PERFORMANCE ANALYSIS OF FUZZY BASED FIELD ORIENTED CONTROL OF

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1 PERFORMANCE ANALYSIS OF FUZZY BASED FIELD ORIENTED CONTROL OF INDUCTION MOTOR DRIVES FOR HYBRID ELECTRIC VEHICLES ABSTRACT 1 Maiam Khan, Student Membe, IEEE and 2 Naayan C. Ka, Membe, IEEE Electical Machine and Dives Reseach Laboatoy Univesity of Windso 1 khan11z@uwindso.ca 2 nka@uwindso.ca Induction motos (IMs) have widely been egaded as one of the most suitable options in automotive industy fo electic populsion systems of hybid electic vehicles (HEVs) due to thei eliability, uggedness and low cost. In the past, poo dynamic esponse of IMs was a key constaint that limited thei capability in applications that equie speed tacking and fast positioning. Howeve, the development of field oiented contol made it possible to decouple the stato cuent into flux and toque poducing components, enabling an independent command on the moto toque fo a simple, moe accuate speed contol. Design of a field oiented contolle equies the knowledge of the phase angle of oto flux. Indiect field oiented contol (IFOC) is a method to detemine this phase angle by estimation which eliminates the equiement of additional sensos. Howeve this estimation inceases the complexity and the computation time of the contol system. Fuzzy logic offes an altenative technique to design such a contol system by making decisions based on human expetise, thus avoiding complex calculations. This pape descibes the implementation of IFOC using both a conventional PI as well as a fuzzy based contolle to compae thei pefomance. Since a fuzzy based contol does not depend on machine equations and pefoms on the basis of linguistic if-else decisions, it poduces a faste speed esponse. Moeove, the toque and speed oscillations wee obseved to be much lowe, as desied in an HEV dive tain. KEYWORDS: Fuzzy logic, Hybid Electic Vehicle, Indiect field oiented contol, Induction moto dive, Pefomance analysis. I. NOMENCLATURE L m L L R R s ω s ω ψ qs ψ ds ψ q ψ d i qs i ds i q i d II. :Mutual inductance :Roto inductance :Roto leakage inductance :Roto esistance :Stato esistance :Synchonous speed :Roto speed :q-axis stato flux :d-axis stato flux :q-axis oto flux :d-axis oto flux :q-axis stato cuent :d-axis stato cuent :q-axis oto cuent :d-axis oto cuent INTRODUCTION The pefomance of a hybid electic vehicle (HEV) depends on the behavio of its electic populsion system that consists of a taction moto and its electical dive. Selection of an appopiate moto plays a cucial ole in the pefomance of the HEV dive tain and is an on-going topic of eseach in the automotive industy. The taction moto dive should offe wide speed anges, high powe, fast toque 1

2 esponse, eliability unde hash opeating conditions of the moto along with low cost and maintenance fo maket acceptability [Zeaoulia and Diallo]. Among the electic motos pesent in the maket, pemanent magnet (PM) synchonous motos, switch eluctance motos (SRMs) and induction motos (IMs) ae possible candidates since they exhibit the chaacteistics desied in taction applications in hybid vehicles. PM synchonous motos have high powe density, low toque ipples, and ae easy to contol but thei high cost and low efficiency at extended speed anges ceates a disadvantage [Williamson et al]. Similaly, dawbacks of SRMs include high acoustic and electomagnetic intefeence (EMI) noise; toque ipples and need fo a special invete topology. Induction motos ae suitable fo HEVs due to thei low cost, simple constuction, minimum maintenance equiement and low weight. They ae extemely eliable and ugged making them well suited fo sevee opeating envionment of HEV taction. They can be ated fo highe powe levels with low acoustic noise and can achieve a wide speed ange opeation beyond base speed though flux weakening. IMs have been used in vaious industial applications fo a long peiod of time. This is why in tems of design, manufactue and contol technique induction motos ae the most matue. Although pevious methods displayed poo dynamic esponse, vecto contol also known as field oiented contol (FOC) of induction machines has enabled the decoupling of stato cuent into toque and flux poducing components that gives independent contol ove the moto toque while maintaining a constant flux that enables an accuate and pecise IM contol. FOC is based on the knowledge of the phase angle of oto flux. In case of diect FOC this field angle is measued using flux sensos o calculated fom teminal voltage. To emove this equiement of sensos, which adds to the cost of the machine, indiect field oiented contol was suggested whee the field angle is estimated using slip speed. Although vecto contol has been successfully implemented using PI compensation, the need to educe the computation time of such contol poblems is desied fo faste esponse. Fuzzy logic offes a substitute method to design a contol algoithm deived fom human intelligence of how the system should espond fo any given input. This pape will demonstate the impovement in the moto dive pefomance by using fuzzy based contol system to implement IFOC. III. INDIRECT FIELD ORIENTED CONTROL OF INDUCTION MOTORS Scala contol stategies fo induction motos exhibit a poo dynamic esponse [Boussehane et al]. This is explained by the deviation of ai-gap flux linkage fom set value in both magnitude and phase. Since scala techniques contol the magnitude and fequency of the stato cuent and have no command ove the phase angle, the moto esponds with high toque and speed oscillations. In ecent yeas, development of field oiented contol has opened the possibility of using AC motos fo pecision contol [Lin and Liaw]. FOC allows the stato cuent to be decoupled into toque poducing and flux poducing components that can be contolled and maintained independent of each othe, making the contol much simila to that of a sepaately excited DC moto. FOC is based on the assumption that the position of the oto flux linkage ψ is at an angle θ f fom the stationay efeence fame as shown in Fig.1 [Kishnan]. Assuming ψ to be on the d-axis of the synchonously otating fame, the stato cuent can be esolved into a field poducing component i ds in phase with ψ, and a pependicula, toque poducing cuent component i qs. The oto voltage equations of the induction moto in the synchonous efeence fame ae given below. d vd = Rid ( ωs ω ) ψ q + dt (1) q v = R i + + q q ( ωs ω ) ψ d dt 2

3 V s i s i qs = i T φ θ T θ f θ sl i ds = i f Ψ Synchonous Refeence Fame θ Stationay Refeence Fame Roto Refeence Fame Fig.1. Phaso diagam of field oiented contol. The slip speed is defined as ω sl = ω ω (2) s Fo a squiel cage induction moto, the d and q axis oto voltages ae zeo. Hence (I) becomes d 0= Ri d ω slψ q + dt q 0= R i + + q ωslψ d dt Roto flux linkages of IM ae given as: ψ = L i + L + L i = L i + L i ψ d q m ds = L i m qs + ( m) d m ds d ( L + L ) i = L i + L i If the oto flux ψ lies on d-axis of the synchonous fame ψ d = ψ ψ q = 0 Applying (5) to (3), the oto voltage equations become: R i R i d q m q + = 0 dt + ω = 0 slψ Roto cuents can be deived fom the flux linkage equations by substituting (5) in (4): Lm iq = iqs L ψ Lm i = d ids L L m qs q (3) (4) (5) (6) (7) 3

4 Solving (6) and (7), the q and d axis stato cuents ae given as: Lψ it = iqs = ωsl R Lm 1 L i = i = f ds ψ + L R dt m Since the cuent component esponsible fo geneating field must be in phase with the oto flux, the d- axis stato cuent is established as i f. Hence the pependicula component i qs must be the toque poducing facto and is named i T. PLUG IN (8) Battey Chage Battey * ω ψ ω ψ L if = + L R L m PI o Fuzzy Contol m dt i f i T Slip Calculato Cuent Magnitude & Phase Calculato ω sl θ sl θ i as i bs i cs 6-Pulse Input to Invete Cuent Contolle Speed Tansduce V DC 3-Phase Invete IM Mechanical Tansmission ICE Fig.2. IFOC of induction moto dive in plug-in HEV application. Fig.2 shows the indiect vecto contol scheme of induction moto. A tansduce sends the oto speed signal to a conventional PI contolle that geneates a toque command based on the deviation fom set speed [Liaw et al]. This toque command is used to calculate the cuent component i T. 3 P Lm Te = ( ψ diqs ψ qids ) (9) 2 2 L Within the nomal age of opeation, flux can be kept constant poducing a constant field component i f [Wijesundea and Jackson]. The field and toque poducing components detemine the magnitude of the stato cuent. i = i + i (10) s Phase of the cuent signal is the sum of θ f and θ T whee θ = tan 1 ( i / i ) (11) T The field angle is the sum of slip angle θ sl and oto angle θ that ae obtained by the integation of slip speed and oto speed espectively. The stato cuent magnitude and phase angle ae sent to a cuent contolle that detemines the 3-phase cuent signal and geneates pulses to dive the PWM invete. PI is one of the most commonly used contol methods due to its simplicity. It depends on the tuning of its 2 f T 2 T f 4

5 popotional gain K p and integal gain K i which can be can be adjusted though tials to give optimum esponse. The PI compensation is given by the equation below. K i Gc ( s) = K p + (12) s Incease in K p educes eo and ise time wheeas highe K i values educe oscillations but incease settling time. Although this contol method is eliable and has been in use extensively fo contol systems application, howeve, it lacks the ability of efficient tacking and egulation simultaneously. Moeove, the complex computation of the IFOC technique and paamete sensitivity is also a concen. The slip speed is calculated using i T which is a function of oto esistance. In a hybid vehicle this esistance is expected to incease as the engine heats up, esulting in deviation fom set speed. IV. FUZZY BASED FIELD ORIENTED CONTROL Fuzzy logic offes a linguistic appoach to develop contol algoithms fo any system. It maps the input-output elationship based on human expetise and hence, does not equie an accuate mathematical model of the system. This consequently makes the fuzzy contol toleant to paamete vaiation. Moeove, the nonlineaities that ae geneally difficult to model o ae ignoed altogethe to educe complexity ae accounted fo in a fuzzy contol system, making it moe accuate and obust. Fig.3 shows the fuzzy contol scheme fo IFOC. The contolle accepts two inputs, eo e between the efeence speed and oto speed; and the ate of change of eo. Both inputs ae mapped on fuzzy sets with a univese of discouse anging fom -360 to 360. Fuzzy sets fo each input consist of 7 membeship functions fom negative lage (NL), negative medium (NM), negative small (NS), zeo (ZO) upto positive lage (PL). Similaly the output has a univese of discouse fom -1 to 1. Gain G in is tuned to map the acceleation to the given ange of fuzzy sets and G out is tuned to scale the contolle output to a coesponding value of i T equied to contol the moto. The fuzzified inputs ae eceived by the ule base that geneates the consequent value fo change in cuent signal, i T, based on the specified if-else ules. The ule base detemines the weight of each membeship function fo the inputs and tigges the coesponding ules. Fo example if both e and ae NL it implies that the oto speed is vey low and it is futhe deceleating, hence i T is set to PL to incease the value of q-axis stato cuent. On the othe hand if e is ZO and is PL it suggests that although the oto has achieved desied speed, it will continue to acceleate and is expected to oveshoot, so i T is educed by setting i T to NL. Thus it is possible to pedict the extent of speed deviation expected fom the moto in the successive time steps. The entie ule base is hence designed based on human peception as to how much the cuent must incease o decease depending on the speed and as well as the acceleation of the moto to educe the deviation aound the efeence signal. Once the ule base is designed, it can be efined fo accuate esults though tials. Fuzzy Logic Contolle G in Fuzzification d dt e Fuzzy Infeence Engine G out du i T ω ef Defuzzification i T ω Fig.3. Block diagam of fuzzy contolle. 5

6 NS NM NS Z0 PS PM PL NS NM NS Z0 PS PM PL (a) (b) Fig.4. (a) Input membeship functions, (b) Output membeship functions. e NL NM NS ZO PS PM PL NL PL PL PL PL PL PL NS NM PL PL PM PM PS ZO NM NS PL PM PS PS NS NM NM ZO PM PM PS ZO NS NM NM PS PM PM PS NS NM NM NL PM PM ZO NS NM NM NL NL PL PS NL NL NL NL NL NL (a) (b) Fig.5. (a) Fuzzy ule base, (b) 3D suface view of the fuzzy ule base. The net weight of the output cuent is computed fom the tiggeed membeship functions using Min aggegation method. The weighted output is tansfomed into equied cuent signal though defuzzification. This is accomplished by the invese tansfomation to map the calculated output fom the fuzzy domain to a cisp eal-time value. The conventional method of defuzzification is the cente of aea (COA), which calculates the cente of the aea epesenting the output fuzzy tem. The output u of the contolle is given by: µ ( xi ) xidu u= (13) µ ( x ) du whee x i is a point in the univese of discouse and µ(x i ) is its membeship value in the membeship function. i 6

7 Since the effective output fom the fuzzy contolle is the amount of incement o decement in cuent signal, i T, it is integated to geneate the net value fo the toque poducing cuent component i T [Hebe]. This fuzzy based contol algoithm was implemented in the Fuzzy Toolbox of Matlab/Simulink. The toolbox allows the use to ceate multiple inputs and outputs, define the ule base in linguistic tems in the Rule Base Edito and is also capable of displaying which ules ae tiggeed fo any given set of inputs to indicate the consequent output geneated. Conventional PI contol has the limitation of being one dimensional. Fuzzy contolle, on the othe hand, can have multiple inputs and multiple outputs. The inputs of the system descibed above not only help to detemine the net eo but also pedict how fast the eo is changing, enabling the contolle to give a bette esponse in time, thus ensuing smalle oveshoots. It can be seen that the fuzzy contolle is independent of any moto paametes and does not equie machine equations making the contol moe obust. V. SIMULATION RESULTS Field oiented contol design fo induction moto was implemented in MATLAB/Simulink. Fig.6 shows the tacking pefomance of PI contol fo a 3 phase, 2 Pole, 37kW squiel cage induction moto unde no load. Given a efeence speed of 1800 pm, the PI contolle takes appoximately 1.65 seconds to each steady state. The speed oveshoots by 500 pm befoe attaining set speed. This oveshoot can be deceased by educing the value of K i, but the esulting esponse will have highe oscillations. This is why the tuning of gain values in the PI contolle is a tade-off between highe oscillation and highe oveshoot with delayed esponse. Pefomance of the fuzzy contolle fo the same efeence signal unde no load is shown in Fig. 7. The fuzzy based contol was able to each set speed in 1 second with a vey small oveshoot. Fo eal-time speed tacking, this fast esponse of fuzzy contolle can ensue apid acceleation of the vehicle in shot duation. Fo the PI contol, the high cuent oscillations sustain fo 1.2 seconds which consequently esults in oscillation of the electomagnetic toque T e. These high toque oscillations poduce fatigue on vehicle components and vibations duing the dive that ae undesiable fo passenges. Fo the fuzzy contolle, on the othe hand, cuent oscillations each the steady state value in 0.4 seconds which is tansfeed into educed toque oscillations, ensuing that the moto uns smoothly. Reseach is cuently in pogess to detemine the behaviou of fuzzy contolle unde applied load changes and paamete vaiations. The aim is to apply a change in the loading condition while moto is opeating in steady state. Unde the opeating conditions of the vehicle, due to highe tempeatues, oto esistance of the induction machine is susceptible to change. Response of the fuzzy based contol system will be analysed fo this change in oto esistance. These esults will be compaed with the esponse of the PI contolle fo the same paametic changes. It is expected that fuzzy contolle will have smalle deviation fom set speed unde change in loading condition and paamete vaiation since it is independent of machine equations. To obseve the pefomance of the fuzzy based contol in eal-time speed tacking, the above mentioned technique will be implemented on an expeimental setup consisting of a vecto contol based induction moto dive. These expeiments ae expected to veify the simulated esults. 7

8 (a) (a) (b) (b) (c) Fig.6. Roto speed (pm), (b) Stato cuent (A) and (c) Electomagnetic Toque (Nm) fo PI contol. (c) Fig.7. Roto speed (pm), (b) Stato cuent (A) and (c) Electomagnetic Toque (Nm) fo fuzzy contol. VI. CONCLUSION The pefomance of fuzzy based IFOC fo HEVs in compaison to a PI contol has been demonstated in this pape. Fom the simulation esults it is clea that fuzzy based algoithm is an efficient substitute contol methodology that gives faste esponse with lowe speed deviation to ensue apid acceleation and smooth dive in automobiles. Lowe toque and cuent oscillations help limit the stesses on the moto as well as the est of the mechanical components of the vehicle. PI contol equies tial and eo fo tuning of its popotional and integal gain, wheeas fuzzy contolle is tuned by intelligent peception. Since the ule base and membeship functions ae identified in linguistic tems, they ae easie to compehend, design and tune. Using ate of change of eo as an input helps in pedicting how much the eo is expected to educe o incease in the next time cycle. This allows the contolle to make an intelligent esponse ahead of time without letting the speed deviate to a lage extent. Moeove 8

9 the contol algoithm is independent of machine equations, making the computation faste and less inticate. VII. ACKNOWLEDGEMENT The wok epoted in this pape was suppoted by National Sciences and Engineeing Reseach Council (NSERC) of Canada. VIII. REFERENCES [1] Boussehanem, I., Hazzab, A., Rahli, M., Kamli, M. and Mazai, B. (2006), Diect Field-Oiented Contol Design using Backstepping Technique fo Induction Moto Speed Contol, 14 th Mediteanean Confeence on Contol and Automation, June. [2] Hebe, B.,Xu, L. and Tang, Y. (1997), Fuzzy Logic Enhanced Speed Contol of an Indiect Field- Oiented Induction Machine Dive, IEEE Tansaction on Powe Electonics, Vol. 12, [3] Kishnan, R. (2001), Electic Moto dives: Modeling, Analysis and Contol, Pentice Hall, New Jesey. [4] Liaw, C., Chao, K. and Lin, F. (1992), A Discete Adaptive Field-Oiented Induction Moto Dive, IEEE Tansaction on powe Electonics, Vol. 7, [5] Lin, F. and Liaw, C. (1993), Contol of Indiect Field-Oiented Induction Moto Dives Consideing the Effects of Dead-Time and Paamete Vaiations, IEEE Tansaction on Industial Electonics, Vol. 40, [6] Wijesundea, D. and Jackson, R. (1992), Obseves fo Field-oiented Contol of Induction Moto Dives, IEE Poceedings on Electic Powe Applications, Vol. 139, [7] Williamson, S., Lukic, S. and Emadi, A. (2006), Compehensive Dive Tain Efficiency Analysis of Hybid Electic and Fuel Cell Vehicles Based on Moto-Contolle Efficiency Modeling, IEEE Tansaction on Powe Electonics, Vol. 21, [8] Zeaoulia, M., Benbouzid, M. and Diallo, D. (2006), Electic Moto Dive Selection Issues fo HEV Populsion Systems: A Compaative Study, IEEE Tansaction on Vehicula Technology, Vol. 55,