Neuro-Fuzzy Control of Chemical Reactor with Disturbances

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1 Neuro-Fuzzy Control of Chemial Reator with Disturbanes LENK BLHOÁ, JÁN DORN Department of Information Engineering and Proess Control, Institute of Information Engineering, utomation and Mathematis Faulty of Chemial and Food Tehnology, Slova University of Tehnology in Bratislava Radlinsého 9, 8 37 Bratislava SLOK REPUBLIC lena.blahova@stuba.s, jan.dvoran@stuba.s bstrat: - This paper presents the ontrol design via the ombination of the neural preditive ontroller and the neurofuzzy ontroller. The neuro-fuzzy ontroller type of NFIS wors in parallel with the neural preditive ontroller and adjust the output of the preditive ontroller, in order to enhane predited inputs. The performane of our proposal is demonstrated on the Continuous Stirred-Tan Reator ontrol problem with disturbanes. Key-Words: - Neuro-fuzzy ontroller, intelligent ontrol, neural networ preditive ontroller, hemial reator Introdution The aim of proess ontrol is to ahieve the target value of given variable. This is mainly the tas of the properly designed ontroller. The ontroller should also provide some flexibility in the ase of unexpeted failure or hange of ondition, et. This paper desribes the above mentioned ombination of two methods of intelligent system ontrolling. By the parallel onnetion of preditive and neural-fuzzy ontroller, we aimed to obtain better results of the referene variable in terms of lowering its overshooting and reduing the ontrol time. The designed system with two onneted ontrollers was tested using the hemial reator in the noal state and in the perturbed state (disturbanes were in the input onentrate of substane, input temperature of reation mixture, input temperature of oolant and flow rate of reation mixture). The hemial reator introdues one of the omplex types of the hemial-tehnologial proess where full sailed ontrol without expressive overshooting is needed. Preditive Control MBPC (Model-Based Preditive Control) is a name of a several different ontrol tehniues []. ll are assoiated with the same idea. The predition is based on the model of the proess (Fig.). The ontroller uses a neural networ model to predit future plant responses to potential ontrol signals. n optimization algorithm then omputes the ontrol signals that optimize future plant performane. The neural networ plant model is trained offline, in bath form, using some of the training algorithms. Fig.. Model-based preditive ontrol sheme The ontroller, however, reuires a signifiant amount of online omputation, beause an optimization algorithm is performed at eah sample time to ompute the optimal ontrol input. The model preditive ontrol method is based on the reeding horizon tehniue. The neural networ model predits the plant response over a speified time horizon. The preditions are used by a numerial optimization program to detere the ontrol signal that imizes the following performane riteria over the speified horizon. N N u J(t,u())= (ym(t + i) yr(t + i)) + λ ( Δu(t + i )) () i= N i= where N, N and N u define the horizons over the traing error and the ontrol inrements are evaluated. The u variable is the tentative ontrol signal, y r is the desired response and y m is the networ model response. The λ value deteres the ontribution of the sum of suares of the ontrol inrements and the performane index. The ontroller onsists of the neural networ plant model and the optimization blo. The optimization blo deteres the values of u that imize J, and then the optimal u is input to the plant. ISSN: ISBN:

2 Euation () is used in ombination with input and output onstraints: u u u Δu y Δy Δu Δu y y Δy Δy () B C (3) 3 Neuro-fuzzy Controller The neural preditive ontroller an be extended with neuro-fuzzy ontroller, onneted in parallel (Fig.). Fig.4. Signifiation sheme of hemial reator Fig.. Neuro-fuzzy ontrol sheme Neuro-fuzzy systems, whih ombine neural networs and fuzzy logi, have reently gained a lot of interest in researh and appliation. speifi approah in neuro-fuzzy development is the NFIS (daptive Networ-based Fuzzy Inferene System) []. NFIS uses a feed forward networ to searh for fuzzy deision rules that perform well on a given tas. Using a given input-output data set, NFIS reates a Fuzzy Inferene System for whih membership funtion parameters are adjusted using a ombination of a ba propagation and least suare method. The NFIS arhiteture of the firstorder Taagi-Sugeno inferene system is shown in Fig.3. The simplified dynamial mathematial model of CSTR is: d = dt db = dt dc = dt dϑ = ϑv dt dϑ = dt ϑ v Bv Cv B C + + ρρ p [ ϑ ϑ ] ϑv ϑ + ρ p Qr + ρ p [ ϑ ϑ ] (4) (5) (6) (7) (8) The rate of reation is a strong funtion of temperature Ei = e Rϑ i i (9) Fig.3. System arhiteture NFIS 4 Experimental 4. CSTR Consider CSTR [3] with first-order irreversible parallel reation aording to the sheme (3). For reation heat gives: Q = Δ H + r ( ) ( Δ ) r r H (0) Temperature of reation mixture ϑ is ontrolled variable and volume flow rate of oolant is input variable. The proess state variables are molar onentration of, B and C (, B and C ) and temperatures of reation mixture ϑ and oolant ϑ. The model parameters are summarized in Table. ISSN: ISBN:

3 ariable Unit alue v mol m -3 4, vb mol m -3 0 vc mol m -3 0 Q m 3-0,05 ϑ v K 38 Ρ g m p J g - K - 4,0 m 3 0,3 v m 3-0,004 ϑ v K 98 ρ g m p J g - K - 4,8 m 3 0, m,5 K J - m - K - 4,8 E /R K 9850 ΔrH J mol - -8, ,55.0 E /R K 09 ΔrH J mol - -, , Table. Parameters of the hemial reator 4. Proess ontrol in the noal state Firstly, CSTR was simulated with neural preditive ontroller (NNPC). To set this ontroller neural networ proess model was needed. Neural networ model of CSTR was trained offline based on nonlinear proess input and output data by Levenberg-Maruardt ba propagation method. When optimization parameters were adjusted, CSTR was further ontrolled by NNPC ontroller. Seondly, CSTR was ontrolled with neuro-fuzzy ontroller (NFC) formed from neural preditive ontroller and NFIS ontroller. NFIS was trained by PID ontroller. PID parameters were designed by Smith- Murrill method in five training periods. NFIS have two inputs: set-point error e and derivation of set-point error de. Twelve membership funtion bell shape were hosen for NFIS input: seven for variable e and five for variable de (Fig.5). The neural preditive and the neuro-fuzzy ontroller were tested in MTLB/SIMULINK environment using neural networ toolbox and fuzzy logi toolbox. This experiment was designed to ompare a neural preditive ontroller with neuro-fuzzy ontroller performane while ontrolling a noal proess. Fig.5. Membership funtions for input variables e and de In Fig.6, set-point hanges of the desired temperature profile were traed with satisfatory results in both onsidered ases. However, it an be seen, that the ontrolled variable (ϑ) profiles exhibit differenes for both ontrollers ompared. The neuro-fuzzy ontroller had more fainting performane that the neural preditive ontroller. Fig.6. Comparison of NNPC and NFC performane for noal plant ISSN: ISBN:

4 4.3 Proess ontrol in the perturbed state Besides the good regulatory performane tested above, traing abilities of ontrollers proposed in the presene of disturbanes is of utmost importane. Disturbanes were applied during the ontrol urse and they were set as step hange of input onentration of substane ( v ), input temperature of reation mixture (ϑ v ), input temperature of oolant (ϑ v ) and flow rate of reation mixture (). Input onentration of substane ( v ) was hange in range ± 0% from the noal value. Input temperature of reation mixture (ϑ v ) was hange in range ± 8K from the noal value. Input temperature of oolant (ϑ v ) was hange in range ± 8K from the noal value. Flow rate of reation mixture was hange in range ± 5% from the noal value. omparison of the neural preditive ontroller and the neuro-fuzzy ontroller performane tested in the presene of proess parameter perturbation is demonstrate in Fig.7, 8 and 9 (the arrows are to show the time instants when disturbanes were applied). Fig.8. Comparison of NNPC and NFC performane for perturbed state step hange of ϑ v + 8K from the noal value, ϑ v 8K from the noal value and v - 0 % from the noal value Fig.7. Comparison of NNPC and NFC performane for perturbed state step hange of v + 0 % from the noal value, ϑ v 8K from the noal value and 5% from the noal value 5 Conlusion In this paper, we present intelligent ontrol system of a ontinuous stirred-tan reator. This intelligent ontrol system is omposed from two individual ontrollers: neural preditive ontroller and NFIS ontroller. The main goal of the resulting ontrol system was to enhane a profile of temperature of reation mixture in the CSTR by manipulating the volume flow rate of oolant. Experimental results obtained demonstrated the usefulness and robustness of the proposed ontrol system, and general advantages of the innovative tehniue in ontrol appliation. Fig.9. Comparison of NNPC and NFC performane for perturbed state step hange of v - 0 % from the noal value, + 5% from the noal value and ϑ v +8K from the noal value nowledgments The authors gratefully anowledge the ontribution of the Sientifi Grant geny of the Slova Republi under the grants /007/09, /0537/0 and the Slova Researh and Development geny under the projet P Referenes: []. asičaninová, M. Baošová,. Mészáros and J. Závaá. Model-based preditive ontrol of a hemial reator. In: 8 th International Congress of Chemial and Proess Engineering, Orgit s.r.o., Praha, Czeh Republi, (008). ISSN: ISBN:

5 [] M. gil, I. Kita,. Yano, and S. Nishiyama. nalysis and pridition of flow from loal soure in a river basin using a Neuro-fuzzy modeling tool. In: Jurnal of Enviromental Management, 85, 5 3, (007). [3] J. Mileš and M. Fiar. Proess Modelling, Identifiation and Control. New Yor: Springer, Berlin Heidelberg (007). ISSN: ISBN: