FUZZY CONTROL OF COMBUSTION WITH GENETIC LEARNING AUTOMATA

Transcription

1 FUZZY CTRL F CMBUSTI WITH GEETIC LEARIG AUTMATA Zoltán Hímer, Géza Dévény 2, Jen Kovács, Urpo Kortela Unversty of ulu, Systems Engneerng Laboratory, P.. Box 43, FI-94 Unversty of ulu, Fnland Fax: , emal: hm@paju.oulu.f 2 Techncal Unversty of Budapest, Department of Power Engneerng Egry József u. 8, Budapest, H- Hungary emal: dgeza@freemal.hu Abstract It s dffcult to acheve effectve control of tme varable and nonlnear plants such a fludzed bed boler. A method of desgnng a nonlnear fuzzy controller s presented. However, ts early applcaton reled on tral and error n selectng ether the fuzzy membershp functons or the fuzzy rules. Ths made t heavly dependent on expert knowledge, whch may not always avalable. Hence, an adaptve fuzzy logc controller such as Adaptve euro-fuzzy Inference System (AFIS) removes ths strngent requrement. Ths paper demonstrates the applcaton of AFIS a nonlnear Mult Input Sngle utput fuel feedng and combuston system and a fuzzy controller desgn for the system wth optmzaton wth Genetc Learnng Automata (GLA). An AFIS model has been developed to determne the exact amount of fuel fed to a combuston chamber. Ths property s mpossble to measure drectly, but t s requred for mprovng combuston control. The control of the combuston base on two Takag- Sugeno type controllers, whch were optmzed by GLA. The control system has been valdated on experment data obtaned n a case-study power plant. The results have shown that the system s able to capture the nonlnear feature of the fuel feedng system. Key words Combuston control, non-lnear systems, AFIS, Combuston control, Genetc Learnng Automata. Introducton In the last decade, the nterest of burnng multfuel has arsen n Fnland usng manly fludsaton technology. The multfuels are usually mxtures of dfferent bo fuels (peat, woodchps, sawdust, and bark) but n some case, coal and muncpal wastes are burned wth. The more ntensve use of multfuels can be explaned by: a) the ncreasng demand of usng domestc fuels (e.g. peat), b) the thermal utlsaton of the hgh calorc-value paper-ndustry by-products (wood chps, sawdust, and bark) whch would be waste and c) dvertng muncpal sold wastes from landfll. Besde the economcal and envronmental advantages, there are several dffcultes wth burnng bo fuels and muncpal wastes. The combuston of those fuels or fuel-mxtures has dfferent propertes compared to the conventonal fuels (coal, gas, and ol). Bo fuels and muncpal wastes are very nhomogeneous. The propertes (heat value, mosture content, homogenety, densty, mx ablty) may vary n a large range. It causes non-steady, agtated combuston condtons; even f steady fuel feed volume s mantaned, leadng to ncrease n the emsson level and varaton of the generated heat flow. Those property varatons are not predctable or drectly measurable, only ther effects on the combuston, on the steam generaton and on the power producton can be observed through the 2 content of the flue gas. Ths paper presents an AFIS system, whch determnes the amount of fuel fed to the combuston chamber. Combned wth a stochometrc model, t predcts the flue gas propertes, ncludng the 2 content. 2. Descrpton of the neuro-fuzzy controller Fuzzy Logc Controllers (FLC) has played an mportant role n the desgn and enhancement of a vast number of applcatons. The proper selecton of the number, the type and the parameter of the fuzzy membershp functons and rules s crucal for achevng the desred performance and n most stuatons, t s dffcult. Yet, t has been done n many applcatons through tral and error. Ths fact hghlghts the sgnfcance of tunng fuzzy system. Adaptve euro-fuzzy Inference Systems are fuzzy Sugeno models put n the framework of adaptve systems to facltate learnng and adaptaton []. Such framework makes FLC more systematc and less relyng on expert knowledge.[2],[3] To present the AFIS archtecture, let us consder two-fuzzy rules based on a frst order Sugeno model: Rule : f (x s A ) and (y s B ) then (k = p ) Rule 2: f (x s A 2 ) and (y s B 2 ) then (k 2 = p 2 )

2 ne possble AFIS archtecture to mplement these two rules s shown n Fg.. ote that a crcle ndcates a fxed node whereas a square ndcates an adaptve node (the parameters are changed durng tranng). In the followng presentaton L denotes the output of node n a layer L. Layer 3: odes n ths layer are also fxed nodes. These are labelled to ndcate that these perform a normalzaton of the frng strength from prevous layer. The output of each node n ths layer s gven by: w 3, w w w 2 =,2 (4) x A A 2 MM w w M MS f L ayer 4: The output of each node s smply constant: w 4, where k s desgn parameter k =,2 (5) y Fg. Construct of AFIS controller Layer : All the nodes n ths layer are adaptve nodes, s the degree of the membershp of the nput to the fuzzy membershp functon (MF) represented by the node:, A x y =, 2 = 3,4, B2 () A and B can be any approprate fuzzy sets n parameter form. For example, f bell MF s used then, B B 2 MM M w2 w2 Layer Layer 2 Layer 3 Layer 4 Layer 5 forwards x c a x 2 A b backwards =,2 (2) where a,b and c are the parameters for the MF. L ayer 2: The nodes n ths layer are fxed (not adaptve). These are labelled M to ndcate that they play the role of a smple multpler. The outputs of these nodes are gven by: x w 2, A B y =,2 (3) The output of each node s ths layer represents the frng strength of the rule. L ayer 5: Ths layer has only one node labelled S to ndcate that s performs the functon of a smple summer. The output of ths sngle node s gven by: wk,5 wk w =,2 (6) The AFIS archtecture s not unque. Some layers can be combned and stll produce the same output. In ths AFIS archtecture, there are two adaptve layers (, 4). Layer has three modfable parameters (a, b and c ) pertanng to the nput MFs [4]. These parameters are called premse parameters. Layer 4 has one modfable parameters (k,). That parameter called consequent parameter. 3. ptmzaton of the Fuzzy controller usng Genetc Learnng Automata Standard genetc or genetc searchng algorthms are used for numercal parameter optmzaton and are based on the prncples of evolutonary genetcs and the natural selecton process [5]. A general genetc algorthm contans, usually, the next three procedures: selecton, crossover and mutaton. These procedures are responsble for the global search mnmzaton functon wthout testng all the solutons. Selecton corresponds to keepng the best members of the populaton to the next generaton to preserve the ndvdual wth good performance (elte ndvduals) n ftness functon. Crossover orgnates new members for the populaton, by a process of mxng genetc nformaton from both parents, dependng of the selected parents the growng of the ftness of the populaton s faster or lower. Among many other solutons, the parent selecton can be done wth the roulette method, by tournament, random and eltst [6]. Mutaton s a process by whch a percentage of the genes are selected n a random fashon and changed. The populaton of the bt strng chromosome s genetc algorthms s replaced by a correspondng strng of bnary-acton learnng probabltes. The value at the th poston of each member of the populaton defnes the probablty of the allele value n the

3 correspondng bt strng of beng at the poston. The probabltes are ntalzed to p ()=.5 for all, so there s equal probablty a or beng selected at each poston. The system therefore has a very hgh degree of randomness for the ntal generaton. A populaton of the bt strngs that drectly determnes the phenotype s generated stochastcally at each generaton by samplng the probablty dstrbuton of the populaton. The probabltes at each poston are regarded as the acton probabltes of a bnary-acton dscrete stochastc learnng automaton. The two actons of the learnng automata are generatng a and generatng a at the correspondng poston n the phenotype strng n each generaton. Snce there are two actons, only the probablty of one of the actons s requred. In ths paper we have defned the probabltes stored n the populaton as beng the probablty of selectng a. Probabltes are updated at each generaton on the wth the Lnear Reward/Penalty algorthm. [7] The probablty p s the probablty of a beng the acton generated at the th poston of the bt strng. Ths s updated at each generaton by the followng f the th poston s at generaton n n p nn p n p (7) f the th poston s at generaton n n p nn p n p (8) In the mplemented algorthm a populaton of 6 ndvduals, an eltsm of 6 ndvduals was used, the crossover of one ste splcng s performed and all the members are subjected to mutaton except the elte. The mutaton operator s a bnary mask generated randomly accordng to a selected rate that s superposed to the exstng bnary codfcaton of the populaton changng some of the bts.[8] Crossover s performed over half of the populaton, always ncludng the elte. The ndvduals are randomly selected wth equal opportunty to create the new populaton. Dynamc crossover and mutaton probablty rate was used n the GLA operaton, as they provde faster convergence when compared to constant probablty rate [9]. 4. Model of combuston The role of the combuston process s to produce the requred heat energy for steam generaton at the possble hghest combuston effcency. The effcency depends on the completeness of burnng and the waste heat taken away n the flue gas by the excess ar flow. The hgher the burnng rate and smaller the waste heat s the hgher effcency. However, excess ar s requred for ensurng complete burnng. The 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 2 content around 3-5 % []. In mult-fuel fred fludsed bed power plants (see Fg. 2), t s a dffcult task due to the nhomogeneous propertes of the fuel. where s the learnng rate parameter and (n) s generated by adjustng the raw ftness n the current generaton. The value of (n) for j th strng at generaton n s gven by j n f mn f f j ( n) mn f max (9) Here s mn(f) and max(f) refer to the mnmum and maxmum raw ftness n the current populaton and f j (n)s the raw ftness of the j th strng. The ftness functon n our case s ) ( y yˆ ) ( y yˆ f j ( n) m* Comb Comb 2 2 () Fg. 2 Fludzed bed power plant The combuston model, utlsng the AFIS structure based on [], calculates the combuston power (P comb ) and flue gas components (C f ), ncludng the oxygen content, from the fuel screw Q Hz, sgnal prmary arflow F p, secondary arflow F s. (see Fg. 3) where the m s a weghtng factor. In our case m=2 to emphasze the mportance of oxygen content whch s drectly related to the flue gas emssons.

4 P comb Fuzzy Fuel and Prmary ar controllers Q Hz F p F s AFIS fuel flow model and Stochometrc combuston and flue gas model C f P comb Degree of membershp Low Mddle Hgh Fuel flow dsturbance Pcombuston Fg. 5 Membershp functon of the Combuston power error Fg. 3 Control system of combuston process. The outputs MFs of the controllers are constants, whch mean n our case sx parameters. The fuel and prmary ar fuzzy controller (see Fg.3) conssts of two parallel Fuzzy controllers. The error sgnal form the oxygen content drves the fuzzy controller of the prmary arflow, whle combuston power s controlled by the flue screw sgnal. 5. Expermental results The reference sgnals for the fuel screw Q Hz, prmary arflow F p and secondary arflow F s sgnals are calculated by the lnearzaton model as a functon of the reference of the combuston power such as: KP.829 Q F F Hz P S.2663Pcomb Pcomb P 4.49 comb () The error sgnal for the controllers dvde n three regon low, mddle and hgh. The membershp functons are show by fg. 4 and 5 The system was optmzed for a power level change and the fuel flow dsturbance. After 392 generaton the optmal parameter for the fuzzy controller was found. KP KP K K K Hgh Mddle Low Hgh Mddle Low The ftness functon result (2).8 hgh mddle low Best Average Poorest Degree of membershp Ftness xygen Fg. 4 Membershp functon of the oxygen error Generatons Fg. 6 Ftness functon by the generaton of the GLA

5 The model have lmtaton on each nputs, the combuston power change has also lmtaton. The set pont functon and the fuel flow dsturbance for the optmzaton were the follow: Tme [s] Set pont [MW] Fuel dsturb [kg] The result s compared by the self-tuned PI and a Genetc Algorthm tuned PI controller [], [3] PI PI wth GA Fuzzy GLA RMSE Comp. tme 32 hours 78 hours The table shows the mprovement of the control by the RMSE value, the drawback s the optmzaton tme. The optmzaton was runnng 78 hour on a Pentum 2.4 GHz computer. Combuston power [MW] ptmzaton of the Fuzzy controller Setpont utput Tme [s] Fg. 5 Fuzzy combuston power controller optmzaton wth GLA ptmzaton of the Fuzzy controller Setpont utput for the combuston power s taken from the measurement data. The smulaton shows that by applyng the new controller structure together wth the AFIS model, much smaller devaton n the oxygen content can be acheved whle satsfyng the same demand for combuston power. Combuston power [MW] Combuston power measurement sgnal Setpont utput Tme [s] Fg. 7 Combuston power response: comparson of the achevement n real process and n the smulated control system. xygen content [%] xygen content measurement sgnal Measurment utput Setpont = 4 % Tme [s] Fg. 8 xygen content response: comparson of the achevement n real process and n the smulated control system. 6. Concluson xygen content [%] In ths paper, AFIS neuro-fuzzy controller was studed va optmzaton by Genetc Learnng Automata. euro-fuzzy controller combnes the theory of artfcal neural networks and fuzzy systems. GLA provdng successful parameter optmzaton for the AFIS controller. The drawback of the method s the tme consumng computaton. Smulaton result revealed that neuro fuzzy model was capable of closely reproducng the optmal performance Tme [s] Fg. 6 Fuzzy xygen content controller optmzaton wth GLA In the followng, the performance of the new controller based on the AFIS model wll be compared to the performance of the real process. The reference sgnal

6 References [] R. Jang, C. Sun, E. Mzutan, euro-fuzzy and soft computaton (Prentce Hall, J,997) [2] Fahd. A. Alturk, Abel Ben Abdennour, eurofuzzy control of a steam boler turbne unt, Proceedng of the 999 IEEE, Internatonal Conference on Control Applcatons, Hawa, USA 999 pp 5-55 [3] E. Ikonen, K.ajm, Fuzzy neural networks and applcaton to the FBC process, IEE Proc.-Control Theory Appl. Vol. 43, May 996 pp [4] S. H. Km, Y. H. Km, K. B. Sm, H. T Jeon, n Developng an adaptve neural-fuzzy control system, Proc. IEEE/RSJ Conference on ntellgent robots and systems Yokohama, Japan, July 993 pp [5] J. H. Holland, Adaptaton n natural and Artfcal System, MIT Press, 992 [6] J.S.Yang & M.L. West, A Case Study of PID Contoller tunnng by Genetc Algorthm Proccedngs of IASTED Internatonal Conference on Modellng and Control, Innsbruck,2 [7] M.Howell Genetc Learnng Automata, Internal report Loughborough Unversty 2 [8] J. Vera, A. Mota, Water Gas Heater onlnear Physcal Model: prmazaton wth Genetc Algorthms Proccedngs of IASTED Internatonal Conference on Modellng Identfcaton and Control, Grndelwald, Swtzerland 24 [9] T. L. Seng, M. B. Khald, Tunnng of a euro-fuzzy Contoller By Genetc Algorthm IEEE Transacton on Systems, Man and Cybernetcs vol.29 no [] K. Leppäkosk & J. Kovács, Hybrd model of oxygen content n flue gas. Proc. IASTED Internatonal Conference on Appled Modellng and Smulaton, ov, 22, Cambrdge, MA, USA, pp [ ] Z. Hímer, V. Wertz, J. Kovács, U. Kortela eurofuzzy model of flue gas oxygen content Proccedngs of IASTED Internatonal Conference on Modellng Identfcaton and Control, Grndelwald, Swtzerland 24 [2] Z. Hímer, G. Dévény, J. Kovács, U. Kortela, Control of Combuston based on euro-fuzzy model Proccedngs of IASTED Internatonal Conference on Appled Smulaton and Modellng,Rhodos Greece 24 [3] H. Ghezelayagh, K.Y.Lee, Tranng euro-fuzzy boler dentfer wth Genetc Algorthm and error-backpropagaton, IEEE 999 AUTHR BIGRAPHY ZLTÁ HÍMER (M.Sc. 2 Budapest, Hungary) s a Ph.D. student snce 2 at the Systems Engneerng Laboratory, Unversty of ulu, Fnland. Hs research nterests nclude fuzzy-neuro modellng and fuzzy control, genetc algorthms, Controller optmsaton and ther applcaton to energy systems and power plant control problems. GÉZA DÉVÉYI (M.Sc. 2 Budapest, Hungary) s a Ph.D. student snce 22 at the Power Engneerng Department, Techncal Unversty of Budapest, Hungary. Hs research nterests nclude power plant atomzaton, fnte element calculaton, hghvoltage swtch gear desgn and ther applcaton to energy systems. JE KVÁCS (M.Sc. 99 Budapest, Hungary, Ph.D. 998 ulu, Fnland) s a senor assstant at the Systems Engneerng Laboratory, Unversty of ulu, Fnland. Hs research nterests nclude adaptve control, constraned control, advanced modellng and ther applcaton to energy systems and power plant control problems. URP KRTELA, born n Fnland, 945, s the head professor of the Systems Engneerng Laboratory, Unversty of ulu, Fnland. He graduated as M.Sc. n Techncal Physcs n 97 at the Unversty of ulu, Fnland. He receved the Lcentate of Technology n 973 at the Unversty of ulu and the Doctor of Technology n 98 at the Unversty of Helsnk, Fnland. Hs nterest les n the research n control engneerng and system theory: state and parameter estmaton and advanced control methods. The applcaton feld conssts of power plant modelng and control, control and fault dagnoss of pulp and paper processes, and feld bus technology.