ample per econd. A mall diturbance i being provided between the time intance 5000,6000,and 7000 o a to enure robutne, the controller enure diturbance rejection and it keep track the et point value a deired. An unit tep repone of ZN tuned PID controller and GA tuned PID controller i obtained for ervo operation and their performance characteritic are compared in term of time domain pecification uch a rie time,peak time, peak over hoot, teady tate value etc., and performance indice uch a ISE and IAE. Table and table how characteritic of time domain pecification and performance indice uch a ISE and IAE of ZN tuned PID controller againt GA tuned PID Controller. Copyright to IJIRSET 584

6 Type of contr ZN PID GA PID Type of controller Set point in cm Settlin g time in econd VI. Table Max Peak over hoot % Table CONCLUSION GAPID controller can cope up with tank non-linear characteritic at variou operating point uch a 4, 4centimeter of water column in the pherical tank. Conventional controller baed on Ziegler Nichol tuning repone i outperformed by GAPID controller with le overhoot and leer ettling time, peak time etc.,. GA tuned PID controller i the baic evolutionary computational method which provide a better atifactory reult a tabulated. The author limited hi work with GA baed tuning alone, further the controller can be tuned by other oft computing technique and implemented in real time o a to compare their performance. GAPID controller can alo be applied for other non linear procee uch a Continuou tirred tank reactor, Yeat fermentation proce, Bio reactor etc to obtain better controller performance characteritic. REFERENCES [] Atrom.K.J and Hagglund.T,(995). PID controller, Theory, deign and tuning nd edition, Intrument Society of America, 995. [] Atrom.K.J and Hagglund.T,(99).Indutrial Adaptive Controller Baed on Frequency Repone Technique, Automatica,. 7(4) [3] AnnaJoeph,J.SamonIaac(03).Real time Implementation of Model Reference Adaptive Controller for a conical Tank.,International Journal on theoretical and applied reearch in Mechanical Engineering,(). [4] Abdel Badie Sharkawy,(006) Genetic fuzzy elf-tuning PID controller for Antilock Braking Sytem, Alexandria Engineering Journal, vol. 45( 6) Analyi of Front End Swi Rectifier in Drive Sytem During Voltage Sag Peak time in eco nd Steady State Value Set point in cm Integral Square Error Integral Abolute Error ZN PID GA PID [5] Dolezel, PetrMare,(009)Self tuning PID Control uing Genetic Algorithm and Artificial Neural Network, ASR Intrument and Control, pp , 009. [6] Dong Hwa Kim, Jae Hoon Cho.(006)A Biologically Inpired Intelligent PID Controller Tuning for AVR Sytem.International Journal of Control, Automation, and Sytem. 4(5) [7] Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won-YongChoe and Hoon Heo,(008)Auto Tuning PID Controller baed on Improved Genetic Algorithm for Revere Omoi Plant, International Journal of Computer Sytem Science and Engineering,. 3(4),3 37. [8] Kumar.S.M.G. Jain.R and Anantharaman.N.(008) Genetic Algorithm Baed PID Controller Tuning for a Model Bioreactor. Indian Chemical Engineering Journal. 50,(3) [9] NeenuThoma P. Poongodi(009) Poition Control of DC Motor Uing Genetic Algorithm Baed PID Controller, Proceeding of the World Congre on Engineering, London,U.K.,vol., [0] Sadaivarao.M.V and Chidambaram,(006)PID Controller tuning of cacade control ytem uing genetic algorithm, Journal of Indian Intrumentation Science. vol. 86, [] Salami.M and Cain.G(995) An Adaptive PID Controller Baed on Genetic Algorithm Proceor. IEEE Genetic Algorithm in Engineering Sytem, Innovation and Application Conference. -4. [] SharifianM.B.B.Rahnavard.RandDelavari.H(0) Velocity Control of DC Motor Baed Intelligent method, Journal of Control Engineering and Technology, (4) [3] Skogetad.S.(003) Simple Analytic Rule for Model Reduction and PID Controller tuning. Journal of Proce Control,(3) [4] PradeepKannan.D, Sathiyamoorthy,(0) Deign and Modelling of State Feedback with Intergal Controller for a Non-Linear pherical tank Proce., International Journal of Emerging Technology and Advanced Engineering, (), [5] Ziegler.J.G and Nichol..N.B,(94).Optimum Setting for Automatic Controller. Tranaction of ASME BIOGRAPHIES D.Pradeep kannan received hi Bachelor Degree in Intrumentation and Control Engineering from Madurai Kamaraj Univerity,India. in 999and Mater degree in Indutrial Engineering in 00 from Madurai kamaraj Univerity..Currently he i an Aociate profeor in the department of Electronic and Intrumentation Engineering in K.L.N. College of Engineering, Madurai, India. He i puruing hi Reearch program at Anna Univerity Chennai India.He ha publihed about 4 paper in reputed Journal andconference. Hi reearch interet include Proce control,fraction order PID controller,tuning of controller for nonlinear procee uing oft computing technique etc. He i a life member of ISTE and ISOI ocietial bodie.hi mail id i pradip_eie@yahoo.co.in. Dr.S.Sathiyamoorthy, Principal of J.J. College of Engineering and Technology ha ixteen year of experience in teaching, reearch and indutry. He ha completed B.E. Degree in Electrical and Electronic Engineering, Regional Engineering College, Tiruchirapalli in 995, and M.E. degree in Control and Copyright to IJIRSET 585

7 Intrumentation at Guindy Engineering College, Anna Univerity, Chennai in 00. He ha received hi Doctorate from National Intitute of Technology, Tiruchirapalli in 008. He ha attended many National and International conference and workhop. He ha publihed five paper in leading international journal. He ha given numerou expert lecture in variou forum and College in area of Neural Network and Fuzzy logic control. Hi area of pecialization are Proce Control and Indutry Automation, Multiphae flow identification uing Electrical Capacitance Tomography. Analyi of Front End Swi Rectifier in Drive Sytem During Voltage Sag Copyright to IJIRSET 586