Rotor Flux Estimation of Induction Motors Using Sliding-Mode Observer

Transcription

1 5th Intenational Confeence on Sustainable Enegy and Envionment Engineeing (ICSEEE 2016) Roto Flux Estimation of Induction Motos Using Sliding-Mode Obseve Yong Feng1,a, Minghao Zhou1,b and Fengling Han2,c 1 Depatment of Electical Engineeing, Habin Institute of echnology, China 2 School of Science, RMI Univesity, Austalia a yfeng@hiteducn, bzhouminghao@hiteducn, cfenglinghan@miteduau Keywods: Roto flux obseves; sliding-mode systems; induction motos Abstact A high-ode nonsingula teminal sliding-mode obseve is pesented fo oto flux of induction motos based on field oiented contol systems in this pape A teminal sliding-mode manifold is chosen fo the obseve and the nonsingula contol laws ae utilized to stabilize the obseve he high-ode sliding-mode contol method is applied to guaantee the stong obustness of the induction moto system and to poduce a smooth contol signal of the obseve he soften signal is diectly used fo the oto flux estimation he effect of the equivalent low-pass filte in the poposed obseve can be optionally egulated he chatteing phenomenon can be attenuated effectively he simulation esults validate the poposed method Intoduction Induction motos (IMs) have been extensively used in many pactical applications in consideation of the simple constuction, lowe epai and maintenance costs, high eliability and elatively low manufactuing cost, [1] he scala contol, the field oiented contol (FOC) and the diect toque contol (DC) ae thee main methods fo the contol of IMs, and especially both the latte two methods can povide high-pefomance contol fo the moto sevo systems he DC method fo IMs applies the bang-bang contol to egulate the stato flux and the toque independently he weakness of this method is that the toque has ipple Nevetheless, in FOC-based IM moto systems the toque and the flux of the moto can be contolled continuously he decoupled toque and the oto flux of an IM can be contolled sepaately like DC motos and a high steady-state and dynamic pefomances of IMs can be achieved [2] he FOC of an IM needs the infomation of the oto flux his infomation can be obtained by eithe diect measuements o indiect estimation methods he special sensos inhibits the pactical applications of the diect measuements while at pesent the indiect estimation methods have been utilized fo obtaining the oto flux [3], ie, the oto flux can be estimated by using the measuements of the stato voltages and cuents A lot of estimation methods have been poposed [4,5,6], etc he obustness to distubances and low sensitivity to the system paamete vaiations ae the attactive advantages of sliding-mode contol [7] and [8] Sliding-mode obseve can be applied fo the estimation of the oto flux of IMs Howeve the chatteing phenomena existing in conventional sliding-mode contol limits its applications [9] and [10] his pape pesents an estimation method fo oto flux of IMs based on high-ode nonsingula teminal sliding-mode contol he oto flux of the IM can be estimated using the smooth contol signal geneated by the obseve he simulation esults validate the poposed method Dynamic Model of Induction Motos he dynamic model of an IM can be descibed in two-dimensional static fame (α-β) as follows [2]: diα s dt = K (uα s Rs iα s ) + K (φα s + ω φβ s ) σ iα s ω iβ s diβ s = K (u R i ) + K ( ω φ + φ ) + ω i i s αs αs dt σ Copyight 2016, the Authos Published by Atlantis Pess his is an open access aticle unde the CC BY-NC license ( (1) 785

2 whee K = 1/(σ Ls ), σ = 1 L2m /(Ls L ),=1/= R/L, uαs and u ae the stato voltages in α-β axes, iαs and i the stato cuents in α-β axes, φαs and φ the stato fluxes in α-β axis, ω the electic angula velocity of the oto, Rs the stato esisto, L, Ls, and Lm the oto, the stato, and the mutual inductance between the stato and the oto, the time constant of the oto he elationship between the oto and the stato fluxes of can be expessed as follows: L φα = L (φα s σ Ls iα s ) m L φ = (φ σ L i ) s β Lm β s (2) whee φα and φβ ae the oto fluxes in α-β axis Fom Eq(1), the infomation of the stato fluxes in an IM ae contained in both K(φαs+ωφ) and K( ωφαs+φ) Consideing the elationship between the oto fluxes and the stato fluxes, it can be seen that these infomation including both the oto and stato fluxes can be obtained Sliding-Mode Obseve fo Roto Flux he sliding-mode obseve-based vecto contol system of an IM is shown in Fig1 he obseve is used to estimate the oto flux of the IM he inputs of the obseve include the stato cuents and voltages of the IM A Estimation of the Stato Cuents An obseve fo the stato cuents is built as follows: ˆ &ˆ ˆ iα s = Kuα s + vα s KRs + σ iα s ω iβ s i&ˆ = Ku + v + ω iˆ KR + iˆ αs s σ (3) whee iˆα s and iˆβ s ae the estimates of the stato cuents iαs and i, vαs and v ae the contol signals of the obseve, which eplace the tems K (φα s + ωφβ s ) and K ( ωφα s + φβ s ) in Eq(1) Fom Eqs (1) and (3), it can be obtained the eo obseve as follows: i& = v KΡ + Νi whee i = iα s, iβ s, iαs = iˆα s iαs P = K (φα s + ωφβ s ), K ( ωφα s +φβ s ) and iβ s = iˆβ s iβ s (4) ae the estimation eos of the cuents in α-β axis,, v = vα s, vβ s, and ωef iq ia iα ib iβ id ic θˆ φˆ ω Fig 1 IM vecto contol system 786

3 + KRs N = σ ω - ω + KRs σ A nonsingula teminal sliding-mode manifold is designed as: s = i + γi& p / q (5) whee s = [sαs, s], γ = diag(γαs, γ), γαs >0, γ > 0 p and q ae odds and satisfy 1<p/q<2 It can be assumed that system (1) and its obseve (3) satisfy v < k1, KΡ& < k 2, whee k1, k2, and ae positive constants he obseve eo i and its deivative in (4) will convege to zeo in finite time, if a NSM manifold is chosen as (5) and the contol stategy is designed as follows: w = v& + v = w γdiag( i& p / q 1, i& (6) p / q 1 )s q & 2 p / q αs i Νi& (k1 + k 2 + µ ) γp γdiag( i&α s p / q 1, i&β s p / q 1 )s (7) whee μ is a positive constant B Estimation of the Roto Fluxes If the ideal sliding-mode motion s=0 is guaanteed to be implemented using heoem 1, the obseve eo and its deivative satisfy i = i& = 0, and (4) can be expessed as: vα s = K (φα s + ωφβ s ) vβ s = K ( ω φα s + φβ s ) (8) he estimates of the stato fluxes can be obtained fom Eq(8): ω ˆ φα s = K ( 2 + ω 2 ) vα s K ( 2 + ω 2 ) vβ s ω φˆ = v + v β s K ( 2 + ω 2 ) α s K ( 2 + ω 2 ) β s (9) Accoding to Eqs (2), the estimates of the oto fluxes can be obtained fom Eqs(3) and (9): L ˆ ˆ ˆ φα = L (φα s σ Lsiα s ) m L φˆ = (φˆ σ L iˆ ) s β Lm β s (10) Consequently both the magnitude and the position of the oto fluxes ae obtained, which can be utilized in the FOC based IM system Simulations A thee phase squiel-cage IM is consideed in the simulation Assume that the paametes of the IM ae: PN=15kW, UN=380V, R=32Ω, Rs=61Ω, L= 0478H, Ls=0478H, Lm=0472H, J=0033kg m2 he design paametes of the oto flux obseve ae: p=5, q=3, γ =1, =0001, k1+k2 =8000 he simulation esults ae shown in Figs 2 and 3 he actual and the estimated oto fluxes of the IM in α axis ae shown in Fig2 he actual and the estimated oto fluxes of the IM ae explained in Fig3 It can be seen fom the simulation esults that the poposed method can estimate the oto flux of the IM quickly and actually 787

4 Fig 2 Actual oto flux and its estimation in α axis Fig 3 Actual oto flux and its estimation Conclusions his pape has poposed a high-ode sliding-mode obseve based estimation method fo the oto flux of IMs A nonsingula teminal sliding-mode suface and a contol stategy of the obseve ae designed to make the obseve tack the stato cuents A smooth contol signal of the obseve can be geneated by utilizing the second-ode sliding-mode technique, and diectly used fo estimation of the oto flux he estimated oto flux can be used fo implementing the FOC of the IM systems he simulation esults have shown the coectness of the poposed method Acknowledgements his wok was financially suppoted by National Natual Science Foundation (NNSF) of China unde Gant ( ) Refeences [1] Maes and J Melkebeek, Speed-sensoless diect toque contol of induction motos using an adaptive flux obseve, IEEE ans Ind Appl, vol36, no3, pp , 2000 [2] S Kwon, MH Shin, and DS Hyun, Speed sensoless stato flux-oiented contol of induction moto in the field-weakening egion using Luenbege obseve, IEEE ans Powe Electon, vol20, no4, pp , 2005 [3] M S Zaky, Stability analysis of speed and stato esistance estimatos fo sensoless induction moto dives, IEEE ans Ind Electon, vol59, no2, pp858-70, 2012 [4] F Chen and M Dunnigan, Compaative study of a sliding-mode obseve and Kalman filtes fo full state estimation in an induction machine, IEE Poc, Elect Powe Appl, vol149, no1, pp53-64, 2002 [5] S Kim, Pak, and G Pak, Speed-sensoless vecto contol of an induction moto using neual netwok estimation, IEEE ans Powe Electon, vol48, no3, pp , 2001 [6] Y Feng, X Yu and F Han, High-ode teminal sliding-mode obseve fo paamete estimation of a pemanent-magnet synchonous moto, IEEE ans Ind Electon, vol60, no10, pp , Oct 2013 [7] Y Feng, X Yu, and Z Man, Non-singula teminal sliding mode contol of igid manipulatos, Automatica, vol38, no12, pp , 2002 [8] Y Feng, X Yu and F Han, High-ode teminal sliding-mode obseve fo paamete estimation of a pemanent-magnet synchonous moto, IEEE ans Ind Electon, vol60, no10, pp , Oct 2013 [9] Y Feng, X Yu, and F Han, On nonsingula teminal sliding-mode contol of nonlinea systems, Automatica, vol46, no6, pp , June

5 [10] Y Feng, X Yu, F Han, "Chatteing fee full-ode sliding-mode contol", Automatica, vol50, no4, pp ,