Real Time Implementation of Enhanced Nonlinear PID Controller for a Conical Tank Process

Transcription

1 Internatonal Journal of Computer Applcatons ( ) Real Tme Implementaton of Enhanced Nonlnear PID Controller for a Concal Tank Process U. Sabura Banu BS Abdur Rahman Unv. P.R. Hemavathy BS Abdur Rahman Unv Lakshmana Prabhu BS Abdur Rahman Unv. Barath Kanna EIE Department BS Abdur Rahman Unv. ABSTRACT Level s one of the most mportant parameter that has to be montored and controlled n any process ndustry. Concal tanks are wdely used n many ndustres due to ts shape whch provdes easy dscharge of water when compared to other tanks. Moreover, lqud level control of a concal tank s stll challengng for typcal process control because of nonlneartes. Snce PID control s the workhorse of almost 9% of the ndustres, an Enhanced Nonlnear PID (EN-PID) controller s proposed whch exhbts the mproved performance than the conventonal lnear fxed-gan PID controller, by ncorporatng a sector-bounded nonlnear gan n cascade wth a conventonal PID control archtecture. To acheve the hgh robustness aganst nose, two nonlnear trackng dfferentators are proposed to select hgh-qualty dfferental sgnal n the presence of measurement nose. The man advantages of the proposed EN-PID controller le n ts hgh robustness aganst nose and ease of mplementaton. And n the proposed technque a EN-PID s desgned and tuned usng the Bee colony optmzaton (BCO) technque. The BCO algorthm s based on the model that s obtaned from the communcatve behavor of the honey bees. Smulaton results performed on a concal tank level process are presented to demonstrate the performance of the developed EN-PID controller. Keywords Bee Colony Optmzaton, Concal Tank Level Process, Nonlnear PID 1. INTRODUCTION Nonlnear PID control s the emergng control mechansm n process ndustres [1,2]. The man feature of nonlnear PID controller s that t can be easly desgned usng wener model as cted by P.K.Bhaba. Although lnear fxed-gan PID controllers are often adequate for controllng a nomnal physcal process, the requrements for hgh-performance control wth changes n operatng condtons or envronmental parameters are often beyond the capabltes of smple PID controllers [3]. In order to enhance the performance of lnear PID controllers, many approaches have been developed to mprove the adaptablty and robustness by adoptng the selftunng method, general predctve control, fuzzy logc and neural networks strategy, and other methods. Amongst these approaches, nonlnear PID (N-PID) control s vewed as one of the most effectve and smple method [6]. The bee colony optmzaton algorthm s nspred by the behavour of a honey bee colony n nectar collecton. Ths bologcally nspred approach s currently beng employed to solve contnuous optmzaton problems [4, ]. The paper deals wth the descrpton of the concal tank level process and also t nvolves the functon of varous components requred for the concal tank level process. Open loop data s generated and the nput-output characterstcs s analysed. An attempt has been made to desgn an Enhanced nonlnear PID controller for the concal tank by BCO based optmzaton technque. 2. CONICAL TANK PROCESS DESCRIPTION The Expermental setup and the schematc dagram of the concal tank system s shown n the fgure 1 & 2 respectvely. The process conssts of a process tank, submersble pump, two dfferental pressure transmtter, overhead sump, nlet valve and outlet valve and nterfacng card. Fg 1 Expermental set up The proposed system conssts of two concal tanks, whch measures cm n heght and n the top end dameter s 4cm, the taperng end s 14cm. It conssts of dfferental pressure transmtter for measurng the pressure and gves n terms of mllamps. The two tanks are connected through an nteractng ppe wth valves. It has a reservor to store water and ths s suppled through the pumps to the tanks. The process tank s n the shape of an nverted cone fabrcated from a sheet metal. Provsons for water nflow and outflow are provded at the top and bottom of the tank respectvely. The heght of the process tanks are cm, the top radus s 4 cm and bottom radus s 14 cm. The Tullu 8 pump s used for dschargng the lqud from the storage tank to Tank1. The nflow to the Tank1 s proportonal to the speed of the pump. The pump dscharges water at a rate of 8 lter/hour and has 6 rpm. 43

2 Internatonal Journal of Computer Applcatons ( ) 1.Zero Crossng Detector Ths transforms the synchronzng sgnal nto a square sgnal. The ZCD s constructed usng opamp. The negatve voltage pulses are removed by usng dode at the output of the ZCD. 2. Ramp Generator Ths s desgned usng a transstor and a RC chargng network. The generated ramp sgnal s gven to a comparator. 3. COMPARATOR A comparator, as ts name apples, compares a sgnal on one output of an op-amp wth a known voltage called the reference voltage on the other nput. Fg 2. Concal tank system set up dagram Gauge pressure s used for lqud level measurement hydrostatc, whch uses pressure head. Ths process s equal to lqud heght above the sensor multpled by the specfc gravty of the lqud. It s ndependent of the volume or vessel shape. In open vessel a pressure transmtter mounted near the bottom of tank wll measure the pressure correspondng to the hgh-pressure sde of the transmtter. The low-pressure sde s vented to the atmosphere. A thn transparent tube made of plastc s provded externally to vew the actual level of the lqud n the tank. A graduated scale placed parallel to the tube ndcates the current level. Gate valves, one at the outflow of the tank1 and the other at the outflow of the tank2 are connected to mantan the level of water n the tanks. Clockwse rotaton ensures the closure of the valve, thus stoppng the flow of lqud and vce versa. A 2-pn male connector s used here to nterface the hardware setup wth the PC. The electrcal output generated from the potentometer s frst converted nto a dgtal value before applyng t to the computer. A solenod value s used to dran the water from the concal tank constantly at a constant rate to the storage tank. Otherwse f t s not kept at a optmum poston, the water wll reach a top poston for lesser pump speed or wll reach a lower poston for a lot hgher pump speed. To cover the entre range of the set up, ths valve poston should be kept properly. The trggerng crcut conssts of the followng modules:. Zero crossng detector(zcd). Ramp generator. Comparator and v. Astable controlled oscllator Fgure 3 shows the block dagram of the Thyrstor trgerrng crcut. In the smplest form, t s nothng more than an open loop opamp crcut. Wth two analog nputs and one dgtal output, the output may be (+) or (-) saturaton voltage, dependng on whch nput s larger. In ths crcut, the comparator s used to compare the ramp wth a d.c voltage Vc whch vares between to volts. The output of the comparator s used for trggerng the thyrstor. Fg 3 Block dagram of thyrstor trggerng crcut 4. OSCILLATOR The man functon of ths s to generate alternatng current or voltage waveform. More precsely, an oscllator s a crcut that generates a repettve waveform of fxed ampltude and frequency wthout any external sgnal. In the trggerng crcut ths s requred to produce a hgh frequency swtchng, so as to reduce thyrstor gate dsspaton. The pulse amplfcaton s done by separate drver crcuts and then fed to the solaton transformer. Based on the error value, the controller generates a hexadecmal equvalent of the voltage that s to be appled to the submersble pump. ths dgtzed value s then appled to an eght-bt dgtal to analog converter(dac) followed by a current to voltage converter wth an output voltage range(- )v.ths voltage sgnal s compared wth the reference voltage usng a comparator crcut. 44

3 Level n cm level(%) level(%) Internatonal Journal of Computer Applcatons ( ) Table 1 Generated data for Inflow rate 1% and 3% 6 Inflow rate - 1% Inflow rate - 3% 4 Tme (Secs) Level (%) Tme (Secs) Level (%) 7 4, Tme n seconds Fg 4 Response for nflow rate 1% The output of the comparator s appled to an Astable oscllator. The man functon of ths oscllator crcut s to generate alternatng current (or) voltage waveform. More precsely, ths crcut generates a repettve waveform of fxed ampltude and frequency wthout any external sgnal. In the trggerng crcut ths s requred to produce hgh frequency swtchng so as to reduce thyrstor gate dsspaton. The pulse amplfcaton s done separately usng drver crcut and then fed to the pulse transformer. 3. DATA GENERATION AND PROCESS MODELING BY CONVENTIONAL TECHNIQUES The data s generated usng the open loop method. Tradtonal methodology for optmzng and tunng PID loops rely on open-loop tests, whereby the loop s placed n manual mode and the controller output s moved, usually n a step-wse fashon Steps Involved In Open Loop Data Generaton 1. Intally the pump s turned on and ts speed s adjusted n the manual mode. 2. Then n the automatc mode, the LABVIEW software s logged n. 3. The flow rate s measured usng the rotameter. 4. Set pont for varous flow rates are gven va the software.. The process s allowed to reach the steady state. 6. The data generated s stored n the excel sheet. 7. Fnally the response for varous nflow rates s obtaned from whch K, τ and θ can be determned. Open loop data are generated n the concal tank system by varyng the nflow rate and notng down the respectve level. Table 1 shows the sample data generated for an nflow of 1% and 3%. Fgure 4 and shows the response of the concal tank for an nflow rate of 1% and 3% tme(sec) Fg Response for nflow rate 3% 3.2. Process Input-Output Characterstcs The nput to tank s vared n steps from mnmum to maxmum and the correspondng steady state levels n the tank are noted. Fnally the obtaned data are plotted. Table 2 shows the steady state characterstcs of the tank wth nput flow to the tank n percentage and level of the tank n cm. From the Input-output characterstcs shown n fgure 6, t s clear that the process s non-lnear. So for the desgn of the controller, the process tank s modeled nto fve lnear. Table 2. Steady state characterstcs for the tank Input n % to Tank Level n Tank n cm (-3)% - REGION 1 (3-4)% - REGION 2 (4-6)% - REGION 3 (6-7)% - REGION 4 (7-9)% - REGION Inflow n % Fg 6 Inflow and level n tank 4

4 Internatonal Journal of Computer Applcatons ( ) 4. ENHANCED NONLINEAR PID FOR CONICAL TANK LEVEL PROCESS Proportonal-ntegral-dervatve (PID) controllers have been the most popular and the most commonly used ndustral controllers n the past years. The popularty and wdespread use of PID controllers are attrbuted prmarly to ther smplcty and performance characterstcs. In order to enhance the performance of lnear PID controllers, many approaches have been developed to mprove the adaptablty and robustness by adoptng the self-tunng method, general predctve control, fuzzy logc and neural networks strategy, and other methods. Amongst these approaches, Nonlnear PID (N-PID) control s vewed as one of the most effectve and smple method for ndustral applcatons. Nonlnear PID control may be any control structure of the followng form: Where K p (.), K (.) and K d (.) are tme-varyng controller gans, whch may depend on system state, nput, or other varables, and u(t) and e(t) are the system nput and error, respectvely. Fgure 7 shows the block dagram of the nonlnear PID controller. The enhancement of the controller s acheved by adaptng ts response based on the performance of the closed-loop control system. When the error between the commanded and actual values of the controlled varable s large, the gan amplfes the error substantally to generate a large correcton to rapdly drve the system output to ts goal. As the error dmnshes, the gan s automatcally reduced to prevent excessve oscllatons and large overshoots n the response. Because of ths automatc gan adjustment, the N-PID controllers enjoy the advantage of hgh ntal gan to obtan a fast response, followed by a low gan to prevent an oscllatory behavor. The nonlnear gan k(e) s a sector-bounded functon of the error e(t), and acts on the error to produce the scaled error f(e) = K(e).e(t). Usng the hgh-qualty dfferental sgnal selected by the developed TDs, the followng enhanced nonlnear N-PID control law s developed as where e(t) and c(t) are expressed as, respectvely, e(t) = Z 1 - Z 3 c(t) = Z 2 - Z 4 Nonlnear systems, where EN-PID control s used to accommodate the nonlnearty, usually to acheve consstent response across a range of condtons. Lnear systems, where EN-PID control s used to acheve performance not achevable by a lnear PID control, such as ncreased dampng, reduced rse tme for step or rapd nputs, mproved trackng accuracy, and frcton compensaton.. BEE COLONY OPTIMIZED ENHANCED PID CONTROLLER FOR CONICAL TANK LEVEL PROCESS The Bees algorthm s developed to obtan the optmal controller parameters such as K, K p, K and K d Then t s mplemented n EN-PID controller to obtan the response. Fgure 8 shows the block dagram of the EN-PID controller optmzed usng bee colony technque. The Bees algorthm s developed to obtan the optmal controller parameters such as K P, K I, K D and K. Fg 7 Block dagram for Nonlnear PID Controller Nonlnear trackng dfferentator, TD(I) s referred to as the followng system: gven a reference sgnal r(t), the system provdes two sgnals Z 1 and Z 2, such that Z 1 = r(t) and Z 2 = ẋ(t). Smlarly TD(II) provdes the output y(t) as two sgnals Z 3 = y(t) and Z 4 = y (t) respectvely. The error e(t) s gven by Z 1 Z 3 and the nonlnear gan s ntroduced to act on error. The proposed enhanced nonlnear PID (EN-PID) controller conssts of a sector-bounded nonlnear gan k(e), a lnear fxed-gan PID controller expressed by K(s) = K p + K /s + K d s, and two nonlnear trackng dfferentators (TDs) where k p, k, and k d are proportonal, ntegral and dervatve gans, whch can be determned by the Zegler Nchols crteron. Fg 8 Block dagram of Non-lnear PID controller usng Bee colony optmzaton technque.1performance Index In ths secton, the feedback controller desgn s formulated as an optmzaton problem and the soluton s sort through steps of Ant Colony Optmzaton (ACO). The technque uses ACO to tune the PID parameters onlne for a mnmum ITAE for each regon separately. Due to the varety of PID control law permutatons, t s necessary to specfy a 46

5 Flow n % Internatonal Journal of Computer Applcatons ( ) mnmum set of attrbutes that s PID controller s assumed to be of non-nteractng form as defned below: 1 Gc () s K p K Kds s By sutable transformaton of the parameters ths form s converted to nteractng form. Mnmzng the followng error crtera generates the controller parameter T ITAE r( t) y( t) t dt where r(t) = reference nput, y(t) = measured varable At frst, the bee,.e. the PID parameters are randomly ntalzed. The ftness functon s defned as 1/ITAE. Smaller the ftness functon, the better performance of the system response wth the specfed PID parameters..1. Algorthm: Bee colony Optmzaton for EN-PID controller tunng 1. Intalze the populaton of solutons x,j 2. Evaluate the populaton 3. Cycle =1 4. Repeat. Produce new solutons (food source postons),j n the neghbourhood of x,j for the employed bees x ( x x ) usng the formula,,,, j j j j k j where k s the soluton n the neghbourhood of I, s a random number and evaluate them 6. Apply the greedy selecton process between x and 7. Calculate the probablty values P for the solutons x by means of ther ftness values usng the P SN 1 ft ft The ftness values of solutons are calculated as 1 f f ft 1 f 1+abs( f) f f < Normalze P values nto [,1] 8. Produce the new solutons ( new postons) for the onlookers from the solutons x, selected depedng on P and evaluate them 9. Apply the greedy selecton process for the onlookers between and x 1. Determne the abandoned soluton (source) f exsts and replace t wth a new randomly produced soluton x for the scout usng x j = mn j + rand(,1)*(max j -mn j ) 11. Memorze the best food source poston (soluton) acheved so far 12. Cycle = cycle Untl cycle = Maxmum cycle Number The termnaton crteron can be n two was: ether by endng the program when objectve functon value reaches a reasonably low value or after a fnte number of teratve steps. In the present case, the program was termnated after 4 teratons. The table 3 shows the optmal controller parameters that can be appled for the non-lnear controller, obtaned usng Bee Colony Optmzaton technque. Table 3 Optmal controller parameters for non-lnear controller K K P K I K D Tme n seconds Fg 9 Response of enhanced non-lnear PID controller 6. CONCLUSION The open loop data s generated by varyng the flows and measurng the respectve levels. The I/O characterstcs s plotted for the process and pecewse lnearzaton s done. The EN-PID controller model s developed and mplemented n the process for non-lnear control. The Bee colony optmzaton algorthm s developed and mplemented n MATLAB to gve optmal values of K, K p, K and K d. Fnally the BCO tuned EN-PID controller s mplemented n the real tme process. 7. REFERENCE [1] George stephanopoulous, Chemcal Process Control, Prentce Hall of Inda Pvt.Ltd.,New Delh,21. [2] Jn Kum Lu, Advanced PID control and MATLAB smulaton, Publshng house of electroncs ndustry, 2 nd edton, September 24. [3] R. Krohlng, J. Rey, Desgn of optmal dsturbance rejecton PID controllers usng Genetc algorthms, IEEE Transacton on Evolutonary computaton, Vol., No.1, Feb 21. [4] Pham DT, Ghanbarzadeh A, Koc E, and Otr S., Applcaton of the Bees Algorthm to the tranng of radal bass functon networks for control chart pattern recognton, Proc th CIRP Internatonal Semnar on Intellgent Computaton n Manufacturng Engneerng (CIRP ICME '6), Ischa, Italy, 26. [] Pham DT, Otr S, Ghanbarzadeh A, and Koc E. Applcaton of the Bees Algorthm to the tranng of learnng vector quantsaton networks for control chart pattern recognton, Proc Informaton and Communcaton Technologes (ICTTA'6), Syra, p , 26. [6] Y.X. Su, Dong Sun,B.Y. Duan, Desgn of an enhanced nonlnear PID controller -Scence Drect journal, pp no:1-124,march 2. 47