HIGH PERFORMANCE CONTROLLERS BASED ON REAL PARAMETERS TO ACCOUNT FOR PARAMETER VARIATIONS DUE TO IRON SATURATION

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1 213 NDIA GROUND VEHICLE SYSTEMS ENGINEERING AND TECHNOLOGY SYMPOSIUM VEHICLE ELECTRONICS AND ARCHITECTURE (VEA MINI-SYMPOSIUM AUGUST 21-22, TROY, MICHIGAN HIGH PERFORMANCE CONTROLLERS BASED ON REAL PARAMETERS TO ACCOUNT FOR PARAMETER VARIATIONS DUE TO IRON SATURATION Jorge G. Cintron-Rivera 1, Ph.D. Caniate Shanelle N. Foster 1, Ph.D. Caniate Wesley G. Zanarelli 2, Ph.D. an Elias G. Strangas 1, Ph.D. 1 Michigan State University -Department of ECE - East Lansing, MI Avance Propulsion - U.S. ARMY TARDEC - Warren, MI 8397 ABSTRACT With the increase in electric power on military groun vehicle platforms, electrically riven accessories are replacing existing hyraulic, belt, an gear-riven loas. Permanent Magnet Synchronous Machines (PMSM are often selecte to rive these accessories, an are uner consieration for the main engine generator, ue to their torue ensity an efficiency being among the highest available. To maximize the efficiency of a PMSM, accurate knowlege of its parameters is reuire across the entire operating range. Efficient control of the onboar electric rives will help reuce fuel consumption in the groun vehicle fleet. This paper presents the effects of iron saturation on the performance of a PMSM rive. Iron saturation epens on the amount of current injecte into the motor an it restricts the amount of flux linkage that can be generate. PMSMs are controlle using a two axis space vector representation. Ieally, the control is ecouple, such that the flux linkage prouction in one axis is not affecte by the current in the other axis. However, iron saturation alters this behavior an the flux linkages become epenent on both axis currents. This paper emonstrates this phenomenon by parametric experimental characterization of two permanent magnet synchronous motors. A simple but epenable metho to approximate an inclue all the saturation effects, base on real parameters, is propose. The effectiveness of the propose metho is valiate through a simulation using the experimentally extracte parameters. INTRODUCTION Future Army groun vehicle platforms are expecte to generate significantly greater levels of onboar electric power, [1]. While traitional alternators can source approximately 6A current at 28VDC (16.8kW, emerging high-voltage generators irectly riven by the engine s crankshaft can prouce nearly an orer-of-magnitue increase in electric power (125-16kW. Benefits of the increase electric power inclue greater electrification of vehicle loas an intelligent power management, incluing some of the most significant loas such as the main engine cooling fan(s an air conitioning compressor. A key challenge remains to ensure that these loas along with the generator operate at maximum efficiency, [2]. Instea of being riven through a set of gears, a belt rive, or a hyraulic system, electrifie accessories len themselves well to variable spee operation an intelligent power management strategies, [3]-[5]. This allows them to run at varying operating points regarless of the main engine spee an they can be power limite on eman to support higher priority loas. While electric rives are generally able to efficiently convert electrical to mechanical power biirectionally, there are still opportunities to further improve this conversion efficiency, reucing the overall thermal buren on the vehicle cooling system. The key to improving the performance an efficiency of a motor rive is to evelop controllers base on real parameters, [6]-[7]. Such controllers are capable of acknowleging the parameters non-ieal behaviors an using them to operate as efficiently as possible, [8]. In [9], a look-up table to implement Maximum Torue Per Amp (MTPA control is propose. This metho oes not UNCLASSIFIED: Distribution Statement A. Approve for public release.

2 Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS inclue saturation effects. PMSMs are usually operate uner saturation [1], neglecting these effects can lea to controller performance egraation [11]. All saturation effects were inclue in both controllers propose in [12] an [13]. In [12], signal injection was use to etermine the parameters neee to evelop lookup tables an in [13], finite element analysis was use to ientify the machine parameters. Neither controller, however, is capable of operating in the fiel weakening region. In this paper, a metho to approximate the parameters of a PMSM is propose. The metho is base on experimental ata an it inclues the saturation effects using piecewise linear functions. The metho was valiate, in the MTPA an fiel weakening regions, using simulations base on real parameters from two 125kW PMSMs. BACKGROUND THEORY AND MODELING Permanent magnet synchronous machines are moele using the euivalent two axis moel shown in Figure 1, referre to as the synchronous frame of reference. This moel is obtaine by applying the Park s transformation matrix to the three phase stator uantities. i v Rs L e The complete machine moel after Park s transformation is given by euations (1 - (5. i v Rsi L el i Rsi e t t (1 i v Rsi L e Rsi e t t (2 Li (3 pm ( v L Rs L Figure 1: Euivalent two axes moel for a PMSM. e e pm 3P T i i (5 Where, are the currents an voltages in the irect an uarature axes. are the flux linkages ue to the permanent magnets an the corresponing axes currents. are the irect an uarature axis inuctances, is the electrical spee of the motor an T is torue Figure 2 shows the orientation frame to which the motor moel, (1-(5, is referre. In this orientation, the flux linkage ue to the magnets lies on the positive -axis, an torue is only prouce by the uarature current. The irect axis current is use as a fiel weakening mechanism an in the case of an interior permanent magnet machine it enables the prouction of reluctance torue. For motoring, PMSMs are generally operate in the secon uarant of the space plane, Figure 2, to perform fiel weakening an evelop the magnetic an reluctance torues. This classical moel (1-(5 is base on ieal conitions where the effects of iron losses, self an cross saturation, are neglecte. To stuy the effects of losses an iron saturation in PMSMs the classical moel is extene in orer to inclue these effects. When an saturate the iron paths in each corresponing axis, the flux linkages prouce by the magnetizing currents are no longer ecouple as shown in the ieal moel (3 an (. Instea, the flux linkages become couple to both axis currents, this coupling effect can be moele as follows, i, i L ( i i L ( i, i i (6 pm i, i L ( i i L ( i, i i (7 where, an are the baseline inuctances for each of the axes. They represent the corresponing axis selfinuctance as a function of the axis current an are calculate assuming no cross saturation from the other-axis current, [6]. an are the cross s axis I s voltage vector i V current vector v x i i, L ( i i x x x x x x x Lxyiy v i pm axis Figure 2: Vector orientation use for moel evelopment an control techniues. ( i, i L ( i i L i x x y x x x xy y Figure 3: Self an cross saturation of the flux linkages i x UNCLASSIFIED Page 2 of 9

3 Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS coupling inuctances for each axis an a the cross saturation effects to the machine moel. This self an cross saturation behavior is illustrate in Figure 3, where the x an y variables represent the an -axis Euations (6 an (7 coul be written in a variety of ways to moel the effect of both currents on the an -axis fluxes. The formulation use in this paper assigns all the cross coupling to the uasi-mutual inuctances an, the rest of the saturation to an, an assumes no effect of saturation of the flux ue to magnets, without ecreasing the moel accuracy. The machine moel incluing the saturation effects is calculate by substituting (6 an (7 into (1-(5. After some algebraic manipulation, the moifie machine moel is given by (8-(1. i i v Rsi L ( i L ( i, i t t L ( i i L ( i, i i e i i v Rsi L ( i L ( i, i t t L ( i i L i ( i, i e pm (8 (9 3P T i, i i i, i i (1 PARAMETER IDENTIFICATION PROCESS This paper is aime to fin an uantify the PMSM parameters, incluing the self an cross saturation effects, in orer to evelop a high performance controller. Knowlege of the non-ieal parameters is essential to evelop a highly efficient motor rive, [1]. To uantify this behavior, the parameter ientification metho propose in [6] was use. This metho is capable of extracting the parameters, incluing the non-ieal characteristics, by collecting an processing experimental ata. Similar methos for parametric ientification have been propose, [7] an they follow the same characterization principle. The ientification process is ivie into two main proceures: Experimental ata collection, as shown in Figure, an off-line ata processing. During the characterization process, the machine is stuie over its entire current operating range. The experimental ata is obtaine at a particular spee, an all possible current an angle combinations are applie to the machine. At every current/angle combination, the phase voltage information, experimental line currents, an rotor position are recore. Then, this information is processe off-line to accurately etermine the machine flux linkages, an e PMSM ABC Inverter V c, using (11 an (12. Given that the information collecte comes from experimental ata, the saturation effects an nonlinear behavior of the PMSM are capture. v i Rs i, i (11 ia, ib, ic Dyno DSP system Controller Boar s i, i e Spee Controlle ata logging an post-process Figure : Experimental Setup e CAN ata flow i R v (12 The flux information obtaine is sufficient to evelop a high performance controller, since an inclue the non-ieal characteristics of the machine. The non-ieal inuctance values can be calculate from this information. EXPERIMENTAL CHARACTERIZATION Two PMSMs, a motor an a generator, were characterize in orer to stuy the effects of iron saturation. The characteristics for each machine are given in table 1. Parameters Motor Generator Rate power 125 kw 125 kw Rate spee 15 RPM 19 RPM Max spee 5 RPM 3 RPM Line voltage 8 8 Max current No. poles 8 Table 1: PMSM parameters The parameters for both machines were etermine at 7 RPM as shown in figures 5-8. This spee is sufficient to generate a measurable back-emf voltage an it is below the base spee. Therefore, it is possible to collect experimental ata for all the rate current combinations of an. UNCLASSIFIED Page 3 of 9

4 L (i L (i (i (i L (i L (i (i (i Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS The experimental results in Figures 5-8, emonstrate that self an cross-saturation are non-ieal characteristics that cannot be ignore or assume to be negligible. For the motor, the flux linkage along the -axis ha as much as 38.5% variation ue to cross saturation, while the -axis ha as much as 23.7% variation. The generator behavior is similar, with flux variations as high as 31.% on the -axis flux an 1.5% on the -axis ue to cross saturation. These non-ieal parametric variations have a negative impact on the torue prouction of the machine, since the torue is irectly proportional to the flux linkages, as shown in (1. Efficiency is also affecte, as the parametric variations will etune the motor controller. For a given operating conition, the controller will not inject the optimal currents to generate the esire torue. 125 kw PM Motor, -axis flux linkage 125 kw PM Genertator, -axis flux linkage Saturation ue to i i x kw PM Genertator, -axis Inuctance Saturation ue to i i x kw PM Genertator, -axis Inuctance 6 Saturation ue to i pm 1.5 Saturation ue to i i i Figure 5: Generator experimentally extracte -axis flux linkage an -axis inuctance. 125 kw PM Genertator, -axis flux linkage Figure 7: Motor experimentally extracte -axis flux linkage an -axis inuctance kw PM Motor, -axis flux linkage Saturation ue to i x kw PM Genertator, -axis Inuctance 8 Saturation ue to i Saturation ue to i kw PM Motor, -axis Inuctance Saturation ue to i Figure 6: Generator experimentally extracte -axis flux linkage an -axis inuctance Figure 8: Motor experimentally extracte -axis flux linkage an -axis inuctance. UNCLASSIFIED Page of 9

5 Inuctance (H Inuctance (H Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS Both machines were also characterize through Finite Element Analysis (FEA. FEA is an excellent tool to etermine the basic operating characteristic of a PMSM. It is capable of incluing both self- an cross-saturation effects. However, the inclusion of cross-saturation effects with FEA reuires lengthy calculation time an a transient-magnetic simulation. Figure 9 an 1 show the axis inuctances for each machine, etermine using a FEA Magneto-static simulation scenario. This type of simulation was use, since it is consierably less time consuming than a full transientmagnetic simulation. These inuctances fit within the experimental inuctances shown in Figures Current(A Figure 9: Generator Finite Element Analysis - an -axis inuctance Generator Inuctances Motor Inuctances L L L L Current (A Figure 1: Motor Finite Element Analysis - an -axis inuctance. PROPOSED PARAMETER APPROXIMATION In orer to evelop a high performance controller, accurate knowlege of the parameters is reuire across the entire operating range. Look Up Tables (LUTs are commonly use to evelop controllers base on real parameters. By using a controller base on a LUT, it is possible to fully inclue the non-ieal parameter behavior shown in Figures 5-8 in the motor controller. The main rawback of a LUT is the reuire memory in the controller. The memory space reuirement is irectly proportional to the resolution of the LUT, [1]. In many applications, Digital Signal Processors (DSPs are use to implement the controller. These DSPs are commercially fabricate with a limite memory capacity. A LUT can be implemente in a DSP controller; however, the LUT resolution must be reuce to fit it in the available memory. This can lea to a ecrease in performance of the controller, as information is remove from the table s entries. An accurate curve-fit metho to approximate the real parameters of the motor an generator is propose in this paper. The metho is a ynamic piecewise linear approximation that inclues the parameters non-ieal characteristics, i.e., the cross-saturation effect. It can perform as well as a full parametric LUT controller, but it will not overstress the DSP/microcontroller memory, nor consume much computation time. For the case of, the true inuctance, shown in Figures 5 an 7, is ivie into two linear sectors, as shown in Figure 11. The first step is to etermine the baseline - axis inuctance from the experimental ata, given by (13. L ( i, i L ( i, i (13 The two linear approximations for (13 are highlighte in Figure 11 by the line with stars markers. Finally, the cross saturation for this case is ae by subtracting from this baseline approximation, as the other axis current increases. It is assume that cross-saturation in the -axis increases linearly with the -axis current. The incremental function is efine as. By using the experimental ata an inspection, it is etermine that the function representing the cross-saturation terms is as shown in (1. Finally, the total inuctance in these two sectors is given by euation (15. L x 1-3 Sector 2 L incluing Saturation an Cross-Saturation L ( i Figure 11: Motor -axis inuctance piecewise linear approximation, incluing cross saturation. ( sec1&2 L i ( i i (1 i rate sec1&1 (, ( ( sector 1 L i i L i i (15 UNCLASSIFIED Page 5 of 9

6 Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS In Figure 11, the two sector linear approximation an the true experimental inuctances are plotte together to illustrate the approximation usefulness. The -axis inuctance reuires more linear sectors, as shown in Figures 6 an 8, since it suffers higher saturation than the -axis uantities. Instea of two sectors to approximate this inuctance, four sectors are use as shown in Figure 12. The linear approximations mae in each sector are iscusse from right to left, beginning with sector. As shown in Figures 6 an 8, the effect from the -axis current is minimal in this sector. Therefore, the inuctance approximation is mae by fining the linear euation that intersects points an. L 1_upper 1_lower 2_lower Cross-saturation 2_upper 3_upper Sector 3 Cross-saturation Sector 1 Sector 2 3_lower x 2 x 3 Sector Cross-saturation x 5 Figure 12: -axis inuctance piecewise linear approximation, incluing cross saturation in four sectors. In sector 3, the cross-saturation effects are ae by introucing a ynamic slope change. In this sector, is a fixe point, but the slope of the baseline inuctance is ajuste as a linear function of, given by. The expressions to etermine the -axis inuctance in sector 3 are given by (16-(18. m( i i x x x x 3_ lower 3_ upper 3_ upper i _ rate ( 3 3 sec.3 3_ upper 3_ lower ( i i 3_ upper irate (16 (17 sec.3 L ( i, i m( i ( i x3 ( i (18 sec.3 In sectors 2 an 1, the linear approximation is mae using the same techniue use for the -axis inuctance, where the slope is constant an the cross-saturation is moele by the linear function. Note that all values of are known from the experimental ata. The complete approximation for the motor -axis inuctance along with the true experimental values are shown in Figure 13. The inuctance approximations for the generator were etermine using the same techniue an the results are similar to those of the motor. L Figure 13: Motor -axis inuctance piecewise linear approximation on top of the experimental -axis inuctance. CONTROLLER PERFORMANCE EVALUATION To evaluate the accuracy of the propose parameter approximation metho, a performance simulation base on experimental ata was evelope for each PMSM. The simulation was performe with four ifferent controllers as shown in Figure 1. For this stuy, only the copper losses were consiere. This leas to high efficiency results, but it serves as a proof of concept. Torue reuest Spee L incluing Saturation an Cross-Saturation Motor Controller Base on: 1. Detaile Parameters 2. Parameters w/o cross saturation 3. Propose Metho. FEA base parameters i, i * * i pm Motor Moel Base on Experimental Data Torue, Losses Figure 1: Simulation base on motor experimental ata. First, a highly etaile controller was evelope using a LUT. This controller contains all the saturation effects of the motor. Therefore, this controller is use as the baseline. The tables resolution has steps of 2.5A from zero to 25A. For each current step there is a table entry that matches a torue comman an a spee to a set of an. The secon controller was evelope using experimental ata, but the cross-saturation effects were ignore. For this case the table s resolution is the same as the first case. The thir controller is evelope using the propose parameter approximation metho. Finally, a controller base on FEA was evelope to compare with the experimental UNCLASSIFIED Page 6 of 9

7 Power Copper Losses Power Copper Losses Power Copper Losses Power Copper Losses Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS parameters. The controllers evelope using the propose an FEA parameters are base on curve fit methos. Each controller was teste in the MTPA an fielweakening regions. For each region, the torue comman was varie from 2 Nm to maximum, an the power copper losses an torue for each operating point was calculate. The results for the performance simulation are shown in Figures w cross-sat (LUT Losses as a function of loaing w/o cross-sat (LUT w propose a Power losses at rate conitions Losses as a function of loaing w cross-sat (LUT w/o cross-sat (LUT w propose b Power losses at 3RPM, fiel weakening Figure 15: Generator (consiering copper losses only, at a rate conitions, an b a eep fiel weakening operation point. put Generator Torue Performance put Generator Torue Performance 32 w cross-sat (LUT w/o cross-sat 3 w propose T 28 out a Rate Conitions b 3 RPM case Figure 16: Generator torue (consiering copper losses only, at a rate conitions, an b a eep fiel weakening operation point Figures 15 an 16 show the performance simulation for the generator. For both operating regions, the controller that performe almost as well as the baseline high resolution LUT controller was the controller esigne with the propose parameter approximation metho. This statement is base on the lower power losses an the torue tracking effectiveness. Figure 15 shows that minimum power losses were achieve with the base line controller an the controller using the propose parameters approximation techniue. On the other han, the controllers esigne using FEA parameters an the parameters ignoring cross-saturation are the controllers that yiele the highest power losses. Similar behavior was note for the torue performance shown in Figure 16 where the controller esigne using the propose parameters follows the etaile LUT controller torue performance Losses as a function of loaing w cross-sat (LUT w/o cross-sat (LUT w propose a Power losses at rate conitions Losses as a function of loaing w cross-sat (LUT w/o cross-sat (LUT w propose b Power losses at 3RPM, fiel weakening Figure 17: Motor (consiering copper losses only, at a rate conitions, an b a eep fiel weakening operation point. The motor exhibite similar behavior as shown in Figures 17 an 18. However, power losses are higher for the motor because it experiences more cross-saturation than the generator. For the motor, the controller esigne using the propose parameter approximation metho ha the closest performance to the etaile LUT controller. UNCLASSIFIED Page 7 of 9

8 Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS put Motor Torue Performance put Motor Torue Performance 32 w cross-sat (LUT 3 w/o cross-sat w propose a Rate Conitions b 3 RPM case Figure 18: Motor torue (consiering copper losses only, at a rate conitions, an b a eep fiel weakening operation point. CONCLUSIONS In this paper, the effects of iron saturation on the performance of a motor rive are stuie using two PMSMs. The flux linkages an inuctances of each machine were etermine through a characterization process an are shown in Figures 5-8. Saturation is evient from these figures an cannot be ignore or assume negligible. It is possible to obtain the parameters reuire to esign a motor controller through FEA simulations or experimental ata collection. The inclusion of cross-saturation effects in the controller evelopment is vital to ensure a high performance, high efficiency controller. A metho to inclue these effects is propose. It was teste against controllers base on high resolution LUT, LUT without cross-saturation, an FEA parameters. Figures emonstrate the valiity of the metho. The simulations showe that the propose metho has low an goo torue performance; both metrics are comparable to the performance of the high resolution LUT controller at both low an high spees. Compare with conventional approaches, the propose metho applie to a 125kW machine contribute to a reuction in copper losses as high as 9W, resulting in an efficiency gain of 1.36%. The propose controller, incorporating a ynamic piecewise linear approximation of the machine flux linkages, is realizable in the majority of motor control DSPs use in high performance PMSM controllers ue to its computational efficiency. The controller helps to improve the ynamic response of the rive an its improve efficiency contributes to a ecrease thermal buren on the cooling system in military groun vehicle applications. REFERENCES [1] Khalil, G., "Challenges of hybri electric vehicles for military applications," Vehicle Power an Propulsion Conference, 29. VPPC '9. IEEE, vol., no., pp.1,3, 7-1 Sept. 29 [2] Yuan Cheng; Trigui, R.; Espanet, C.; Bouscayrol, A.; Shumei Cui, "Specifications an Design of a PM Electric Variable Transmission for Toyota Prius II," Vehicular Technology, IEEE Transactions on, vol.6, no.9, pp.16,11, Nov. 211 [3] Estima, J.O.; Marues Caroso, A.J., "Efficiency Analysis of Drive Train Topologies Applie to Electric/Hybri Vehicles," Vehicular Technology, IEEE Transactions on, vol.61, no.3, pp.121,131, March 212 [] Seok-Myeong Jang; Seon-Ik Hwang; Kyoung-Jin Ko; Jang-Young Choi; So-Young Sung, "Driving performance evaluation of interior permanent magnet (IPM motor using circuit parameter estimation," Electrical Machines an Systems (ICEMS, 21 International Conference on, vol., no., pp.125,128, 1-13 Oct. 21 [5] Fajkus, P.; Klima, B.; Hutak, P., "High spee range fiel oriente control for permanent magnet synchronous motor," Power Electronics, Electrical Drives, Automation an Motion (SPEEDAM, 212 International Symposium on, vol., no., pp.225,23, 2-22 June 212 [6] J. G. Cintron-Rivera, A. S. Babel, E. E. Montalvo-Ortiz, S. N. Foster an E. G. Strangas, A Simplifie Characterization Metho Incluing Saturation Effects for Permanent Magnet Machines, 212 International Conference on Electrical Machines (ICEM, pp , 212. [7] Babel, A.S.; Foster, S.N.; Cintron-Rivera, J.G.; Strangas, E.G., "Parametric sensitivity in the analysis an control of permanent magnet synchronous machines," Electrical Machines (ICEM, 212 XXth International Conference on, vol., no., pp.13,1, 2-5 Sept. 212 [8] S. Kim, Y. Yoon, S. Sul, K. Ie, "Maximum Torue per Ampere (MTPA Control of an IPM Machine Base on Signal Injection Consiering Inuctance Saturation," Power Electronics, IEEE Transactions on, vol.28, no.1, pp.88,97, Jan [9] Y. Nanfang, L. Guangzhao, L. Weiguo an W. Kang, Interior Permanent Magnet Synchronous Motor Control for Electric Vehicle Using Look-up Table, 212 IEEE 7 th International Power Electronics an UNCLASSIFIED Page 8 of 9

9 Proceeings of the 213 Groun Vehicle Systems Engineering an Technology Symposium (GVSETS Motion Control Conference, vol. 2, pp , June 2-5, 212. [1] T. Herol, D. Franck, E. Lange an K. Hameyer, Extension of a - Moel of a Permanent Magnet Excite Synchronous Machine by incluing Saturation, Cross-Coupling an Slotting Effects, 211 IEEE International Electric Machines an Drives Conference (IEMDC, pp , May 211. [11] Seok-Myeong Jang; Seon-Ik Hwang; Kyoung-Jin Ko; Jang-Young Choi; So-Young Sung, "Driving performance evaluation of interior permanent magnet (IPM motor using circuit parameter estimation,"electrical Machines an Systems (ICEMS, 21 International Conference on, vol., no., pp.125,128, 1-13 Oct. 21 [12] S. Kim, Y. Yoon, S. Sul, K. Ie, "Maximum Torue per Ampere (MTPA Control of an IPM Machine Base on Signal Injection Consiering Inuctance Saturation," Power Electronics, IEEE Transactions on, vol.28, no.1, pp.88,97, Jan [13] Z. Li, H. Li, "MTPA control of PMSM system consiering saturation an cross-coupling," Electrical Machines an Systems (ICEMS, th International Conference on, vol., no., pp.1,5, 21-2 Oct. 212 [1] J.G. Cintron-Rivera, S.N.. Foster, C.E. Nino-Baron an Elias G. Strangas, High Performance Controllers for Interior Permanent Magnet Synchronous Machines Using Look-up Tables an Curve-fitting Methos, IEMDC 213 Ohare, Illinois. UNCLASSIFIED Page 9 of 9