University of Sidi Mohammed Ben Abdellah Fez, Morocco

Transcription

1 Matlab & Simulink Simulation with FPGA-Base Implementation Sliing Moe Control of a Permanent Magnet Synchronous Machine Drive BADRE BOSSOUFI (Stuent Member IEEE) 1)2), MOHAMMED KARIM 1), SILVIU IONIłĂ (Senior Member IEEE) 2), AHMED LAGRIOUI 1), GABRIEL V. IANA 2) 1) EVIA Team, Faculty of Sciences Dhar El Mahraz University of Sii Mohamme Ben Abellah Fez, Morocco 2) Center of Moeling an simulation of the systems, Faculty of Electronics, Communications University of PITEŞTI, Romania Bare_isai@hotmail.com, karim_lessi@yahoo.fr, silviu.ionita@upit.ro, lagrioui71@gmail.com, gbiana2000@gmail.com Abstract: This paper starts with an overview of FPGA technology evelopment, followe by a presentation of esign methoologies, evelopment tools an relevant CAD environments, incluing the use of portable harware escription languages an system level programming/esign tools. In this paper, a new contribution for the FPGA-Base implementation of controls electrical. This approach is base on concept moularity an reusability. In this paper is presents a etaile escription of the structure by Inirect Sliing Moe of Permanent Magnet Synchronous Machine PMSM. Experimental results carrie from a prototyping platform are given to illustrate the efficiency an the benefits of the propose approach an the various stages of implementation of this structure in FPGA. Keywors: Permanent Magnet Synchronous Machine (PMSM), FPGA, Inirect Sliing Moe Control, Power System Control, Systems Generator, Reusability, PWM. 1. Introuction The Permanent magnet synchronous Motor is an electric actuator very robust an has a low moment of inertia compare to a DC machine. This characteristic confers to him a ynamics characterize by weak constants of times what makes it possible to esign controls in torue, of spee an in position with a better precision an very satisfactory ynamic performances[1, 2, 3]. Currently, two of the best techniues for controlling electrical machines have high performance for the Control of PMSM, namely the Direct Torue Control an the Space Vector Moulation Control. Invente by twentieth century, its operating principles are totally ifferent but the goals are the same. its main objectives an control of torue an current to force the target to follow instructions given by the user with high accuracy an stability, but regarless of the variation of machine parameters an isturbances submitte by outsie [4]. However, specific harware technologies such as fiel programmable gate arrays (FPGAs) can also be consiere as an appropriate solution in orer to boost the performance of controllers. Inee, these generic components combine low cost evelopment (owing to their reprogrammability), use of convenient software tools, an more an more significant integration ensity [5-8]. FPGA technology is now consiere by an increasing number of esigners in various fiels of application such as wire an wireless telecommunications [9], an image an signal processing [10, 11], where the always more emaning ata throughputs take avantage of the ever increasing ensity of the chips. Still, more recently, other application fiels are in growing eman, such as meical euipment [12], robotics [13] [15], automotive [16], an space an aircraft embee control systems [17]. For these embee applications, reuction of the power consumption, thermal management an packaging, reliability, an protection against solar raiation are of prime importance an electrical control systems. This last omain, i.e. the stuies of control of electrical machines, will be presente in this paper. The principal avantages of the igital solutions are as follows: High flexibility of changing structures of control; ISSN: Issue 3, Volume 6, March 2011

2 Immunity against isturbances; No problems of variations of control parameters. With technological avancement, increase integration of FPGA evices is increasing. Nowaays, the ensity of FPGA components can achieve the euivalent of 10 million logic gates with switching freuencies of aroun 500 MHz. This allows the implementation of complex algorithms control in their entirety with a small perio of time to loa. The inherent parallelism of FPGA components offers the possibility to run several algorithms in parallel control an configure them accoring to the efine criteria. Dynamic configuration between the algorithms control has as objective to select the appropriate algorithms epening on your point of operation. It may be useful also to ensure continuous operation in case of faults (sensors, switches...). This paper presents the realization of a platform for Sliing Moe control (SMC) of PMSM using FPGA base controller. This realization is especially aime for future high performance applications. In this approach, not only the architecture corresponing to the control algorithm is stuie, but also architecture an the ADC interface an RS232 UART architecture. Consiering the complexity of the iversity of the electric control evices of the machines, it is ifficult to efine with universal manner a general structure for such systems. However, by having a reflexion compare to the elements most commonly encountere in these systems, it is possible to efine a general structure of an electric control evice of machines which is show in Fig.1: 2. Principle of Variable Structure Systems The principle of variable structure systems has been stuie primarily in the Soviet Union. Subseuently, much research on power systems control fiel has been mae elsewhere to complement the theoretical stuy an fin some possible applications. The sliing moe control is a particular operating moe of variable structure system. Using this comman has been limite longer ue to oscillations to the phenomena of slip an limitations of the switching freuency of power switches. There are ifferent regulatory structures by sliing moe current in systems base on variable structure sliing moe control. Consier the following controlle system (1): y = h( x) + G( x) u (1) t Where u is the input vector of imension, m, y is the state function of imension, n, h is the state function escribing the system evolution over time an G is a matrix of imension nm. For the synthesis of a regulatory structure by sliing moe, it is necessary to efine initially the switching function S(y) of imension m. S y) = S ( y)... S ( y) m, where S i (y) is the i th ( 1 [ ] t switching function S(y). 3. Moeling of the Synchronous Permanent magnet Machine The motor consiere in this paper is an interior PMSM which consists of a three phase stator winings an a PM rotor. The voltage euations in a synchronous reference frame can be erive as follows, Fig.1: Architecture Sliing Moe Control Fig.2: Scheme of the synchronous machine Φ u = rs. i + ω. Φ (2) t ISSN: Issue 3, Volume 6, March 2011

3 u Φ. ω Φ (3) t = rs +. Where the irect an uarate axis flux linkages are, Φ = L. i + Φ (4) f Φ = L. i (5) The electromagnetic torue of the motor can be evaluate as follows, [. I + ( L L ). I I ] 3 Ce = p φ f. (6) 2 The motor ynamics can be simply escribe by the euation (7). Ω Ce Cr = J. + f. Ω (7) t With: Ω: rotation's spee mechanical of the PMSM ω: rotation's spee electric. p: Number of pairs of poles. J : Total moment of inertia brought back on the tree of the PMSM. f : Coefficient of viscous friction. C r : Resistive torue. f: flux prouce by the permanent magnet. Φ : axis stator magnetic flux, Φ : axis stator magnetic flux, L : axis stator leakage inuctance, L : axis stator leakage inuctance, r s : stator wining resistance, C e : electromagnetic torue, 4. The control law base on sliing moe control of the inverter evelopment The control law sliing moe must simultaneously satisfy the conitions of invariance an attractiveness. To o this the switching function S (y) must satisfies [5]: S( y) = 0 - The invariance conition:. (8) S( y) = 0 - The attractiveness conition:. S i ( y) p 0 si Si ( y) f 0 for( i = 0... m) (9). S i ( y) f 0 si Si ( y) p 0 These conitions lea to etermining a new vector control: u = u + u (10) e att The vector control given by euation (10) comprises two terms [7]: - The first is the control vector specifying the euivalent control for the system to stay on the sliing surface. - The secon is the vector control that ensures the attractive control system outsie the sliing surface. It also reuires the system ynamics starting from an initial point until it reaches the sliing surface (Fig.3) [9]. Fig.3: The state of Sliing Moe trajectory 5. Inirect control by PMSM sliing moe stator current 5.1. Synthesis of a-inirect control by sliing moe The inirect control by sliing moe stator current vector of a permanent magnet synchronous machine ensures the calculation of irect an inverse components of the reference voltage vector expresse in the - plane. These components are then applie across the phases of the stator PMSM through an intermeiate stage of the PWM. The evelopment of such law control must satisfy simultaneously the conitions of invariance an attractiveness given by euations (8) an (9). The terms ω Φ an ω Φ are consiere as terms of electromotive forces inuce on the axis an an the expressions of the erivatives of the switching function Ṡ i an Ṡ are given by euations (11) an (12). Thus, the inirect control ISSN: Issue 3, Volume 6, March 2011

4 by sliing moe an components of stator current can be carrie out by taking on each axis an. Therefore, each component V an V is compose by two terms as shown in euation (10). The first term is the euivalent voltage vector which is active in steay state, while the secon term is the voltage vector which is attractive assets in transition. V = Ve + Vatt (11) V = Ve + Vatt For trajectories currents i an i remaine on their sliing surfaces (S i =0 an S =0), apply the voltage vectors V e an V e on the axis an axis. These vectors can be calculate taking into account the following invariance conitions: S. S i i V = ( i = 0 e i = r i s ) = 0 ω Φ i = i S i 1 = ( V t L = r i s ω Φ e r i s + ω Φ (12) ) = 0 S S i. S. S i rs = S L rs = S L 2 i 2 A S A S i sgn( S sgn( S i ) K S ) K S 2 i 2 (16) In summary: V Φ i ω L 0 = r s V Φ i ω L (17) A 0 sgn( Si ) K 0 Si ( + ) 0 sgn( ) 0 A S K S The following figure shows the sliing moe correction block iagram, satisfying the attractiveness an invariance conitions: S. S V = ( i = 0 e i = r i s ) = 0 + ω Φ = S 1 = ( V t L = r i s + ω Φ e r i s ω Φ (13) ) = 0 (a) Consiering the erive of switching functions an the control formulas, the new components V an V will be: Si V = rsi ωφ L = Ve + Vatt t (14) S V = + Φ = + rs ω L Ve Vatt t From this attractive voltage vector system of reference voltage vector involves the switching function erivative Ṡ i an Ṡ. A structure of attractiveness is chosen at a constant spee an proportional action, which gives: V V att att = L ( A sgn( S = L( A sgn( S i ) + K S ) + K S i ) ) (15) By applying the reference voltage vector given by the previous system, the result of the prouct of each of switching functions Ṡ i an Ṡ its own erivative is given by the following system: (b) Fig.4: Block iagram of the corrector inirect sliing moe (a) i, (b) i. Fig. 5: Inirect Sliing Moe Control applie to a PMSM ISSN: Issue 3, Volume 6, March 2011

5 For a given value of the reference current, the current i trajectory escribe by the system from Fig.4 is shown in Fig.6. The trajectory obtaine is characterize by two stages: the attractiveness moe an sliing moe. (a) (b) Fig.6: Trajectory characterizing the inirect control moe by sliing (a) Continuous operation (b) Discrete operation From this entire process, systems with variable structure controlle by an inirect sliing moe control have several properties: - The system oesn t epenent only on the sign of the switching function, but also it epens on its value. - The ynamics of the system controlle by such control epens essentially on the coefficients choice of the attraction moe matrices K an A. - The theory of inirect sliing moe is appropriate to systems whose control is iscontinuous Results of simulations The Fig. 7 shows the general structure of sliing moe control of the PMSM stator current in the reference. The i an i currents are subjecte to the transformation of Concoria for components i sα an i sβ. Each component is controlle by a sliing moe corrector that provie the reference U an U epenant by the electromotive forces of voltages. The result is applie to the Pulse With Moulation (PWM) component use for controlling the voltage inverter, which generates three-phase voltages V a, V b an V c that are subject to a Park transformation. Finally, the V an V are applie irectly in PMSM. Fig. 7: Block iagram of inirect sliing moe control for PMSM ISSN: Issue 3, Volume 6, March 2011

6 i s1 i s2 i s3 (A) Fig.8: Stator current Fig.11: Voltage V s1 Fig.9: Instea of the current vector in the plane (α β) Fig.12: Spee Rotor Fig.13: Torue electromagnetic Sliing Moe Attractiveness Moe Sliing Moe In the Fig. 8 to 13 are show the simulation result of inirect control by sliing moe stator when the current is applie between +I sn an -I sn (E=380V, freuency PWM=5 KHz, K = K = A = A = 320). It shoul be note that the ynamics of the transient is lower than that obtaine with other commans. However, the current has better uality control in steay state with fewer oscillations. The choice of coefficients A, A, K an K was selecte by follows criteria: Fig.10: Quaratic Current i ISSN: Issue 3, Volume 6, March 2011

7 - The moule reference voltage vector must not excee the maximum amplitue that can generate voltage of the inverter. - Coefficients chosen provie goo robustness against parameter variations where the higher coefficients provie better control. The coefficients shoul not cause strong current oscillations. The chosen coefficients are the result of several simulations where the selection criteria is it a goo factor. These coefficients allow controlle uantities to follow their references to an error of about 99% on the PMSM parameters (L, L an r s ). 6. Development of the esign methoology 6.1. FPGA evices There are several manufacturers of FPGA components such: Actel, Xilinx an Altera etc. These manufacturers use ifferent technologies for the implementation of FPGAs. These technologies are attractive because they provie reconfigurable structure that is the most interesting because they allow great flexibility in esign. Nowaays, FPGAs offer the possibility to use eicate blocks such as RAMs, multipliers wire interfaces PCI an CPU cores. The architecture esigning was one using with CAD tools. The escription is mae graphically or via a harware escription language high level, also calle HDL (Harware Description Language). Is commonly use language VHDL an Verilog. These two languages are stanarize an provie the escription with ifferent levels, an especially the avantage of being portable an compatible with all FPGA technologies previously introuce. Fig.14: Programming FPGA evisee The Fig.14 summarizes the ifferent steps of programming an FPGA. The synthesizer generate with CAD tools first one Netlist which escribes the connectivity of the architecture. Then the placement-routing optimally place components an performs all the routing between ifferent ISSN: Issue 3, Volume 6, March 2011

8 logic. These two steps are use to generate a configuration file to be ownloae into the memory of the FPGA. This file is calle bitstream. It can be irectly loae into FPGA from a host computer. In this paper an FPGA XC3S500E Spartan3E from Xilinx is use. This FPGA contains 400,000 logic gates an inclues an internal oscillator which issuer a 50MHz freuency clock. The map is compose from a matrix of 5376 slices linke together by programmable connections (Fig.15). Control Car PMODOD1 RS232 Connection with the PC & Power 5V USB Converter A/D ADCS7476MSPS 12-bit FPGA XC3S500 E Input / Output Connectors Reconfigurable Buttons Fig.15: The FPGA XC3S500E Spartan 6.2. Simulation Proceure The simulation proceures begin by checking the control algorithm functionality trough a functional moel using Simulink s (System Generator for Xilinx) blocks. For this application, the functional moel consists in a Simulink moel of the Inirect Sliing moe Control algorithm associate with a voltage inverter an PMSM moel. Fig.16 gives a global view of the functional moel. Fig.16: The schematic bloc of functional moel The escription of the ifferent moules is etaile below: The blocks of coorinate s transformation: the transformation of Park Inverse (abc-to); The blocks of coorinate s transformation: the transformation of Park (-to-abc); The PWM block is the most important, because can provie control pulses to the IGBT voltage inverter in the power section from well-regulate voltages; Two blocks Sliing Moe Corrector for the regulation of currents I an I from the comparison of measure values an reference values of stator currents; ISSN: Issue 3, Volume 6, March 2011

9 The block for FEM calculation an spee estimator; The block encoer interface IC allows the aaptation between the FPGA an the acuisition boar to iniuity the rotor position of the PMSM; The ADC interface allows the connection between the FPGA an the analog-igital converter (ADCS7476MSPS 12-bit A / D) that interfaces two Hall Effect tranucers for the stator currents machine acuisition; Block "Timing" which controls the synchronization between blocks, which allows the refresh in the voltages reference V 10, V 20 an V 30 at the beginning of each sampling perio; The RS232 block provie the signal timing an recovery of signals viewe, create by another program on Matlab & Simulink to visualize the esire output signal. 7. Experimental Set-up To implementing the control system by Sliing moe Control is it use a XC3S500E Spartan3E, ADC (analog to igital convertor) interface (Fig.17). The control unit architecture ensures a control moule for an A/D interface, an encoer interface an the control Sliing moule. The A/D interface moule an encoer interface are activate simultaneously at the beginning of each sampling perio. Then, after a elay conversion from analog to igital conversion t ADC, the control unit activates the control moule inirect sliing moe. This moule is controlle by its own control unit. First times, the Park transformation moule will calculate the components of i an i (t abc- ). Then, when the processing moule abc- inicates the en of its calculation, the estimation moule of the FEM is activate, has to calculate ω anω. It is Φ Φ running for t FEM time. Then the SM_I an SM_I moules are enable computing in parallel the tensions U an U (t SM_ ). Thereafter, when the moules inicate the en of the calculation, inverse Park transformation moule is activate an calculates the reference voltages U sa, U sb an U sc (t -abc ). After the PWM moule is enable. Latter has a computational time eual to t PWM an can calculate an refresh the reference voltages V 10, V 20 an V 30 which will be compare to a triangular carrier signals that generate control signals C 1, C 2 an C 3. Fig.17: FPGA base harware ISMC The following table shows the performance of computing time an resource consumption, obtaine uring the control Sliing Moe architecture implementation. The resources consume are obtaine for a fixe point format 13/Q12. The total computing time t SMI, in comman moule is eual to 1.04µs. By aing the analog to igital conversion ISSN: Issue 3, Volume 6, March 2011

10 time t A/D, total time Tex architecture brought ives euals 3.48µs. Moule Latency Time Calculation Interface A/D 120 t A/D =2.4 µs IC Interface 2 t Co =0.04 µs Park 16 t abc- =0.30 µs FEM 15 t C = 0.24 µs SM_I 8 t SM_ = 0.75 µs Park-Inverse 14 t -abc=0.30 µs SM_I 18 t SM_ = 0.75 µs PWM 5 t PWM =0.014µs t SMI = t abc- + 2t SM_ + t -abc + t PWM t FOC = 1.04 µs Run time T ex =T A/D + t SMI t ex =3.48 µs Resources Number of Slices 1344 e 5376 (25%) Consume Wire Multipliers 8e 16 (65%) Memory RAM 7% Table1: FPGA Performance for ISMC To test the controller, a prototyping platform for a Permanent magnet Synchronous Machine was assemble.. FPGA PMSM Fig.19: Prototyping platform control LOAD The Fig.20 show the experimental results obtaine uring the implementation of the Sliing Moe inirect control. It presents the control signals state for the switches of the inverter voltage in the area where there is the reference voltage vector. These results are similar to those presente in the theories. Furthermore, the control signals generate from the FPGA boar will be filtere before being injecte into the voltage inverter. The above figures show that the phases are balance an emonstrate the proper functioning of the PWM. Sector 0 Sector 1 Sector 2 Sector 3 Fig.18: Experimental setup of the testbe Sector 4 Sector 5 Fig.20: Switching states of control signals C 1 an C 2 ISSN: Issue 3, Volume 6, March 2011

11 The Fig.20 shows that control system satisfy the basic reuirements of the control strategy an valiate therefore the goo functionality of the system. In fact, It can be note that: The switching freuency is limite to the sampling freuency of the control algorithm to guarantee safe operation of the semiconuctor power evices. The switching freuency increases weakly when the stator current vector magnitue ecreases. The inirect sliing moe control is synthesize using the sliing moe theory. In this case, a reference voltage vector is applie to the machine. This voltage vector is compose by a vector voltage euivalent vali on the sliing surface an a vector attraction voltage vali outsie the sliing surface (transient). The application of the vector reference voltage to PMSM reuires an intermeiate stage of pulse with moulation. The switching freuency is fixe eual to the freuency of the PWM. The inirect control by sliing moe ensures better uality control currents in steay state with a consierable reuction of the oscillations. The implementation of the inirect control by sliing moe on FPGA evices is characterize by a reuce operation time. Fig.21: Stator current locus for ISMC Fig.23: -axis an -axis current in the PMSM Fig.24: the a-axis an b-axis voltage stator In figures 21, 22, 23 an 24 the experimental results of Inirect Sliing Moe PMSM with the FPGA platform are shown. Upate freuency for this implementation is 20kHz. All results were extracte from the FPGA by the ChipScope tool of Xilinx. This figures show that control system satisfies the basic reuirements of the control strategy an valiates therefore the goo functionality of the system. In fact, It can be note that: The switching freuency is limite to the sampling freuency of the control algorithm to guarantee safe operation of the semiconuctor power evices. The switching freuency increases weakly when the stator current vector magnitue ecreases. Implementing the ISMC control in FPGA has the rawbacks: The switching freuency is variable. It is limite to half the sampling freuency of the control algorithm an maximum at very low spee. The zero voltage vectors are not applie. Fig.22: abc-axis current in the PMSM ISSN: Issue 3, Volume 6, March 2011

12 8. Conclusion In the case of a Sliing moe controlle by current stator of permanent magnet synchronous machine, it is reuire the use of the PWM techniue. This paper presents the implementation of Sliing Moe Control architecture on FPGA for Permanent Magnet Synchronous Machine (PMSM). The evelopment of the corresponing esign has rigorously followe an appropriate methoology which offers consierable avantages an allows the creation of a library for optimize reusable moules. Among the avantages of this control structures, the switching freuency is fixe an there is compliance with the eight vector voltages that can provie the voltage inverter. However, it has isavantages because the general structure of the control algorithm is complex to implement an parameters of the control algorithm epen on the sampling perio. References: [1] Y.Y. Tzou, H.J. Hsu: FPGA Realization of Space-Vector PWM Control IC for Three Phase PWM Inverters, IEEE Trans, Power Electron, vol.12, n 6, pp , nov [2] E. MONMASSON, an M. Cirstea FPGA Design Methoology for Inustrial Control Systems A Review, IEEE Trans In. Electron.., vol.54, no. 4, pp , August [3] Y. Kebbati, Y.A. Chapuis an F. Braun, Reuse methoology in FPGA/ASIC Digital Integration Solution for Vector Control of Motor Drives, in Proceeing of IEEE International Symposium on Signal, Circuit an Systems (SCS 2001), pp , Romania, [4] X. Lin-Shi, F. Morel, A. M. Llor, B. Allar an J.M. Retif Implementation of Hybri Control for Motor Drives, IEEE Tran. In Electron., vol.54, no.4, pp , August [5] H. T. moon, H. S. Kim an M. J. Youn, A Discret Time Preictive Current Control for PMSM IEEE Trans. Power Electronic., vol.18, no.1, pp , Janvier [6] B.BOSSOUFI, M.KARIM, S.IONITA, A.LAGRIOUI, The Optimal Direct Torue Control of a PMSM rive: FPGA-Base Implementation with Matlab & Simulink Simulation Journal of Theoretical an Applie Information Technology JATIT, pp63-72, Vol. 28 No.2, 30th June [7] M.W. NAOUAR, «Commane numériue à base e composants FPGA une machine synchrone», algorithmes e contrôle u courant, Thèse e Doctorat, Ecole Nationale Ingénieurs e Tunis et l Université e Cergy Pontoise, Tunis, [8] E. Monmasson; B. Robyns; E. Menes, B. De Fornel, Dynamic reconfiguration of control an estimation algorithms for inuction motor rives, in Proc. IEEE ISIE Conf., 2002, pp [9] A.Lagrioui; H.Mahmoui; Current an Spee Control for the PMSM Using a Sliing Moe Control 2010 IEEE 16th International Symposium for Design an Technology in Electronic Packaging (SIITME), Pitesti, Romania. [10] G.R. Walker, Digitally-Implemente naturally sample PWM suitable for multilevel converter control, IEEE Trans. In. Electron., vol. 18, n 6, pp , Nov [11] K. Tazi, E. Monmasson an J-P. Louis, The use of FPGAs to buil an AC rive specific harware- software library. The case of Park s transformation, in Proc. EPE-PEMC 2000 Conf., 2000, vol. 7 pp [12] E. Monmasson; B. Robyns; E. Menes, B. De Fornel, Dynamic reconfiguration of control an estimation algorithms for inuction motor rives, in Proc. IEEE ISIE Conf., 2002, pp [13] B.BOSSOUFI, M.KARIM, S.IONITA, A.LAGRIOUI, Performance Analysis of Direct Torue Control (DTC) for Synchronous Machine Permanent Magnet (PMSM) in Proc. IEEE-SIITME 2010, pp , Sep 2010, Pitesti, Romania. [14] Altera ata book, [Online]. Available: [15] S. Velusamy, W. Huang, J. Lach, M. Stan, an K. Skaron, Monitoring temperature in FPGA base SoCs, in Proc. Comput. Des. Conf., 2005, pp [16] N. P. Ligocki, A. Rettberg, M. Zanella, A. Hennig, an A. L. e Freitas Francisco, Towars a moular communication system for FPGAs, in Proc. Electron. Des., Test an Appl. Workshop, 2004, pp [17] D. E. Johnson, K. S. Morgan, M. J. Wirthlin, M. P. Carey, an P. S. Graham, Persistent errors in SRAM-base FPGAs, in Proc. MAPLConf., 2004, CD-ROM. ISSN: Issue 3, Volume 6, March 2011