Rotor Stationary Control Analysis Based on Coupling KdV Equation Finite Steady Analysis Liu Dalong1,a, Xu Lijuan2,a

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1 204 Intrnational Confrnc on Computr Scinc and Elctronic Tchnology (ICCSET 204) Rotor Stationary Control Analysis Basd on Coupling KdV Equation Finit Stady Analysis Liu Dalong,a, Xu Lijuan2,a Dpartmnt of Mchanical and Elctrical and Information Enginring, Huali Collg of Guangdong Univrsity of Tchnology, Zngchng Guangdong 5325, China 2 Huashang Collg Guangdong Univrsity of Financ & Economics, Dpartmnt of Information Enginring, Guangdong Zngchng 5300, China a liudalongliudal@63.com Kywords: nonlinar; KdV quation; stability solution; control Abstract. In th turbin rotor baring systm, th stady control is ncssary, accurat mathmatical modl is stablishd to nsur th stabl opration of th nonlinar control systm. Th traditional control mthod uss fuzzy PID control algorithm, bcaus of th nonlinar coupling charactristics of control systm, rsulting in th fuzzy control ruls is difficult to guarant th stabl solution of quation. A rotor baring systm control mthod is proposd basd on nonlinar coupld KdV quations finit stady analysis. Th transfr function of rotor dlay coupling systm is stablishd, gain and phas margin tuning mthod of paramtrs is dsignd, two frdom dgr coupld nonlinar KdV controllr is constructd, finit stabl solutions of th KdV quation is obtaind. Th control algorithm is ralizd. Numrical simulation rsults show that th control modl has good control prcision, and it has good stability and suprior prformanc. Introduction Turbin baring systm is a ky componnt in larg rotating machinry, it has complx structur, and it works in high tmpratur and high spd nvironmnt, rquirmnts of turbin baring systm of control algorithm is xtrmly high, th control of two ordr control objct of th shaft vibration and shaft displacmnt componnts rquirs vry high. With th dvlopmnt of modrn industry, som complx control systms ar dvlopd, th accurat modl is obtaind[-3]. It has crtain difficultis to gt th stabl solution, and th traditional control mthod cannot achiv th stabl control. With th dvlopmnt of modrn control thory and mathmatical thory, th fuzzy control and nural ntwork control systm hav mad grat progrss, and gradually dvlop a lot of xprt control systm, th xprt systm is stablishd basd on xprt xprinc and th accumulation of yars of fild work practic, th controlld objct is takn with th structurd procssing, it can b dscribd as uncrtain prturbation dviation dgr systm, bcaus of th nonlinar coupling charactristics of control systm, rsulting in th fuzzy control ruls is difficult to guarant th stabl solution of quation. A rotor baring systm control mthod is proposd basd on nonlinar coupld KdV quations finit stady analysis. Th transfr function of rotor dlay coupling systm is stablishd, gain and phas margin tuning mthod of paramtrs is dsignd, two frdom dgr coupld nonlinar KdV controllr is constructd, finit stabl solutions of th KdV quation is obtaind. Th control algorithm is ralizd. Numrical simulation rsults show that th control modl has good control prcision, and it has good stability and suprior prformanc[4,5]. Nonlinar coupld KdV quations and control law dsign In this papr, th nonlinar coupld KdV quation is constructd, and th finit stability analysis of th rotor is takn, to improv th stady control prformanc of rotor. In th dsign of rotor control systm, th nonlinar coupld KdV quations is obtaind in finit stability, th algorithm is th cor of ralization of control systm, using intrnal modl control ida in th dsign of two 205. Th authors - Publishd by Atlantis Prss 3

2 dgr frdom PID controllr, a kind of two dgr frdom IMC-PID controllr is formd. A turbin rotor dlay coupling systm is stablishd, th systm transfr function is: 30s 27s G ( s) G ( s 2 = 7s + 8s + 25s 28s G ( s G ( s s + 9s + () Th intrnal modl control concpt is takn into considration, on th basis of gain and phas margin amplitud margin and phas margin) paramtrs tuning mthod, th two dgr frdom coupld nonlinar KdV controllr is dsignd, forming a two dgr frdom IMC-PID controllr, th controllr structur diagram is shown in Figur. d r Q () s - P(s) M(s) - y Q () s 2 Fig. Structur diagram of nonlinar coupling KdV controllr In th control systm shown in Figur, r is input vctor for turbin rotor controllr, y is th output of rotor controllr, d is th intrfrnc signal, it is assumd to b a group of Gauss whit nois signal in th systm. P(s) is a practical mathmatical modl of th controlld procss, th coupld nonlinar KdV quation is constructd: i= n ( Tmis+ ) λ2s + i= C() s =, C2() s = λs+ Km( λ2 + Lm) s (2) Th closd loop transfr function of th systm is dsignd, and th inrtia link indpndnt dlay l of th systm is procssd by Taylor approximation, th systm function is: Lm s ( λ2s+ Lm ) s Ys () = Rs () + Ds () ( λs+ ) ( λ2s+ ) (3) In th rotor stady control procss, powr gain of turbin rotor unstady control is K= KK m, K > 0, th condition that th systm rmains stabl is: λ2 0< K < + Lm (4) Th input data squnc is un ( ), output of discrt linar systm is xn ( ), thus th rotor stady control ADRC data trackr is constructd, its input and output rlation is: p m xn ( ) + axn i ( k) = bun r ( r) k= r= 0 (5) Th PID algorithm is usd for rotor stady control, fuzzy adaptiv KvD coupling mmbrship transfr function is obtaind: fh = fhan( x( k) v( k), x2( k), r, h0) x( k+ ) = x( k) + hx2( k) x2( k+ ) = x2( k) + hfh (6) In th formula, v is th input signal is input; x is th signal aftr procssing; x 2 is a drivativ of th input signal, h is th stp lngth, stp lngth is smallr, thn th nois is smallr, known lngth of rotor control input data squnc is N, th sampling tim intrval is T, th discrt rotor f f group of stat control fatur transform scal is N. Th fuzzy mmbrship infinit lngth fatur is xtractd, and th autocorrlation function is calculatd, dnotd as ra ( m ). With th ral rotor control charactristics of autocorrlation function, th following rlationship is dscribd: ra( m) = rx( m), m p (7) 32

3 p r ( m) = a r ( m k), m > p a k a k = (8) In th rotor stady control systm, in ordr to improv th systm xpansion ability, G0 and α0 ar th systm rspons and link charactristics of th initial dsign, and th actual charactristics of G systm is computd, th snsitivity function is dfind as: S G α () s = G G α α (9) Whr, G=G0+ΔG,α=α0+Δα,nonlinar coupld limitd stability is analyzd basd on KdV quation, th stat quation is obtaind basd on fuzzy mmbrship dgr calculation, and th fuzzy control rul is: = z y z = z2 b z 2 = z3 b2fal(,0.5, δ) z 3 = b3fal(,0.25, δ) + bu (0) In th formula, z, z z 2 is th first ordr drivativ stimation of th systm input, 3 is th nw variabl disturbanc to systm. b, b2, b3, δ,b ar th adjustabl paramtrs. Th fuzzy control ruls ar mbddd into th systm, it lays th foundation for th ralization of th systm. 2. Paramtr tuning of rotor unstady control dsign In th turbin control systm, according to th control modl of th coupld nonlinar KdV quation finit stability, w nd to stablish a prcis mathmatical modl for paramtr tuning, according to th turbin rotor control stady stat spac modl, th KdV control quation is obtaind: x f(, txu, ) = y = gtxu (,, ) () In th abov formula, t is control tim, x is th running stat of th rotor, u rprsnts th input paramtrs of th control modul, y is control modul output paramtrs, including: x= [ φθψ,,, PQRUVW,,,,,, X,, ] T Y Z (2) Rspctivly, thy ar rotor angl of roll angl, pitch angl, roll angl, roll angl, pitch angl rat, th rat of dviation angl rat, body coordinat axis vlocity componnt, vrtical displacmnt, latral displacmnt, hight; u = [ δ,,, ] T δa δr δt, th paramtrs ar turbin rotor angl, ailron dflctions, rotor unstady control cofficint. Th paramtric modl rlationship is shown in Figur 2. Im (, 0) θ M ϕ s G R Fig. 2 Constant control paramtr rlation modl On th basis of small prturbation thory, th motion modl of th rotor angl is: x = Ax + Bu y = Cx + Du (3) Th tim rror of fixd output signal control modul is: = P p g (4) 33

4 According to th abov formula, output signal P is convrtd into a tim rror compnsation signal, th tim rror is th stat variabl of th control systm, th nw stat modl of turbin control systm is: z = Az + Bµ (5) Whr: 0 Cc Dc z=, µ = ua, =, B= p 0 A c B c (6) Through th abov analysis, th limitd stability of th nonlinar coupld KdV quations analysis is obtaind, and th turbin rotor unstady control is ralizd. Control tst and simulation analysis Finally, through th control systm, th prformanc of th systm is tst, 2 ordr undrdampd control systm of turbin rotor is prsntd in this papr, th stady control systm is dsignd, th control ruls of fuzzy controllr is obtaind, and th r(t) is th stp signal, th output of th systm t is c(t), dviation is ( ) = rt ( ) ct ( ), phas rsistor is 3.234Ω, phas inductanc is mh, ratd spd is 2000r/min, polar logarithmic is 6, damping cofficint is Th initial stat of th systm is X = [ ] T, according to th abov paramtrs, control simulation xprimnt is takn, control curvs ar shown in Figur 3 basd on traditional mthod and nw mthod, th control prcision numrical analysis rsults ar shown in Tabl. From th figurs and th rsults in tabl, it shows that th nw mthod has bttr control accuracy, rotating angl of th turbin rotor and spd control accuracy ar improvd, it shows th supriority of th control mthod in this papr. Figur 3. Rotor rotation angl control comparison Tabl Control accuracy rsults of diffrnt algorithms Numbr of xprimnts (tim) Traditional control algorithm/% Nw control algorithm /% Conclusions In this papr, a rotor baring systm control mthod is proposd basd on nonlinar coupld KdV quations finit stady analysis. Th transfr function of rotor dlay coupling systm is stablishd, gain and phas margin tuning mthod of paramtrs is dsignd, two frdom dgr coupld nonlinar KdV controllr is constructd, finit stabl solutions of th KdVquation is obtaind. Th control algorithm is ralizd. Numrical simulation rsults show that th control modl has good control prcision, and it has good stability and suprior prformanc. 34

5 Acknowldgmnts In this papr, basd on th quality of ducation dpartmnt of guangdong provinc in 202, mchanical and lctrical projct comprhnsiv skills training cntr. Rfrncs [] Sshagiri S, Khalil H K. Robust output fdback rgulation of minimum-phas nonlinar systms using conditional intgrators[j]. Automatica, 2005, 4( ): [2] SHAN Dong-hong, ZHAO Wi-ting. Rsarch on Intrusion Dtction Systm Nural Ntworks and Principal Componnt Analysis[J]. Computr Simulation. 20; 28(6): [3] HUANG Kai- fng, ZHAO Tao. Application of Particl Swarm Optimization Clustring in Ntwork Scurity[J]. Computr Simulation. 202; 29(2): [4] LIU Kzhi. Wirlss Communication Bas Station Enrgy Aaving Rsarch Basd on Intllignt Frquncy Convrsion[J]. Bulltin of Scinc and Tchnology. 202; 28(8): [5] HE Binhui. Study on Application of Elvator for Th Gntic Algorithm in Th Prsnt Situation[J]. Bulltin of Scinc and Tchnolog, 202,4(28):