COMPUTATIONALLY INTELLIGENT MODELLING AND CONTROL OF FLUIDIZED BED COMBUSTION PROCESS

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1 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp Introducton COMPUTATIONALLY INTELLIGENT MODELLING AND CONTROL OF FLUIDIZED BED COMBUSTION PROCESS by Žarko M. ]OJBAŠI] *, Vlastmr D. NIKOLI], Ivan T. ]IRI], and Ljubca R. ]OJBAŠI] Faculty of Mechancal Engneerng, Unversty of N{, N{, Serba Orgnal scentfc paper: UDC: /.377:519.62/.63 DOI: /TSCI ] In ths paper modellng and control approaches for fludzed bed combuston process have been consdered, that are based on the use of computatonal ntellgence. Proposed adaptve neuro-fuzzy-genetc modellng and ntellgent control strateges provde for effcent combnng of avalable expert knowledge wth expermental data. Frstly, based on the qualtatve nformaton on the desulphurzaton process, models of the SO 2 emsson n fludzed bed combuston have been developed, whch provdes for economcal and effcent reducton of SO 2 n fludzed bed combuston by estmaton of optmal process parameters and by desgn of ntellgent control systems based on defned emsson models. Also, effcent fuzzy non-lnear fludzed bed combuston process modellng strategy by combnng several lnearzed combuston models has been presented. Fnally, fuzzy and conventonal process control systems for fuel flow and prmary ar flow regulaton based on developed models and optmzed by genetc algorthms have also been developed. Obtaned results ndcate that computatonally ntellgent approach can be successfully appled for modellng and control of complex fludzed bed combuston process. Key words: computatonal ntellgence, fludzed bed combuston, fuzzy systems, neural networks, genetc algorthms In fludzed bed combuston (FBC), besdes fuel combuston chamber contans a quantty of partcles of nert materal such as sand or ash. The combuston ar enterng from below lfts mxed materal keepng t n constant movement and formng a turbulent bed, whch behaves lke a bolng flud. Ths essental feature s the bass for many excellent propertes of the FBC technology but t also makes the process hghly complex [1-3]. To match the process complexty, several aspects of the applcaton of powerful computatonal ntellgence technques for FBC process modellng and control have been consdered n ths paper. Harmful flue gas emssons such as sulphur oxdes, ntrogen oxdes, and carbon monoxde are result of the complex burnng phenomena and the constructon features of the plants. In addton to the developments n the plant constructon and flue gas cleaners, also the optmzaton of the process operatng condtons s an mportant and cost-effectve way to affect these emssons, especally snce possblty to reduce emssons s one of the man *ncorrespondng author; e-mal: zcojba@n.ac.rs

2 322 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp features of FBC technology. But to be able to optmze the plant operaton, models for the varables of the overall cost functon are requred. Wth that and other ams concernng control of FBC plant n mnd [4-6], n ths paper models for the SO 2 emssons based on the computatonal ntellgence technques are consdered. Also, n ths study conventonal control process models lnearzed around dfferent operatonal ponts have been combned by means of hybrd fuzzy model, whch extends the model usablty for wde range of plant workng regmes. Suggested fuzzy model, based on Takag-Sugeno-Kang (TSK) fuzzy reasonng, makes smooth nterpolaton of several lnear models and therefore overcomes ther rgd lmtatons. Fnally, genetc optmzaton has been consdered for obtanng usable conventonal and fuzzy controllers for regulaton of the man FBC plant operatonal loops. Conventonal proportonal-ntegral-dervate (PID) controller and alternatve fuzzy proportonal-dervatve (PD) controller desgn approaches have been consdered, where controller parameters were optmzed by real coded genetc algorthms. Quck response and modest overshoot of a closed loop system s of vast mportance havng n mnd energy effcency, flue gas emsson, and plant safety. Computatonally ntellgent modellng and control approach [7-9] appled n ths paper s based on fuzzy logc, neural networks, genetc algorthms, and fuzzy clusterng methodologes. Hybrd approaches have been used, such as tranable neuro-fuzzy structure that combnes the theory of artfcal neural networks (ANN) and fuzzy systems and that can beneft from both qualtatve and quanttatve avalable nformaton. Learnng methods of ANN enable these systems to learn from gven tranng data sets, and due to the massve parallelsm of the ANN real-tme processng of larger data sets and graceful degradaton of performance n the case of damage are provded. The fuzzy set theory enables the neuro-fuzzy systems to deal wth the ambguous or ll-defned data effectvely and to present the learned nformaton n a more human understandable form. Soft computng models and control systems consdered n ths paper present extensons of the results that the authors obtaned [4-6, 10] n the feld of neuro-fuzzy-genetc modellng and control of FBC process and flue gas emssons. Besdes that, group of authors [3, 11, 12] developed fuzzy-relaton models of flue gas emsson, adaptve prototypes for onlne NO x emsson dentfcaton and Wener logcal models of FBC process, as well as genealogcal decson trees and dstrbuted logcal processors for multvarable control of FBC. Other authors [13, 14] consdered bnary coded genetc optmzaton and genetc learnng automata for conventonal and fuzzy control based on a neuro-fuzzy models of combuston process. In some papers [15, 16] robust FBC control wth predctve model based on fuzzy model and pecewse quadratc Lyapunov functons that guarantees stablty n every work regme s suggested. Some novel results [17] consderng advanced control of FBC are based on human-smulated ntellgent control that can overcome conventonal control dsadvantages. Combnng numercal and lngustc nformaton nto system s the key-strategy obtaned by computatonally ntellgent approach, snce complexty of the FBC process makes applcaton of conventonal modellng and advanced control strateges dffcult [4, 10, 13]. Fludzed bed combuston, expermental data and methodology Fludzed bed combuston Combuston ar enterng from below n fludzed bed combuston [1, 2] lfts partcles such as sand or ash that are present n combuston chamber, formng a turbulent bed and keepng them n constant movement when the fuel s added to the bed. Released heat from the

3 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp materal burnng mantans the bed temperature, whch s also kept unform through the bed by the turbulence. The heat capacty of the sold bed partcles gves the system thermal stablty, whch makes varatons n fuel propertes less crtcal than wth many other combuston systems [1, 18]. Normal operatng temperature of the bed s relatvely low, so the ash and most fuels do not melt or snter and consequently fuel propertes lke ash content, partcle sze and mosture are of less mportance. Besdes low operatng temperatures ( C), the fludzed bed combustor s also characterzed by hgh excess ar levels ( 30%), ntermedate partcle szes (1-3 mm), long resdence tmes (several mnutes) and vgorous partcle moton that domnates heat transfer and reacton processes [1]. Expermental data Expermental data used n ths paper orgnate from several prevous researches concernng FBC, conducted at the Thermal engneerng and Mechatroncs and Control departments of the Mechancal Engneerng Faculty of the Unversty of Nš, N{, Serba [2, 19-23]. For example, some data sets obtaned n these experments were measured from a laboratory FBC plant, of 120 mm dameter crcular cross-secton, 1500 mm heght and 20 kw power (fg. 1). Fgure 1. Schematc representaton of two laboratory expermental fludzed beds

4 324 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp Durng these experments ol shale was used as fuel. Sgnals were measured wth a frequency of 1 Hz, and the process was operated changng the values of parameters. A sample of obtaned measurement data s shown n fg 2. Concentraton of SO 2 was drectly measured and then recalculated as percent of SO 2 removal from flue gas, whch was used as tranng data for model output. Computatonal ntellgence technques used for FBC modellng and control Ths secton summarzes man computatonal ntellgence technques used for FBC modellng and control n ths study, namely the basc archtecture and the hybrd learnng algorthm of adaptve neuro-fuzzy nference system (ANFIS) [9], modfed mountan clusterng (MMC) technque for ntal neuro-fuzzy model structure determnaton [8, 24] as well as real-coded genetc algorthms [25]. ANFIS structure Fgure 2. A set of expermental data used for tranng of neuro-fuzzy model Consder a frst-order TSK fuzzy nference system that conssts of two rules: Rule 1: If X s A 1 and Y s B 1 then f 1 p 1 x q 1 y r 1, and Rule 2: If X s A 2 and Y s B 2 then f 2 = p 2 x +q 2 y + r 2. If f 1 and f 2 are constants nstead of lnear equatons, we have a zero-order TSK fuzzy model. Fgures 3(a) and (b) llustrate the fuzzy reasonng mechansm and the correspondng ANFIS archtecture, respectvely. Node functons n the same layer of ANFIS are of the same functon famly. Note j that O denotes the output of the th node n layer j. Layer 1: Each node n ths layer generates membershp grades m of a lngustc label. For nstance, the node functon of th node mght be:

5 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp Fgure 3. Frst-order TSK fuzzy model usng trapezodal membershp functons and correspondng ANFIS archtecture O 1 A x a d x ( x) max. mn.,1,, 0 b a d c (1) where x (and also y) s the nput to node ; A (and also B ) the lngustc label (small, large, etc.) assocated wth ths node, and a, b, c, and d the parameter set that changes the shape of the trapezodal membershp functon. Parameters n ths layer are referred to as the premse parameters. Layer 2: Each node n ths layer, labeled wth P, calculates the frng strength of each rule va multplcaton: 2 O w ( x) ( y), 1, 2 A Layer 3: The th node of ths layer, labelled wth N, calculates the rato of the th rule s frng strength to the sum of all rules frng strength: 4 w O w, 1, 2 w w Layer 4: Node n ths layer has the followng node functon: 1 B O w f w ( p x q y r ) (4) where w s the output of layer 3 and p, q, and r s the parameter set. Parameters n ths layer wll be referred to as the consequent parameters. Layer 5: The sngle node n ths layer computes the overall output as the summaton of all ncomng sgnals overall output: The hybrd BP/RLSE learnng algorthm O wf overall output w 5 w f The hybrd learnng algorthm of ANFIS conssts of two alternatng parts: (2) (3) (5)

6 326 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp (1) Back propagaton/gradent descent (BP/GD) whch calculates error sgnals (defned as the dervatve of the squared error wth respect to each node output) recursvely from the output layer backward to the nput nodes, and (2) the recursve least squares estmate (RLSE) method, whch fnds a feasble set of consequent parameters. We observe that, gven fxed values of premse parameters, the overall output can be expressed as a lnear combnaton of the consequent parameters: f w1 f1 w2 f2 ( w1 x) p1 ( w1 y) q1 ( w1 ) r1 ( w2 x) p2 ( w2 y) q2 ( w2 ) r 2 (6) Equaton (6) can be recast as a matrx equaton AX = B (7) where X s an unknown vector whose elements are the consequent parameters. Least-squares estmate (LSE) of, namely X *, s sought to mnmze the squared error AX - B 2 Sequental formulas are employed to compute the LSE of X. Specfcally, let the th row vector of matrx A defned n (7) be at h and the th T element of B be b. Then T T T Sa 1a 1S 1 1a 1( b 1 a 1 ), 1 S, 0,1,..., P 1 T 1 a 1Sa 1 X X S X S where S s often called the covarance matrx and the least-squares estmate X * s equal to.x p. The condtons to ntalze (8) are X 0 = 0 and S 0 = gi, where s a postve large number and I s the M M dentty matrx, where M s the number of consequent parameters. For gven fxed values of premse parameters, the estmated consequent parameters are known to be globally optmal. MMC clusterng The purpose of clusterng s to dstl natural groupngs of data from a large data set, producng a concse representaton of system behavour. The quck subtractve or MMC clusterng technque was developed by Yager/Flev and modfed by Chu [19]. The clusterng of I/O data produces a set of cluster centers, and each cluster center acts as a prototypcal data pont that descrbes a characterstc mode of the system, and can be consdered as the nucleus of a fuzzy f-then rule. In that way parttonng of the nputs and determnaton of the ntal mnmal fuzzy rule base can be performed. Namely, f a collecton of n-normalzed data ponts {x 1, x 2,..., x n } n an M-dmensonal space s consdered, measure of the potental of data pont can be defned as: n P exp( x x ), j j 1 The constant r a s effectvely the radus defnng a neghbourhood. After the potental of every data pont has been computed, the data pont wth the hghest potental s selected as the frst cluster center. If x * 1 s the frst cluster center wth potental P * 1, the potental of each data pont s revsed by: * j P P P exp( x x ), a r 4 2 rb (8) (9) (10)

7 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp where r b s a postve constant larger than r a n order to avod hgh densty of the cluster centers [19]. Real coded genetc algorthm The genetc algorthms (GA) are computatonal ntellgence technque, nspred by Darwn s theory of bologcal evoluton, that represent an alternatve to the tradtonal optmal search approaches n whch t s hard to fnd the global optmum for non-lnear and multmodal optmzaton problems. GA mantans and manpulates a populaton of solutons and mplements a survval of the fttest strategy n ts search for better solutons. The fttest ndvduals of any populaton tend to reproduce and survve to the next generaton thus mprovng successve generatons. Implementaton of the GA requres the determnaton of sx fundamental ssues: chromosome representaton, selecton functon, genetc operators, ntalzaton, termnaton and evaluaton functon. Chromosome representaton scheme determnes how the problem s structured n the GA and also determnes the genetc operators that are used. Each ndvdual or chromosome s made up of a sequence of genes. Among varous types of representatons of an ndvdual or chromosome, real-coded representaton stands out for ts effcency and precson wth more consstent results [25]. Also, real codng makes t possble to use large and even unknown domans for varables. Selecton of ndvduals plays a sgnfcant role n a GA snce t determnes whch of the ndvduals wll survve and move on to the next generaton. A probablstc selecton s performed based upon the ndvdual s ftness so that the superor ndvduals have better chances to be selected. There are several schemes for the selecton process: roulette wheel selecton and ts extensons, scalng technques, tournament, normal geometrc, eltst models, and rankng methods. The basc search mechansm of the GA s provded by the two types of operators: crossover and mutaton, whch are used to produce new solutons based on the exstng solutons n the populaton. Crossover takes two ndvduals as parents and produces two new ndvduals whle mutaton alters one ndvdual to produce a sngle new soluton. An ntal populaton s needed to start the GA procedure. The ntal populaton can be randomly generated or can be taken from other methods. The computatonal flowchart of the real coded genetc algorthm (RCGA) optmzaton process employed n ths paper s shown n fg. 4. The GA moves from generaton to generaton untl a stoppng crteron s met. The Fgure 4. Flowchart of genetc algorthm

8 328 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp stoppng crteron could be maxmum number of generatons, populaton convergence crtera, and lack of mprovement n the best soluton over a number of generatons or target value for the objectve functon. Evaluaton functons or objectve functons of many forms can be used n a GA so that the functon can map the populaton nto a partally ordered set. Computatonally ntellgent FBC modellng Neuro-fuzzy desulphurzaton modellng Process operatng condtons are an mportant and cost-effectve way to affect FBC harmful flue gas emssons contanng sulphur oxdes. To be able to optmze the plant operaton, neuro-fuzzy models have been consdered for predcton of the SO 2 emssons based on the values of the most nfluental (changeable,. e. adjustable) parameters. Sulphur-doxde removal from flue gas durng the combuston process s possble by addng lmestone n bed, whch s consdered to be one of the most mportant advantages of FBC. Harmful gaseous emssons are converted to sold materal, whch s elmnated from combuston bed, and there are also possbltes for ts later usage. Degree of bndng of sulphur s dependent on many parameters, where most mportant are: combuston temperature, molar rato Ca/S, bed heght, fludzaton velocty, excess ar rato, prmary/secondary ar rato, characterstcs of lmestone, sze of partcles of lmestone, heatng velocty of the lmestone partcle, etc. [1, 20, 21, 26]. Input sgnals for SO 2 flue gas content model were selected based on a pror knowledge on the condtons affectng the formaton and reducton of SO 2 n FBC process. Four model nputs selected were: molar rato Ca/S, bed temperature TB, excess ar rato, and fludzaton velocty v 0, whle model output was percent of SO 2 removal from flue gas, denoted as SO 2. Rato Ca/S s n practcal operaton of FBC expermentally near-optmally determned, and s selected as greater than one snce desulphurzaton s mproved when more lmestone s added n bed than theoretcally needed. Influence of bed temperature on flue gas SO 2 content s sgnfcant snce below optmal temperature porosty of CaO s decreasng due to substantally smaller calcnaton of lmestone, whle on hgher temperatures ntense snterng occurs, closng pores and decreasng desulphurzaton. Excess ar does not nfluence desulphurzaton process drectly, but t has ndrect postve effect. When fludzaton velocty ncreases, tme of contact of SO 2 and lmestone partcles decreases, so desulphurzaton s lowered. It was assumed that geometrcal parameters of the fludzed bed plant cannot be changed, as well as fuel type or lmestone qualty and lmestone partcle sze, so those nfluental parameters were not consdered as possble model nputs. To model FBC desulphurzaton, TSK fuzzy models [7] have been used havng rule structure wth fuzzy antecedent and functonal consequent parts, whch thereby qualfy to be treated as mxed fuzzy and non-fuzzy models. TSK fuzzy models have the ablty to represent both qualtatve knowledge and quanttatve nformaton and allow for applcaton of powerful learnng technques for model dentfcaton from data. To develop models, the structure dentfcaton and parameter adjustment [8, 15, 24] tasks needed to be solved. The former determnes I/O space partton, rule antecedent (. e., premse) and consequent varables, the number of IF-THEN rules, and the number and ntal postons of membershp functons. The latter dentfes a feasble set of parameters under the gven structure. For the problem of structure dentfcaton, a clusterng technque presented n

9 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp prevous secton was used [5]. Exponental potental functon was used to rank and select most representatve cluster centers from plant I/O data, and these cluster centers are then used to generate an ntal TSK fuzzy model. Also another approach was consdered parttonng based on expert process knowledge. Gaussan membershp functons have been used. Model parameters adjustment was performed usng effcent ANFIS neuro-fuzzy scheme [9] overvewed n prevous sectons. Usng ANFIS ntal TSK models obtaned from the structure dentfcaton phase have been represented as generalzed feed forward neural networks and traned wth plant I/O data, thereby adjustng the parameters of the antecedent membershp functons as well as those of the functonal consequents wth hybrd learnng scheme. Several versons of the ANFIS model structures were consdered. Frst, versons wth two (Ca/S, T B ) and four nputs (Ca/S, T B,, v 0 ) were tested, whle model output was SO 2. n all consdered cases. One realzed approach wth four nputs s shown n fg. 5(a). Fgure 5. (a) ANFIS network wth 4 nputs and 14 rules and (b) output surface for traned fuzzy model wth two nput (Mfs membershp functons) Also, nterpretablty of the obtaned results was ssue of nterest. Besde the fact that qualtatve knowledge about the process was used along wth avalable numercal data thanks to appled neuro-fuzzy modellng approach, obtaned results after tranng can also be transformed nto understandable nformaton. For example n fg. 5(b) output surface for fuzzy model wth two nputs and modest number of prmary fuzzy sets wth Gaussan membershp functons, after tranng, s presented. It s obvous that some theoretcal knowledge can be confrmed from such results, as the fact that there s optmal bed temperature whch provdes for maxmal SO 2 removal, after whch further ncrease degrades SO 2 removal process, and so on. Also, rules wth traned optmal parameters can be arranged n readable form provdng understandable conclusons that were extracted from data by the model [4]. Among several tests performed, one expermental verfcaton of accuracy of model wth four nputs and 14 rules from fg. 5(a) s presented n fg. 6, for 250 expermental data samples not used for model tranng. Possblty to perform mult-crtera optmzaton of the obtaned models by applcaton of genetc algorthms n order to acheve ncreased accuracy and/or nterpretablty of the models has been also tested. For ths purpose presented GA wth real codng have been used [5, 10].

10 330 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp Fgure 6. Expermental verfcaton of accuracy of traned fuzzy model wth four nputs Hybrd fuzzy FBC model For development of the FBC plant man control loops, a basc combuston process model s requred. Control orented non-lnear [27] and lnear [11, 12] mathematcal models of FBC process are based on mass and energy transfer. Combuston model nputs are fuel flow Q c [kgs 1 ], prmary ar flow F p and secondary ar flow F s [Nm 3 s 1 ]. Measurable system varables are bed temperature T B [K], freeboard temperature T F [K] and flue gas oxygen content C F [%]. In ths paper, a computatonal ntellgence model based on fuzzy nference mechansm s proposed. The suggested fuzzy model ntellgently nterpolates lnear models that are the result of the Lyapunov lnearzaton around several characterstc operatng ponts, n the form: d x ( t) dt Ax( t) Bu( t), y( t) Cx ( t) (11) The dea was to overcome rgd lmtatons of the lnear model, where the model s only vald near the operatng pont. By means of fuzzy model such lmtatons can be overcome and the fuzzy model can produce correct output for an arbtrary operatng pont. Ths approach allows the usage of lnear models from [11, 12] and optmzaton of models explaned n [4-6, 10]. Decsve fuzzy model nputs are measurable state varables, namely bed and freeboard temperatures T B and T F and flue gas oxygen content C F, whch defne operatng ponts of the lnearzed models. Other fuzzy model nputs are outputs of lnear models y, value of combuston power P comb, that are ntellgently blended by the fuzzy model n order to generate overall model output y. Snce the suggested fuzzy model s used as an nterpolatng supervsor of several dfferently lnearzed models, the TSK fuzzy reasonng was used [7], wth lnear dependences n the consequental part of fuzzy rules, and free members equal to

11 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp zero. For realzaton wth m submodels, lnearzed around m operatng ponts and wth outputs y 1, y 2, y m, mplemented k-th fuzzy rule s: k m Rule operatng pont yˆ a y a y a y (12) k 1 2 s :f then k1 k2... km All parameters a k1, a k2, a km of the fuzzy rule are equal to zero, except for one whch equals one. Every fuzzy rule defnes one lnear model for approprate operatng pont dentfed n the antecedent rule part, selectng approprate lnear model for each characterstc operatng pont. Fgure 7. Fuzzy model Model actvates more than one fuzzy rule for dfferent values of nput but wth dverse actvaton levels, so t s obvous that suggested realzaton makes smooth nterpolaton of sngular lnear models. Also, fuzzy model produces approprate model output for the operatng ponts that are not ncluded n several optmally adjusted lnear models. A scheme of fuzzy model based on non-lnear model lnearzed around 4 characterstc operatng ponts s shown n fg. 7. Intellgent FBC control Intellgent control of FBC desulphurzaton Computatonally ntellgent desulphurzaton models developed n prevous secton are ntended to be used as approxmators for determnaton of optmal process parameters n relaton to flue gases SO 2 removal. Models are to be ntegrated n FBC boler's control system at supervsory level, and have the task of estmatng parameters for basc control loops. Optmzaton of emssons demands compromses between dfferent ams, and proposed models provde nputs for the optmzaton cost functon whch defnes optmal balance between plant's thermal effcency and emssons. Besde descrbed usage, followng the deas from [3, 6, 11, 28] developed models can be ntegrated n an expert system, whch advses plant operators when lmts for NO x, SO 2, and CO emssons are reached and helps to stablze burnng condtons. Such a system

12 332 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp provdes easy access to the knowledge concernng emssons and helps operators to act quckly and effcently, whle effects of actons can be clearly seen. Such a system can be used not only n plant operaton, but also for tranng. Its structure s shown n fg. 8. Fgure 8. Expert system for montorng emssons n FBC boler plant The man power of the proposed approach les n centralzed acquston of all sources of nformaton about the process, whether they orgn from the operators' experence, theoretcal knowledge about the process or measured data. Expert system can also potentally be based on computatonal ntellgence,.e. t can also be fuzzy. Besde proposed statc models of the emsson of SO 2 n bolers wth FBC, dentfcaton of dynamc fuzzy models for the sake of applcaton n the framework of adaptve control of FBC process has been consdered as potentally feasble concept. For dynamc modellng of the emsson wdely used strategy of external dynamcs has been appled. Ths concept allows for the effcent applcaton of fuzzy models that represent statc approxmators for modellng of dynamc systems, whch has applcaton n control systems as ts fnal am. Term external dynamcs orgnates from the fact that non-lnear dynamc model can be dvded nto two parts: non-lnear statc approxmator and external bank of delay elements. Fgure 9 shows the extenson of the basc dea of Fgure 9. Dynamc fuzzy model of the SO 2 emsson wth FBC statc modellng to a dynamc verson of a model.

13 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp GA optmzed conventonal and fuzzy control of FBC Effcency of combuston process depends on the burnng completeness and on the waste heat taken away n the flue gas by the excess ar flow. The hgher the burnng rate and the smaller the waste heat, the hgher the effcency. However, excess ar s requred for ensurng complete combuston. The O 2 content of the flue gas s drectly related to the amount of excess ar. The am of the combuston control, from the effcency pont of vew, s to keep the O 2 content around 3-6% [3]. In mult-fuel fred FBC power plants, ths s a dffcult task due to the nhomogeneous propertes of the fuel. In [13] the dea of usage of the bnary coded genetc algorthm for the optmal FBC PD controller tunng s presented. To the contrary to that work, n ths paper real coded genetc algorthms for optmal PID controller and fuzzy PD controller tunng were suggested, along wth mproved ftness functons and dfferent plant model. The combuston model used, based on the lnear model developed n [11, 12] calculates combuston power (P comb ) and flue gas components (C F ) ncludng the oxygen content, from the fuel flow, prmary ar flow F p, and secondary arflow F s. The oxygen and combuston power controller conssts of two parallel PID controllers. The fuel flow controller s drven by the oxygen content error sgnal. The second PID controller regulates combuston power by changng prmary arflow. The structure of the PID controller s: U 1 () s K K sk E s P d where modfable parameters are PID controller proportonal (K p ), ntegral (K ), and dervatve (K d ) gans, U(s) and E(s) are Laplace transforms of control and error sgnals u(t) and e(t), whle s denotes Laplace s complex varable. System s lnearzed at operatng pont Q C = 2.6 kg/s, F P = 3.1 Nm 3 /s, FS 8.4 Nm 3 /s, W C = 165 kg, C B = 0.042, C F = 0.031, T B = 749 C, T F = =.650 C, and P = 21.1 MW. The RCGA were used for tunng PID controller gans through genetc algorthms optmzaton varables set Θ = [θ 1, θ 2, θ 3, θ 4, θ 5, θ 6 ] = [K p1, K 1, K d1, K p2, K 2, K d2 ], as shown n fg. 10. (13) Fgure 10. RCGA for PID controller parameter optmzaton

14 334 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp In the mplemented algorthm a populaton of 60 ndvduals, an eltsm of 2 ndvduals, ntal range [0, 50] and a scattered crossover functon were used. All the members were subjected to adaptve feasble mutaton except for the elte. The ndvduals were randomly selected by the Roulette method. The ftness functon used was sum of oxygen content relatve error, combuston power relatve error and relatve value of maxmum oxygen content overshoot (n order to addtonally penalze overshoot and therefore try to suppress oscllatory behavour): y yˆ y yˆ max( y ) f ( ) k k k M M M O O P P O yˆ O 1 yˆ P yˆ O 2 2 where k 1, k 2, and k 3 are weght factors an M s the number of samplng data ponts. In our case k 1 = 2, k 2 = 1, and k 3 = 1, emphaszng mportance of oxygen content drectly related to the flue gas emssons, combuston qualty, and energy effcency. Stablzaton of system wth ntal dsturbances, where the flue gas oxygen content s 2.1%, and the ntal plant power s 24 MW for 8 mnutes controlled by PID controllers wth RCGA tuned parameters s shown n fg. 11. PID parameters were obtaned by careful alteratons of the stated RCGA parameters. After several optmzaton runs, optmal parameters for two PID after 500 generatons were K p1 = 83.20, K 1 = 67.53, K d1 = 87.45, K p2 = 5.13, K 2 = , K d2 = and the fnal optmal responses are shown n fg. 11 by full lne. (14) Fgure 11. PID controllers (a) flue gas oxygen content and (b) combuston power stablzaton As an alternatve to the conventonal PID controller desgn approach, the fuzzy control [7, 8] for FBC control was also consdered, namely two parallel fuzzy PD controllers for fuel and prmary ar were desgned. The twn fuzzy PD controllers had the same nputs and tasks as wth PID controllers. The error sgnal and error dervate for the controllers were normalzed and dvded n three regons each: low, medum, and hgh. The output membershp functons of the controllers were sngletons.

15 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp Optmal fuzzy controller normalzaton gan values K 11, K 12, K 13, K 21, K 22, and K 23 (two for nputs and one for output per controller) were determned by RCGA. In the mplemented algorthm a small populaton of 30 ndvduals, an eltsm of 3 ndvduals, ntal range [0, 50], a scattered crossover functon, adaptve feasble mutaton and Roulette selecton were used. The ftness functon was: f M y yˆ y yˆ max( y ) M O O P P O ( ) M, yˆ yˆ yˆ 1 O 1 P 2 2 where the frst element mnmzes the oxygen content relatve error, second mnmzes combuston power relatve error and thrd element dmnshes oxygen content overshoot. After 500 generatons the followng parameters were obtaned: K 11 = , K 12 = , K 13 = , K 21 = , K 22 = , K 23 = Stablzaton of closed loop fuzzy controlled system wth ntal dsturbances, where the ntal flue gas oxygen content s 2.1%, desred oxygen content s 3.1%, the ntal plant power s 24 MW and desred plant power s 22 MW for 10 mnutes s shown n fg. 12. O (15) Fgure 12. Fuzzy controllers (a) flue gas oxygen content and (b) combuston power stablzaton Both PID and fuzzy controllers perform well, whch ndcates that RCGA optmzaton s useful tool n FBC controller tunng. Fuzzy control was tested as an alternatve to conventonal control as t opens possblty to relatvely easly ncorporate specal actons regardng plant safety, energy effcency, flue gas emsson and others when certan crcumstances occur n the system [4]. Conclusons Modellng and control problem that was studed n the paper orgnates from the fludzed bed combuston process, whch s hghly non-lnear and complex thus makng conventonal modellng and control of FBC plants dffcult. Frstly, models for the flue gas SO 2 content were dentfed usng computatonal ntellgence. Appled ANFIS networks were capable of capturng the non-lneartes n

16 336 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp process data, the tranng was effcent and predcton accuracy of the obtaned models was good. That goes along wth other features, such as nterpretablty of the models, use of all sources of nformaton on the process, etc. Concsely recaptulated, trple usage of the developed computatonally ntellgent models of the emssons n FBC has been proposed for ntellgent control of FBC bolers. That are, namely: applcaton of statc fuzzy models of emssons n order to provde for nput values for optmzaton crtera, on the bass of whch reference values for basc control loops are calculated; applcaton of statc fuzzy models n expert system that has the task of centralzed treatment of nformaton on harmful gaseous emssons and also to provde recommendatons to plant operators; and applcaton of dynamc fuzzy models of emsson and ther nverses for desgn of control n the framework of adaptve fuzzy control wth nternal model and fuzzy predctve control. Proposed hybrd fuzzy FBC model based on the TSK fuzzy reasonng gves the optmal state of model output for the operatng ponts that are not ncluded n several optmally adjusted lnear models that t uses. It makes smooth nterpolaton of lnear models there fore overcomng ther rgd lmtatons. The proposed fuzzy model represents an extenson of the publshed results n a feld of the FBC process modellng wth control tasks n mnd. Stablzaton of system wth the ntal dsturbances controlled by PID controllers wth optmally tuned gans as well as controlled by alternatve fuzzy PD controllers wth optmally adjusted parameters has also been presented. Real coded genetc algorthms were used for numercal calculaton of optmal PID controller gans and fuzzy controller parameters. Both closed loop systems have rapd response and small overshoot. Such response s of vast mportance havng n mnd energy effcency, flue gas emssons and plant safety. A slower response ncreases chances for ncomplete combuston that can lead to a major plant falure. Based on the results reported n ths paper, as well as on prevous results publshed by the authors and others, t could be concluded that applcaton of computatonal ntellgence for modellng and control of fludzed bed combuston has both proven ts potental and opened nterestng drectons for future research. Above all, combnatons of neuro-fuzzygenetc methodologes could be further explored to provde for more effcent ntegraton of avalable expert knowledge about the process wth other sources of nformaton, such as measured data. Nomenclature Ca/S molar rato, [ ] C F flue gas oxygen content, [ ] F p prmary ar flow, [Nm 3 s 1 ] F s secondary ar flow, [Nm 3 s 1 ] f rule (lnear equaton output) j O node functon P comb combuston power, [MW] Q c fuel flow, [kgs 1 ] T B bed temperature, [K] T F freeboard temperature, [K] u system nput v 0 fludzaton velocty, [m 3 s 1 ] w rules frng strength y system output Greek symbols SO 2 SO 2 removal from flue gas, [%] excess ar rato, [ ] Acronyms ANN artfcal neural network ANFIS adaptve neuro-fuzzy nference system BP/GD back propagaton/gradent descent FBC fludzed bed combuston MMC modfed mountan clusterng PD proportonal dervatve PID proportonal-ntegral-dervatve RLSE recursve least squares estmate

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18 338 THERMAL SCIENCE, Year 2011, Vol. 15, No. 2, pp [26] Manovć, V., Grubor, B., Ilć, M., Sulfur Self-Retenton n Ash, a Gran Model Approach, Thermal Scence, 6 (2002), 2, pp [27] Leppäkosk, K., Paloranta, M., Ikonen, E., Comparng Two Nonlnear Structures for Secondary ar Process Modellng, Proceedngs, Control 2004, Bath, UK, 2004, ID-68 [28] Leppäkosk, K., Mononen, J., Kortela, U., Kovács, J., Integrated Optmsaton and Control System to Reduce Flue Gas Emssons, Proceedngs, 4 th IFAC/CIGRE Symposum on Power Plants & Power Systems Control 2000, Brussels, 2000, pp Paper submtted: December 5, 2010 Paper revsed: January 9, 2011 Paper accepted: March 16, 2011