ISSN: 2277 – 9043                             International Journal of Advanced Research in Computer Science and Electroni...
ISSN: 2277 – 9043                           International Journal of Advanced Research in Computer Science and Electronics...
ISSN: 2277 – 9043                           International Journal of Advanced Research in Computer Science and Electronics...
ISSN: 2277 – 9043                            International Journal of Advanced Research in Computer Science and Electronic...
ISSN: 2277 – 9043                              International Journal of Advanced Research in Computer Science and Electron...
ISSN: 2277 – 9043                International Journal of Advanced Research in Computer Science and Electronics Engineerin...
ISSN: 2277 – 9043                                International Journal of Advanced Research in Computer Science and Electr...
Upcoming SlideShare
Loading in …5
×

125 131

290 views

Published on

Published in: Business, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
290
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
3
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

125 131

  1. 1. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 Direct torque control of induction motor using discrete events of a hybrid system B. M. Manjunath, A. vinay Kumar comparators, a flux and torque estimator and a voltage Abstract— In this paper, the direct torque control (DTC) is vector selection table. The torque and flux are controlledemployed for fast and slow torque and flux control of induction simultaneously by applying suitable voltage vectors, andmotor coupled to an inverter (Inv-IM). This paper describes acombination of direct torque control (DTC) and space vector by limiting these quantities within their hysteresis bands,modulation (SVM) for an adjustable speed sensor-less induction de-coupled control of torque and flux can be achieved.motor (IM) drive. The motor drive is supplied by a two-levelinverter. The inverter reference voltage is obtained based on However, as with other hysteresis bases systems, DTCinput-output feedback control, using the IM model in the stator drives utilizing hysteresis comparators suffer from high– axes reference frame with stator current and flux vectors torque ripple and variable switching frequency. . Thecomponents as state variables. We first model the DTC of torque and flux are controlled simultaneously by applyingInv-IM as a hybrid system (HS). Then, we abstract the suitable voltage vectors, and by limiting these quantitiescontinuous dynamics of the HS in terms of discrete events. We within their hysteresis bands, de-coupled control ofthus obtain a discrete event model of the HS. And finally, we use torque and flux can be achieved. However, as with otherSupervisory Control Theory of discrete event system (DES) to hysteresis bases systems, DTC drives utilizing hysteresisdrive Inv-IM. comparators suffer from high torque ripple and variable switching frequency. The most common solution to thisIndex terms- direct torque control (DTC), discrete event problem is to use the space vector modulation depends onsystem (DES), inverter coupled induction motor(INV-IM), supervisory control theory (SCT). the reference torque and flux. The main advantages of SVM-DTC are minimal torque response time and the absence of coordinate-transform, voltage modulator I. INTRODUCTION block, controllers such as PID for flux and torque for these advantages, DTC is the control method adopted inThe main advantage of Induction motors (IM) is that no this paper.electrical connection is required between the stator and the We propose a three-step method to model the DTC ofrotor, they have low weight and inertia, high efficiency and a Inv-IM. In a first step, we model the DTC of Inv-IM as ahigh overload capacity [1]. There exist several approaches to hybrid system (HS) with a discrete event dynamicsdrive an IM. Induction motor control methods can be defined by the voltage vectors used to control IM; and abroadly classified into scalar control and vector control. continuous dynamics defined by continuous equations onIn scalar control, V/F control is the important control the stator flux vector(Φs) and the electromagnetictechnique, it is the most widespread, reaching torque(Г).approximately 90% of the industrial applications. The Hybrid system in the sense that it consist of discretestructure is very simple maintaining a constant relation component (inverter) and the continuous componentbetween voltage and frequency and it is normally used (induction motor).without speed feedback, hence this control does not In a second step, we abstract the continuous dynamics ofachieve a good accuracy in both speed and torque the HS in terms of discrete events. Some events are usedresponses mainly due to the fact that the stator flux and to represent the entrance and exit of the torque Γ and thethe torque are not directly controlled. Vector control is a amplitude Φs of in and from a working point region.technique that can reach a good accuracy, but its main And some other events are used to represent the passagedisadvantage is the necessity of a huge computational of the vector Φs between different zones. By thiscapability and of a good Identification motor parameters. abstraction, the continuous dynamics of the system IMThe method of Field acceleration overcomes the is described as a discrete event system (DES).computational problem of vector controllers by achieving In a third step, we use Supervisory Control Theorysome computational reductions [2][4]. And the technique of (SCT) to drive Inv-IM.Direct Torque Control (DTC) been developed by Takahashi[5][6][7][8] permits to control directly the stator flux and the II.INVERTER AND ITS DISCTERT EVENTtorque by using an appropriate voltage vector selected in a MODELlook-up table. And the technique of Direct Torque Control(DTC) been developed by Takahashi [5][6][7][8] permits to The inverter (Fig.1) is supplied by a voltage Uo andcontrol directly the stator flux and the torque by using an contains three pair of switches for i = a, b, c.appropriate voltage vector selected in a look-up table. The The input of the inverter is a three-bit value (Sa Sb Sc)conventional DTC drive contains a pair of hysteresis where each Si can be set to 0 or 1. A value 0 of Si sets to (close, open), and a value 1 sets it to (open, 125 All Rights Reserved © 2012 IJARCSEE
  2. 2. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 A. Model of torque and fluxclose). The output of the inverter is a voltage vector Vsthat drives IM. The inverter vector s is determined by With DTC, the voltage vector VS generated by theEquation (1), and thus, depends uniquely on Uo and (Sa inverter is applied to the IM to control the flux Φs andSb Sc). the torque Γ. Let us first see how and Φs, Γ can be expressed. In a Stationary reference frame, the flux s = ]… vector Φs is governed by the differential Eq. (3), where(1) Rs is the stator resistance and Is is the stator currentThe inverter can produce eight vectors k = 0, 1,…7) vector. Under the assumption that , is negligiblecorresponding respectively to the eight possible w.r.t VS (realistic if the amplitude of Φs is sufficientlyvalues(0=000 to 7=111) of (Sa Sb Sc).from equation high); we obtain Eq. (4) which approximates the(1),we obtain easily equation (2) that computes the eight evolution of Φs from Φso after a delay t.vectors , k=1,2,..7. Note that v0 and v7 are null.Figure (2) represents the six non-null voltage vectors inthe D-Q axes which represent the stationary referenceframe fixed to the stator. B. evolution of flux and torque Eq. (4) implies that the application of a vector voltage generates a move of the end of Øs in the direction of . Note that consists of a radial vector (parallel to ) and a tangential vector (orthogonal to ). Increases (resp. decreases) the flux Øs (i.e., the amplitude of ) if it has the same (resp. opposite) direction of . rotates clockwise (resp. counterclockwise) if the angle from to is +π/2 (resp. –π/2). From Equation (5). We deduce that increases (resp. decreases) the torque ГThe inverter can be modeled by a 8-state automaton if the angle from to is π/2 (resp. –π/2).who’s each state qk (k = 1... 7) means: “Vk is the currentvoltage vector”. To adopt the terminology of hybridsystems, the term mode will be used as a synonym ofstate. The transition from any mode q⋆ to a mode qkoccurs by an event Vk which means “starting to applyVk”. III. INDUCTION MOTOR AND ITS CONTINUOUS MODELThe induction motor is a continuous system because itsbehavior is modeled by algebraic and differentialequatons on two continuous variables, the stator flux(Φs) and the electromagnetic torque(Γ). Figure 3 illustrates the evolution of when have the same direction as and the angle from to is +90 degrees. Therefore, in this example both the flux Øs and the torque Г increase. As proposed in [5] to divide the possible global locus of into the six zones Z1, Z2... Z6 of Fig. 4. Table I shows how the flux magnitude Øs and the torque Г evolve when is in Zi (i = 1,.6) under the control of each of the eight vectors (k = 0, 7, i − 2 · · · i+3), where indices are defined modulo 6 (and not modulo 8). Symbols ↑, ↓ and = mean 126 All Rights Reserved © 2012 IJARCSEE
  3. 3. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012“increases”, “decreases” and “is constant”, respectively. and under the control of i-2, i-1, i+1, i+2, 0We see that under the control of i-2, i-1, i+1, i+2, and 7, the evolution of Øs and Г is thus the one already 0 and 7, the evolution of Øs and Г is known. But indicated in Table I or Zi. Table II shows the evolutionvectors i and i+3 are problematic because they can of Øs and Г in zone Zi,j under the control of i and i+3.both increase and decrease the torque Г in the samezone Zi, depending if Øs is in the first or the second 30degrees of Zi. This problem will be callednon-determinism of the six-zone division. IV. MODELING OF IM AS DES BY ABSTRACTING ITS CONTINUOUS DYNAMICS Let us show how the continuous dynamics of IM presented in Sect. III is abstracted in terms of discrete events. The first abstraction consists in translating by events the entrance and exit of (ØS, Г) in and from a working point region. The second abstraction consists in translating by events the passage of the vectorC. solving the non-determinism of six-zone division between orientation zones.In this two approaches were proposed to solve the A. Abstracting the entrance and exit of (Øs, Г) non-determinism of the 6-zone division. The firstapproach is based on the observation that the Let Øwp and Гwp the flux magnitude and the torquenon-determinism occurs when is in a zone Zi while defining the targeted working point. That is, the aim of control will be to drive IM as close as possible to (Øwp,one of the control vector i or i+3 is applied A solution Гwp). We define a flux interval [Øwp-, Øwp+] centered inis to leave non-determinism as soon as it appears, by Øwp, and a torque interval [Гwp, Гwp] centered in Гwp. Weapplying a control vector different from i and i+3. partition the space of (Øs, Г) into sixteen regions Ru,vWe suggest to select the control vector to be applied for u, v = 1, 2, 3, 4, as shown in Fig. 6. The objective ofamong the four control vectors i-2, i-1, i+1, i+2 the control will be to drive IM into the set of regionsbecause these four vectors permit to obtain all the {Ru,v : u, v = 2, 3} (shaded in Fig. 6) and to force it tocombinations of the evolution of (Øs, Г) (see Table I). remain into this set. We define the event that represents a transition from Ru,v to Ru′,v for any v, and the event that represents a transition from Ru,v to Ru,v′ for any u. Since only transitions between adjacent regions are possible, the unique possible events are the following: if u<4, if u>1, if v<4, if v>1. With the above abstraction, the evolution of (Øs, Г) can be described by a 16-state automaton, whose states are noted (u, v) and correspond to the sixteen regions Ru,v, u, v = 1, 2, 3, 4. The transitions between states occur with the events defined above , , , . B. Abstracting the passage of between orientation zonesA second approach to solve the non-determinism is touse twelve zones by dividing each of the six zones Zi In Sec. III-B and III-C, we have shown how to partitioninto two zones Zi,1 and Zi,2 comprising the first and the the global locus of into six or twelve zones (Figs. 4second 30 degrees, respectively [13], [1]. Figure 5 and 5). This partitioning is very relevant, because werepresents the twelve-zone division. In each zone Zi,j have seen that from the knowledge of the current zone 127 All Rights Reserved © 2012 IJARCSEE
  4. 4. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012occupied by . interpreting Table I, we determine the transitions of MkWe can determine the control vector to be applied as follows, where Vk is the control vector currently applied by the inverter. From state (u, v, i)k of Mk :for obtaining a given evolution of (Øs, Г) (Tables I and i′ • The event can occur when u < 4 and ØSII). With the 6-zone partition, we define the event Zi increases, i.e., when k is equal to one of the followingthat represents a transition from Zi to Zi’. Since only values: i−1, i+1, i, 0 if i is odd, 7 if i is even. This eventtransitions between adjacent zones are possible, the leads from (u, v, i)k to (u+1, v, i)k.unique possible events are the following: , ,where i-1and i+1 are defined modulo 6. We can thus • The event can occur when u > 1 and ØS decreases, i.e., when k is equal to one of the followingabstract the evolution of by a 6-state automaton,whose states are noted (i) and correspond to the zones values: i−2, i+2, i+3,0 if i is odd. This event leadsZi, i = 1…6. The transitions between states occur with from (u, v, i)k to (u−1, v, i)k.the events defined above: , , We can use the • The event can occur when v < 4 and Γ increases,same approach with the 12-zone partition, by defining i.e., when k is equal to one of the following values: i+1,the event that represents a transition from Zi,j to i +2, i, i+3. This event leads from (u, v, i)k to (u,Zi′,j′ . Since only transitions between adjacent zones are v+1, i)k.possible, the unique possible events are the • The event can occur when and v > 1 and Γfollowing: , , , , where i−1 and i+1 decreases, i.e., when k is equal to one of the followingare defined modulo 6. We can thus abstract the values: i−2, i−1, i, i+3. This event leads from (u, v,evolution of by a 12- state automaton, whose states i)k to (u, v−1, i)k.correspond to the zones Zi,j , i = 1 ···12 and j = 1, 2. • The event can occur when rotates clockwise, i.e., when Γ increases, i.e., when k is equal to one ofC. modeling IM as a DES i+1the following values: i+1, i+2, i, i+3. This event leads from (u, v, i)k to (u, v, i+1)k.In Sec. IV-A, we have shown how to abstract theevolution of , Г) by a 16-state automaton. In Sec. • The event can occur when rotates counterIV-B, we have shown how to abstract the evolution clock-wise, i.e., when Γ decreases, i.e., when k is equal to one of the following values: i−2, i−1, i, i+3. Thisof by a 6-state or 12- state automaton. In the sequel,we consider uniquely the 6- state automaton because it event leads from (u, v, i)k to (u, v, i−1)k.reduces the state space explosion which is inherent to Due to the non-determinism of Sect. III-B, the eventsthe use of automata. As we have seen in Sect. III-C, the depending on the evolution of Γ ( , , ,6-zone partition necessitates to apply a control vector ) are potential but not certain when k is equal to i ordifferent from Vi and Vi+3 when Øs is in Zi. We will i+3.explain in Sect. V how this requirement can beguaranteed by supervisory control of DES. V. USE OF SCT TO DRIVE IMLet us see how the two automata (16-state and 6-state) A. introduction to SCTare combined into an automaton Mk that abstracts thebehavior of IM when a given control vector Vk is In supervisory control, a supervisor Sup interacts with aapplied by the inverter. DES (called plant) and restricts its behavior so that it respects a specification. Sup observes the evolution of P (i.e., the events executed by the plant) and permits only the event sequences accepted by S. To achieve its task, Sup will disable (i.e., prevent) and force events. The concept of controllable event has thus been introduced, meaning that when an event e is possible, then Sup can disable it if and only if e is controllable; e is said uncontrollable if it is not controllable [9]. We will also use the notion of forcible event, meaning that when an event e is possible, then Sup can force e to preempt (i.e., to occur before) any other possible event, if and only if e is forcible; e is said unforcible if it is not forcible [14]. A method has been proposed to synthesize Sup automatically from P, S and the controllability and forcibility of every event [9]. B. The Plant Inv-IM Modeled as a DESA State of Mk is noted (u, v, i)k since it is a combinationof a state (u, v) (corresponding to Ru,v) and a state i The plant to be controlled is the system Inv-IM (i.e.,(corresponding to Zi ). Mk can therefore have at most 6 inverter with IM). In Section II, we have modeled the× 16 = 96 states (u, v, i)k, (u, v = 1…4, i = 1…6). By inverter by an automaton A with 8 states qk (k = 0…7) 128 All Rights Reserved © 2012 IJARCSEE
  5. 5. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012Corresponding to the 8 control vectors Vk, respectively. added an event Null in the model of IM. The interface GAnd in Section IV-C, when a given VK is applied by the generates these events.inverter to the IM, we have modeled the evolution of IM Sup observes the events Z, Г, Ø, Null. Since theseby an automaton MK that can have at most 6 × 16 = 96 events are generated by IM through G, Sup has nostates (u, v, I)k, (u, v =1,…4,i=1,…6).Therefore, the control on them. Hence, these events are uncontrollablesystem Inv-IM can be modeled by replacing in A each and unforcible. Sup generates the events VK, and thus,mode qk by the automaton Mk . The transition from any has all control on them. Hence, these events arestate (u, v, i)* to a state (u, v, i)k occurs by an event Vk . controllable and forcible.The obtained automaton, noted P , can therefore have atmost 8 × 96 = 768 states. The initial state is (1; 1; 1)0, VI. CONCLUSIONthat is, initially: the flux and the torque are in RegionR1,1, the flux vector is in zone Z1 and the null control In this control method, a much better behavior of thevector Vo is applied. The set of marked states is { (u; v; DTC-SVM performance is presented , achieving one ofi)k : u, v = 2, 3},because the objective of the control is to the main objectives of the present work, which was todrive Inv-IM into the set of regions {Ru,v : u, v = 2, 3} control the torque by reduce the torque ripple and(i.e., the set of states { u; v; i k : u, v = 2, 3}), and then to consequently improve the motor performance comparedforce it to remain into this set. For the purpose of to classical DTC. This control method shows bettercontrol, we define an undesirable event Null meaning results in high as well as in low speed also as shown inthat the flux or the torque has decreased to zero, and a results for low speed. As a future work, we intend tostate E reached with the occurrence of Null .We will see improve our control method by using a hierarchicallater how Null and E are necessary. Therefore, the control and a modular control, which are very suitableautomaton P has actually at most 769 (768+ the state ), to take advantage of the fact that the event based modeland its alphabet Σ is: of the plant has been constructed hierarchically and modularly.C. control architectureWe propose the control architecture illustrated in Figure7. The interaction between the plant and the supervisoris realized through two interfaces A and G.A: In Sect. II, we have modeled the inverter by anautomaton executing the events Vk, where k = 0,.…7.The interface A translates every event Vk generated bythe supervisor into (Sa Sb Sc), which is the 3-bit code of VII. SIMULATION AND RESULTSk. And the inverter translates (Sa Sb Sc) into the controlvector Vk, which is applied to IM.G: In Sect. IV, we have modeled IM by an automatonexecuting the events Z, Г, Ø. and in Sect. V-B, we have 129 All Rights Reserved © 2012 IJARCSEE
  6. 6. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012Fig: 8. simulation diagram for DTC of IM Fig: 9. Simulation results for Torque, current IABC, speed and flux in DQ axis. 130 All Rights Reserved © 2012 IJARCSEE
  7. 7. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 AUTHORS B. M. Manjunath received his B.Tech (Electrical and Electronics Engineering) degree from the Jawaharlal Nehru Technological University, and M.Tech (Power Electronics) from the same university. He is currently an Asst. Professor of the Dept. Electrical and Electronics Engineering, Rajeev Gandhi Memorial College of Engg. & Tech, Nandyal. His field of interest includes renewable energy sources and Power electronics & Drives. (E-mail: manjumtech003@gmail.com). Nandyal , Andhra Pradesh, India. A. Vinay Kumar received his B.Tech (Electrical and Electronics Engineering) degree from the Jawaharlal Nehru Technological University in 2009 and M.Tech (Power Electronics) pursuing from the same university. His field of interest includes power systems and fig.10: flux on XY plot power electronics. (E-mail: coolvinay207@gmai.com). Nandyal, Andhra Pradesh, India. REFERENCES[1] A. A. Pujol. Improvements in direct Control of Induction Motors.PhD thesis, Department of Electronical Engineering, PolytechnicalUniversity of Catalunya, Terrassa, Spain, November 2000.[2] J. L. Romeral. Optimizaci´on de Modelos de Control Digital ParaMotores (AC). PhD thesis, Department of Electronical Engineering,Polytechnical University of Catalunya, Terrassa, Spain, June 1995.[3] Simulink implementation of induction model –a modular approachby burak ozpineci and Leon m. Tolbert[4] S. Yamamura. AC Motors for high-performance applications.Analysis and Control. Marcel Dekka, Inc., 1986.[5] I. Takahashi and T. Noguchi. A new quick response and highefficiency control strategy of induction motors. IEEE Transactions onIndustry Applications, 22(5):820–827, Sept.-Oct. 1986.[6] I. Takahashi and S. Asakawa. Ultra-wide speed control ofinduction motor covered 10a6 range. IEEE Transactions on IndustryApplications, 25:227–232, 1987.[7] I. Takahashi and T. Kanmashi. Ultra-wide speed control with aquick torque response AC servo by DSP. In EPE, pages 572–577,Firenze, Italy, 1991.[8] T. G. Habetler and D. M. Divan. Control strategies for directtorque control using discrete pulse modulation. IEEE Transactions onIndustry Applications, 27(5):893–901, 1991.[9] P.J. Ramadge and W.M. Wonham. The control of discrete eventsystems. Proc. IEEE, 77:81–98, January 1989.[10] I. Boldea and S. A. Nasar. Vector Control of AC Drives. CRCPress Inc., 1992.[11] P. Vas. Sensorless Vector and Direct Torque Control of ACMachine. Oxford Univ. Press, London, U.K., 1998.[12] I. Takahashi and S. Ohimori. High performance direct torquecontrol of an induction motor. IEEE Transactions on IndustryApplications, 25(2):257–264, 1989.[13] I. Ludtke. The Direct Control of Induction Motors. PhD thesis,Department of Electronics and Infomation Technology, PolytechnicalUniversity of Glamorgan, Wales, U.K., May 1998.[14] C. H. Golaszewski and P.J. Ramadge. Control of discrete eventprocesses with forced events. In 26th CDC, pages 247–251, LosAngeles, CA, USA, 1987. 131 All Rights Reserved © 2012 IJARCSEE

×