Model Reference Adaptive System Sensorless Vector Control of an Induction Motor Using a Novel Fractional Order PI Controller Adaptation Mechanism

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1 215 IJSRSET Volume 1 Issue 3 Pint ISSN : Online ISSN : Themed Section: Engineeing and Technology Refeence Adaptive System Sensoless Vecto Contol of an Induction Moto Using a Novel Factional Ode PI Contolle Adaptation Mechanism Aami Hashim Obeid Ahmed, Giddani Kalcon, Nagm Eldeen Abdo Mustafa Hassanain School of Electical and Nuclea Engineeing, College of Engineeing, Sudan Univesity of Science and Technology, Khatoum, Sudan ABSTRACT Recently, speed sensoless contol of Induction Moto (IM) dives eceived geat attention to avoid the diffeent poblems associated with diect speed sensos. Among diffeent oto speed estimation techniques, Refeence Adaptive System (MRAS) schemes ae the most common stategies employed due to thei elative simplicity and low computational effot. In this pape a novel adaptation mechanism is poposed which eplaces nomally used conventional Popotional-Integal (PI) contolle in MRAS adaptation mechanism by a Factional Ode PI (FOPI) contolle. The pefomance of two adaptation mechanism contolles has been veified though simulation esults using MATAB/SIMUINK softwae. It is seen that the pefomance of the induction moto has impoved when FOPI contolle is used in place of classical PI contolle. Keywo: Induction Moto, Speed Sensoless, Refeence Adaptive System, Popotional-Integal Contolle, Factional Ode PI contolle I. INTRODUCTION Electic motos fo vaiable speed dives have been widely used in many industial applications. High pefomance electic moto dives equie decoupled toque and flux contol. In the past, Diect Cuent (DC) motos wee commonly pefeed. Because toque and speed contols of DC motos ae easie than Altenating Cuent (AC) motos. In DC moto dives toque is popotional to amatue cuent, so DC moto dive may diectly contol the toque by using a cuent contol loop. Also flux contol is easy in DC dives. The toque and flux contols ae independent fom each othe. Howeve, DC motos have the disadvantage of bush eosion, maintenance equiements, envionmental effects, complex stuctues and powe limits. On the othe hand, the thee phase induction motos have been the most widely used and ae often viewed as the wokhose of moden industy in fixed speed applications fo easons of cost, size, weight, eliability, uggedness, simplicity, efficiency and ease of manufactue. In contast to the commutation DC moto, it can be used in aggessive o volatile envionments since thee ae no isks of coosion o spaks. Howeve, because of the involved model high nonlineaities, multivaiable, highly coupled, the electical oto vaiables ae aely measuable and its paametes vay with opeating conditions; these equie much moe complex metho of contol, moe expensive and highe ated powe convetes than DC motos [1]. The development of enabling technologies was slow until the intoduction of semiconducto powe switches in the 195 s, allowing the development of commecial vaiable fequency invetes in the 196 s. It then became viable to use vaiable speed induction motos in some low pefomance vaiable speed applications. The seach fo simple contol schemes simila to those used fo DC dives, has led to the so-called Vecto Contol (VC) o Field Oiented Contol (FOC) schemes, in IJSRSET Received: 14 May 215 Accepted: 5 June 215 May-June 215 [(1)3: ] 211

2 which by means of a vaiable tansfomation to a otational fame, it is possible to obtain two cuent components to poduce the toque and the flux espectively. Futhemoe, these cuent components can be independently contolled so as to achieve a decoupled contol. By using these techniques, vecto contolled induction motos have poved to outpefom the DC ones. Since then, the induction moto has eplaced the DC moto in many demanding high pefomance motion contol applications, offeing many advantages when compaed with DC moto. Thee ae essentially two geneal metho of VC. One called the diect o feedback method, and the othe, the indiect o feedfowad method. Indiect vecto-contolled (IVC) induction moto dives ae inceasingly used in high pefomance systems due to thei elative simple configuation compaed to Diect Vecto Contol (DVC) scheme which equies flux and toque estimatos. Implementation of the vecto contolled induction moto dive techniques equies the moto speed infomation. Tachogeneatos, esolves, incemental o optic encodes ae usually used to detect the oto speed. Unfotunately the need of speed sensos in ode to apply effective vecto contol algoithms is one of thei main constaints. Indeed, thee ae seveal disadvantages of those sensos such as highe numbe of connection between moto and its dive, additional cost, susceptibility to noise and vibations, exta space, volume and weight on the oveall actuato [2-7]. Theefoe, vecto contolled induction moto metho in the absence of any speed senso have been investigated by many eseaches. The advantages of speed sensoless induction moto dives ae educed hadwae complexity and lowe cost, educes size of the dive machine, elimination of the senso cable, bette noise immunity, inceased eliability and less maintenance equiements. Recently, seveal metho have been poposed fo speed estimation of sensoless induction moto dives based on the moto model. A compehensive study of the diffeent speed estimation techniques and thei specific meits and demeits as well as thei feasibility fo estimating the oto speed ae pesented and compaed in. These stategies make use of the instantaneous values of stato voltages and cuents to estimate the moto speed. efeence adaptive systems offe simple implementation and equie less computational effot compaed to othe metho and ae theefoe the most popula stategies used fo sensoless contol. Roto flux, back EMF and eactive powe techniques ae popula MRAS stategies which have eceived a lot of attention. Howeve, Roto Flux based Refeence Adaptive System (RF-MRAS), fist poposed by Schaude, is the most popula MRAS stategy and a lot of effot has been focused on impoving the pefomance of this scheme. Conventional RF-MRAS schemes use PI contolle as the adaptive mechanism fo speed estimation. The eason is that the conventional PI contolle is easy to implement eithe by hadwae o by softwae, inexpensive cost, and no deep mathematical theoy is necessay to undestand how the conventional PI contolle woks. In spite of the majo featues of the conventional PI contolle, it has some disadvantages such as the high peak oveshoot and esponse will be sluggish when thee is sudden load distubance [8-13]. This pape poposes a novel adaptation mechanism to eplace the classical PI contolle used in MRAS speed estimation schemes which ae based on oto flux to educe these poblems. The poposed novel adaptation mechanism is based on FOPI contolle stategy. The pefomance of both contolles is simulated and compaed using MATAB/SIMUINK softwae package. It will be seen that the novel adaptation mechanism scheme has bette pefomance when compaed to conventional PI contolle. II. DYNAMIC MODES OF INDUCTION MOTOR In this pape, the dynamic model of a thee phase induction moto can be expessed as a set of diffeential equations as follows [14]: di v i dt d q a diqs vqs i dt qs d q a d d R i dt d q dq R i dt qs d q d P T dt 2 4 J J (1) Intenational Jounal of Scientific Reseach in Science, Engineeing and Technology (ijsset.com) 212

3 Whee: R R 2 s m 2 a a R m 2 a m a R 2 m ; m a s 3Pm iqs q i d (2) Whee i, i qs, d and q ae espectively the stato cuents and the oto fluxes expessed by thei d-q othogonal components; is the oto angula speed; v and v qs ae the d-q stato voltages; s and ae the stato and oto inductances; m is the mutual inductance; a is the edefined leakage inductance. R s and R ae the stato and oto esistances, espectively; J is the moment of inetia of the moto; T is the toque of extenal load distubance; P is the numbe of pole; and T is the time constant of the oto dynamics. An easy way to comply with the confeence pape fomatting equiements is to use this document as a template and simply type you text into it. III. CASSICA RF-MRAS SPEED OBSERVER The basic scheme of the classical oto flux based model efeence adaptive system configuation is given in Figue 1. The scheme consists of two models; efeence and adjustable ones and an adaptation mechanism. The efeence model o the voltage model geneates the efeence value of the oto flux components in the stationay efeence fame fom the monitoed stato voltage and cuent components and these ae obtained fom the efeence model as follows [15-18]: d di ( v R s i s ) dt dt m q di qs ( v qs R s i qs s ) dt dt m (3) Whee is leakage coefficient which is given as: 2 1 m (4) s V V qs i i qs Figue 1: Classical RF-MRAS speed obseve The Adjustable o adaptive o cuent model descibes the oto equation and the oto flux components ae expessed in tems of stato cuent components and the oto speed. The adaptive model can be expessed in tems of the following equations [15-18]: ˆ d m 1 i ˆ ˆ ˆ dt T T d q ˆ q m 1 i ˆ ˆ ˆ dt T T ˆ Refeence Adaptive qs q d d q ˆd (5) Afte developing efeence and adjustable models, the adaptation mechanism is to be designed which foms the vey impotant pat of the RF-MRAS Obseve. The adaptation mechanism is designed in a way to geneate the value of the estimated speed used so as to minimize the eo between the efeence and estimated fluxes. In the conventional RF-MRAS scheme, this is pefomed by defining a speed tuning signal to be minimized by a PI contolle (adaptation mechanism) which geneates the estimated speed which is fed back to the adaptive model. This pocess continues till the eo between two models ten to zeo. The expessions fo the speed ˆq + - Adaptation Mechanism (IOPI Contolle) Intenational Jounal of Scientific Reseach in Science, Engineeing and Technology (ijsset.com) 213

4 tuning signal and the estimated speed can be given as follows [15-18]: ˆ ˆ (6) q d d q K I ˆ ( K P ) (7) p Whee K P and K I ae the popotional and integal constants espectively and ^ signifies the estimated value. IV. FC AND FOPI CONTROER Intege Ode PI (IOPI) contolle belongs to the dominating fom of feedback industial contolles and thee is a continuous effot to impove thei quality and obustness. Design and tuning IOPI contolle have been a lage eseach hoizon eve since Ziegle and Nichols pesented thei metho in Specification, stability, design, applications and pefomance of the IOPI contolle have been widely teated since then. In ecent yeas, thee ae inceasing inteests to enhance the pefomance of IOPI contolle by using the concept of Factional Calculus (FC). The histoy of the FC coves ove thee hunded yeas, simila to that of classical diffeential calculus. In last two decades, the FC has become much popula among the eseaches of diffeent steams. FC is a genealization of integation and diffeentiation to non-intege (factional) ode fundamental opeatos epesented by D a t ; whee a and t ae espectively the lowe and uppe limits; and is the ode of factional diffeentiation o integation. Fo positive it denotes deivative and fo negative it denotes integal actions. The continuous integodiffeential opeato (D) is defined as follows [19]: a D t d ; dt > 1; = t d ; < a Thee ae seveal definitions of factional ode integation and diffeentiation. Some of the definitions extend diectly fom intege ode calculus. The most (8) often used ae Riemann iouville and Gunwald- etnikov definitions. Recently the concept of FC is widely intoduced in many aeas in science and engineeing [1]. FOPI contolle can be witten as PI. The tansfe function of the FOPI contolle is obtained as [2-23]: K s U ( s) I G ( s ) K K Ks FOPI E( s) P P I (9) Whee E(s) is an eo and U(s) is contolle's output. K P and K I ae the popotional and integal gain values of the FOPI contolle and is the nonintege ode of the factional integato. It is obvious that the FOPI contolle not only nee design two paametes K P and K I, but also design one ode λ of integal contolle. By taking the value of as 1, the FOPI contolle is conveted to the odinay IOPI contolle. The FOPI contolle in time domain is epesented by [2-23]: u ( t ) K P e( t ) K D I t e( t ) (1) The block diagam of the novel RF-MRAS speed obseve employing FOPI contolle adaptation mechanism is shown in Figue 2. V V qs i i qs ˆ Refeence Adaptive d q ˆd Figue 2: Novel RF-MRAS speed obseve In Equation (9), s - has factional ode which is not diectly compatible with MATAB softwae and it becomes difficult to ealize hadwae of the FOPI contolle. Theefoe, thee ae seveal intege ode ˆq + - Adaptation Mechanism (FOPI Contolle) Intenational Jounal of Scientific Reseach in Science, Engineeing and Technology (ijsset.com) 214

5 Speed (ad/sec) Speed (ad/sec) appoximation metho available fo factional ode elements. In MATAB FOPI contolle is implemented using FOMCOM toolbox whee Oustaloup's appoximation is ealized [24]. V. RESUTS AND DISCUSSION In ode to veify the effectiveness and feasibility of estimating oto speed using novel and conventional adaptation mechanism techniques, a simulation model has been developed in MATAB/SIMUINK platfom. The paametes of the induction moto used in simulations ae given in Table I. TABE I PARAMETERS OF THE INDUCTION MOTOR Paametes Values Roto esistance, R.72 Stato esistance, R s.55 Roto inductance,.68 H Stato inductance, s.68 H Magnetizing inductance, m.63 H Moment of inetia, J.5 kg.m 2 Viscous fiction coefficient, B.2 Nms -1 Extensive simulation tests wee caied out to compae between the two adaptation mechanisms schemes unde diffeent opeating conditions such as constant speed command; vaiable speed command; invesion of the speed command; moment of inetia mismatch; and oto esistance mismatch. The esults ae pesented in the following sections. A. Constant Speed Command Figue 4 shows the behavio of induction moto speed estimation whee the induction moto otates at a constant speed (7ad/sec) without load toque. The simulation is pefomed fo eight secon. In tems of the estimated speed contol tajectoies shown in Figue 3, two adaptation mechanisms have a simila pefomance in tem of fast tacking of the desied speed without steady state eo. Also, in Figue 3 it can be easily obseved that the speed esponse of the IM dive with new adaptation mechanism shows no sign of oveshoot as obseved with conventional PI contolle thus educing the settling time. Futhemoe, as can be seen fom the wavefoms the speed eo between the actual speed and estimated speed is less with FOPI contolle when compaed to the contol of the IM dive with the conventional PI contolle. Howeve, the ise time fo the conventional PI contolle is faste than fo the FOPI contolle Refeence Speed Estimated Speed using FOPI Contolle Estimated Speed using PI Contolle Figue 3: Estimated constant speed using two adaptation mechanism contolles B. Vaiable Speed Command In this case, the induction moto dive is tested unde vaiable speed command with no load toque. The speed command is 3ad/sec fo the fist two secon, followed by 5ad/sec fo the next two secon, then 8ad/sec fo the next two secon followed by 1ad/sec fo the last two secon. Figue 4 shows the speed esponse of sensoless contolled induction moto dive with FR-MRAS using two adaptation mechanisms. Fom Figue 4 it is clea that FOPI contolle povided optimum pefomance in tems of oveshoot and settling time. Only ise time emained to be good fo conventional PI contolle Refeence Speed Estimated Speed using FOPI Contolle Estimated Speed using PI Contolle Figue 4: Estimated vaiable speed using two adaptation mechanism contolles Intenational Jounal of Scientific Reseach in Science, Engineeing and Technology (ijsset.com) 215

6 Speed (ad/sec) Speed (ad/sec) Speed (ad/sec) C. Invesion of Speed Command Figue 5 shows the simulation esult obtained fo speed inveting fom 8ad/s to -8ad/s without load toque Refeence Speed Estimated Speed using FOPI Contolle Estimated Speed using PI Contolle Figue 5: Estimated spee using two adaptation mechanism contolles with evesing speed efeence When the speed is changed, the esponse of the induction moto dive shows oveshoot and undeshoot in case of conventional PI contolle wheeas in FOPI contolle estimated speed settles smoothly without any emakable oveshoot and undeshoot. In addition, the settling time fo FOPI contolle is shote than fo conventional PI contolle. Based on ise time chaacteistic, it can be said that the conventional PI contolle is able to esponse quickly compaed to FOPI contolle. The last chaacteistic is the steady state eo whee the two adaptation mechanisms have almost zeo steady state eo. D. Paametes Vaiation Fo high pefomance applications the new adaptation mechanism contolle should be obust to paametes vaiation. Changes in the moment of inetia (J) and the oto esistance (R ) ae investigated though simulation tests. The simulation tests ae undetaken by changing one paamete at a time while keeping othe paametes unchanged. The induction moto is commanded to acceleate fom est to efeence speed of 7ad/sec unde no toque load. Figue 6 shows the induction moto esponses of FOPI and conventional PI contolles when the moment of inetia is inceased by 1% of its oiginal value, whilst Figue 7 depicts the estimated speed esponses when the oto esistance inceased by 14% of its oiginal value. It is vey much clea fom Figues 6 and 7 that the new adaptation mechanism contolle is less sensitive to paametic vaiations and a obust tacking pefomance is achieved in pesence of the uncetain paametes. Futhemoe, when caefully study Figue 6 and 7 accoding to the settling time, oveshoot and speed eo, the best pefomance belongs to new adaptation mechanism contolle. Although, the ise time fo the conventional PI contolle is still faste than fo FOPI contolle Refeence Speed Estimated Speed using FOPI Contolle Estimated Speed using PI Contolle Figue 6: Response of the IM using two adaptation mechanism contolles with vaiation in the moment of inetia Refeence Speed Estimated Speed using FOPI Contolle Estimated Speed using PI Contolle Figue 7: Response of the IM using two adaptation mechanism contolles with vaiation in the oto esistance VI. CONCUSION In this pape a novel adaptation mechanism using FOPI contolle, which eplaces conventionally used PI contolle in the adaptation mechanism of the RF-MRAS based speed obseve fo the sensoless contol of induction moto is poposed. Simulation esults have been pesented to compae both the FOPI Intenational Jounal of Scientific Reseach in Science, Engineeing and Technology (ijsset.com) 216

7 and conventional PI contolles and it was found that FOPI contolle shows bette tansient pefomance when compaed to conventional PI contolle. Also as can be seen fom the diffeent speed wavefoms the speed eo between the efeence speed and estimated speed is low when FOPI contolle is used in place of conventional PI contolle. Robustness of the two contolles against system paametes vaiation is also veified. Simulation esults show that the FOPI contolle shows bette pefomance than the classical PI contolle in the face of system paametes vaiation. Howeve, the application of the new adaptation mechanism contolle does not consideably impove the ise time pefomance. VII. REFERENCES [1] Dubey, Fundamental of Electical Dives Fundamental of Electical Dives, Naosa Publication, Second Edition, 211. [2] Dheeaj and Meghna, Compaison of Vecto Contol Techniques fo Induction Moto Dives, Indian Jounal of Electical Biomedical Enginee, Vol. 1, 213. 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