induction motor (IM) was based on hysteresis controllers and. Switching ...... [17] J. N. Nash, âDirect Torque Control, Induction Motor Vector Control without an ...
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Torque Control of Induction Motor Drives Based On One-Cycle Control Method Abstract.- The first work on direct torque control (DTC) of induction motor (IM) was based on hysteresis controllers and Switching Tables. Although it has the advantage of simplicity, it has a few drawbacks such as current, torque and flux distortions, and variable frequency operation. Posterior DTC works have solved most of these problems, but with added complexity to the control algorithm. This paper presents a new flux and torque controllers, for DTC of IM drives, based on One Cycle Control (OCC) hardware technique. Present work rescue original OCC features, such as average model, control and hardware simplicity, constant switching frequency, applying to DTC drives. In this sense, OCC hardware principles are emulated by software DSP. The proposed control method (DTC-OCC) is capable of solving most of the original problems of DTC such as operation at fixed frequency with reduced ripple on flux, torque and current, while recovering at the same time, the simplicity of the DTC algorithm. As OCC has been considered as a generalized PWM modulator, the theoretical foundations of the new method are provided from both PWM and OCC approaches. Simulation and DSP-based experimental results show good performance of the proposed control and confirm the theoretical analysis and assumptions. Index Terms—Direct Torque Control, One Cycle Control, Induction Motor, DSP.
I.
INTRODUCTION
Direct Torque Control directly implements flux control estimating the (rotor or stator) position flux and its magnitude, while torque control is realized directly once the flux control is established. The first work on DTC [1], reported by Takahashi utilized flux and torque hysteresis controllers and a switching table (ST) to achieve a fast and robust torque response. However, in spite of the simplicity, it has variable switching frequency and distortions in flux, torque and current [2]. DTC controllers based on Space Vector Modulators (SVM) utilize closed-loop schemes to control flux and torque motor quantities [3]. Neither varying switching frequency nor above mentioned distortions are characteristics of this method. First reported work on DTC-SVM uses also dead-beat control [4] to improve its dynamic behavior. Some others reported control methods used with DTC-SVM are: adaptive control [5], artificial intelligence strategies [6], multi-level SVM [7], [8]. Other control strategies improved the hysteresis control, reducing switching frequency variation and flux and torque distortion, by using of additional variable hysteresis bands [9], [10] but lost also at least a bit of the simplicity of Takahashi original method. On the other hand, One Cycle Control (OCC) is a hardware technique, averaged model, related to pulse width modulation (PWM) techniques; primarily used in dc-dc converters and power factor corrector (PFC) rectifiers [11], [12]. To generate drive pulses, OCC compares the averaged
modulating waves to a varying amplitude triangular-carrier, controlled by integral of control output variable [12] i.e. voltage dc link for PFC rectifiers. This is done in a switching cycle or period Accordingly, for IM drives, OCC systems could be faster than SVM (PWM) systems, since control variables (as motor flux and torque) can be averaged in a switching cycle, instead of a stator (or rotor) frequency cycle [3], [4]. This feature is applied in present proposal to fast control response, and also reduce torque ripple. Hence, unlike DTC-SVM or hysteresis-bands based DTC, proposed DTCOCC controller does not need other control methods to improve its dynamic or stationary performance. In accordance, conventional OCC features as average model and control simplicity could be satisfied in proposed controlled. However, hardware simplicity still presents some issues, since DTC drives need d-q transformation as well as torque and flux estimators. To satisfy full DTC drives requirements, a microcontroller or DSP system is necessary [1-4]. In this sense, to add some hardware simplicity in a DTC-OCC drive, OCC is integrated into DSP system; keeping OCC hardware principles. Constant switching frequency is another important OCC characteristic. Meanwhile, to satisfy varying OCC carrier-amplitude in modern DSPs (so far) carrier frequency must change in a similar way [13]. Thus, an equivalent method is adopted. Above all, proposed drive features the following:
average model control simplicity hardware simplicity DSP control constant switching frequency
Although proposed controller is quite simple, see Fig.5, the rest of the paper is devoted to apply OCC hardware ideas to DTC-DSP based drives. In this sense, an important problem is application of OCC principles to DTC control. This is done in present work, approaching at first DTC by classical control theory and then associating to OCC principles. II. SVM (PWM) CONTROL APPROACH Equations (1) through (6) constitute the space vector model of IM with single rotor cage and negligible core loss [14]. d (1) V S RS i S S j x S dt d (2) 0 RR i R R j ( x m ) R dt (3) S LS i S Lm i r
R LR i r Lm i S me
3 * P. Re j S .i S 2
(4)
(5)
2 J d m me m L p dt
(6)
a), so (12) can take the form
where the symbol indicates space vector; RS, RR are stator and rotor resistances, respectively; LS, LR, Lm are stator, rotor and magnetizing inductance, respectively; x is an arbitrary speed, S is magnetic flux speed; m is mechanical speed; p is the pole pair number, J is shaft inertia; me and mL are electrical and mechanical load torques, respectively. Space vectors quantities defined as X [ X a aX b a 2 X c ] j 2 ( ) ae 3
[17] see Fig.2. Therefore dSd / dt kSd k1 Sd dt , k1=k(k-
(7)
where X represents either stator voltage, stator current, rotor current, stator or rotor flux. The quantities Xk (with k = a, b, c) represents the instantaneous values with respect to a neutral point. It was shown in [15] that there is a relationship between SVM and PWM control schemes. In this sense, the DTC-SVM
V Sd kSd k1 Sd dt R S i Sd
which can be expressed as a PI controller: ˆ ) K ( * ˆ ) dt R i v d* K P1 ( S* S i1 S S S Sd
(13) (14)
The term RS iSd can be seen as a coupling term between both flux controller and voltage reference vd*, similar to the Stator FOC [18]. On the other hand, from (11) with iSd set to zero gives: (15) me K e Sd iSq Then, from (10) and former equation VSq
K1me S S S
(16)
Then, if flux is constant (i.e. steady state) equation above can be expressed as a PI controller as: ˆ vq* K P 2 (me* mˆ e ) K i 2 (me* mˆ e )dt ˆ S S
(17) A constant flux assumption is not new in high performance drivers [16-18], since these controllers emulate independent dc motor control and flux control could be seen as equivalent to field control. Expressions (14) and (17) support the control system shown in Fig. 5, where; vd* control stator flux and vq* controls electrical torque, respectively. Fig.1. Control system for DTC-SVM (PWM)
reported in [3] can be interpreted as a DTC-PWM modulator since it uses the same flux and torque references, as shown in Fig. 1. Also, the voltage, current and stator flux can be referred to a general dq frame moving at an arbitrary angular speed x, so these quantities can be expressed using matrix or vector notation, respect to dq axes, as (Y=VS, iS,S) Y Yd jYq
(8)
Thus, if x =S is taken in (1) V Sd R S i Sd VSq
d Sd S Sq dt
d RS i Sq Sq S Sd dt
(9) (10)
and from (5)
me K e (Sd iSq Sq iSd )
(11)
Assuming Sd=S, Sq=0 (see Fig.2), and from (9) d (12) V Sd R S i Sd Sd dt Note that a second derivative of a function y can be expressed and a first as y´´(t k ) k ( y´(t k ) y´(t k 1 )), k=1/(tk-tk-1) derivative of y is given by y´(tk 1) k ( y(tk 1) y(tk 2 )) . Assuming y’(tk-1) is a constant value y(tk-1)=ay(tk-2) then, y´´(t k ) ky´(t k ) k ( k a ) y (t k 1 )) . Thus, if y´´(t k ) dSd / dt , * y´(t k ) Sd , S =S vq d can be kept constant in DTC [16],
Fig.2. References frames and space vectors, is the angle between S and iS, S =St.
III. OCC SYSTEM APPROACH Fig.1 shows a DTC-PWM control system for IM with torque and flux controllers. In general, in a control system there is an input and output variable, i.e. mimo or miso systems. For a DTC control as in Fig.1, it is difficult to identify the input and output variables. This issue is important, due to one cycle control premise: OCC integrates the output Y(t) until it matches the average input X(t) in only one switching cycle [19], see Figs.3 (a), (b). However, as in reference [19] OCC premise is only used for dc-dc converters, for more complex control systems as DTC control, a vector or matrix approach makes necessary, see Figs.3(c). Thus, input and output control should be identified from Fig. 1. In present work, average torque motor is identified as input (a faster variable) while flux is identified as output (a slower variable); analogously to an OCC-PFC rectifier, where the input X(t) is average phase current and output Y(t) is the integral of dc link voltage [12].
3 va* K , * va K , v* K , b * vb K , v* K , c vc* K ,
q1 1 q1 0;
(23)
q3 1 q3 0; q5 1 q5 0
where K=K(t) is triangular carrier. Substituting (22) into former expression
Fig.3. (a) Original OCC block diagram [19]. (b) Associated waveforms. (c)Proposed DTC-OCC block diagram. (b) Related waveforms.
To show how the present proposal is deduced, consider the block diagram shown in Fig.1 that is utilized for DTCSVM (PWM) controller. As it can be observed, the voltage references for PWM modulator depends on flux, torque controllers, and also from estimated flux angle, so this relation can be written as: va* * vb vc*
Cos Sin * v ACos( 2 / 3) Sin( 2 / 3) d* v Cos( 2 / 3) Sin( 2 / 3) q
(18)
where is electrical stator angle, A is an arbitrary sinusoidal amplitude wave. Equation (17) can be written as va* Cos( ) * * 2 * 2 v A v v Cos ( ) ( ) ( 2 / 3 ) d q b vc* Cos( 2 / 3) arctg(vq* / vd* ).
(19) (20)
Stator flux must be constant during control operation, even when torque varies roughly due to a change in speed or torque command i.e. motor stops or reverses speed. One way to achieve this goal is that output flux variations are very much less than output torque variations. This can also be noticeable from the second term of Equations (13) and (16), where in general RSiSd
