Model reference adaptive vector control for induction motor without speed sensor

Transcription

1 Special Issue Aticle Model efeence adaptive vecto contol fo induction moto without speed senso Advances in Mechanical Engineeing 207, Vol. 9() 4 Ó The Autho(s) 207 DOI: 0.77/ jounals.sagepub.com/home/ade Bo Fan,2, Zhi-Xin Yang 3, Xian-Bo Wang 3,LuSong and Shu-Zhong Song Abstact The wide applications of vecto contol impove the high-accuacy pefomance of altenating cuent (AC) adjustable speed system. In ode to obvese the full-ode flux and calculate the eal-time speed, this aticle intoduces the moto T equivalent cicuit to build a full-ode flux obseve model, whee the cuent and flux vaiables of stato and oto ae adopted. Model efeence adaptive contol is intoduced to build the AC moto flux obseve. The cuent output is used as feedback to build the feedback matix. The calculation method of moto speed, which is pat of the inputs of flux obsevation, is applied to ealize the adaptive contol. The concept of chaacteistic function is intoduced to calculate the flux, of which the foundation is the vaiables of composite fom of voltage and cuent models. The chaacteistic function is deduced as a elative-state vaiable function. The feedback matix is impoved and designed to ensue the moto flux obseve is a smooth switch between cuent and voltage model in low and high speeds, espectively. Expeimental esults show that the feedback and chaacteistic model ae feasible, and the vecto contol with speed sensoless based on the full-ode flux obseve has bette pefomance and anti-distubance. Keywods Vecto contol, full-ode flux obseve, speed sensoless, model efeence adaptive contolle, induction moto Date eceived: 25 June 206; accepted: 2 Novembe 206 Academic Edito: Pak Wong Intoduction Magnetic field oientation is vital in vecto contol (VC) method fo induction moto s speed egulation. Magnetic field oientation elates tightly to the oto paametes. How to ecognize and calculate the oto paametes with high accuacy has become a hot issue in academia. The common method is adopting the closed-loop and installing a speed senso in moto shaft so as to get a goup of moe accuate oto paametes. Howeve, in eal applications, the installation of speed senso faces the following limits: 3 The installation of speed senso educes the simplicity and obustness of the system; The speed senso with high pecision is usually costly; In some specific hash situations (e.g. high tempeatue and moist), the installation educes the eliability of the system; The impope installation would become a new souce of the fault. College of Infomation Engineeing, Henan Univesity of Science & Technology, Luoyang, China 2 CITIC Heavy Industies Co., Ltd, Luoyang, China 3 Depatment of Electomechanical Engineeing, Faculty of Science and Technology, Univesity of Macau, Macau, China Coesponding autho: Zhi-Xin Yang, Depatment of Electomechanical Engineeing, Faculty of Science and Technology, Univesity of Macau, Macau , China. zxyang@umac.mo Ceative Commons CC-BY: This aticle is distibuted unde the tems of the Ceative Commons Attibution 3.0 License ( which pemits any use, epoduction and distibution of the wok without futhe pemission povided the oiginal wok is attibuted as specified on the SAGE and Open Access pages ( open-access-at-sage).

2 2 Advances in Mechanical Engineeing In ode to solve these poblems, VC without speed senso has been poved a pomising altenative method. The speed sensoless vecto contol (SSVC) is pesented fist by R Joetten and G Maede 4 in 983, who pompted the development of altenating cuent (AC) tansmission technology up to a new level. Nowadays, thee ae many kinds of methods, which can be divided into seveal categoies: 5 7 model efeence adaptive-contol system (MRAS) method, dynamic speed estimation (DSE) method, atificial neual netwoks (ANNs), adaptive speed obseve (ASO) method, popotional-integal (PI) egulato method, high fequency injection (HFI) method, and oto slot hamonic (RSH) method. SSVC has many meits such as saving the speed senso and educing the constuction and maintenance cost. It achieves a simila dynamic pefomance as the conventional VC with speed-loop method. Especially, SSVC impoves the low-speed chaacteistics, the speed egulation ability in vaiable load situation. This method gets a stonge stating toque than conventional VC method. This chaacteistic bings obvious advantages in high fiction and inetia load, so as to ealize the complete decoupling contol. Moeove, the scheme of SSVC is elatively bief. Simila to the conventional VC, SSVC includes the speed contol loop, toque contol loop, and flux contol loop. 8 0 The egulatos of speed and flux also adopt the PI egulatos. Unlike the conventional VC method with speed senso, SSVC must build a flux obseve and a speed obseve so as to detect the eal-time magnetic field oientation. SSVC also has a shotcoming;,2 its demeit is that the oto time constant affects geatly on the accuacy of oto s flux detection in flux-loop, which influences the dynamic pefomance of speed egulation. The SSVC system is put fowad based on the VC in geneal, in which the speed senso and encode ae eliminated. The paametes of flux and speed of induction moto ae obtained by an online o offline obseve. In ecent yeas, the scholas ae devoted to the study on speed sensoless contol system because of the advantage of VC method to pefom with high accuacy, which is simple constuction scheme and has gadually become a hot topic in moto contol field. The contol system pefomance with SSVC depends on the accuacy and ange of speed identification. How to obtain the speed and othe paametes accuately plays an impotant ole in this contol method. The common acquisition method fo flux values and field oientation angle is using diect method of magneto sensitive and the detecto coil detection. Moeove, the indiect method of obsevation model is also adopted. The diect method equies the installation of hall element in the inne suface of moto stato side, and the detecto coil needs to locate in the moto slot. Although these methods ae of high pecision, the installation of detection element in the inteio of moto is constained by the technology and pocess poblems, and it is vulneable to the impact of the slot. The detected aw signals contain a lot of ipple components. The diect method is used only to the specific moto, not to move to othe motos without detection device. It is not convenient to wide applications. At pesent, the indiect method is moe pominent, which adopts the obsevation model. With the easily measued quantities, such as the stato s voltage and cuent, the flux obsevation model is applied to calculate the oto flux vecto and othe paametes. 3 A typical dynamic system, of which state vaiables ae obtained though the measuement of extenal vaiables (i.e. the input and output vaiables), is also known as the state econstuction device. In the ealy 960s, in ode to ealize the state feedback contol system o othe equiements, DG Luenbege and RW Bass poposed the concept and constuction method of the state obseve. The poblem on the state unmeasued diectly is solved by econstucting method. The emegence of the state obseve povides a pactical possibility of state feedback and has been applied in many aspects of contol engineeing, fo example, copying distubance to achieve the full compensation fo distubance. MRAS is intoduced to meet the equiements of ealtime contol. This model includes the efeence model, the contol object, and the adaptive adjustment mechanism. It takes the output of efeence model as the standad output; the adaptive mechanism compaes the eo between the efeence model and the contolled object so as to detemine the adaptive ule. With constant adjustment of the paametes o a cetain auxiliay signal, the contol object is constained to change with the efeence model changes. Adaptive paamete identification is to put the contolled object in the position of efeence model; the adaptive mechanism does not change the adjustable paametes continuously with the eo until it appoaches zeo, and then the final adjustable model conveges to the contolled object model. This aticle intoduces the stato flux (usually defined as vitual flux.) into the thee-phase pulse width modulation (PWM) ectifie. Accoding to the eseach of vitual-oiented VC and estimation of instantaneous powe, this study poposes a diect powe stategy without gid voltage sensos. This stategy combines the vitual flux diect powe contol method to the space vecto modulation. The est of this aticle is oganized as follows. Section The oto flux obsevation model pesents the ototille flux obseve model, such as cuent model and voltage model. Section The full-ode flux obseve model of the induction moto gives the fullode flux obseve model of the induction moto. Sections The full-ode flux obseve based on MRAS and The design of the feedback matix in the

3 Fan et al. 3 full-ode flux obseve explain the full-ode flux obseve based on MRAS. Section Expeimental and esults analysis discusses the expeimental esults of the famewok and its compaisons. Section Conclusion concludes the study. The oto flux obsevation model Magnetic field contol fo thee-phase asynchonous moto is an impotant issue in speed-contol system. The constant ai gap flux of AC moto needs to be maintained in contol unde the fundamental fequency, while the weak magnetic contol needs to be kept in highe fundamental fequency. The position and size of the oto magnetic field is necessay to be ecognized if the AC moto is contolled by the oto magnetic field oientation. It means that the moto magnetic field is contolled in eal time. Fist, the magnetic field oientation can be detected. Diect detection is difficult to achieve due to engineeing envionment and technological complexity. In geneal, the obsevation method is used. The most basic method on oto flux obsevation includes the voltage model and the cuent model. The cuent model is divided into the two types of coodinate conditions: the one is in twophase ab stationay coodinate and the othe is in dq otating coodinate. The cuent model Cuent model of the two-phase stationay coodinate system. The cuent model in two-phase ab stationay coodinates is shown in Figue : the stato voltage equation is obtained by the two-phase ab stationay coodinates mathematical model voltage equation of AC induction moto di sa u sa = R s i sa + L s dt di sb u sb = R s i sb + L s dt + L m di a dt, + L m di b dt ðþ The oto flux components on ab stationay coodinates ae shown in equation (2) c a = L m i sa + L i a, c b = L m i sb + L i b ð2þ whee i a = L ðc a L m i sa Þ, i b = L c b L m i sb ð3þ Let u a = u b = 0 and substitute them into equation (3), then we get the oto flux cuent model c a = T p + L mi sa vt c b, c b = T p + L mi sb + vt c a ð4þ whee T is the oto electomagnetic time constant, T = L m =R. Cuent model in two-phase otating coodinate system. The cuent model in two-phase dq otating coodinates is shown: the oto flux cuent model fist detected the stato cuents and velocity, and then the oto flux is calculated. The thee-phase stato cuents ae tansfomed to its excitation component i sa and toque component i sb by 3s=2. The VC equations ae shown as follows v s = L mi st T c, c = L m T p + i sm ð5þ The moto slip v s and stato fequency v ae calculated fom the above equations and then v = v s + v. The oto flux can also be obtained. Figue 2 shows the cuent model of oto flux on dq otating coodinates. The voltage model Equation (6) is obtained by the mathematical model of voltage equation of AC induction moto on two-phase ab stationay coodinates Figue. Cuent model oto flux on two-phase ab stationay coodinates. Figue 2. Cuent model of oto flux on dq otating coodinate.

4 4 Advances in Mechanical Engineeing _x = Ax + Bu, Y = Cx ð9þ Accoding to the model of the contolled object, the simulation system with the same dynamic equation as equation (9) is built as follows as _^x = A^x + Bu, ^y =C^x ð0þ Figue 3. Voltage model of oto flux. di sa di a u sa = s i sa + L s + L m dt dt, u sb = s i sb + L s di sb dt + L m di b dt ð6þ Then i sa and i sb ae eplaced in equation (2), thus we obtain L m dc a = u sa s i sa L s L2 m disa L dt L dt, ð7þ L m dc b = u sb s i sb L s L2 m disb L dt L dt Moto magnetic flux leakage coefficient s = L 2 m =(L sl ) is substituted in equation (7), which is integated on both sides. Figue 3 shows the voltage model of oto flux c a = L ð ðu sa s i sa Þdt sl s i sa, L m c b = L ð ð8þ u sb s i sb dt sls i sb L m The full-ode flux obseve model of the induction moto The basics of full-ode states obseve If the contolled object is obseved, its input and output ae applied to ebuild the states with the states obseve. If the dimension of the ebuilt state vectos equals the contolled object state vectos, this obseve is called as a full-ode flux obseve. Full-ode adaptive state obseve is also called Luenbege obseve. This method belongs to the ange of MRAS. 4 Setting the induction moto itself as a efeence model, the fullode state obseve is used as the adjustable model. This method has meits of avoiding the pue integal poblem, ensuing the accuacy of the efeence model and educing the sensitivity to moto paametes. The dynamic state equation of the contolled object is set as equation (9) whee ^x and ^y ae the state estimation value and output value of this simulation system, espectively. The initial states of the two systems (the contolled object and the simulation system) ae always diffeent, that is, even if thei paametes ae identical. It exists as the state s eo between the estimation and the actual object, which leads to failue in ealizing the accuate states obsevation. Howeve, the state s eo esults in the output s eo. Accoding to the theoy of feedback contol, the output s eo between the contolled system and simulation system is built with negative feedback and contolled as soon as it appoximates to zeo, hence the state s eo appoximates to zeo. The fullode flux obseve is built based on the above theoy _^x = A^x + Bu + H(^y y), ^y = C^x ðþ whee u and y ae the inputs, ^x is the output, and H is the feedback matix of the obseve output. The obseve pole assignment is applied to impove the dynamic pefomance and lets the state s eo appoximation to zeo as soon as possible. H can be chosen as the abitay pole assignment, which detemines the decay ate of the state s eo. The state space model of AC induction moto The equivalent cicuit of AC induction moto has thee kinds of foms: T cicuit, invese G cicuit, and G cicuit. Among these thee types of cicuits, T cicuit is widely used. In this aticle, T equivalent cicuit is applied to deive the state space model of AC induction moto. The steady state equivalent T cicuit model in otating dq coodinates with abitay angula velocity v k is shown in Figue 4. On the pemise of neglecting tempeatue change, skin effect, and excitation satuation, as the oto speed is a elatively slow change in the amount of cuent and flux, it is seen as the constant. Theefoe, the AC moto model is descibed by a fouth-ode linea equation. The constuction of the state space model needs to choose the appopiate vaiable. The stato cuent and the oto flux ae chosen to the oientation of oto flux. The stato flux and the oto flux ae chosen to diect toque contol. The state equation of AC moto in abitay angula velocity with otating coodinate system is built as follows

5 Fan et al. 5 Figue 4. T cicuit with abitay angula velocity in dq coodinate. The complex fom of AC moto equation The complex vecto fom of AC moto equation: the AC moto states equation, accoding to the stato flux and oto flux, is built by T equivalent cicuit and equation (2) 2 jv t s _z = 6 4 s t i s = L s L s t s t jðv k v m Þ z z + 0 u s, whee z=½c s c Š T, s=(l ss +L s )=(L m +L ss +L s ), t 0 s =(L ss +L s )=R s,andt 0 =sl m=r s. k =L m =L is the oto magnetic coupling facto. R s =R s +k 2R is the equivalent esistance. t 0 =sl m=r s is the instantaneous time constant. The stato cuent and oto flux ae used as the state vaiables, x=½i s c Š T, then the state Figue 5. The pinciple diagam of the full-ode flux obseve equation is shown in equation (4). In addition, this of AC moto. eo can be seen as the feedback coection. A feedback 2 R s + s 3 L m L m v k v sl s st sl s L t sl s L i sd d i sq v k R s + s L 2 3 m L i u sd m sd sl s v 6 7 dt 4 c sd 5 = sl s st sl s L sl s L t i sq L m c (v k v ) sd 5 + u sq sl s 6 7 c sq 6 t t 4 L m 0 (v k v ) 7 c sq 5 0 t t ð2þ ð3þ whee the total leakage inductance coefficient is s =(L s L L m 2 )=L s L, the total leakage inductance is L = sl s, the oto time constant t = L =R, v is the oto electic angula fequency, and v e is the synchonous fequency. The full-ode flux obseve based on MRAS The pinciple of the full-ode flux obseve is shown in Figue 5. The AC moto is the efeence model and the eo between the moto cuent and the obseved cuent is intoduced to coect the elative moto state fo obsevation. 5 7 The full-ode flux obseve of induction moto is the moto itself as a efeence model. The state equation is built to estimate the moto flux and stato cuent; the stato cuent is used as the output cuent; and the actual eos estimated cuent is intoduced as feedback coection. The gain of the feedback matix of the coection tem is adjusted to impove the pefomance of the full-ode flux obseve. matix gains is egulated with this coection to impove the pefomance of the full-ode flux obseve. Moeove, the stato cuent and the estimation cuent ae feedbacked in eal time to the obseve, which pomotes adjustment of its paametes. This eo tends to zeo as soon as possible to achieve the pupose of accuate speed identification 2 _x = 6 4 t s jv k i s = ½ 0Šx k jv L s t L m jðv k v t t s x + L s 0 Þ u s, ð4þ The mathematic model of the full-ode flux obseve to AC induction moto Accoding to the state equation of AC induction moto, when the stato flux and oto flux ae used as the state vaiables, the full-ode flux obseve is expessed with the intoduction of the cuent feedback, then

6 6 Advances in Mechanical Engineeing 2 ^t 3 jv k s ^t s _^z= s 5^z+ u s +Li s ^i s, 0 ^t ^t jðv k ^v Þ ^i s = ^t ^t ^z ð5þ s s whee ^z = ½ ^c s ^c Š T, L = ½ l s l Š T is the feedback matix, and l s = l sd + jl sq and l = l d + jl q. The subtaction between equations (3) and (5) can be obtained as the eo equation 82 ^t 3 >< jv k s ^t s _e = 6 4 s >: ^t ^t jðv k ^v Þ e i = ^t ^t e s s 7 5 l s ^t s l ^t s 9 >= e 0 >; j^c, ð6þ In the otating coodinate system, the full-ode fluxes obseve model of T equivalent cicuit is built with the addition of the cuent feedback 2 ^t k jv k ^t 3 j^v k _^x = s L s 6 L m ^t 7 4 5^x jðv k ^v Þ ^t ð7þ ^L s 5u s + K i s ^i s, ^i s = ½ 0Š^x 0 whee _^x = ½^i s k Š T, ^t s = ^L s =(^R s + ^R ), K = ½ k s k Š T, k s =(l s l )=L s, k = l. The eo equation is obtained as follows 02! 3 k jv k jv^ _e ic = t^s L^s t^ 6 L m K½ 0Š B A e ic j v k v^ t^ t^ jc ^ 6 L 4 s 7 5e v, e i = ½ 0Še ic ð8þ ^ jc whee e ic = ½e is, e icr Š T, e v = v ^v is the speed eo, e i = i s ^i s is the cuent eo, e cs = c s ^c s is the stato flux eo, and e c = c ^c is the oto flux eo. The speed acquisition method Since the AC moto speed cannot be obtained diectly, it is identified by the adaptive ate with the detection data. The identification equation based on the fullode flux obseve is as follows Ð ^v = k p + k i edt, e =Im ei^c R ð9þ whee e is the adaptive signal of AC moto speed, k p denotes the popotional coefficient, k i indicates the integal coefficient, and ^c R is the conjugate of ^c R. The adaptive algoithm of equation (9) is shown in Figue 5, and paametes (K p and K i ) ae selected with expeimental method. SSVC based on the full-ode flux obsevation Based on the conventional pinciple of VC, SSVC depends on the online o offline paametes identification to obtain the flux and speed. Recently, moe scholas and eseaches ae inteested in this contol field and mainly focus on how to identify the paametes, 8,9 such as speed, flux, and oto time constant. These identification accuacies and extensions detemine the contol pefomance. MRAS is applied to online identification of AC induction moto paametes in this aticle. The efeence model and the adjustable model ae built. The adaptive mechanism is used to adjust the paametes of the adjustable model and maintain the eo between the efeence model and the adjustable model to zeo. This method has the bette pefomance even if the system has dynamic changes and distubances. The estimation of speed is intoduced to the VC system with sensoless. The contol system model, in this aticle, is built with the full-ode flux obseve based on MRAS. The stato cuent excitation and toque components have been completely decoupled befoe the space vecto pulse width modulation (SVPWM). This contol system model is shown in Figue 6. The design of the feedback matix in the full-ode flux obseve The complex fom of oto flux obseve The chaacteistic function F(s) is intoduced to design the flux calculation model. In the fequency domain, one of any kinds of oto flux obseve is expessed to the complex fom fo the cuent model flux obsevation and the voltage model flux obsevation. The calculation model of the flux, obseved by the cuent model flux obsevation in fequency domain, is expessed as ^c Rv = s + ^t ^R R i s + jðv k ^v m Þ ð20þ Well, the calculation model of the flux, obseved by the voltage model flux obsevation in fequency domain, is expessed as ^c Rc = u s ^R s i s ^L s jv k^l s i s s + jv k ð2þ

7 Fan et al. 7 DC ω ψ ^ ψ T e ASR AψR L /(n p L m ) i sm i st PI PI u M u T C 2/3s u A u B u C SVPWM Theephase Invete u A u B u C Theephase AC Moto ^ ω Figue 6. Division of decoupling vecto contolling system. Theefoe, the complex fom of the flux obsevation is as follows ^c a = F(s)^c Rva + ð F(s) Þ^c Rva ð22þ ^c b = F(s)^c Rvb + ð F(s) Þ^c Rvb The deivation of the chaacteistic function In the flux calculation model, the chaacteistic function combines the voltage model and cuent model as F(s)= s + ^t s ð ^Ls ^c s = ð s + + jvk + ks Þ s + ^ts 3 us^r si s^l sjv k ^L si s s + jv k ð ^Ls 3 ð s + + jvk + ks Þ s + 3 ^ts ^R Ri s s + ^t + j vk^vm ^R Rk Þðs + jv k Þ ð ^t + jðvk^vm ÞÞ ð^lss + ^Ls Þ ^R Rk ð Þ ð ^t j^vm ^R Rk Þðs + jv k Þ ð ^t + jðvk^vm ÞÞ ð^lss + ^Ls Þ ^R Rk Þ ð Þ ð ^t j^vm ð Þ ð27þ Theefoe, the chaacteistic function is deduced as ^R ^L R k ð s + jvk Þ s + jv k + k s s + ^t + jðv k ^v m Þ ^L s ^R R k Þ! ð28þ ^t j^v m a efeence function. Its deivation pocess is obtained with the tansfomation of equation (6) u s = ^R s + jv k ^L ss + ^L s ^i s + ^L ss + ^L s _^i s + ^R R^i s ^t j^v m ^c R ð23þ k s ^L ss + ^L s is ^i s u s s + ^t + jv k i s + ^L s s ^L ss + ^L s = s + ^t + jv k + k s i s ^i s s _^c R = ^R R^i s ^t + jðv k ^v m Þ j^v m ^c ^t R ð24þ ^c R + k i s ^i s ð25þ s + ^t + jðv k ^v m Þ ^c R ^R R i s = l ^R R is ^i s ð26þ The flux calculation equation of the full-ode flux obseve is as follows In ideal conditions, the paametes of the full-ode flux obseve ae designed easonably. This flux obseve can be close to the cuent model flux obseve at low speed, while can smoothly switch to voltage model flux obseve at high speed. The design of feedback matix Fom the full-ode flux obseve vecto model, it can be seen that, when the feedback matix is zeo, the smooth switching of this full-ode flux obseve could not be ealized between the voltage model and cuent model. Moeove, the ovedamped appeas in this flux obseve at high speed. The feedback matix must be designed to esolve this smooth switching, in ode to meet the application equiements of this full-ode flux obseve, whose vaiables ae the stato flux and oto flux at the synchonous otating coodinate. The conventional feedback matix gains is L = ½R s R R Š T o L = ½R s Š T ½R s R Š T. The feedback matix is designed accoding to the two matices: the stato flux is the pue voltage model and the oto flux is the cuent model and voltage model. The second method is the negative infinity, which is unable to ealize and is eplaced by R. A new impoved

8 8 Advances in Mechanical Engineeing Figue 7. Compaison between actual speed and identification speed and the compaison between actual flux and obseved flux, speed is set to 200 /min, feedback matix is set to zeo. method of the feedback matix is poposed in this aticle, shown in equation (29), which is designed to the linea inceasing gains following the AC moto speed, to ealize the smooth switching between the cuent model and voltage model L = R s + k f ^L s ð29þ R R k b jv m j whee k b =(R R + R)=v b, k f = 2jv e j, and R = 5R R. The feedback matix, designed with this method, can ealize the smooth switching to the voltage model and cuent model in the full-ode flux obseve. When AC moto speed is low, this obseve can appoximate to the cuent model flux obsevation. With the incement of AC moto speed, the paametes elative to speed also incease, this obseve can achieve close to the voltage model flux obsevation. Expeimental and esults analysis The feedback matix used in the full-ode flux obseve veified the efficiency and accuacy. The paametes involved in this flux obsevation model ae aanged to simulate. The full-ode flux obseve is applied to the expeiments including high, middle, and low speed of AC moto. The feedback matix is set to zeo and equation (29). The AC moto adopts the VC with speed feedback. The set value of oto flux is 0.88 Wb. The set values of speed ae 200, 600, and 30 /min, espectively. The compaisons between the actual flux and obseved flux with these values of speed ae shown in Figues 7 2. Fom the calculation model of feedback matix and chaacteistic function, it is known that when the moto speed is low, the flux obsevation is close to the cuent model; when the moto speed is elatively high, the calculation model is close to the obsevation of the voltage model. As the moto speed is low, the identification speed can be vey good to follow the actual speed; the actual flux and obsevation flux ae basically coincident. These simulation esults ae elative to that the feedback matix can be good to make the full-ode flux obseve close to cuent model flux obseve in moto low-speed unning aea, and the stability of cuent model flux obseve in moto lowspeed unning is bette. At the same time, when the feedback matix is not zeo, the speed esponse inceases compaed with the feedback matix is zeo, which impoves the anti-intefeence ability and the convegence. This aticle intoduces a compound fom of cuent voltage model, of which an instantiated cuent voltage feedback matix loop is applied on the moto mathematical model. By means of feedback matix, the model of moto is close to the cuent system model in low otating speed and matches to voltage system in high otating speed. In this aticle, the full-ode flux obseve based on MRAS is adopted to obseve the flux and estimate the speed. The diagam of VC system without sensos is shown in Figue 3. MATLAB/Simulink is applied to veify the poposed VC of speed sensoless with the full-ode flux obseve based on MRAS. This simulation paametes of AC induction moto ae as follows: ated powe is 4 kw, ated voltage is 380 V, ated fequency is, the pole

9 Fan et al. 9 Figue 8. Compaison between actual speed and identification speed and the compaison between actual flux and obseved flux, speed is set to 200 /min, feedback matix is set to equation (29). Figue 9. Compaison between actual speed and identification speed and the compaison between actual flux and obseved flux, speed is set to 600 /min, feedback matix is set to zeo. numbe is 2, stato esistance is O, stato leakage inductance is mh, oto esistance is 0.86 O, oto leakage inductance is 0.00 mh, mutual inductance is mh, and moment of inetia is 0.9 kg m 2. The simulation esults ae shown as follows. Figue 4(a) shows the actual speed and identification speed in ated fequency 50 Hz. It is obvious fom Figue 4(b) that the speed eo conveges apidly and is nea zeo fom 0.5 s. The toque wavefom of AC moto is shown in Figue 4(c). Expeiments ae accomplished in the AC moto contol system platfom to test the pefomance of VC with speed sensoless based on MRAS. Space vecto modulation switching bidge signals with dead time ae

10 0 Advances in Mechanical Engineeing Figue 0. Compaison between actual speed and identification speed and the compaison between actual flux and obseved flux, speed is set to 600 /min, feedback matix is set to equation (29). Figue. Compaison between actual speed and identification speed and the compaison between actual flux and obseved flux, speed is set to 30 /min, feedback matix is set to zeo. shown in Figue 5(a): switching fequency is 9.4 khz and dead time is.4 ms. Figue 5(b) and (c) shows the invete output voltage and cuent wavefoms of phase u. With the analysis of these expeimental esults, the contol system that applied the poposed method has bette pefomance and dynamic esponse ability. Fom these figues, it is obvious that the estimated speed can well follow the actual speed of the moto, which achieves a good identification esult, and the system eo can get convegence, which veifies the stable opeation of the system and explains the design of VC system is feasible.

11 Fan et al. Figue 2. Compaison between actual speed and identification speed and the compaison between actual flux and obseved flux, speed is set to 30 /min, feedback matix is set to equation (29). Figue 3. A vecto contol system with speed sensoless block diagam. Conclusion The main poblem in VC of AC dive is the paametes identification, such as esistance, inductance, and flux of stato and oto. The SSVC system pays moe attention to flux obsevation and speed estimation. The full-ode flux obseve is impoved fo obsevation on flux. The dual-model composite method is applied to estimate flux. The obsevation model and speed estimation model ae built based on model efeence adaptive contol. The feedback

12 2 Advances in Mechanical Engineeing Figue 4. The moto toque and speed wavefoms: (a) actual speed and identified speed, (b) speed eo, and (c) toque wavefom of AC moto. matix is intoduced to impove the feedback gains, in ode to meet the smooth switching of obsevation model, in which the cuent model is obtained in low speed and the voltage model is used in high speed. Accoding to this identification method, the VC system with speed sensoless based on full-ode flux obseve is poposed in this aticle. The identification esults of speed and flux ae used as inputs to egulate

13 Fan et al. 3 Figue 5. The output cuent and voltage of invete: (a) SVPWM signals, (b) output voltage of invete, and (c) output cuent of invete. the vaious contol quantities. The decoupling cicuit, 2/3s tansfomation and SVPWM ae applied to ealize the VC of AC moto. Expeimental esults show that the poposed method has bette dynamic esponsibility and anti-distubance. Declaation of conflicting inteests The autho(s) declaed no potential conflicts of inteest with espect to the eseach, authoship, and/o publication of this aticle. Funding The autho(s) disclosed eceipt of the following financial suppot fo the eseach, authoship, and/o publication of this aticle: This wok was suppoted by the National Natual Science Foundation of China (U40452 and 64735) and the Poject of Luoyang Science and Technology Development Plan (4007A). This wok was also suppoted by the Univesity of Macau unde Gants (MYRG FST). Refeences. Holtz J. Sensoless contol of induction moto dives. Poc IEEE 2002; 90: Kim J-H, Choi J-W and Sul S-K. Novel oto-flux obseve using obseve chaacteistic function in complex vecto space fo field-oiented induction moto dives. IEEE T Ind Appl 2002; 38: Wai R-J and Chang J-M. Intelligent contol of induction sevo moto dive via wavelet neual netwok. Elect Pow Syst Res 2002; 6: Joetten R and Maede G. Contol methods fo good dynamic pefomance induction moto dives based on cuent and voltage as measued quantities. IEEE T Ind Appl 983; IA 9: De Almeida Souza D, de Aagao Filho WC and Sousa GCD. Adaptive fuzzy contolle fo efficiency optimization of induction motos. IEEE T Ind Appl 2007; 54: Hilaiet M, Auge F and Bethelot E. Speed and oto flux estimation of induction machines using a two-stage extended Kalman filte. Automatica 2009; 45: Foo GHB and Rahman M. Diect toque contol of an IPM-synchonous moto dive at vey low speed using a sliding-mode stato flux obseve. IEEE T Powe Elect 200; 25: Riveos JA, Yepes AG, Baeo F, et al. Paamete identification of multiphase induction machines with distibuted windings pat 2: time-domain techniques. IEEE T Enegy Conve 202; 27: Wang X, Yang Z, Fan B, et al. Contol stategy of theephase photovoltaic invete unde low-voltage idethough condition. Math Pobl Eng 205; 205: (23 pp.). 0.FanB,YangZ,XuW,etal.Rotoesistanceonline identification of vecto contolled induction moto basedonneualnetwok.math Pobl Eng 204; 204: (0 pp.).. Patel C, Ramchand R, Sivakuma K, et al. A oto flux estimation duing zeo and active vecto peiods using cuent eo space vecto fom a hysteesis contolle fo a sensoless vecto contol of IM dive. IEEE T Ind Electon 20; 58: Vaclavek P, Blaha P and Heman I. AC dive obsevability analysis. IEEE T Ind Electon 202; 60: Foo G and Rahman M. Sensoless sliding-mode MTPA contol of an IPM synchonous moto dive using a sliding-mode obseve and HF signal injection. IEEE T Ind Electon 200; 57: Hinkkanen M and Luomi J. Stabilization of egeneating-mode opeation in sensoless induction moto dives by full-ode flux obseve design. IEEE T Ind Electon 2004; 5: Hofmann H and Sandes SR. Speed-sensoless vecto toque contol of induction machines using a two-time-scale appoach. IEEE T Ind Appl 998; 34: Zaky MS, Khate MM, Shokalla SS, et al. Wide-speedange estimation with online paamete identification schemes of sensoless induction moto dives. IEEE T Ind Appl 2009; 56:

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