Open Access Modeling and Optimization Control for Aircraft AC Generator Brushless Excitation System Based on Improved Adaptive PSO

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1 Send Orders for Reprins o reprins@benhamscience.ae The Open Auomaion and Conrol Sysems Journal, 2015, 7, Open Access Modeling and Opimizaion Conrol for Aircraf AC Generaor Brushless Exciaion Sysem Based on Improved Adapive PSO Ruofa Cheng*, Wenlong Zhao, Hongfeng Deng and Xiaozhou Jiang School of Informaion Engineering, Nanchang Hangkong Universiy, Nanchang, , China Absrac: The brushless exciaion sysem of aircraf AC generaor is a srong coupled and nonlineariy dynamic sysem which is ofen being subjeced o surbances. Therefore, he convenional PID conroller is unable o mee he brushless exciaion sysem conrol requiremens of More Elecric Aircraf (MEA) or All Elecric Aircraf (AEA). A new brushless exciaion compound conrol conroller (RBFPID) is proposed in his paper based on racal basis funcion (RBF) neural neworks and he convenional PID conrol. Because he new brushless exciaion compound conroller (RBFPID) has a number of muually coupled parameers ha needs o be se, he improved adapive paricle swarm opimizaion (APSO) algorihm is used o opimize muually coupled PID parameers Kp, Ki, Kd and RBF parameers!,!, m, n on line. In order o validae performances of he new brushless exciaion compound conroller based on muli-parameer opimizaion by he improved APSO, he simulaion model of he aircraf brushless exciaion sysem is implemened in MATLAB/SIMULINK accorng o fferenial equaions of each componen of brushless exciaion sysem. The simulaion resuls show ha he opimized adapive compound exciaion conroller (APSORBFPID) exhibis quick response speed, shor adjusmen ime and high seady sae accuracy. Keywords: Aircraf generaor, brushless exciaion sysem, modeling and opimizion conrol, PSO, RBF neural nework. 1. INTRODUCTION Wih he rapid developmen of More Elecric Aircraf (MEA) and All Elecric Aircraf (AEA) echnology, he srucure and conrol funcion of aircraf elecrical sysem has become much more complex. The brushless exciaion conrol sysem is a criical componen of he aircraf elecric power sysem, and is performance recly affecs he whole aircraf power sysem sabiliy and reliabiliy. Thus i is very imporan and necessary o design a sable and reliable exciaion conroller for aircraf AC generaor. The raional Proporional Inegral Derivaive (PID) conroller has been widely applied o he exciaion conrol of synchronous generaor [1, 2], because i has he advanages of simple srucure, good robusness, easy o implemen, no seady sae error. However, i is hard o build he accurae mahemaical model for complex MEA/AEA exciaion conrol sysem due o he challenge of nonlineariy, muli-variable, srong coupling and ime-varying. Therefore, i is fficul o obain saisfacory conrol effeciveness in complex MEA/AEA power sysem by using he raional PID conrol sraegy based on mahemaical model. In recen years, many scholars have sued some new exciaion conrol sraegies and parameer opimizaion for complex power sysem, such as fuzzy conrol [3], geneic algorihm (GA) [4], paricle swarm opimizaion (PSO) [5]. Bu fuzzy conrol effeciveness depends largely on membership funcion and *Address corresponng o his auhor a School of Informaion Engineering, Nanchang Hangkong Universiy, Nanchang, Jiangxi, , China; Tel: ; cjbyong@126.com fuzzy rules; Geneic algorihm or paricle swarm opimizaion is prone o local opimum, premaure convergence. Neural nework echnology has made grea progress in recen years and has been widely applied in conrol field, especially racal basis funcion (RBF) [6, 7], which is a neural nework based on local learning. RBF neural nework has many aracive characers such as adapabiliy, nonlinear approximaion abiliy, easy o realize and so on. I is more suiable for nonlinear real-ime complex conrol sysem. RBF and PID compound conrollers have he characerisics of high precision, good real-ime and robusness, bu oo many parameers need o be adjused in conrol process. I is fficul o une because of coupling among he parameers. If improper selecion of parameers will obain bad conrol effeciveness, and even cause he sysem o be unsable. The lieraure [8] demonsraed ha fixed gain PI conroller can achieve locally finie sabiliy when he sysem has RBF esimaion bias or random surbance. The lieraure [9] uses IPSO for PID conroller opimal design. The GA is used for PID conroller opimizaion in lieraure [10]. The lieraure [11] has pu forward a hierarchical learning rae facor, which is inroduced ino RBF learning. The above lieraures obained some good resuls, bu hey d no consider he coupling and coornaive opimizaion of fferen conrol parameers among RBF and PID. In order o overcoming he afore menioned shorcomings, an innovaive muliparameer coornaive opimizaion scheme for PID and RBF compound exciaion conrol is proposed in his paper, which is based on adapive paricle swarm opimizaion algorihm. This paper is organized as follows. Brushless exciaion sysem model for aircraf AC generaor is esablished in Sec / Benham Open

2 22 The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 Cheng e al. Fig. (1). PID and RBF adapive conroller based on PSO. ion 2. In Secion 3, he new RBF and PID compound exciaion conroller is designed based on APSO muli-parameer opimizaion. Then simulaion experimen and resul are demonsraed in Secion 4. Finally, he paper is concluded in Secion EXCITATION SYSTEMN MODEL 2.1. Aircraf Generaor Brushless Exciaion Sysem A presen, hree-sage AC synchronous generaor brushless exciaion sysem is used in large and meum-sized aircraf, which includes he auxiliary excier, main AC excier and main generaor [12]. The main generaor is a roaing magneic pole synchronous generaor. The main generaor field curren is provided by he oupu of he roaing recifier, which is se in he same roaing spindle wih roaing armaure of he AC excier. The auxiliary excier is a permanen magne synchronous moor (PMSM) ha is a roaing magneic pole synchronous generaor. The srucure of hreesage aircraf AC generaor brushless exciaion sysem is shown in Fig. (1). The main excier and exciaion conroller are provided wih DC power supply, which is he recificaion oupu volage of permanen magne synchronous generaor. The exciaion conroller adjuss main AC excier exciaion curren wih some conrol algorihm. Therefore, he main generaor erminal volage is conrolled inrecly. This paper focuses on he conrol opimizaion algorihm for aircraf AC generaor brushless exciaion sysem, so he permanen magne synchronous generaor (auxiliary excier) and is recifier are replaced by DC power supply [13] Main Synchronous Generaor Model The aircraf main generaor of hree-sage brushless AC exciaion sysem is a wound roor salien pole synchronous generaor wih damper winngs. Accorng o adoping he generaor convenion, he volage equaions of each phase winngs of he saor, roor and he flux linkage equaions in ABC frame are acquired wihou considering he synchronous generaor sauraion, hyseresis and oher facors. The model of main synchronous generaor in dq0 frame is esablished as follows hrough he Park's ransformaion [14]. # u dm =!R s i dm + L q " em i qm! M sq " em i Q! L dm d + M f sf + M D sd u qm =!R s i qm! L d " em i dm + M sf " em i f! L qm q + M sd " em i D + M Q $ sq v f = R f i f! M dm sf + L f f + M D fd 0 = R D i D! M dm sd + L D D + M f fd 0 = R Q i Q! M qm sq + L Q Q & Where, u, i, R, L, M are volage, curren, resisance, self-inducance, muual inducance of he main generaor in dq0 frame, respecively; The subscrip symbol s denoes he main generaor saor winngs; dm, qm denoe he rec and quadraure axis of saor winngs, respecively; Subscrip symbol f denoes he exciaion winngs; D, Q denoe he rec and quadraure axis of he exciaion winngs, respecively Main Excier Model The main excier is a salien pole synchronous generaor ha does no have wo damper winngs in d-q axis as compared o he main synchronous generaor. Accorng o adoping he generaor convenion, he model in dq0 frame of main excier is esablished as follows: (1)

3 Modeling and Opimizaion Conrol The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 23 # u de =!R se i de + L qe " ee i qe! L de de + M ex se u qe =!R se i qe! L de " ee i de + M se " ee i ex! L qe $ qe u ex = R ex i ex! M de se + L ex ex & Where, u, i, R, L, M denoe volage, curren, resisance, self inducance, muual inducance of he main excier in dq0 frame, respecively; Subscrip symbols se, ex denoe he main excier saor winngs, exciaion winngs, respecively; de, qe denoe he rec and quadraure axis of he saor winngs, respecively. 3. DESIGN OF ADAPTIVE CONTTOLLER BASED ON MULTI-PARAMETER OPTIMIZATION 3.1. Improved Adapive Paricle Swarm Opimizaion Algorihm Paricle swarm opimizaion (PSO) is he sochasic opimizaion algorihm based on bionic swarm inelligence which was proposed by Kennedy and Eberhar in The soluion space of he problem is analogous o a flock of birds foraging over cerain areas, and each bird is modeled as a paricle wihou mass or volume. Each paricle represens a candae soluion o he problem wih is own posiion and velociy. PSO can rapidly find he soluion of he problem hrough he muual cooperaion among he bionic swarm inelligence paricles. PSO is very suiable for solving nonlinear opimizaion problem in high-mensional space, because i has an inheren parallel compuaional srucure, and i does no require he derivaive of he objec funcion. PSO is preferred o oher opimizaion algorihms for i has rapid convergence speed, easy implemenaion and fewer parameers o be adjused. In PSO, a swarm of paricles are represened as poenial soluions, and each paricle i is associaed wih he velociy vecor V i = [v i,1,v i,2,!v i,d ] and he posiion vecor X i = [x i,1,x i,2,!x i,d ], where d denoes he mension of he soluion space. The velociy and he posiion of each paricle are iniialized by random vecors wihin he corresponng ranges. During he evoluionary process, he velociy and posiion of he i paricle on jh mension are updaed as: v i, j ( +1) =!v i, j () + c 1 r 1 [ p i, j! x i, j ()] + c 2 r 2 [ p g, j! x i, j ()] (3) x i, j ( +1) = x i, j () + v i, j ( +1) j = 1,2,...,d (4) (2) Where, ω is he ineria weigh; c 1, c 2 denoe posiive acceleraion coefficiens, r 1 r 2![0,1] are random numbers; d denoes he mension of he soluion space; In order o preven he opimal soluion ou of he opimizaion range, he general assumpion is v![v min v max ], x![x min x max ]. The ineria weigh (! ) of PSO is an imporan parameer ha influences he convergence speed of PSO algorihm and decides he paricle global search abiliy. Therefore, he proper selecion of! is crucial o he opimizaion qualiy of he PSO algorihm. The consan beween [0.2, 1.2] or a linearly decreasing weigh! is adoped in many lieraures.! =! max " (! max "! min ) # g / G max (5) However, he PSO algorihm is used in a nonlinear dynamic process o search soluion space in his paper. Therefore, he adapive ineria weigh is adoped, so ha i is only relaed o curren paricle objecive funcion value. $! =! + (! "! )(J " J ) max min min & J # J min J avg " J avg min & '! max J > J avg (6) Where,! max and! min are he maximum and minimum ineria weigh, respecively; J is he curren paricle objecive funcion value; J avg and J min are average and minimum objecive funcion values of all paricles, respecively. The adapive weigh is inroduced ino PSO algorihm, which can produce good global search abiliy, improve he effeciveness of rapid algorihm. Meanwhile, he opimal preservaion sraegy is adoped o ensure he algorihm converging quickly. During he process of opimizaions, he wors invidual in he curren populaion is replaced by he bes invidual so far Design of RBFPID Conroller Based on Muliparameer Opimizaion The Raal Basis Funcion (RBF) neural nework is a kind of local approximaion of he neural neworks. I is more suiable for nonlinear real-ime complex conrol sysem. Considering he nonlineariy, srong coupling and imevarying characers of brushless exciaion conrol sysem of aircraf AC generaor, i is fficul for raional Proporional Inegral Derivaive (PID) conrol o ge good conrol performance. A compound exciaion conrol sraegy based on RBF and PID is designed in his secion. To overcome he problem ha he parameers of PID and RBF compound conroller are fficul o be se, a new kind of muli-parameer adapive opimizaion scheme is pu forward based on adapive paricle swarm opimizaion (APSO) algorihm. The srucure of RBFPID adapive exciaion conroller is as shown in Fig. (2). As you can see in Fig. (2), PID acs as a feedback conroller which can suppress he inerference and ensure he

4 24 The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 Cheng e al. Fig. (2). PID and RBF adapive conroller based on PSO. sabiliy of he conrol sysem. RBF neural nework is a feedforward conroller which can improve sysem response speed. The improved adapive paricle swarm algorihm is used o opimize muliple and muual coupling conrol parameers of he compound RBFPID exciaion conroller, inclung learning rae (! ), ineria weigh (! ), cener vecor ( m ), Gauss funcion wih ( n ) of RBF neural nework, and he proporional coefficien ( Kp ), inegral coefficien ( Ki ), fferenial coefficien ( Kd ) of PID. Adapive muliparameer opimizaion enhances he conrol sysem dynamic sabiliy, self-adapive operaion. The compound conroller of RBFPID can adap well o he change of conrol sysem conions and uncerain facors, so as o improve he conrol qualiy of he exciaion sysem. In conrol sage, he adapive exciaion conroller of RBFPID real-ime deecs he oupu volage of main generaor, and calculaes and changes he conrol signal U c (k) (proporional o he duy raio of PWM) accorng o he volage error. The enlarged PWM signal conrols he exciaion curren of main generaor, and regulaes generaor oupu volage. The conrol oupu of RBF neural nework is expressed as follows. 2 h j = exp[! x(k)! c j ] j = 1,2,...p (7) 2 2" j n U n (k) = "! j h j j = 1,2,...p (8) j=1 Where, x is p mension of inpu vecor, x!r n. c j is he jh cenral poin of he raal basis funcion;! j is he firs of neurons in he hidden layer raal basis funcion wih; The oal oupu U c (k) of he compound conroller is he sum of he RBF conroller oupu U n (k) and PID conroller oupu U p (k) which are opimized by APSO. U c (k) = U n (k) +U p (k) (9) A he end of each conrol cycle, he conrol sysem eners he learning sage, in which connec weighs are adjused accorng o he sysem error. The weighs adjusmen formula of RBF nework is as follows: E(k) = 1 2 (u c (k)! u n (k))2 (10)!"(k) = #$ E(k) " j (k) = $(u (k) # u (k))h (k) (11) n c j!(k) =!(k "1) + #!(k) + $(!(k) "!(k "1)) (12) Where η is he learning rae of RBF neural nework, E(k) is racking error of he conrol sysem, he purpose of learning minimizes he sysem error E(k) Algorihm Implemenaion Seps Assume P represens he h generaion of he popula- ion. Bes is he bes invidual among P 0, P 1,..., P ; LBes is he bes invidual in P. The flow char of muliparameer opimizaion based on APSO is as shown in Fig. (3). STEP 1: Accorng o he general experience, he ranges [min,max] of seven opimized parameers are o be deermined. Oher parameers such as he number of maximum ieraion G max, populaion size N are o be se in he same ime;

5 Modeling and Opimizaion Conrol The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 25 STEP 3: Each invidual is decoded ino he corresponng conrol parameers. The resul of sysem error e() is obained under he conrol of each se of decoded parameers; STEP 4: Accorng o he formula (14), he value J of he cos funcion is calculaed for each invidual, he finess value is defined as 1/J. If e()! 0, he cos funcion J is defined as he formula (15). ( ) 2 J =! w 1 e # & (14) 0 " $! J = " (w 1 e() 2 + w 2 e() ) (15) 0 Where, e() is he sysem error; w 1, w 2 are he weighs value, and, e ( ) = y( ) y( 1), y() is he sysem oupu; he formula (15) is a penaly funcion which is used o avoid an overshoo; STEP 5: Accorng o he finess value of each invidual, he bes and wors inviduals are seleced and saved o LBes and LWors, respecively; STEP 6: Bes and LBes are compared, if LBes!Bes, hen Bes! LBes and LWors! Bes STEP 7: Adjus he adapive conrol parameers of PSO algorihm accorng o he formula (5) or formula (6); STEP 8: Updae paricle velociy and posiion accorng o he formula (3) and formula (4), respecively and obain +1 P ; STEP 9: Judging wheher he ieraions imes reaches he prese value G max or no. If so, end of program, else reurns o sep 3. STEP 10: The bes invidual Bes afer many generaions of evoluion is decoded as opimal conrol parameers. Fig. (3). Muli-parameer opimizaion based on APSO flow char. STEP 2: I randomly generaes N invidual paricles o form he iniial populaion P 0. Each of acual parameer is iniialized as formula (13). K = min+ (max! min) " rand (13) Where, rand!( 0,1) is a random number; he seven parameers form ( K p, K i, K d,!,!, m, n ) invidual; 4. SYSTEM SIMULATION ANALYSIS Accorng o he mahemaical model of main excier and main generaor in secion 2, he simplified exciaion sysem simulaion model of aircraf AC generaor is esablished in SIMULINK as shown in Fig. (4) (upper par), in which he auxiliary excier is replaced by DC volage source. The PID and RBF conroller model based on APSO muli-parameer opimizaion for brushless exciaion sysem of aircraf AC generaors is shown in Fig. (4) (lower par). RBF and PID conrollers are implemened hrough he wo MATLAB funcions, respecively. The sysem given volage U ref is 115V; U ou sands for he volage effecive value (RMS) of aircraf AC generaor hree-phase oupu volage; The simulaion parameers: T s = 1e! 5s, n N = rpm, U DC = 60V, p = 2. The ranges of adapive parameers are

6 26 The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 Cheng e al. Fig. (4). Brushless exciaion simulaion conrol model for aircraf generaor. Fig. (5). Exciaion simulaion sep response. m = [80 120], n = [0 10], Kp![50,650], Ki![0,10], Kd [0,30], η [0.0,0.5],! "[0.0,0.5], respecively Simulaion of Raising Volage From Zero The simulaion experimen of raising volage from zero is used o validae reliabiliy and rapiy of he proposed exciaion conrol scheme for aircraf AC generaor. The simulaion ime is 0.2s. Fig. (5) is he aircraf AC generaor erminal volage of raising volage from zero simulaion under he conrol of APSORBFPID., The simulaion resuls under he adapive PSOPID conroller (APSOPID) is also given in Fig. (6) for comparison. Compared Fig. (5) wih Fig. (6), i can be seen ha he proposed APSORBFPID conroller has he faser conrol speed han he APSOPID conroller a he same experimenal conions. The simulaion RMS volage curves of he raising volage from zero experimen are shown in Fig. (7) (he red curve represens he erminal RMS volage under he proposed algorihm of APSORBFPID, he green one is he erminal RMS volage under he APSOPID conroller, he doed line is he given volage 115V). As can be seen from he Fig. (7), he rise ime of he PSOPIDRBF conroller is shorened obviously, only 21.5ms. Meanwhile he rise ime of he PSOPID conroller is 31.8ms. The conrol accuracy of he former is higher han ha of he laer. The conrol parameers and conrol performance of wo exciaion conrollers are given in Table 1. From he Table 1, i can be seen ha he erminal volage error of aircraf AC generaor is only V under he conrol of APSORBFPID, and i is far less he error V under he conrol of APSOPID. I also can be seen from he Table 1, he overshoo of he sysem volage is only 0.17 under he conrol of APSORBFPID. Comparaive analysis incaes ha he GAPIDRBF conroller achieves beer performance.

7 Modeling and Opimizaion Conrol The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 27 Fig. (6). Exciaion simulaion sep response. Fig. (7). Exciaion simulaion sep response. Table 1. Comparison of he sep response resuls of wo exciaion conrollers. Conrol Parameers and Performance Parameers Conroller Kp Ki Kd!! m n J E (V) M Tr/ms APSOPID / / / / APSORBFPID Simulaion of Plus/Minus Load In order o validae ani-inerference capabiliy of he proposed exciaion conrol scheme, he 20 raed load is suddenly conneced o he sysem model a he ime 0.25s. A he ime 0.35s, he 20 raed load is suddenly sconneced o he sysem model. The AC volage curves are given in Fig. (8), Fig. (9) under he conrol of PID conroller and APSORBFPID conroller, respecively. In Fig. (8), when 20 raed load is suddenly added a ime 0.25s, he erminal AC volage experiences an obvious decrease. While 20 load is shaded a he ime 0.35s, he erminal AC volage increases quickly. Comparing wih Fig. (8), From Fig. (9), i can be seen ha he erminal AC volage change is very small under he conrol of APSORBFPID, wheher 20 raed load is suddenly conneced a he ime 0.25s, or sconneced a he ime 0.35s. The RMS volage curves are given in Fig. (10) under he conrol of wo conrollers. From Fig. (10), he proposed APSORBFPID conrol scheme no only has more rapid he response speed and also has higher conrol precision. The erminal volage error under he APSORBFPID conrol is smaller han ha of APSOPID. The oupu conrol signals of APSORBFPID and AP- SOPID conrollers are given in Fig. (11). From Fig. (11), he

8 28 The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 Cheng e al. Fig. (8). Oupu conrol signal under he model uncerain. Fig. (9). Oupu conrol signal under he model uncerain. Fig. (10). Oupu conrol signal under he model uncerain.

9 Modeling and Opimizaion Conrol The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 29 Fig. (11). Oupu volages under he model uncerain. conrol signal oupu of APSORBFPID conroller is always more quickly racking any change of he sysem load han ha of APSOPID conroller. CONCLUSION This paper presens an effecive muli-parameer opimizaion scheme o design a new RBF and PID exciaion conroller (APSORBFPID) for hree-sage aircraf AC generaor based on adapive paricle swarm opimizaion (APSO). The new conrol sraegy combines all advanages of adapive paricle swarm opimizaion, RBF neural nework and PID conroller. The simulaion resuls show he proposed compound APSORBFPID exciaion conroller for aircraf AC generaor has smaller volage error, shorer adjusing ime, and faser response han he convenional PID exciaion conroller. Meanwhile, he novel muli-parameer opimizaion based on APSO overcomes he problem ha muliple parameers are fficul o une because of muual coupling in convenional compound conroller. CONFLICT OF INTEREST The auhors confirm ha his aricle conen has no conflic of ineres. ACKNOWLEDGEMENTS This work was suppored by he Naional Naural Science Foundaion of China under Gran No and No , Naural Science Foundaion of Jiangxi Province under Gran No BAB201019, S&T Pillar Projec of Jiangxi Province under 20142BBE REFERENCES [1] L. Cheng, J. Zhang, Y. Sun, X. Guan, C. Wu, and W. Li, Closedloop opimum design mehod for PID conroller of exciaion sysem in large-scale power sysem, Power Sysem Technology, vol. 31, no. 3, pp , [2] A.P. Memon, M.A. Uqaili, Z.A. Memon and N.K. Tanwani, Suiable feed forward arificial neural nework auomaic volage regulaor for exciaion conrol sysem, Universal Journal of Elecrical and Elecronic Engineering, vol. 2, no. 2, pp , [3] H. Jie, J. Kang, and P. Li, Fuzzy PID conroller based on variable universe for exciaion sysem, Elecric Power Auomaion Equipmen, vol. 38, no. 2, pp , [4] L. Sun, H. Song, C. Gong and K. Ma, Disurbance signal for parameer idenificaion of exciaion sysem and accuracy analysis, Waer Resources and Power, vol. 31, no. 6, pp , [5] J. Zhao, and J. Chen, Design of he fuzzy neural PID conroller based on hybrid PSO, Journal of Xian Universiy, vol. 35, no. 1, pp , [6] L. Zhang, and Y. Bo, PID adapive conrol in he applicaion of he inducion moor sysem based on he RBF neural nework inverse, Journal of Applied Mechanics and Maerials Research, vol , no. 2014, pp [7] J. Zhang, G. Wen, Y. Wei, and G. Yin, RBF neural nework pid for bilaeral servo conrol sysem, Journal of TELKOMNIKA, vol. 11, no. 9, pp , [8] W. Nie, and Z. Wang, Design of rec orque conrol sysem of moor based on RBF neural nework supervision, Journal of Indusry and Mine Auomaion, vol. 39, no. 10, pp , [9] H. Fang, and Z. Shen, Opimal hydraulic urbogeneraors PID governor uning wih an improved paricle swarm opimizaion algorihm, Proceengs of he CSEE, vol. 25, no. 22, pp , [10] J. Liu, Advanced PID Conrol and MATLAB Simulaion, Elecronic Indusry Press, Beijing, [11] X. Zhang, and Y. Wang, Research on improved on-line learning algorihm of RBF neural nework, Journal of Changzhou Universiy (Naural Science Eion), vol. 26, no. 1, pp , [12] M. Gunes and N. Dogru, Fuzzy conrol of brushless exciaion sysem for seam urbogeneraors, IEEE Transacions On Energy Conversion, vol. 25, no. 3, pp , 2010.

10 30 The Open Auomaion and Conrol Sysems Journal, 2015, Volume 7 Cheng e al. [13] B. Liang, Y. Li, and M. Xue, Modeling and simulaion of hreesage aircraf synchronous generaor sysem, Journal of Compuer Simulaion, vol. 30, no. 10, pp , [14] A. Baraka, S. lim Tnani, G. Champenois, and E. Mouni. A new approach for synchronous generaor erminal volage conrol Comparison wih a sandard indusrial conroller. Elecric Power Sysems Research, vol. 81, no. 7, pp , Received: Sepember 16, 2014 Revised: December 23, 2014 Acceped: December 31, 2014 Cheng e al.; Licensee Benham Open. This is an open access aricle licensed under he erms of he Creaive Commons Aribuion Non-Commercial License (hp://creaivecommons.org/licenses/by-nc/4.0/) which permis unresriced, non-commercial use, sribuion and reproducion in any meum, provided he work is properly cied.