Furthermore, some experimental results which con-firm the validity of the proposed control method are given.II. MACHINE EQUATIONSThe dynamic behavior of an induction machine is describedby the following equations written in terms of space vectors ina stator reference frame(1)(2)(3)(4)whereand represent the stator and rotor resistances;, and self and mutual inductances;rotor angular speed expressed in electricalradians.The electromagnetic torque is expressed in terms of stator androtor fluxes as(5)where is the pole pair number andIn (5) the symbol represents the scalar product. By elimi-nating and from (1)–(4) leads to the state-variable form ofthe induction machine equations with stator and rotor fluxes asstate variables(6)where and .III. DIRECT TORQUE CONTROL PRINCIPLEThe basic functional blocks used to implement the DTCscheme are represented in Fig. 1.
The instantaneous values offlux and torque are calculated from stator variables by usinga closed loop estimator [18]. Stator flux and torque can becontrolled directly and independently by properly selecting theinverter switching configurations.In voltage source inverters, eight switching combinations canbe selected, two of which determine zero voltage vectors and theremaining generate six equally spaced voltage vectors havingthe same magnitude.Fig. 2 shows the voltage vectors which are usually employedin DTC scheme when the stator flux vector is lying in sector 1.According to the principle of operation of DTC the selectionof a voltage vector at each cycle period ismade in order tomain-tain the torque and the stator flux within the limits of two hys-teresis bands (Figs. 3 and 4). In particular, the selection is madeFig. 1. Basic DTC block diagram.Fig. 2. Voltage vectors utilized in basic DTC scheme when stator flux is inSector 1.on the basis of the outputs of torque ( ) and flux ( ) hysteresiscomparators.The basic criteria adopted to select the proper switching con-figurations are related to the following considerations.The flux amplitude can be controlled according to (1), as-suming the voltage drop small. The stator flux vectormoves in the direction of the stator voltage . Then, selectingstep-by-step the voltage vector appropriately, it is possible todrive along a prefixed path with a high dynamic. In steady-state conditions, the stator flux vector describes a circular locus,except for the ripple due to the switching effects.From (2)–(4) it is possible to determine the first-order differ-ential equation linking the stator flux to the rotor flux, given by(7)This equation clearly shows the nature of rotor flux dynamicresponse for changes in stator flux.In steady-state conditions the stator and rotor flux vectorshave the same angular speed and the angle between these vectorsdetermines the torque value, as expressed in (5). In response to a TABLE IBASIC SWITCHING TABLEFig. 3. Flux hysteresis comparator.Fig. 4. Torque hysteresis comparator.positive torque step command, the control algorithm applies tothe machine an opportune voltage vector, driving the stator fluxvector in advance with respect to the steady-state conditions.
Owing to the first order, low-pass filtering action expressedby (7), the rotor flux vector follows the stator flux vector witha time delay related to the time constant . This determines aquick increase of the angle between the two flux vectors and thusof the torque. After the transient, the displacement angle willassume the new value corresponding to the torque command.Taking the previous considerations into account, the torqueand stator flux control can be obtained acting respectively on thetangential and the radial component of , defined with respectto the locus described by the stator flux vector.Assuming the stator flux vector lying in sector 1 of the –plane, the switching table shown in Table I was proposed in [1]and used by many authors.In Table I the symbol represents one of the two zero-voltagevectors and . The most opportune is selected in order tominimize the inverter switch commutations. The selection algo-rithm represented in Table I and in Figs. 3 and 4 is very simpleto implement and gives good results. However, the digital im-plementation of the algorithm may determine a drive behaviorwhich is not optimized in terms of torque and current ripple.This because the effects produced by a given voltage vector in asampling period are quite different at high and low speed (e.g.,the torque reduction produced by a zero voltage vector is muchmore evident at high speed than at lowspeed). These phenomenabecome very important in the case of low sampling frequency.In Section IV, a detailed analysis is carried out in orderto determine the inherent relationships between the appliedvoltage vector and the corresponding variations of stator fluxand torque, taking the motor operating conditions into account.By using the results of this analysis it is possible to define moreaccurate switching tables.Fig. 5. Graphical representation of the torque variation  T .IV. ANALYSIS OF TORQUE AND FLUX VARIATIONSThe induction machine discrete equations in state-variableform can be determined by developing (6). For small values ofthe sampling period the stator and rotor flux at time canbe expressed as(8)(9)Equation (8) clearly shows the variation of the stator flux dueto the applied voltage vector, for given operating conditions.Neglecting the stator resistance effects, (8) reduces to the wellknown relationship(10)From (10), it appears that the stator flux variation has thesame direction of the applied voltage vector and an amplitudewhich is proportional to and .With reference to the electromagnetic torque, at time (5)may be rewritten as(11)Substituting (8) and (9) in (11) and neglecting terms propor-tional to the square of , the torque at time is given by(12)where(13)(14)The first contribution is due to stator and rotor resis-tances and acts in order to reduce the absolute value of thetorque. This contribution is proportional to the torque value attime and is independent of and . The second contri-bution represents the effect of the applied voltage vectoron the torque variation and is dependent on the operating con-ditions. For a given voltage vector this contribution is mainlyaffected by the rotor speed through the dynamic emf .A graphical representation of (14), is given in Fig. 5. Thestator flux vector is assumed lying on the -axis. The dis-placement angle between and is defined by the torquevalue . The bold-faced line represents the locus of the stator Fig. 6. 感应电动机直接转矩控制算法英文文献和中文翻译(2):http://www.751com.cn/fanyi/lunwen_63585.html