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ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009 Improved DTC relying on Hybrid Fuzzy-self tuning PI Regulator for the Permanent Magnet Synchronous Machine K. Nabti. K. Abed. H. Benalla Electrotechnic's laboratory of Constantine, faculty of engineering sciences Mentouri University, Campus Zerzara, Constantine, ALGERIA. E-mail : Idor2006@yahoo.fr Abstract start-up. Several techniques developed to improve the We propose in this paper a Self-adaptation PI for speed DTC performance [3], [4], [5], [6], [7].In paper [8] the regulation based on direct torque control (DTC) of authors replace the conventional PI by the fuzzy logic Permanent Magnet Synchronous Machine (PMSM). regulator when the output is the torque reference. In Speed regulation with a conventional PI regulator paper [9] fuzzy logic is used to replace the switching reduces the speed control precision, increases the torque table of DTC which make possible to choose the very fluctuation, and consequentially causes low performances suitable voltage vector. The paper [6] realizes Fuzzy-PI of the whole system. Using fuzzy logic method, by self- speed regulation for induction machine; we utilize this adaptation of conventional PI regulator parameters gives idea for PMSM in this paper. The fuzzy control is the appropriate Kp and Ki (proportional and integral nonlinear and adoptive in nature, giving robust coefficients respectively) which improve the system performances in the face of parameter variations and load performance. Simulation results show that the ripples of disturbance effects. The regulator inputs are speed error both torque and flux are reduced remarkably, small and its change. Self-adaptation PI regulator, based on overshooting and good dynamics of speed and torque. conventional PI regulator; consist to adjust dynamically the conventional PI parameters kp and ki. Simulation Keywords: Permanent Magnet Synchronous Machine, results show that the method improves the Direct Torque Direct Torque Control, Fuzzy PI regulator. Control system performances. This paper consists of mathematical model of PMS machine, direct torque 1. Introduction control principle; fuzzy logic technique applied to DTC, The PMSM control difficulty resides in the coupling of simulation results with interpretation, and finally control variables such as flux and electromagnetic torque. conclusion. Two principal strategies were developed almost at the same time in two different research centers, Direct 2. Motor equations in the α, β reference Torque Control strategy was first introduced by I. frame Takahashi, in 1986 [1]. M. Depenbrock, develop a In the stationary α-β reference frame, the model can be similar idea in 1988 under the name of Direct Self expressed as [8]: Control [2]. The DTC is one of the recent researched dψ α control schemes based on the decoupled control of stator uα = Rs .iα + dt flux and torque providing a quick and robust response (1) with a simple implementation in AC drives. DTC has the dψ β u β = Rs .iβ + advantages of simplicity, good dynamic performance, dt and insensitive to motor parameters except the stator ⎡ψ α ⎤ ⎡cosθ r − sinθ r ⎤ ⎡ψ d ⎤ resistance. In DTC strategy, the speed sensor is not ⎢ψ ⎥ = ⎢ ⎥ .⎢ ⎥ (2) essential for the flux and torque estimation. Direct ⎣ β ⎦ ⎣ sinθ r cosθ r ⎦ ⎣ψ q ⎦ Torque Control employs two hysteresis controllers to ψ d = Ld .id + ψ m regulate the stator flux and torque, which results an (3) ψ q = Lq .iq approximate decoupling between the flux and the torque control. The key issue of DTC scheme is how to choose a ⎡ψ α ⎤ ⎡ Ld .iα ⎤ ⎡cosθ r ⎤ ⎢ψ ⎥ = ⎢ L .i ⎥ + ψ m .⎢ ⎥ (4) suitable stator voltage vector to keep the stator flux and ⎣ β⎦ ⎣ q β⎦ ⎣ sinθ r ⎦ torque in their hysteresis band. The conventional DTC The mechanical equation given by: disadvantages are the high torque ripples and the slow transient response to the step changes in torque during 45 ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009 dω r p = (Tem − TL − Bmω r ) (5) dt J In addition, the electromagnetic torque expressed as follow: 3 2 ( Tem = p ψ α .iβ −ψ β .iα ) (6) Where (uα, uβ), (iα, iβ) and (ψsα, ψsβ) are the stator voltages, stator currents, and stator flux linkages in α, β reference frame, Ld, Lq are the d,q axes inductance, Rs is the stator resistance. ψm is the flux linkage of permanent magnet, p is the number of pole pairs, Tem is the electromagnetic torque, TL is the load torque, Bm is the damping coefficient, ωr is the rotor speed and J is the moment of inertia. Figure1. Stator flux variation in stationary (α, β) frame 3. Direct torque control principles 3.1. Flux and torque estimation and control In the DTC technique, the inverter switches obtained In stationary reference frame, the machine stator voltage using the flux and torque errors, and the position of the space vector is represented as follows: stator flux within the six-region control of the flux. The dψ s flux and torque errors evaluated as follows: Vs = Rs ⋅ i s + (7) dt Δψ = ψ sref − ψ s (14) ⎡ ⎛ 2π ⎞ ⎛ 4π ⎞ ⎤ Vs = usα + jusβ = 2⎢ ⎜ j⋅ ⎟ ⎜ j⋅ ⎟ VaN + VbN ⋅ e⎝ 3 ⎠ + VcN ⋅ e⎝ 3 ⎠ ⎥ (8) ΔT = Tref − Tem (15) 3⎢ ⎥ ⎣ ⎦ ⎛ψ β ⎞ θ = tg −1 ⎜ ⎟ (16) ⎜ ⎟ Where: Rs, is, ψs stator resistance, current and flux ⎝ψ α ⎠ respectively. VaN, VbN, VcN the three phase voltage Where θ is the angle between stator flux vector and α inverter outputs given as follows: axis, ψ sα , ψ sβ are the stator flux components in (α, β) Uc VaN = Vsa = (2 ⋅ C1 − C 2 − C3 ) reference frame. 3 U (9) 3.2. Switching table: VbN = Vsb = c (2 ⋅ C 2 − C1 − C 3 ) In order to determine the inverter switching pattern using 3 Uc flux and torque errors, two hysteresis controllers are VcN = Vsc = (2 ⋅ C3 − C 2 − C1 ) employing. The inverter is switched based on these errors 3 Uc is the inverter DC supply voltage, C1, C2, C3 are the and the position of the stator flux within the six-region switching table outputs, and they are relevant to the control as can be seen from Table 1, in such a way that switching strategy. the inverter output voltage vector minimizes the flux and From (7) we can estimate the stator flux as follow: torque errors and determines the flux rotation direction. ψ s = ψ s 0 + ∫ (Vs − Rs ⋅ i s ) (10) So we can write: n ψ sα = ∫ (v sα − Rs i sα )dt Flux Couple 1 2 3 4 5 6 (11) ψ sβ = ∫ (v sβ − Rs i sβ )dt KCem=1 V2 V3 V4 V5 V6 V1 Kψ=1 KCem=0 V7 V0 V7 V0 V7 V0 The module of the stator flux is: ψ s = ψ s2α + ψ s2β (12) KCem=-1 V6 V1 V2 V3 V4 V5 KCem=1 V3 V4 V5 V6 V1 V2 ψ s is the stator flux vector, and ψ s 0 is its initial value. Kψ=0 KCem=0 V0 V7 V0 V7 V0 V7 For simplicity, it is assumed the stator voltage drop Rs.is is small and neglected, the stator flux variation can be KCem=-1 V5 V6 V1 V2 V3 V4 expressed as: ∆ψs ≈ Vs.∆t. Table.1. DTC switching table. We can estimate the electromagnetic torque using the following relation: 4. Control structure 3 2 ( Tem = p ψ α .iβ −ψ β .iα ) (13) Figure (2) illustrates the PMSM drive scheme considered in this investigation. The drive consists of a Fuzzy PI We can be controlled the change of torque by keeping the speed controller, flux and torque controllers, space flux amplitude of the stator flux linkage constant and by position, and PMSM. The rotor speed wr compared with controlling the rotating speed of the stator flux as fast as the reference speed wref. The resulting error and its rate of possible. We show in this section that both of the change are processed in the fuzzy PI speed controller for amplitude and rotating speed of the stator flux controlled each sampling interval. The output of speed regulator by selecting the proper stator voltage vectors as shown in considered as the reference torque Tref. fig.1. The primary voltage vector Vs, is defined by the equation (8) 46 ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009 Ri: If Eω is Ai, ΔEω is Bi then KP is Vi, KI is Wi. Where Ai, Bi, Vi and Wi denote the fuzzy subsets. Kp, Eω Ki NL NM NS ZE PS PM PL N L, M, S, M, S, M, L, ΔEω Z S M L M S Z Z L, M, L, Z, L, M, L, Z S M L M S Z P L, M, L, Z, L, M, L, Z M L L L M Z Tab1e. 2- Fuzzy Rules Base The inference method used in this paper is Mamdani’s procedure (inference) based on min-max decision. The Figure2. A direct torque control scheme firing strength (applied fuzzy operators) αi, for ith rules is 5. Fuzzy controller given by: Speed error “Eω,” and its rate of change ΔEω are using ( α i = min μ Ai (Eω ), μ Bi (ΔEω ) ) (17) as inputs to the fuzzy controller. Proportional coefficient By fuzzy reasoning, Mamdani’s minimum procedure Kp and integral coefficient Ki are the outputs of the fuzzy gives: controller. The number of fuzzy segments is chosen to have maximum control with a minimum number of rules. ( ) μVi (KP ) = min α i , μVi (KP ) ' (18) μW (KI ) = min (α i , μW (KI )) Triangle and trapezoidal membership functions have ' been used. The fuzzy membership functions of input and i i output variables are shown in (Fig. 3) [6]. Where µA, µB, KP and KI are membership functions of sets A, B V and W of the variables Eω, ΔEω, Kp and KI, respectively. Thus, the membership functions µv and μw of the outputs KP and KI are given by: 21 ' ( μV (KP ) = max μVi (KP ) i =1 ) (19) (KI ) = max(μ (KI )) 21 ' μWi Wi i =1 The Maximum criterion method is used for defuzzification. The final single-valued output is obtained by this method. 6. Simulation results To verify the technique proposed, digital simulations based on MATLAB/SIMULINK have been implemented. The PMSM used for the simulations has the following parameters [10]: Figure3. The fuzzy membership functions of input and output variables. Uc[V] 350 f[Hz] 50 From the experience of simulation and experiment, the range of coefficients kp and ki are [1, 5] and [0.005, 0.02], Rs[Ω] 0.3 respectively [6].The speed error universe of discourse is Ld[mH] 3.366 divided into seven fuzzy sets. {NL (negative large), NM Lq[mH] 3.366 (negative middle), NS (negative small), ZE (zero), PS J [Kg/m2] 10.8e-5 (positive small), PM (positive middle), PL (positive Bm[Nm/rad/s] 0 large)}. rate of change ΔEω includes 3 fuzzy subsets, it is ψm[V/rad/s] 0.0776 not necessary to subdivide it, because it's changes quickly p 5 in DTC. Output membership KP and KI, both contain Table3. PMS motor parameters four fuzzy subsets as shown in (fig. 3). There are total of 21 rules as listed in table 2. Each Conventional PI regulator coefficient: control rule can be described using the inputs variables ki = 0.0553; kp =1.441. speed error “Eω”, it rate of change ΔEω, and output For proposed DTC and conventional DTC the dynamic variables (controller parameters ki and kp). The ith rule Ri responses of speed, flux, and torque for the starting can be expressed as: 47 ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009 process without load Tl=0, we applied an load torque equal to Tl=7Nm at 0.6s, at t=1.7s we remove the load torque. We Inverse the speed at t=1s. 10 10 Electromagnetique torque (N.m) Electromanetic torque (N.m) 5 5 0 0 -5 -5 -10 -10 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 t(s) t(s) (a2) (a1) 100 100 50 50 Speed (rad/s) speed (rad/s) 0 0 -50 -50 -100 -100 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 t(s) t(s) (b1) (b2) 0.254 0.254 0.253 0.253 0.252 0.252 0.251 0.251 stator flux (Wb) stator flux (Wb) 0.25 0.25 0.249 0.249 0.248 0.248 0.247 0.247 0.246 0.246 0.245 0.245 0.244 0.244 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 t(s) t(s) (c1) (c2) Figure4. (a1) Torque response, (b1) speed response, (c1) flux Figure5. (a2) Torque response, (b2) speed response, (c2) flux response, for DTC with conventional PI regulator. response, for DTC with fuzzy PI regulation. 48 ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009 We compare between speed response for DTC with conventional regulator and fuzzy PI speed regulator. Fuzzy PI 100 4 Conventional PI 3.5 50 Proportional coefficient kp 3 Speed (rad/s) 0 2.5 -50 2 1.5 -100 0 0.5 1 1.5 2 2.5 1 t(s) 0 0.5 1 1.5 2 2.5 t(s) (a) Figure6. Speed responses for DTC conventional PI regulator and DTC fuzzy PI regulator. 0.019 0.018 0.017 0.252 Integral coefficient ki 0.016 0.251 Zoom stator flux (Wb) 0.015 0.25 0.014 0.249 0.013 0.248 0.012 0 0.5 1 1.5 2 2.5 0.247 t(s) 1.4468 1.4469 1.447 1.4471 1.4472 1.4473 1.4474 1.4475 1.4476 (b) t(s) Figure9. Proportional and integral coefficient estimated using fuzzy PI regulator. Figure7. Comparison between stator flux, dashed line stator flux using conventional PI regulator and solid line using fuzzy PI regulator. The simulation results show that flux and torque responses are very fast for two DTC methods. By proposed DTC technique, the ripple of torque and flux in steady state is reduced remarkably compared with 7.4 conventional DTC that reduce the acoustic noise and 7.3 vibrations. Zoom Electromagnetic torque (Nm) 7.2 In fuzzy PI regulation good dynamic responses of torque with neglected influence of load disturbances in speed 7.1 which restored its reference quickly. 7 Figures 7 (a) and (b) represent the estimated parameters 6.9 kp and ki of the PI regulator, we observe that kp ∈ [1, 5] 6.8 and ki ∈ [0.005, 0.02], as shown in section 5. 6.7 7. Conclusion 6.6 In this paper, a fuzzy logic direct torque control scheme 1.5712 1.5713 1.5713 1.5714 1.5714 1.5715 using fuzzy PI regulator technique is presented. Using t(s) fuzzy logic technique, the kp and ki can be obtained dynamically that gives a fast speed response. The Figure8. Comparison between electromagnetic torque, dashed line simulation results suggest that FLDTC can achieve stator flux using conventional PI regulator and solid line using fuzzy PI precise control of the stator flux and torque .Compared to regulator. conventional DTC, presented method the steady performances of ripples of both torque and flux are considerably improved. 49 ICGST-ACSE Journal, ISSN 1687-4811, Volume 8, Issue III, January 2009 8. References 9. Biographies [1] I. Takahashi, and T. Noguchi. A new quick-response NABTI .K (Master) was born in and high- efficiency control strategy of an induction 11/03/1979 Constantine, machine. IEEE Transactions on Industry Applications. ALGERIA. Received an engineer 22 (5), 820- 827, 1986. from the University of Constantine [2] M. Depenbrock. Direct self-control (DSC) of / Algeria in 2003; a master degree inverter-fed induction machine. IEEE Transactions on in electrical machines control. Power Electronics. 3(4), 420-429, 1988. Prepare doctoral degree in [3] F. Jawad, M.B.B. Sharifian. Comparison of different electrical engineering. His switching patterns in direct torque control technique professional research in fuzzy logic of induction motors. ELSEVIER, Electric Power and field oriented control and direct torque control for Systems Research. 60 (2001), 20, 63–75. August AC machines drives. From July 2004 to November 2005 2001. he worked at VSI (verrier Silice international) . [4] Z. Longji, R. Wang. A novel direct torque control system based on space vector PWM. Power ABED .K (Master) was born in Electronics and Motion Control Conference, IPEMC 06/02/1979 Constantine, 2004. The 4th International. Vol.2, Page(s) 755 – 760, ALGERIA. 14-16 Aug 2004. Received an engineer from the [5] X. Del Toro, S. Calls, M. G. Jayne, P. A. Witting, A. University of Constantine / Arias, and J.L. Romeral, Direct torque control of an Algeria in 2003; a master degree induction motor using a three-level inverter and fuzzy in electrical machines control. logic. Industrial Electronics, 2004 IEEE International Prepare doctoral degree in Symposium. On Vol. 2, Page(s):923 – 927, 4-7 May electrical engineering. His 2004. professional research in fuzzy logic and field oriented [6] J. Yang, and J. Huang, Direct torque control system control and direct torque control for AC machines drives. for induction motors with fuzzy speed PI regulator. Proceedings of the Fourth International Conference BENALLA. H (Professor) was on Machine Learning and Cybernetics, Guangzhou. born in Constantine, Algeria in 568-573, 18-21 August 2005. 1957. He received the MS, and [7] M. Zelechowski, M. P. Kazmierkowski, and F. Doctorate engineer degrees in Blaabjerg, Controller design for direct torque power electronics, from the controlled space vector modulated (DTC-SVM) National Polytechnic Institute of induction motor drives. Industrial Electronics ISIE Toulouse, France, respectively, in 2005, Proceedings of the IEEE International 1981, and 1984. In 1995, he Symposium. On Vol. 3, Page(s) 951 – 956, 20-23 received the PHD degrees in June 2005. Electrical Engineering from university of Jussieu-Paris [8] Y. Sayouti, A. Abbou, M. Akherraz, H. Mahmoudi. VI; France. Since 1996, he is currently professor of Fuzzy speed control of induction motor with DTC- Electrical Engineering in Department of Electrical based neural networks. Journal of Theoretical and Engineering at Constantine University Algeria. Applied Information Technology in volume 04, Issue 08. [9] R.Toufouti S.Meziane ,H. Benalla. Direct Torque Control for Induction Motor Using Fuzzy Logic. ACSE journal, volume (06), Issue (2), June, 2006. [10] Xi Zhu, Z. Zi-Qiang., and H. David. Application of full-order and simplified EKFs to sensorless PM brushless AC machines. International journal of automation and computing 2, 179-186, 2005. 50

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