00103436 - An Adaptive Hy Steresis-Band Current Control Technique of a Voltage-Fed PWM Inverter for...

7/28/2019 00103436 - An Adaptive Hy Steresis-Band Current Control Technique of a Voltage-Fed PWM Inverter for Machine D

1/7

402 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 31, NO . 5 , OCTOBER 1990

An Adaptive Hy steresis-Band Current ControlTechnique of a Voltage-Fed PW M Inverterfor Machine Drive SystemAbstract-A Hysteresis-band instantaneous current control PWMtechnique is popularly used because of its simp licity of im pleme ntation ,fast current control respo nse, and inherent peak current limiting capab il-

ity. H oweve r, a current controller with a fixed hysteresis hand has thedisadva ntage that the mod ulation frequency varies in a band and, as aresult, generate s nonop timum current ripple in the load. T his paperdescribes an adaptive hysteresis-band current control method where theband is modulated with the system parameters to maintain the m odula-tion frequency to be nearly constant. Although the technique is applica-ble to general ac drives and other types of load, an interior permanentmagnet (IPM) synchronous machine load is considered. Systematicanalytica l expre ssions of the hysteresis band are derived as func tions ofsystem parameters. An IPM machine drive system with a voltage-fedcurrent-controlled PWM inverter has been simulated on computer tostudy the performance of the proposed method.

I. INTRODUCTIONINCE the introduction of the general sine-triangle voltageS WM technique by Schonung and Stemmler [9] around

two-and-a-half decades ago, the literature in power electron-ics abounds with various PWM techniques and their imple-mentation. For ac machine drive applications, the PWMvoltage control is usually associated with stator current con-trol because the current directly relates to the developedtorque of a machine. Besides, the control of current ampli-tude is particularly important for power semiconductor de-vices of the inverter. A PWM voltage-controlled invertermay have either scalar or vector current control in outerloops. Scalar current control may be adequate for a simplelow-performance drive system. In a high-performance vectoror field-oriented drive control system, the vector currents Zqs(torque component of current) and Ids (flux component ofcurrent) are controlled independently to control the torqueand flux, respectively. The different PWM voltage controltechniques, such as sine-triangle and notch angle look-uptable, are generally difficult to implement. Besides, the cur-rent feedback loops may have delay, which will not permitinstantaneous-peak current control of a device. Asynchronoussine-triangle PWM voltage control can be used in conjunctionwith instantaneous current feedback control to solve theabove problem. However, in this method, the current looperrors will be nearly sinusoidal in nature, and the response

Manuscript received July 17, 1989.The author is with the Department of Electrical Engineering, U niversity ofTennessee, Knoxville, TN 37996-2 100.IEEE Log Number 9038039.

will be somewhat limited by the stability requirement of thefeedback loops. Besides, multiple crossings of the triangleramp by the current error may become a problem when timerate of change in the current error becomes greater than thatof the ramp. Predictive voltage control techniques [13] toachieve balance between instantaneous command and feed-back currents have been forwarded. Although these tech-niques tend to give optimum performance in terms of re-sponse time and accuracy, these are very complex to imple-ment.

Among the various PWM techniques, the hysteresis-bandcurrent control PWM method is popularly used because of itssimplicity of implementation. Besides fast-response currentloop and inherent-peak current limiting capability, the tech-nique does not need any information about system parame-ters. However, the current control with a fixed hysteresisband has the disadvantage that the PWM frequency varieswithin a band because peak-to-peak current ripple is requiredto be controlled at all points of the fundamental frequencywave. As a result, the load current contains excess harmon-ics, which cause additional machine heating. Besides, thedifficulty of vector conversion of harmonic rich feedbackcurrents and phase lag of the fundamental current withrespect to the reference wave make high-performance ma-chine control difficult. Consider a battery-fed inverter drivesystem where the battery voltage in the worst case may varyby a factor of two (see Table 11) from full motoring to fullregeneration. Since maximum inverter switching frequency isa limiting factor and switching frequency tends to increasewith the increase of battery voltage for a fixed hysteresisband, the band is to be designed on worst-case basis, i .e. , forthe maximum battery voltage. This means that most of thetime, the drive system will operate with nonoptimum statorcurrent ripple. Malesani and Tenti [3] have proposed aprogrammable hysteresis-band current control method byusing a phase-locked loop (PLL) technique to constrain theinverter switching at a fixed predetermined frequency. ThePLL loop with large LP filter tends to create stability prob-lem. Besides, during large transients, the PLL tends to losesynchronization.

The paper describes an adaptive hysteresis-band currentcontrol PWM technique where the band can be programmedas a function of load and supply parameters to optimize thePWM performance. Although various criteria of optimizationare possible, the paper illustrates a case where the modula-

0278-0046/90/1OOO-0402$01.OO 0 990 IEEE


2/7

I

BOSE: ADAPTIVE HYSTERESIS-BANDCURRENT CONTROL TECHNIQUE 403

I ' I A C M AC HIN E '

MICRO

Fig. 1. Three-phasePWM nverter ac machine drive with hysteresis-bandcurrent controller.tion frequency is held nearly constant. Modem high-perfor-mance ac drive systems invariably Use microcomputer controlwhere all the system variables are already available in thememory. An algorithm relating the hysteresis-band with thesystem variables can be easily computed and updated to adedicated hardware hysteresis-band current control for aninterior permanent-magnet synchronous machine drive appli-cation. An analytical derivation of the band has been madeand then verified by simulation on computer.

n. SYSTEM ANALYSISFig. 1shows a three-phase PWM inverter feeding an ac

machine load where each machine phase is represented by acounter emf in series with inductance and resistance. Sinu-soidal command currents ( i ; , i t , F) are compared with therespective machine phase currents (i , , i ,, i c ) , and the result-ing errors through hysteresis-band current controllers com-mand the transistor base drives, as is shown. The hysteresisbands that are normally fixed and the same for all phases in aconventional system are shown being updated from a micro-computer in the proposed adaptive band system. The band(HB) can be modulated at different points of the fundamentalfrequency cycle to control the PWM switching pattern of theinverter. For symmetrical operation of all the three phases, itis expected that the band profiles HB,, HB,, and HB, willbe same, but phase will be displaced.A . Case I : Neutral Connected with Pure Inductance Load

Consider a simple case where a wye-connected machineneutral is C O M & ~ ~ o the center tap of the supply battery,and the load is purely inductive, i.e., the counter emf andresistance are neglec td. In this case, each phase is indepen-dent and is supplied by a half-bridge inverter leg. Fig. 2shows the PWM current and voltage waves for phase a. Thecurrent i , tends to cross the lower hysteresis band at point 1,where the transistor Q1 i s switched on. The linearly risingcurrent ( i , +) then touches the upper band at point 2, wherethe transistor Q4 is switched on. The following equations can

+ -0.5VFig. 2. Current and voltage waves with hysteresis-band current control(machine neutral connected).be written in the respective switching intervals t , and t, :

di+dtL =0 . 5VB

did di;i.e.- - 0dt dt (3)where L =phase inductance, and i , + and i , - are therespective rising and falling current segments.From the geometry of Fig. 2, we can write

did di;dt dt

di; di*- t2 - L t , = -2HBdt dt

- t l - t l =2HB (4)( 5 )

1tl + t, = T, =- (6)f,where t , and t , are the respective switching intervals, and f,is the modulation frequency.

Adding (4) nd (5 ) and substituting (6), we can writedid di; 1 di ;

dt f, dtt , x + t, - --- =0 .Subtracting (5 ) from (4),we get

di+ di; di2dt dt4HB = t l L 2- - ( t l - t , ) ~ .

Substituting (3)n (8), we getdit di;dt

1 did di;4HB = (tl +t2)- - tl - 2 ) ~

( 4 - 2)-&.-- -f, dtAgain, substituting (3) in (7) nd simplifying


3/7

II

404 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 3 1, NO. 5 , OCTOBER 1990

IY

t

W3sLLz0a130

Fig. 3. Sensitivity of modulation frequency with the supply voltage.

II

Fig. 4. Sensitivity of modulation frequency with the command currentslope.Substituting (10) in (9) gives

r

Substituting (1) in (11) and simplifying

the frequency f c in Fig. 4 will be modulated at twice thesignal frequency. The corresponding maximum and minimumvalues of f c can be derived as

O.125VB a 3aat wt =- --,etc. (14)fcmax = (HB)L 2 ' 2and

Therefore, for constant hysteresis-band control, the band isto be designed for f,,, which corresponds to the highest V,and rn =0 point of the cycle. This indicates large harmonicdistortion of current, and especially, the problem becomessevere with large variation of dc voltage. Equation (12)indicates that HB can be modulated as a function of V, andrn so that the modulation frequency fc remains constant.This will improve the PWM performances substantially.B. Case 2: Neutral Connected with Counter emf Load

The machine always develops a counter emf at a speed,and therefore, this type of load is more practical. The counteremf wave is sinusoidal and is at a phase angle with respect tothe fundamental frequency applied voltage. During a modula-tion period, the emf magnitude can be considered to beconstant. The following equation can be written from Fig. 2:

di: 1dt L- - - - 0.5VB- ~ f )

di; 1- -d t - - ( O w B +U ~ )where u f = counter emf.

Note that the magnitudes of the current slopes are differentbecause the counter emf ur is subtractive in positive slopebut additive in negative slope. The general equations (7) and(8) of Case 1 will be valid here. Substituting (16) and (17) in(7), we get

tl t2 1 diz--(0.5VB - u J ) - -(0.5VB +ur ) - -- =0(12) L L f c dtf c Li.e.

where rn =di:/dt is the slope of command current wave.

0.5 V,i.e. --Lor t , - , = --

Equation (12) shows the band as a function of modulationEquation (13) indicates that for a fixed band, the modulationfrequency will vary with V, and rn. Fig. 3shows the

Substituting (16), (17), and (18) in (8), we get4H B =- 0. 5VB- uf )frequency, supply voltage, and the slope of the i; wave. tlL

t2 2Lsensitivity of f c with V indicating that the modulation +-(0.5VB +u f ) --frequency increases with the dc voltage. Fig. 4 shows the Lsensitivity of f c with the slope of command current wave.Since i.e., HB = ~

u t ) =0.5w2Zi(1+c o s 2 w t )I' where rn is substituted for d i z ld t .


4/7

STATIONARYFRAME

Fig. 5. Phasor diagram of interior permanent magnet synchronous ma -chine.Equation (19) is similar to (12), except the counter emf

parameter is introduced. In this equation, the variables vfand m depend on the type of load machine and its operatingcondition.An interior permanent-magnet synchronous machine load

will be considered here, although (19) is valid for any type ofac machine. Fig. 5 shows the phasor diagram [ll]of an IPMmachine. In forward direction of motion, the phasor diagramcan be considered to be rotating counter clockwise at syn-chronous speed (U,) with respect to the stationary referenceframe dS axis, and at any instant, the angle between themagnet axis (de) and d S axis is 8 =o,t . The armaturereaction flux ' ka adds with the magnet pole flux qf toconstitute the stator flux 'k,, which is aligned at an angle 6(torque angle), as shown. The stator phase voltage V , andinduced emf V are at quadrature to the respective fluxcomponents 'ksand q f .A new set of d er- qe' axes thatalign with 'k, and V is shown in the figure. The machinephase current Z, is shown at arbitrary lagging power factorangle Cp. This current can be resolved as an Zds-Zq, pair onde -qe axes or an Zm-ZT pair on de'-qe' axes. The in-phasecurrent IT contributes to machine torque, whereas the reac-tive current ZM controls the stator flux. From the phasordiagram, the following equation can be written:

uf = Vfm in0, (20)i s =I, , sin (e, +6 - p)zqs=I, , cos (6 - a) (21)(22)Ids=I, , sin ( 6 - +) (23)

whereVfm =J2Vf =J2\ kf~ , and I, , =J2Zs.

The phase current is (i.e., i,) can be considered to betracking accurately with respective commanded current (it)with the hysteresis-band current control. Therefore, differen-tiating (21)

di ,dtm = - = w , [ ~ ~ ~COS 6 -+)

-sin e,Z, sin (6 -+)] (24)

and then substituting (22) and (23)m = zqsCOSe, - zdS in e,). (25)

Substituting (20) and (25) in (19), the complete expression ofHB can be derived to be0.125VB 4L2w2, J 2 q f ~ ,HB =-1-7(- L - ZfcL

BOS E: AJ M F TW E HYS TERES I S - BAND CURRENT CONTROL T E C H N I Q U E 405

A T I

Equation (26) can be written in the formHB =

- {( - Ids sin 8 +ZqsCOS 8 (27),where wb =base frequency (rad/@, XL = =0.5(Xq,+Xds), and VfB='kf b' The IPM machine has somesaliency but only the average reactance is taken into consider-ation. Substituting the trigonometrical relation( A in e, +B COS e)

=o . ~ ( A '+B ' ) [ I - COS^(^,+ a)]and simplifying (27) can also be written in the form

where

0 . 2 5 ~ ~,B =fcvB

and

Fig. 6 shows the typical plot of (28) for a fixed modulationfrequency, where it is given in phase relation with the phasecurrent and induced voltage. Evidently, modulation of HBoccurs at twice the stator frequency with the average valueA-B.C. Case 3: Isolated Neutral with Counter emf Load

Since machines normally operate with isolated neutral , thisis the most practical case. Unfortunately, with isolated neu-tral, the machine phase voltages interact and can no longer be0.5 VB as with a connected neutral. The derivation of theexact expression of HB is somewhat difficult in this case. nFig. 1, the phase voltages with floating neutral can be given


5/7

406 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 31,NO . 5 , OCTOBER 1990

n n

ADAPTIVE HYSTER ESIS BAND(A-B ) t B C o s Z ( O + o )

FIXED HYSTERESIS BAND(WORST CASE)

Fig. 6. Adaptive hysteresis-band profile for constant modulation showingrelation phase current and induced voltage w aves.

LOCKED OUT PULSE '

l-lmn&/2TABLE ISWITCHINGODES F T H E INVERTERA N D PHASE IMPRESSEDOLTAGES

MODE O N - D E V I C E PHASE a VOLTAGE1 Q I Q(, Q5 +113V132 Q I Qh Q23 Q I Q3 Q5

+113Vu Fig. 7 . Typical PWM voltage waves when the machine neutral is isolated.0

4

65 Q-1 Qb Q Z

QI Q(, Qz +2 / 3 V 130

Q A 4 3 Q 5 - 2 /3v1{7 Q-1 Q iQz - 1 / 3 V 38 $4 (21, QS - 1 /3V l{

as V I(29)

(30)

(31)

2 1

2 1' a n = -'a0 - ? ( ' b o + CO)"bn = - u b o - ?( 'a , + CO)

2 1' c n = -'CO - ?('a." + ' b o )

Table I gives all the switching modes of the inverter, andFig. 7 shows [2] typical PWM voltage waves in the isolatedneutral case. When Q1 is on, the possible phase-a voltagemay be 0, 113, or 2/3VB, and when Q4 is on, the corre-sponding voltage may be 0, -113, or -2/3VB. TypicalPWM phase voltage and current waves during a modulationcycle are shown in Fig. 8 . With the assumed polarity ofcounter emf when Q1 is on, the phase current in a timesegment will rise or fall, respectively, depending on thedominating phase voltage or counter emf, but the current will

ON ONFig. 8. Typical PWM phase voltage and current waves in a modulationcycle in isolated neutral case .Therefore, summing up the total current

always fall during the Q4-on period. The general expressionof incremental current rise AHB during Q1-on period is(33)1

4given by

InAH B = - ( a V B - ur ) - l nm (32) The general expression of incremental current fall during theQ4-on period is given bywhere 1 2 di; t2 na =0, - or - and m =- -AHB = -(at', +U,.) - Z n m . (34)3 3 dt


6/7

BOSE ADAPTIVE HYSTERESIS-BANDCURRENTCONTROLTECHNIQUE

. I I

407Therefore, the total fall is

-2HB =C - AH B =C[ -t2,,( m +z)- xt2,,aV,1

(35)The average current rise and fall during the periods t , and

t , , respectively,are shown by the dotted lines in Fig. 8. Theslope of these lines will be determined by the weightedaverage supply voltage. In (33) and ( 3 3 , the second term canbe expressed as

or

Zt,,aV, = t , d V,Zt2,aV, = t2a"V, (37)

(39)where a and a" are the respective applied voltage coeffi-cients. Although the average applied voltages in the twointervals may have some asymmetry, we will assume thesesame (i.e., d =a")as in Case 1 and Case 2 for computa-tional simplicity. The computation of HB on this assumptionwill give a smal l amount of inaccuracy. The parameters a,a', and a" will typically vary between 1/3 and 2/3, and thelater is the worst case. Combining (33), (3 3, (38), and (39),we get

0.25a' V, L2HB = -[l f c L - -(y'VB' L +- 1 4 . (40)

Equation (40) is same as (19) except 0.5 VB has beenreplaced here by a' V,. Therefore, the complete expressionof HB or the isolated case of IPM machine is

0.25a'V,wb [ X i (u , ) ~HB = 1 - 7 -f ,XL ". wb ,(A ' - B') +B'cos2(Be +a) (41)

whereA ' = 2 d A

BB' =-a''The A, B, and a parameters have been defined in (28).

III. CONTROLMPLEMENTATION AND SIMULATIONThe hysteresis-band HB in (41) can easily be implementedby microcomputer in a high-performance drive system whereall the essential parameters may exist in the memory. In this

equation, the parameters a', w b , f , , X , , and VrB can be

ON

Fig. 9 . Block diagram for implementation of adaptive hysteresis-bandcurrent contro l.treated as constants, whereas the terms V, ,we, Ids , Zqs , and8 are variables at any steady-state operating condition.

Fig. 9 shows the block diagram for the implementation of(41). The absolute position of the machine rotor is sensed byan analog resolver and then converted to speed ( U , ) andposition (e) outputs by a resolver-to-digital converter. The8, signal is then converted to cosB, and sine , signals bylook-up tables. The stator phase currents are converted tosynchronously rotating frame signals Ids and Zq s using thecos Be and sin Be unit vectors. Note that the HB signals(HB,, HBb, HB,) for all the phases are symmetrical butphase shifted by 60".A digital signal-processor-type TMS32W25 by Texas Instruments is ideally suited for the controlimplementation. Because of the symmetry, a segment of HBfor the interval 0" to 180" can be computed and stored in theform of a look-up table, which can then be retrieved sequen-tially for each phase. The table is to be refreshed everysampling interval in steady-state condition. The algorithm forimplementation is as follows:

0 Sample the variables V,, we, Id s , and Zq s every 2 ms.0 With the known parameters a', w b , f,,X , , and Vf,,

compute HB every 5" interval for 0 to 180" (36 sam-ples) and load the table every 2 ms.

0 Using the 5" interval pulse train, retrieve the HB look-uptable (with the help of phase location pointers) and loadHB,, HB,, and HB,.

The 180" pulse train as shown is used for synchronizationpurposes. Since the algorithm is not valid for transient opera-tion, which is indicated by the current loop error exceedingthe band, the automatically worst-case HB (Fig. 6) is com-manded.

The adaptive hysteresis-band current control for the iso-lated neutral case of the IPM machine drive system has beenimplemented in digital simulation using the SIMNON (LundInstitute of Technology, Sweden) language. The details of thedrive system are described in [ll] and [12]. Table 11 showsthe parameters of the drive system. Fig. 10 shows thesimulation result of phase current waves and HB profile forf,=4 KHZ, V, =204 V and d =2/ 3 (wont case).

The inaccuracy of the a parameter will cause some spreadof modulation frequency, and a conservative a' value inpractical implementation will result in the maximum modula-tion frequency below that of the optimum value. The re-

_ _ _ - -l-


7/7

408 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 31, NO. 5 , OCTOBER 1990\TABLE II \PARAMETERSF THE IPM MACHINE RIVE YSTEM

70 hp, 4-Pole, Wye Connected Neodymium-Iron-Boron(Crum ax 30A) Machine*Base Speed (01,) =710.48 radis (elec.) (3394 RPM)Magnet f lux ( w b y t ) =40.2 Volts(at 75C)Rated Stator Flux ( w i ) y b r ) =58.5 V o l t sBattery Voltage VI^) =204 Volts (nomina l) --135 264 Volts variation) - --Rated Stator Curr ent (Isr)=315 Amps a Stator Resistance (R,) =0.00443 O hmsStato r Leakage Reactance (wbLqs) =0.0189 Ohms

A V E R A G E SUPPLY V O L TA G E C O E F F I C I E N TFig. 11. Real-time search of parameter a for optimum hysteresis band.

jOBl

De-Axis Magnetizing Reactance (wbLdm) =0.0785 OhmsQe-Axis M agnetizing Reactance (obLqm)=0.1747 Ohms

*At Battery Voltage of 135 Volts

, I/ 0

l A D A FHE 1 VE

J I 0. 1T I M E (secs)

current control.Fig. 10. Simulation phase current wave with adaptive hysteresis-band

band is modulated as a function of system parameters tomaintain the modulation frequency to be nearly constant.Systematic mathematical analysis has been presented, andband expressions have been derived as a function of the loadmachine and supply parameters for connected and isolatedneutral cases. An IPM machine drive system with the pro-posed adaptive band has been studied by digital simulation.

finement of the above method by real time search of the aparameter is at present under investigation and is indicated inFig. 11. In the beginning, HB is computed on the basis ofconservative value a =2 /3 . The a parameter is then iter-ated on the basis of actual average modulation frequencycounting the transistor base drive logic transition of a phaseleg of the inverter over a full cycle.f c ( a v ) until f c ( a v ) =fc(opr).he f c ( a v ) can be determined by

IV .CONCLUSIONA novel adaptive hysteresis-band current control PWM

technique has been described in the paper. A hysteresis-bandcurrent control PWM method is popularly used because it issimple to implement by dedicated hardware, has fast re-sponse, and device peak current is automatically limited. Theconventional fixed hysteresis-band current control generatesexcessive current ripple because modulation frequency varieswithin a band. In an adaptive hysteresis-band method, the

REFERENCES[ l ][2]

B. K. Bose, Power Electronics and AC Drives. E n g l e w d C lif fs ,NJ: Prentice-Hall, 1986.A. B. Plunkett, A current controlled PWM transistor inverter drive,in Proc. Conf. Rec. IEEEIIAS 1979 Ann. Mtg., 1979, pp.L. Malesani and P. Tenti, A novel hysteresis control method forcurrent-controlled VSI PWM inverters with constant modulation fre-quency, in Proc. Conf. Rec. IEEEIIAS Ann. Mtg., 1987, pp.H. Le-Huy and L. A. Dessaint, An adaptive current controller forPWM inverters, in Proc. Conf. Rec. IEEEIPESC Conf., 1986,

[5] A. Kawamura and R. G. Hoft, Instantaneous feedback controlledPWM inverters with adaptive hysteresis, IEEE Trans. IndustryD. M. Brod and D. W. Novotny, Current control of VSI-PWMinverters, IEEE Trans. Industry Appl., vol. IA-21, pp. 562-570,1985.

785-792.[3 ]

851-855.[4 ]

pp. 610-616.

Appl., vol. IA-20, pp. 769-775, 1984.[6 ]

I[7] G. Pffaf, A. Weschta, and A. Wick, Design and experimentalresults of a brushless ac servo drive, in Proc. Conf . Rec.IEEEIIAS Ann. Mtg., 1982, pp. 692-697.A. Nabae, S. Ogasawara, and H. Akagi, A novel control scheme ofcurrent-controlled PWM inverters, in Proc. Conf. Rec. IEEEIIASAnn. Mtg., 1985, pp. 473-478.[9] A. Schonung and H. Stemm ler, Static frequency changers withsubharmonic control in conjunction with reversible variable speed acdrives, Brown Boveri Rev., pp. 555-577, 1964.[IO] B. K. Bose and H. Suthe rland, A high-performance pulsewidthmodulator for an inverter-fed drive system using a microcomputer,

IEEE Trans. Industry Ap pl ., vol. IA-19, pp. 235-243, 1983.B. K. Bose, A high performance inverter-fed drive system of aninterior permanent magnet synchronous machine, in Proc. Con f .Rec. IEEEIIAS Ann. Mtg., 1987, pp. 269-276.B. K. Bose and P. M. Szcze sny, A microcomputer-based controland simulation of an advanced IPM synchronous machine drivesystem for electric vehicle propulsion, in Proc. IECON 87, 1987,pp. 454-463.J. Holtz and S . Stadtfeld, A predictive controller for the statorcurrent vector of ac machine-fed from a switched voltage source, inProc. Int. Power Electron. Conf. Rec. (Tokyo), 1983, pp.B. K. Bose, Pow er electronics-an emerging technology, IEEETrans. Ind. Electron., vol. 36, pp. 403-412, Aug. 1989.

[8]

[ l l ]

[I21

[I31

1665-1675.[14]

00103436 - An Adaptive Hy Steresis-Band Current Control Technique of a Voltage-Fed PWM Inverter for...

Documents

Transcript of 00103436 - An Adaptive Hy Steresis-Band Current Control Technique of a Voltage-Fed PWM Inverter for...