Neuro-Fuzzy DC Motor Speed Control Using Particle Swarm Optimization

Transcription

1 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA *, Abdellah LAOUFI, Brahm GASBAOUI, and Abdessalam ABDERRAHMANI Department of Electrcal Engneerng, Bechar Unversty, B.P 47 BECHAR (08000) Algera E-mals: * Correspondng author: elec_allaouabf@yahoo.fr Abstract Ths paper presents an applcaton of Adaptve Neuro-Fuzzy Inference System (ANFIS) control for DC motor speed optmzed wth swarm collectve ntellgence. Frst, the controller s desgned accordng to Fuzzy rules such that the systems are fundamentally robust. Secondly, an adaptve Neuro-Fuzzy controller of the DC motor speed s then desgned and smulated; the ANFIS has the advantage of expert knowledge of the Fuzzy nference system and the learnng capablty of neural networks. Fnally, the ANFIS s optmzed by Swarm Intellgence. Dgtal smulaton results demonstrate that the degned ANFIS-Swarm speed controller realze a good dynamc behavor of the DC motor, a perfect speed trackng wth no overshoot, gve better performance and hgh robustness than those obtaned by the ANFIS alone. Keywords DC Motor speed control; Neuro-Fuzzy controller; Swarm collectve ntellgence; ANFIS controller usng PSO.

2 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI Introducton In spte of the development of power electroncs resources, the drect current machne became more and more useful. Nowadays ther uses sn t lmted n the car applcatons (electrcs vehcle), n applcatons of weak power usng battery system (motor of toy) or for the electrc tracton n the mult-machne systems too. The speed of DC motor can be adjusted to a great extent as to provde controllablty easy and hgh performance [, ]. The controllers of the speed that are conceved for goal to control the speed of DC motor to execute one varety of tasks, s of several conventonal and numerc controller types, the controllers can be: PID Controller, Fuzzy Logc Controller; or the combnaton between them: Fuzzy-Neural Networks, Fuzzy-Genetc Algorthm, Fuzzy- Ants Colony, Fuzzy-Swarm. The Adaptve Neuro-Fuzzy Inference System (ANFIS), developed n the early 90s by Jang [3], combnes the concepts of fuzzy logc and neural networks to form a hybrd ntellgent system that enhances the ablty to automatcally learn and adapt. Hybrd systems have been used by researchers for modelng and predctons n varous engneerng systems. The basc dea behnd these neuro-adaptve learnng technques s to provde a method for the fuzzy modelng procedure to learn nformaton about a data set, n order to automatcally compute the membershp functon parameters that best allow the assocated FIS to track the gven nput/output data. The membershp functon parameters are tuned usng a combnaton of least squares estmaton and back-propagaton algorthm for membershp functon parameter estmaton. These parameters assocated wth the membershp functons wll change through the learnng process smlar to that of a neural network. Ther adjustment s facltated by a gradent vector, whch provdes a measure of how well the FIS s modelng the nput/output data for a gven set of parameters. Once the gradent vector s obtaned, any of several optmzaton routnes could be appled n order to adjust the parameters so as to reduce error between the actual and desred outputs. Ths allows the fuzzy system to learn from the data t s modelng. The approach has the advantage over the pure fuzzy paradgm that the need for the human operator to tune the system by adjustng the bounds of the membershp functons s removed. The PSO (partcle swarm optmzaton) algorthm used to get the optmal values and parameters of our ANFIS s based on a metaphor of socal nteracton. It searches a space by

3 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 adjustng the trajectores of ndvdual vectors, called partcles, as they are conceptualzed as movng as ponts n multdmensonal space. The ndvdual partcles are drawn stochastcally towards the postons of ther own prevous best performances and the best prevous performance of ther neghbors. Snce ts ncepton, two notable mprovements have been ntroduced on the ntal PSO whch attempt to strke a balance between two condtons. The frst one ntroduced by Sh and Eberhart [4] uses an extra nerta weght term whch s used to scale down the velocty of each partcle and ths term s typcally decreased lnearly throughout a run. The second verson ntroduced by Clerc and Kennedy [5] nvolves a constrcton factor n whch the entre rght sde of the formula s weghted by a coeffcent. Ther generalzed partcle swarm model allows an nfnte number of ways n whch the balance between exploraton and convergence can be controlled. The smplest of these s called PSO. Ths proposes an applcaton of ANFIS-Swarm. PSO algorthms are appled to search the globally optmal parameters of ANFIS controller. The best range and shapes of member shps functons obtaned wth ANFIS are adjusted agan usng PSO. Smulaton results are gven to show the effectveness of ANFIS-Swarm controller. Model of DC motor DC machnes are characterzed by ther versatlty. By means of varous combnatons of shunt-, seres-, and separately-excted feld wndngs they can be desgned to dsplay a wde varety of volt-ampere or speed-torque characterstcs for both dynamc and steady-state operaton. Because of the ease wth whch they can be controlled systems of DC machnes have been frequently used n many applcatons requrng a wde range of motor speeds and a precse output motor control [6, 7]. In ths paper, the separated exctaton DC motor model s chosen accordng to hs good electrcal and mechancal performances more than other DC motor models. The DC motor s drven by appled voltage. Fgure show the equvalent crcut of DC motor wth separate exctaton. The characterstc equatons of the DC motor are represented as: 3

4 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI d dt d dt d dt R ex ex =. ex. Vex L + ex L () ex R. L +.w. +. V Lndex Cr fc =. ex. nd + +. w r J J J (3) nd ndex nd = nd r ex nd L nd L nd L () nd w r Symbols, Desgnatons and Unts: Symbols Desgnatons Unts ex and end Exctaton current and Induced current. [A] w r Rotatonal speed of the DC Motor. [Rad/Sec] V ex andv nd Exctaton voltage and Induced voltage [Volt] R ex andr nd Exctaton Resstance and Induced Resstance. [Ω] L ex,l nd and Exctaton Inductance Induced Inductance and Mutual L ndex Inductance. [mh] J Moment of Inerta. [Kg.m ] Cr Couple resstng. [N.m] fc Coeffcent of Frcton. [N.m.Sec/Rad] From the state equatons (), (), (3) prevous, can construct the model wth the envronment MATLAB 7.4 (R007a) n Smulnk verson 6.6. The model of the DC motor n Smulnk s shown n Fgure. The varous parameters of the DC motor are shown n Table. Vnd /Lnd s Rnd Lndex /Lnd 40 Vex /Lex s Rex /Lex Wr s fc Lndex Cr /J Fgure. Model of the DC Motor n Smulnk 4

5 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 Table. Parameters of the DC Motor V ex =40[V] L nd =0.0[mH] V nd =40[V] L ndex =.8[mH] R ex =40[Ω] J =[Kg.m ] R nd =0.6[Ω] Cr =9.[N.m] Adaptve Neuro-Fuzzy MODE Speed Controller Adaptve Neuro-Fuzzy prncple A typcal archtecture of an ANFIS s shown n Fgure, n whch a crcle ndcates a fxed node, whereas a square ndcates an adaptve node. For smplcty, we consder two nputs x, y and one output z. Among many FIS models, the Sugeno fuzzy model s the most wdely appled one for ts hgh nterpretablty and computatonal effcency, and bult-n optmal and adaptve technques. For a frst order Sugeno fuzzy model, a common rule set wth two fuzzy f then rules can be expressed as: Rule : f x s A and y s B, then z = p x + q y + r (4) Rule : f x s A and y s B, then z = p x + q y + r where A and B are the fuzzy sets n the antecedent, and p, q and r are the desgn parameters that are determned durng the tranng process. As n Fgure, the ANFIS conssts of fve layers [8]: Fgure. Correspondng ANFIS Archtecture 5

6 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI Layer : Every node n the frst layer employ a node functon gven by: O = µ A (x), =, O = µ B= (y), = 3, 4 where µ A and µ B can adopt any fuzzy membershp functon (MF). (5) Layer : Every node n ths layer calculates the frng strength of a rule va multplcaton: O = w = µ (x ). µ ( y),, (6) A B = Layer 3: The -th node n ths layer calculates the rato of the -th rule s frng strength to the sum of al rules frng strengths: where w O w = w =,, (7) w + w 3 = s referred to as the normalzed frng strengths. Layer 4: In ths layer, every node has the followng functon: where w O 4 + = w z = w (p x + q y r ) =, (8) s the output of layer 3, and { p, q, r } s the parameter set. The parameters n ths layer are 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, whch s expressed as: O 5 = = w z = w z w + w z + w (9) The output z n Fg. 3 can be rewrtten as [9, 0]: x )p + (w y)q + (w )r + (w x )p + (w y)q (w ) r z = (w + (0) Adaptve Neuro-Fuzzy controller The ANFIS controller generates change n the reference voltage V ref, based on speed error e and dervate n the speed error de defned as: e = ω ref - ω () de = [d(ω ref - ω)]/dt () where ω ref and ω are the reference and the actual speeds, respectvely. 6

7 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 In ths study frst order Sugeno type fuzzy nference was used for ANFIS and the typcal fuzzy rule s: f e s A and de s B then z = f(e, de) (3) where A and B are fuzzy sets n the antecedent and z = f(e, de) s a crsp functon n the consequent. The sgnfcances of ANFIS structure are: Layer : Each adaptve node n ths layer generates the membershp grades for the nput vectors A, =,, 5. In ths paper, the node functon s a trangular membershp functon: 0, e a e a, a e b b a O = µ A (e ) = c e (4), b e c c b 0, c e Layer : The total number of rule s 5 n ths layer. Each node output represents the actvaton level of a rule: O = w = mn( µ (e), (e)), =,, 5 (5) A µ B Layer 3: Fxed node n ths layer calculate the rato of the -th rule's actvaton level to the total of all actvaton level: O 3 w = w = n w j = j Layer 4: Adaptve node n ths layer calculate the contrbuton of -th rule towards the overall output, wth the followng node functon: O 4 + (6) = w z = w (p e + q de r ) (7) Layer 5: The sngle fxed node n ths layer computes the overall output as the summaton of contrbuton from each rule: O 5 = = w z = w z w + w z + w (8) The parameters to be traned are a, b and c of the premse parameters and p, q, and r of the consequent parameters. Tranng algorthm requres a tranng set defned between 7

8 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI nputs and output [3]. Although, the nput and output pattern set have 50 rows. Fgure 3.a shows optmzed membershp functon for e and de after traned. Fgure 3.b shows Surface plot showng relatonshp between nput and output parameters after traned. Fgure 3.c shows The ANFIS model structure. Fgure 3.a. Membershp functons for e and de after traned output(u) nput(de) nput(e) Fgure 3.b. Surface plot showng relatonshp between nput and output parameters 8

9 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 Fgure 3.c. The ANFIS model structure The number of epochs was 00 for tranng. The number of MFs for the nput varables e and de s 5 and 5, respectvely. The number of rules s then 5 (5 5 = 5). The trangular MF s used for two nput varables. It s clear from (4) that the trangular MF s specfed by two parameters. Therefore, the ANFIS used here contans a total of 95 fttng parameters, of whch 0 (5 + 5 = 0) are the premse parameters and 75 (3 5 = 75) are the consequent parameters. The tranng and testng root mean square (RMS) errors obtaned from the ANFIS are and respectvely. Partcle Swarm Optmzaton (PSO) PSO s a populaton-based optmzaton method frst proposed by Eberhart and Colleagues [, ]. Some of the attractve features of PSO nclude the ease of mplementaton and the fact that no gradent nformaton s requred. It can be used to solve a wde array of dfferent optmzaton problems. Lke evolutonary algorthms, PSO technque conducts search usng a populaton of partcles, correspondng to ndvduals. Each partcle represents a canddate soluton to the problem at hand. In a PSO system, partcles change ther 9

10 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI postons by flyng around n a multdmensonal search space untl computatonal lmtatons are exceeded. Concept of modfcaton of a searchng pont by PSO s shown n Fgure 4. k V k X + k X k + V Gbest V Pbest V Pbest Gbest (X k : current poston, X k+ : modfed poston, V k : current velocty, V k+ : modfed velocty, V Pbest : velocty based on Pbest, V Gbest : velocty based on Gbest) Fgure 4. Concept of modfcaton of a searchng pont by PSO The PSO technque s an evolutonary computaton technque, but t dffers from other well-known evolutonary computaton algorthms such as the genetc algorthms. Although a populaton s used for searchng the search space, there are no operators nspred by the human DNA procedures appled on the populaton. Instead, n PSO, the populaton dynamcs smulates a brd flock s behavor, where socal sharng of nformaton takes place and ndvduals can proft from the dscoveres and prevous experence of all the other companons durng the search for food. Thus, each companon, called partcle, n the populaton, whch s called swarm, s assumed to fly over the search space n order to fnd promsng regons of the landscape. For example, n the mnmzaton case, such regons possess lower functon values than other, vsted prevously. In ths context, each partcle s treated as a pont n a d-dmensonal space, whch adjusts ts own flyng accordng to ts flyng experence as well as the flyng experence of other partcles (companons). In PSO, a partcle s defned as a movng pont n hyperspace. For each partcle, at the current tme step, a record s kept of the poston, velocty, and the best poston found n the search space so far. The assumpton s a basc concept of PSO []. In the PSO algorthm, nstead of usng evolutonary operators such as mutaton and crossover, to manpulate algorthms, for a d- varable optmzaton problem, a flock of partcles are put nto the d-dmensonal search space 0

11 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 wth randomly chosen veloctes and postons knowng ther best values so far (Pbest) and the poston n the d-dmensonal space. The velocty of each partcle, adjusted accordng to ts own flyng experence and the other partcle s flyng experence. For example, the -th partcle s represented as x = (x,,x,,, x,d ) n the d-dmensonal space. The best prevous poston of the -th partcle s recorded and represented as: Pbest = (Pbest,, Pbest,,..., Pbest,d) (9) The ndex of best partcle among all of the partcles n the group s gbest d. The velocty for partcle s represented as v = (v,,v,,, v,d ). The modfed velocty and poston of each partcle can be calculated usng the current velocty and the dstance from Pbest,d to gbest d as shown n the followng formulas [3]: v + ) ( t ) ( t ) ( t ) = w.v + c * rand () * (Pbest x ) + c * Rand () * (gbest x ) (0) ( t,m,m,m ( t + ) ( t ) ( t + ) x,m = x,m + v,m =,,,n; m=,,,d () where: n = Number of partcles n the group, d = dmenson, t = Ponter of teratons ( t ) mn max (generatons), v = Velocty of partcle I at teraton t, ( t ),m Vd v,d V w = Inerta weght d, ( t ) factor, c,c = Acceleraton constant, rand() = Random number between 0 and, x,d Current poston of partcle at teratons, Pbest = Best prevous poston of the -th partcle, gbest = Best partcle among all the partcles n the populaton.,m The evoluton procedure of PSO Algorthms s shown n Fg. 5. Producng ntal populatons s the frst step of PSO. The populaton s composed of the chromosomes that are real codes. The correspondng evaluaton of a populaton s called the ftness functon. It s the performance ndex of a populaton. The ftness value s bgger, and the performance s better. The ftness functon s defned as follow: m,m = PI = MIN _ offset e where PI s the ftness value, e s the speed error and MIN_offset s a constant. () After the ftness functon s calculated, the ftness value and the number of the generaton determne whether the evoluton procedure s stopped or not (Maxmum teraton number reached?). In the followng, calculate the Pbest of each partcle and gbest of populaton (the best movement of all partcles). The update the velocty, poston, gbest and pbest of partcles gve a new best poston (best chromosome n our proposton).

12 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI Start Generate Intal Populatons Calculate parameters of ANFIS Controller (member shp functons, Ke and Kde) Calculate the ftness functon Calculate the Pbest of each partcle and gbest of populaton Update the velocty, poston, gbest and pbest of partcles No Maxmum teraton number reached? Yes Stop Fgure 5. The evoluton procedure of PSO Algorthms Optmal ANFIS Controller Desgn To desgn the optmal ANFIS controller, the PSO algorthms are appled to fnd the globally optmal parameters of the ANFIS. The structure of the ANFIS controller wth PSO algorthms s shown n Fgure 6. In ths paper, the chromosomes of the PSO algorthms contans two parts: the range of the membershp functons (Ke and Kde) and the shape of the membershp functons (e~e5 and de~de5). It gves the optmal output voltage, such that the steady-state error of the response s zero. The genes n the chromosomes are defned as: [Ke, Kde, e, e, e3, e4, e5, de, de, de3, de4, de5] (3) Fgure 7 shows the membershp functons of the ANFIS controller wth PSO Algorthms. Table lsts the parameters of PSO algorthms used n ths paper.

13 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 PSO Algorthms Reference Speed + _ Ke Kde ANFIS DC Motor Output Speed Fgure 6. ANFIS wth PSO Algorthms structure Fgure 7. Membershp functon of ANFIS controller wth PSO Table : Parameters of PSO Populaton Sze 50 Number of Iteratons 00 w max 0.6 w mn 0. c = c.5 Mn-offset 00 Ke and Kde [ ~ 0.005] e [0 ~ 0.05] e [0 ~ 0.05] e3 [0.05 ~ 0.043] e4 [0.05 ~ 0.067] e5 [0.043 ~ 0.067] de [-0.06 ~ 0.04] de [-0.06 ~ 0.075] de3 [0.04 ~ ] de4 [0.075 ~ 0.084] de5 [ ~ 0.084] 3

14 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI Computer Smulaton Three dfferent controllers are desgned for the computer smulaton. Frst, the fuzzy logc controller s desgned based on the expert experence. Second, the fuzzy logc controller s desgned based on the neural networks to fnd the optmal range of the membershp functons (ANFIS). After that, the optmal fuzzy controller (ANFIS) s desgned based on the PSO to search the optmal range of the membershp functons, the optmal shape of the membershp functons (ANFIS wth PSO). After the prmtve smulaton process, the optmal values of Ke and Kde n ANFIS are calculated as and 0.005, respectvely. The best chromosomes n ANFIS wth PSO are pursued as: [ , , , 0.040, 0.035, , , , , , , ] (4) The optmal membershp functons ANFIS wth PSO are shown n Fgure 8. Let the command sgnal be a step for the speed of the DC motor at 7.93 Rad/Sec. The smulaton results are obtaned for 0.0 second range tme. The speed response of FLC (Fuzzy Logc Controller) s shown n Fg 9. The speed response of FLC usng neural networks (ANFIS) s shown n Fg 0. The speed response of the optmal ANFIS controller usng PSO s shown n Fg. The performances of three controllers are lsted n Table 3. Accordng to our MATLAB model smulaton, we llustrate that the steady state error equal zero n one case: ANFIS controller wth PSO (ANFIS-Swarm); the overtakng value s zero n the three cases that means the FLC used s robust. The rsng tme of DC motor speed step s less mportant n FLC usng neural networks (ANFIS) compared wth FLC alone and t s have the mnmal value n The ANFIS controller wth PSO (ANFIS-Swarm). In the present work, the ntellgent controller based on ANFIS-Swarm optmzaton gve a good agreement wth the step reference speed. In the Adaptve Neuro-Fuzzy (ANFIS) DC motor control, the optmzaton of membershp functons became very necessary, t s mportant shown n the mnmal rsng tme of speed response, so the membershp functons are adjusted n optmal values to gve a steady state error speed value equal zero. The computer MATLAB smulaton demonstrate that the ANFIS controller assocated to the Swarm ntellgence approach became very strong, t gves a very good results and possesses good robustness. 4

15 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 Fgure 8. The optmal membershp functons ANFIS wth PSO Speed Wr [Sec] Tme [Sec] Fgure 9. The speed response of Fuzzy Logc Controller 5

16 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI 40 0 Speed Wr [Rad/Sec] Tme [Sec] Fgure 0. The speed response of FLC usng neural networks (ANFIS) Table 3. Performances of three controllers Results Fuzzy Logc FLC usng neural Controller(FLC) networks (ANFIS) Rsng tme [Sec] Overtakng [%] Steady state error[%] ANFIS controller wth PSO (ANFIS-Swarm) Conclusons In ths paper, the optmal ANFIS controller s desgned usng Partcle Swarm Optmzaton algorthms. The speed of a DC Motor drve s controlled by means of three dfferent controllers. Accordng to the results of the computer smulaton, the Adaptve Neuro- Fuzzy (ANFIS) controller effcently s better than the tradtonal FLC. The ANFIS-Swarm s the best controller whch presented satsfactory performances and possesses good robustness (no overshoot, mnmal rse tme, Steady state error = 0). The major drawback of the fuzzy controller presents an nsuffcent analytcal technque desgn (choce of the rules, the membershp functons and the scalng factors). That we chose wth the use of the Neural Networks and Partcle Swarm Optmzaton for the optmzaton of ths controller n order to control DC motor speed. Fnally, the proposed controller (ANFIS-Swarm Controller) gves a very good results and possesses good robustness. 6

17 Leonardo Electronc Journal of Practces and Technologes ISSN Issue 5, July-December 009 p. -8 References. Hénao H., Capolno G. A. Méthodologe et applcaton du dagnostc pour les systèmes électrques. Artcle nvté dans Revue de l'electrcté et de l'electronque (REE), (Text n French) 00, 6, p Raghavan S. Dgtal control for speed and poston of a DC motor. MS Thess, Texas A&M Unversty, Kngsvlle, Jang J. S. R. Adaptve network based fuzzy nference systems. IEEE Transactons on systems man and cybernetcs 993, p Sh Y., Eberhart R. A modfed partcle swarm optmzer. Proc. 998 Int. Conf. on Evolutonary Computaton The IEEE World Congress on Computatonal Intellgence, Anchorage 998, p Clerc M., Kennedy J. The partcle swarm-exploson, stablty, and convergence n a multdmensonal complex space. IEEE Trans. Evolutonary Computaton 00, 6, p Halla A. Étude des machnes à courant contnu. MS Thess, Unversty of LAVAL, (Text n French), May Capolno G. A., Crrncone G., Crrncone M., Henao H., Grsel R. Dgtal sgnal processng for electrcal machnes. Invted paper, Proceedngs of ACEMP'0 (Aegan Internatonal Conference on Electrcal Machnes and Power Electroncs), Kusadas (Turkey), 00, pp Ln C. T., Lee C. S. G. Neural fuzzy systems: A neuro-fuzzy synergsm to ntellgent systems. Upper Saddle Rver, Prentce-Hall, Constantn V. A. Fuzzy logc and neuro-fuzzy applcatons explaned. Englewood Clffs, Prentce-Hall, Km J., Kasabov N. Hy FIS, Adaptve neuro-fuzzy nference systems and ther applcaton to nonlnear dynamcal systems. Neural Networks, Kennedy J., Eberhart R. Partcle swarm optmzaton. Proc. IEEE Int. Conf. on Neural Network 995, 4, p Yoshda H., Kawata K., Fukuyama Y., Takayama S., Nakansh Y.. A partcle swarm optmzaton for reactve power and voltage control consderng voltage securty assessment. IEEE Trans. on Power Systems 000, 5(4), p

18 Neuro-Fuzzy DC Motor Speed Control Usng Partcle Swarm Optmzaton Boumedene ALLAOUA, Abdellah LAOUFI, Brahm GASBAOUI and Abdessalam ABDERRAHMANI 3. Gang Z. L. A partcle swarm optmzaton approach for optmum desgn of PID controller n AVR system. IEEE Trans. Energy Converson 004, 9, p