[ieee 2007 international symposium on computational intelligence and intelligent informatics -...

5

Click here to load reader

Upload: me

Post on 28-Feb-2017

218 views

Category:

Documents


5 download

TRANSCRIPT

Page 1: [IEEE 2007 International Symposium on Computational Intelligence and Intelligent Informatics - Agadir, Morocco (2007.03.28-2007.03.30)] 2007 International Symposium on Computational

Speed Sliding Control ofPMSM Drives

M. Kadjoudj*, A.Golea**, N.Golea*, M.E. Benbouzid*** senior member IEEE*Department of electrical engineering, Batna University" Department of electrical engineering, Biskra University

* * *Department GEII, University of Brest, French

Abstract- The current controlled voltage source inverter fed Among the current control strategies, fixed band hysteresisPMSM has received wide spread interest in high performance current control is probably the simplest technique and thevector control and motion control applications. Hysteresis most extensively used method to control the phase motorcontrollers are intrinsically robust to system parameters, exhibit currents for AC machine drives. Some significant advantagesvery high dynamics and are suitable for simple implementation. of hysteresis controllers over other types of controllersThe main drawback of the hysteresis controller is a limited designed with linear or non-linear control techniques are ascontrol on switching frequency. Very high switching frequency follows:may be resulted from the use of three independent controllers.In this paper, both the fixed band and the sinusoidal bandcurrent controllers are presented and their performances * fast response and good accuracy because it actsevaluated. In addition, a mixed mode controller of a sinusoidal quickly.band added to a fixed band is proposed. For comparison * switching behaviour of the power inverter can bepurposes, the harmonics spectra of the phase currents are directly taken into account at the design level .obtained using the fast Fourier transformer (FFT). This paper * robustness to load and motor parameters variations.presents also a detailed analysis and simulation of speed sliding simple hardware implementation.mode control (SMC). The effectiveness is demonstrated fordifferent operating conditions. ld*=O labe* E

I. INTRODUCTION Wr controller Current

Recent developments in power electronic, motion controland magnetic materials provide an excellent opportunity touse AC motors in high performance drive applications [1]. WrAs a result PMSM drive became competitor to other

classes of AC drives due to its advantages features for PMSMadjustable synchronous speed and high performance Fig. 1. Block diagram of the proposed controlapplications. It is characterised by high torque to current ratio,high power to weight ratio, high efficiency and robustness Nevertheless, a current controller with fixed hysteresis[2]. band has two main disadvantages. The switching frequencyThe vector control technique can be implemented by using varies during the fundamental period, resulting in irregular

current and speed controllers with fast response and high operation of the inverter. The current ripple is relatively largeaccuracy. A typical closed loop vector control scheme for the and theoretically can reach a double value of the hysteresisPMSM drive is shown in figure 1. Vector control for PMSM bands. As a result, the load current contains harmonics thatdrives provides the decoupling control between the torque and cause additional machine heating [6] [7] [10].flux components, and is able to obtain good performance An other hysteresis current controller employs a band,characteristics similar to that of a DC motor, so vector control which sinusoidally varies with the fundamental period. Thusis a popular control method for PMSM. Performance of the ripple can be varied with the current magnitude therebyvarious current controller schemes for VSI inverter feeding reducing current ripple content. A lessened ripple wouldAC motors have been investigated and reported in the result in a lower harmonic content, keeping intact the fastliterature [3] [4]. The most common strategies of current response and simplicity of implementation of hysteresiscontrollers can be classified as hysteresis , ramp comparator curncotles[6[9[1]

.. ... ... . . . . ~~~~~~Theaim of this paper iS to present a mixed band currentand ~~ ~~ ~ ~~, hyrdcnrles.ahsheehsisonavnae controller scheme with improved performance over the entireand drawbacks with regard to accuracy and dynamic response rag ofsedTh pooedcnolrshmeia

over the entire peed ranges [5].combination of a fixed band and sinusoidal band hysteresiscontrollers in order to take advantage of the position features

1-4244-11 58-0/07/$25.OO © 2007 IEEE.137

Page 2: [IEEE 2007 International Symposium on Computational Intelligence and Intelligent Informatics - Agadir, Morocco (2007.03.28-2007.03.30)] 2007 International Symposium on Computational

3rd International Symposium on Computational Intelligence and Intelligent Informatics - ISCIII 2007 - Agadir, Morocco * March 28-30, 2007

of both the fixed band and the sinusoidal band hysteresis pulsation and noise in the motor and fast response in order tocontrollers. The simulation results are presented and provide high dynamic performance [1].discussed. The speed sliding mode control has been widely The voltage vector corresponding to the active states areutilised as speed controller in the PMSM drives. It is shown in figure 2. The six commands VI - V6 correspond tocharacterised by high accuracy, fast response and robustness. active voltage vectors, the remaining two Vo and V7

correspond to the zero voltage vector. In hysteresis currentII. BASIC CONCEPT controller, the load current is forced to follow a reference

current within an hysteresis band by the switching action ofThe voltage equations in a synchronous reference frame the inverter.

can be derived as followsV3(-l,l,-l) A,/ V2(1,1,-1)

Vd RS + PLd -r Lq Id 0 IKq ILrAZ.d Rs+pLq iLq~ + or]-(1where R, and Ld,q are the stator resistance per phase and d-q V4(-l,l,l)axis inductances, Vdq and Id,q are respectively the statorvoltages and currents, co, is the angular speed, 0 is the rotor V00, , )position, np is the number of pole pairs and p is thedifferential operator. From the above relations, the developedtorque can be written as,

KV5(Tl,-l,) V6(1,-T,l)

Cem KT Iq + T .(Ld - Lq )VdIq (2) Fig.2. Switching states of the output VSI under currentqOf controller.

KT 3-.n Oqf (3) The upper and lower bounds of the hysteresis band are set2 for the motor current. Although simple and extremely robust,

The motor dynamics can be simply described by the the control technique exhibits several unsatisfactory features.equation (4) The main one is that it produces a varying modulationJ dr + f r C -C (4) frequency for the power converter. It is, in general,ndt or -em st responsible for various problems [5][6].

The switching frequency varies over the fundamentalperiod and the inverter operation is irregular and hence the

By using the concept of the field orientation, it can be switching losses also increase. It is well known that a threeassumed that the d-axis current is controlled to be zero. Under phases VSI will not work properly if controlled by threethis assumption, the contribution of the second term of the independent hysteresis loops due to the inherent couplingelectric torque equation becomes effectively negligible and between the three phases of the inverter. Figure 3 shows thatthe reduced dynamic model of the PMSM is given by the the use of individual controllers provides mutual interactionfollowing equations. of the controllers [9].

dIq Rs *Iq f (5)= .V- Sj 0)(5

dt Lq q Lq q Lq r

dt T -q COp r Cst (6) X

III. FIXED BAND CURRENT CONTROLLER

In the vector control scheme, the current controller hasdirect influence on the drive performance and its design needsspecial consideration. The basis requirements from the current Fig.3. Block diagram of independent hysteresis controllerscontrollers are low harmonics to reduce losses, torque

138

Page 3: [IEEE 2007 International Symposium on Computational Intelligence and Intelligent Informatics - Agadir, Morocco (2007.03.28-2007.03.30)] 2007 International Symposium on Computational

M. Kadjoudj, A. Golea, N. Golea, M. E. Benbouzid Speed Sliding Control of PMSM Drives

IV. VARIABLE BAND HYSTERESIS Van = (2ShiSh2-Sh3)CONTROLLERS 6

Based on the hysteresis band conventionally, there are two Vbn=£ (-Shl+2Sh2-Sh3) (23)types of hysteresis controllers, namely, fixed band and 6sinusoidal band hysteresis controllers. In the sinusoidal band Vcn (-Shl-Sh2 +2Sh3)case, the hysteresis band varies sinusoidally over the 6fundamental period [1].

V. MODELLING RESULTS

Iaref =Imax.sin(@.t) ~~~~(19)Jaref =Imax.slfln (0). t) A. A. Simulation Results of the Speed SMCIupp={Iax +AIsin sin ((). t) (20)Low {Imax-Asin }sin(co. t) B. (21) Using the procedure described in section 3, a rigorous

simulation is carried out for the speed servo drive with sliding

In a fixed band controller, the lateral distance of the upper mode control. Figure 5-6 show the system response for a stepand the lower waveforms are not uniform. The switching change in the speed command at rated load and with samplingfrequency is low around the peak values and high around the period Te=lms. The speed response exhibits no overshoot.zero crossing points of the reference current [5]. The However, during the initial period, the current Iq is restrictedsinusoidal band scheme limits the harmonic to lower values by the maximum torque limit until it reaches the sliding line.for a given band but forces higher switching frequency near In figure 6-h, X2=f(t) shows that the estimation by thezero crossing [7][8]. observer is very fast and accurate, and than good SMC can be

The advantages of both the controllers can be combined to achieved.give a variable band controller. The instantaneous band heightmay be produced by 150

Alcomb=AI+Alsin.Sin((o. t) (22) Cem

a bFigure 4 shows the various band structures of hysteresis 0.4 .

0 0.2 0.4 0 0.2 0.4current controllers. t(sec) t(sec)

0.2 10

M_ag_b_)_=_ 0.1 ------------------X

- 1 500 .0050.010.0150.02r- 00 0|-----------------------------------------------------------

11-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Id 0 IqMag(pu) 0 ---0.1----- -o-----4--

-1 Ca) - r r 10.20 c d

------------I--------------------2-------- 0.2

-00 0.2 0.4 0 0.2 0.40 0.005 0.01 0.015 0.02 t(sec) t(sec)

compagr1Fig. 5. Performance ofPMSM with speed command(pu) 0-------------------------------------- -

200S

0 0.005 0.0 1 0.015 0.02 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-10000-----------

------------------------h------------------------------------------------s-----n------

2 - F ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-2000------------fMag c(pu) 002 0.4 002 0.4

mo)e issenclalyi tephst(sec) t(sec)

10000 10000X2 X2

0 0. 005 0.01 0.015 0.02

t(se c) 5000 - -----5000 --- -I-----------

Fig.4. Band shapes of various hysteresis controllers.hg~~~~~~~~~(a) Fixed band (b) Sinusoidal band (c) mixed band 0

-200 -100 0 0 02 0.4xi t(sec)

Page 4: [IEEE 2007 International Symposium on Computational Intelligence and Intelligent Informatics - Agadir, Morocco (2007.03.28-2007.03.30)] 2007 International Symposium on Computational

3rd International Symposium on Computational Intelligence and Intelligent Informatics - ISCIII 2007 - Agadir, Morocco * March 28-30, 2007

acceleration versus speed error. It is clear that the speed in controllers are given by a mixed band hysteresis currentsteady state is chattering free. controller.

10 r C r 1 - -

-100 -10-.05---------2-0.5-0.-0.3-0.

1CC-~~~~CeWr 1Ge

-O -1 .---5-----I- --- -- t'_ --- |i i illhlh

-5 ------ 0h

,00 --- bS0

4iC b l 4lo 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-10

0 0.4 0 02 0.4 A .t(sec) t(sec)

0.2 10 4----------C ref 5

-0 ------------ ------------- 40 --- 0.2-.4--0.5--------.2-.25 0.3 0.3-0.

id00.1 - __ 1 - 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 0.2 0.4 0 0.2 0.4 Cern ___ __t(sec) t(sec)

0 0.4f~~~~~~~~~~~x

- -

the~ Fi 7efrac Spee inverusicrenontrles 200nindFg8 Promneo aial adcnrle

------------0-0.5-0.-0.5-0.-0.2-0.-0.3-0.

earlier, the most advantages of the hysteresis currentcontrollers is the fast reaction time. Figure 8 shows the The current is tracked within the sinusoidal bands. It is alsoperformance of the mixed band current controller based clear that the average and maximum switching frequency isPMSM drive for a command speed of 150 rad/sec at rated higher with sinusoidal bands. Results for the hysteresisload condition. It is to be noted that drive system accurately controller with ± 0.-A sine bands are shown in figure 10. Thefollows the reference speed with no overshoot during current ripple is lower compared with the ± 0.1A fixed bandtransient conditions. For the phase current and electric torque, case. The higher order harmonics present with the ± 0.1lAit is evident that the performance of the controller is quite fixed band controller are suppressed to a large extent. Figuregood. It is observed that the current can successfully follow 10 indicates that most of the higher order harmonics with thethe command current both in steady state and transient fixed band controller are suppressed in the sinusoidal bandperiods, controller. For the variable band current controller, the phaseThe steady state current waveforms and the corresponding current waveform has almost uniform current ripple, and a

harmonic distribution for different hysteresis bands are switching frequency is almost held in 1.05 kHz, and thus thepresented in figures 9-11. The spectral distribution is a direct harmonic components of phase current are concentratedfunction of the number of pulses per fundamental period of around the 1 kHz. The mixed band current controller have thethe reference current. The pulses number depends on the band lowest number of pulses for the same band height at zeroheight. Some of the higher order harmonics have a significant crossing points. In figure 11, the spectral distribution showsmagnitude [1 1 ]. that for variable band controller the dominant harmonics are

Figures 9-10 show that the fixed band controller has less distributed and shifted to the left (close to the fundamental).maximum frequency, whereas sinusoidal band controller has This type of band is especially suitable for drives using highbetter spectral behaviour. The advantages of both the speed switching where the band can be reduced with

increased maximum switching frequency as necessary [12].

140

Page 5: [IEEE 2007 International Symposium on Computational Intelligence and Intelligent Informatics - Agadir, Morocco (2007.03.28-2007.03.30)] 2007 International Symposium on Computational

M. Kadjoudj, A. Golea, N. Golea, M. E. Benbouzid Speed Sliding Control of PMSM Drives

4________________________ _____ that the current ripple with mixed band current controller is4 A L ~ A ~b^, *^ g §reduced. Also, the higher order harmonics have a lower

2 -g---- - ----------------- ,- -,- ---- -'\ shR li { magnitude. The dominant harmonics are distributed andla ---j-\---- -------- shifted to the left and then close to the fundamental. The

-2 - variable band hysteresis controller is especially suitable for_4 drives using high performance. This paper demonstrates also0.25 0.26 0.27 0.28 0.29 0.3 the application of the SMC to the robust control of a PMSM.1

c

The SMC guarantee robust behaviour for all type of referenceMag signals, fast convergence and a good performance of both low

(pu) 4 .and high speeds. The SMC has presented a low chatteringlevel.

0 REFERENCES0 1000 2000 3000 4000 5000fr(Hz) [1] M.N. Uddin, T.S.Radwan, G.H.George,

Fig.9. Drive response for fixed band controller M.A.Rahman, "Performance of current controllers4 __________ __________ ____ for IPMSM drive," IEEE transaction on industry

applications, vol. 36 No. 6, November 2000, pp.1531-1538.

01e- --------- 1 [2] Kadjoudj, M.E. Benbouzid, C. Ghennai, D.Diallo,-2_ ------------------ ------------"ARobust hybrid control for PMSM drives," IEEE

A4X__ X__ n Xtrans. Ener. conver., vol. 19 No 1. Marsh 2004, pp.0.25 0.26 0.27 0.28 0.29 0.3 109-115.

t(sec)1 [3] S.K.Chung and al., "A new instantaneous torque

Mag control ofPMSM for high performance drive(pu) l l lapplications," proc. IEEE Feb. 97, pp. 721-727.

0- ~--------------------------------------------

[4] S.Buso , L. Malesani, P.Mattavelli, "Comparison ofO__ - L _I _current control techniques for active filter," IEEE

0 1000 2000 3000 4000 5000 trans. IE, vol. 45, No. 5 Oct 98, pp. 722-729.fr(Hz) [5] K.A. Corzine, "A hysteresis current regulated control

Fig. 1O. Drive response for sinusoidal band controller for multilevel drives," IEEE Trans. Energy

4 Conversion, vol. 15, n02, June 2000, pp. 169-175- 0 0 hhl ^ [6] M.P.Kazmierkowski, L.Malesani, "Current control2.------ k----------------->------ - ----------------1 - --

la 0 Jln ^j1 J \ LR4 techniques for 3 phases VSI PWM converters,IEEE trans. IE, vol.45, No.5 Oct. 98, pp.691-703.

-2 [7] J. Xu, F.Wang, S.Xie,J.Xu and J.Feng, "A new4 0 0 0 0 control method for PMSM withobserver" _proc. of025 026 027 028 029 03 the 35th annual IEEE power electronics specialists1 tlslc) conference, Aachan Germany 2004, pp. 1404-1409.

mag [8] A.Golea, N.Golea, M.Kadjoudj, N.Benounnas,(pu) ^ "CAD of sliding mode control of PMSM," proc. of

.- the IEEE intemat. Symp. USA, 1999, pp. 602-606.[9] M.Kadjoudj, M.Benbouzid, R.Abdesemed,

o ! !C.Ghenai, "Current control ofPMSM fed by two and0 1000 2000 3000 4000 5000 three levels VSI," EPE, Slovakia Sept. 2000, vol. 7,

Fig.11. Drive response for mixed band controller pp. 69-74.[10] A.Tripathi, P.C. Sen, "Comparison of current control

techniques for active filter applications," IEEE trans.

VI. CONCLUSION on Indus. electr, vol.45, No.5 Oct.98, pp. 722-729.[11] A.Benchaib and al., "Real time sliding modeobserver and control of an induction motor," IEEEA variable band hysteresis current controllers and speed trans. JE Feb.99, vol. 46, No. 1, pp.128-138.

sliding mode control are presented in this paper for a high [12 B.J Kag'..iw Rbsthseei urnperformance vector control of PMSM drives. The mixedband controlled PWM scheme with fixed switchinghysteresis controller is useful because of its lower average frequency," IEE proc. Electr. Power appl., vol. 148,frequency. The harmonic spectrum of the load current iS No. 6November 2001, pp. 503-512.generated using fast Fourier transformer (FFT). It is apparent

141