High Performance Sensor Less Control of IM Drives for Industry Applications

8/14/2019 High Performance Sensor Less Control of IM Drives for Industry Applications

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High Perform ance Sensorless Control of Induction Motor Drives for Industry ApplicationsG.Grim*, C. las**, J.F.Eastham***, F.Profumo* , P. Vranka"* * *

* Dipartimento di Ing egneria Elettrica, Politecnico di Torino, C.so Duca d egli Abruzzi 24, 10129, Torino, Italy,Fax: +3 9- 11-564.7199, Tel. : +3 9-11-564.7 159, e-mail: grivag(iathena.po1ito.it** Dept. of Electrical En gineering, Polytechnic of Bucharest, S pl. Independentei 313, 77206 B ucharest, Rom ania,Fax. +40-1-3 120412, Tel . : +40-1-4.100.400. e-mail: [email protected]*** School of Electrical and Electronic Engineering, Bath University. Claverton Dow n, Bath B A2 7AY, U.K.,Fax: +44 -1225426.305, Tel . : +44-1225-826.056, e-mail : J .F.Eastham(ibath.ac.uk**** Dept. of Electrical Engineering, University of M iskolc, Egyetemavaros, 35 15 Miskolc, Hungary,Fax: +36-46 -361.740, Tel.: +36-46-365.111 , e-mail: elkvp(igold.uni-miskolc.hu

Abstract - This paper deals with some aspectsconcerning the implem entation of a sensorless inductionmotor control for industry applications. The proposedcontrol method uses an adaptive rotor flux observer anda suitable adaptation law for the speed estimation. Thetheoretical analysis of this method has been presented in[l-51. It has been found that this method is superior tomany other methods when the performance versuscomplexity criterion is considered [l ], [4]. Theadaptation law is obtained by a general one, valid forany induction motor parameter estimation [5].A comp arison between the flo ating and the fixed pointDS P implementation of the proposed method ispresented. In fact, the appearance of new and powerfulfixed point DSP microcontrollers makes the fixed pointsolution very attractive for many industrial applications,such as the retrofit ones, the conveyors control, and a lotof m anufacturing process control. D ifferent algorithmimplemen tation issues. such as the on-line compu tationof the observer gain m atrix and of the discrete mo tormodel are discussed in this paper. Simulation andexperimental results fo r the two cases (fixed and floatingpoint DSP implementation) are shown.IntroductionSensorless drive systems have a structure similar to thatof the classical field oriented drives, but instead ofmeasuring the rotor speed, the shaft speed is onlyestimated. The absence of the shaft sensor leads toseveiral benefits, but reduces the speed range operationand mak es the control algorithm m ore comp lex [l-51. Tohave a simultaneous estimation of the rotor flux an d thespeed, several solutions have been proposed in the lastten years. In [4], it was shown that the solution using anadaptive linear state observer (Lu enberger Observer) andan adaptation mechanism can be a very attractivesolution, in respect to the performan ce versus com plexitycriterion. This method has a thorough theoretical basis[3], lhaialso explains its superiority to other methods [2].For industrial applications, some improvements have tobe done in the algorithm implementation in such a waythat a cheaper controller system can be designed andused. It is expected that the new fixed-point DSPmicrocontroller TMS320C240 would becom e a verypopular solution for industry applications during the n extyears, since it reduces all the control hardware to onechip [6]. Although this processor has a reasonablecompu tation power, the simplicity of the controlalgorithm is a benefit for at least two reasons: it allowsmore other functions (such as com mun ication, automaticgeneration of reference) to be performed by the systemand it norm ally leads to smaller comp utation errors dueto truncation. For a lot of control algorithms, includingmost of the speed estimation ones, the accuracy alsodepends drastically on the sampling time, so that thealgorithm simplicity has a do uble effect on precision.

In this paper a very simple speed and flux estimationalgorithm is presented. The algorithm is implem ented inboth fixed and floating point representation, and the twosolutions are compared in simulations andexperimentally.The Simplified Speed and Flux Estimation AlgorithmAs the four electrical equations of an induction motorform a linear system with a variable parameter (the rotorspeed), the Extend ed Luenberger Ob server (ELO) [1,4],that is an adaptive linear observer, can be used toestimate the state vector. The motor an d the observer aredescribed by the following equations:

X = A x + B u (Obs.):y = C x(Motor):(1)The matrices A, B, and C describe the induction motorelectrical equations, where the model output y is thestator current, while L is the observer gain matrix. Thestate vector x has as elements the orthogonalcomponents, in the fixed reference frame, of the statorcurrent and roto r flux: (id?, qsrhdr nd hqr).The A matr ix

depends on the rotor speed. If the rotor speed isestimated-and used by the observer, its matrix will bedenoted A instead of A, as they are distinct due to thedifference between the estimated and the real speed.Because of this variation with speed o f the matrix A theselection of the observer gain matrix L is not astraightforward problem. A traditional approach [2], [3 ]uses a gain matrix whose elements depend on the rotorspeed so that the eigenvalues of (A - LC) areproportional with those of A, so that the observer is astable system. The speed is estimated by an adaptationmechanism obtained from the hyperstability theory [5]:

-where A -A = (orGr)A, and ey = y -In Fig.1, the scheme of the speed sensorless FOCinduction motor drive, with Extended LuenbergerObserver (ELO) speed estimation.

Fig. 1. Speed sensorless FOC ind uction motor drive, withExtended Luenberger Observer @LO) speedestimation.

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For our schem e this means:w ,. = w ,. = KJ'e;Aer %it = KS[-e,,,id, + elds&]dt

(2 )where K >O is an arbitrary constant.In a digital implementation the discrete equivalent ofEq.1 and Eq.2 has to be used. The state equation in thelinear observer will be:

( 3 )

A -

?(k + 1) = Ad?(k) +B du +Ld (y (k )- (k) )with the matrices given by:

AhA , = e , hBd =J;, AtB d t

A 2 h 22!e A h z I+&+-- +... (4 )

If the gain matrix L for the continuos time observer iscomputed according to the traditional approach, then thediscrete gain matrix L, is obtained from L by a similarrelation. Due to the com plex structure of A, it is notpossible to find simple formulae to com pute the L,elements so that the eigenvalues proportionality is kept.The algorithm simplification starts with theimplementation of Eq.4 . If only the first th e e terms inthe series are retained, an analytical expression of A, canbe obtained. It has the following form:[ C I 1 C 1 2 W r c;, +c:,C;;; c,4W , 1

where c are constants depending on the A coefficientsand on b e sampling t ime h , whi le 6,.s the estimatedrotor speed. Using this relation the discrete equivalentof A can be easily obtained by only eightmultidica tions. In a sim ilar wav it can be found that B1s practically independent on t h i speed. so it is no ne1to compute it on-line. Using these results (Ad - LdC)obtained to be:

This form suggest that L, may be chosen as :

S

with 1, desired eigenvalue. In this wa y (A, - L C) willhave as eigenvalues A ( two times) and d e twoeigenvalues given by the block in the lower right comer.It can be proved that for small sampling times the

eigenvalues of this block are always stable, so that theobserver is stable if h is correctly chosen.In this way the alg orih m f or speed and fluxes estimationis reduced to the following ope rations:0 compute the A, matrix according to the last value ofthe estimated speed ( j r , by eight multiplications,according to Eq.5:0 compute the new coefficients of the L, matrix, bytwo multiplications, according to Eq.6:0 compute the new estimate of th e sta te vector (statorcurrents and rotor fluxes) according to Eq .3;0 compute the new estimate of the rotor speedaccording to Eq.2.The evaluation of the integral in Eq.2 can be done by asimple rectangular approximation without affecting theprecision.Simulation ResultsThe algorithm implementations in floating point andfixed point have been tested by simulation on the samespeed sensorless scheme of the field oriented inductionmotor drive on which the experimental results have beenobtained Th e induction motor rated quantities andparameters are shown in the Appendix, while thestructure of the sensorless drive is presented in Fig 1 Tosimplify the analysis. the following assumptions havebeen made- ideal inverter (the voltage references are applied- parameters tuning,- absence of noise on the measured stator currents andFig 2 show s the results obtained for no-load startingconditions (0 to 1000 rpm speed reference step).followed by a torque step (at the rated value) after 0 56secondsAs i t can be seen, the estimation errors are larger in thecase of the fixed point algorithm, which makes all thecalculations for the flux and speed estimation and for thecontrol tasks using 16 bit integers Th ere is quite arelevant error for the shown estimated quantities. 1 espeed and stator currents As a consequence, theestimated speed tends to have oscillations that could leadto an undulate motor speed To avoid this situation theproportional term in the PI regulator on the speed loopha s to be kept not too high, with a negative impact onthe dynamic performance of the system To allow thecomparison of the results, the PI regulator parameters f orthe floating point implementation have been set at thesame value of those used for the fixed point oneTo increase the global precision of the estimation weneed to represent some of the variables in the algorithmon 32 bits Th e equations that are susceptible of greatererrors due to the finite length representations are the flusand the speed equation If either of these are estimatedwith the variables expressed on 32 bits, the globalprecision increases very much For example, in Fig 3 arepresented the results obtained for the same testconditions. when the speed estimation is done on 32 bitsThe estimated quantities are now very close to the realones and the system behavior is quite similar to thatusing the floating point algorithm As a directconsequence the coefficients of the speed regulator canbe increased. so that the dynamic performalice isimproved Again, for comparison purposes. the PIregulator parameters for the floating point scheme havebeen set at the same value of those used for the fixedpoint one (th e value of the proportional gain is higherthan the one used to obtain the results shown in Fig 2)

directly to the motor terminals):voltages

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1200

1000

8 0 06 0 0400

20 0

0

-200

1 5

10

50

-5-10- 1 5

-2 0

a) time (s) ~0 2 0 4 0 6 0 8 1

0 1 0 2 0 3 0 4

r - -I

0 0.1 0 2 0.3 0.4Fig.2: Sim ulation results for the sensorless induction motor drive using the floating point (a, c) and respectively thefixed point (b, d) algorithm implementation. In the fixed point implementation all variables are represented on16bits:a, b: real (solid line) and estim ated (dashed line) speed;c, d: real (solid line) and estimate d (dashed line) stator current on the stationary d axis.

0 0 1 0.2 0 3 0 4

1 0 0 0I:c800 I---- - - - + - - - - + - - - - + - - - -

II_ - -

20 ,

Fig.3: Sim ulation results for the sensorless induction motor drive using the floating point (a, c) and respectively thefixed point (b, d) algorithm implem entation, In the fixed point implementation the variables in the speedestimation equation are represented on 32 bits:a, b: real (solid line) and estim ated (dashed line) speed;c, d: real (solid line) and estim ated (dashed line) stator current on the stationary d axis.

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Experimental ResultsThe floating point and fixed point algorithms have alsobeen tested experimentally on the field orientedinduction motor drive that has been previously simulated(induction motor rated quantities and parameters shownin the Appendix). The structure of the sensorless drive isagain the one of Fig. 1. All the control and estimationtasks for either the floating point and the fixed pointimplementations of the described sensorless schemehave been performed using a floating point DSP, theTMS320C30 by Texas Instruments. This DSP allows toperform op erations either in floating point or in fixedpoint (and the data length can be chosen by the user).The sampling time for the acquisitions, for the outputsand for the calculations has been set at 200 ps. The timeneeded to perform all the input/output and calculationtasks is 180~s .A BJT inverter has been used, with the main switchesrated 1200 V. 50 A. The switching frequency is 2.5 kHz.Fig.4 shows the experimental results obtained for thesame conditions that have been tested in simulation, i.e.no-load starting conditions (0 to 1000 rpm speedreference step). followed by a torque step (at the ratedvalu e). The stationary d ax is current (Fig.4c.d) is shownin stationary conditions with no load. Again, the fixedpoint implementation has been made using 16 bit data

for the flux and speed estimation and for the controltasks. These results are quite similar to those shown inFig.2, with larger estimation errors in the case of thefixed point algorithm. It can be seen that even in thefloating point implementation there are estimation errorswhich are larger than those in Fig.2a,c (where idealconditions have been supposed). This is due to thepresence of noise on the measured quantities andprobably to detuning on the motor parameters, as it wasshown in the 'analysis on t he no i se a nd pmne te r sdetuning effects, made in [ l] .The proportional gain inthe PI regulator on the speed loop has been kept not toohigh to avoid too large speed ripple in the fixed pointalgorithm (for compar4son. the PI gains used in thefloating point implementation are set a t the same valuesused for the fixed point implem entation).In Fig.5 are presented the eqerimental results obtainedfor the same test and operating conditions. when th espeed estimation is performed on 32 bits. Again, thee,xperimental results are very similar to those shown inFig.3. except for the prese nce of non-idealities. asalready mentioned in the comment to Fig.4 Theestimated qu'mtities are very close to the real ones Theproportional g g n in the PI regulator on the speed loop ishigher than that used in the fixed point 16 bitimplementation, leading to a better dynamic behavior.

II 21)1

Fig.4: Eqerimental results for the sensorless induction motor drive using the floating point (a, c) and the fixed point(b. d) algorithm imp lementation. In the fised point iniplernentation all variables are represented on 16 bits:a. b: real (solid line) and estimated (dashed lin e) speed: time scale: 250 m s/div: vertical scale: 200 rpnddiv:c. d: real (solid line) and estiniated (dashed line) stator current on the stationary 'd' axis: time scale: 50 ms/div:vertical scale: 5 Aldiv.

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i

1 1 I 1 c) ~I 11 I JI II I II I ~ d)J

ConclusionsIn this paper the possibility of using the fixed pointprocessors in high performance sensorless inductionmotor drives has been discussed. T he subject has becom eof greater relevance due to the appearance of new fixedpoint DSP microcontrollers expected to become astandard for the industry applications during the nextyears. The speed estimation m ethod chosen fo r the fixedpoint implementation is the on e that has been previouslyfound optimal in respect with the performance versuscomplexity criterion. Further simplifications in thealgorithm have been proposed to decrease thecomputation time and to minimize the errors due to thefinite length representation. The simulation tests haveshown that it is no important difference between theperformance of the sensorless system using the fixedpoinl and respective the floating point im plementation.AppendixThe iinduction motor parameters are:Rated Output Power:Rated TorqueRated Voltage:Rated Frequency:Rated Flux:Poles:Rated Speed:Max Speed:Rated Power Factor:Rated efficiency:Inertia:

420250500.6114143030000.870.850.006

kWNmVHzv s

kg m2

Stator Resistance: 0.6592 RRotor Resistance: 0.472 RStator Leakage Inductance: 4.29 mHMain Inductance 58.2 mHRotor Leakage Inductance: 4.29 mH

References[ 11 C.Ilas, A.Bettini, L.Ferraris, GGriva, F.Profumo:Comparisonof Different Schemes without Shaft Sensorsfor Field Oriented Control Drives, Conf.Rec.IEEE-IECON94, Bologna, Italy, S eptember 1994, pp. 1579-1589, published on Sensorless Control of AC MotorDrives edited by K.Rajashekara, A.Kawamura,K.Matsuse, IEEE press, pp.30-39.[2] H.Kubota, K.Matsuse: Speed Sensorless Field-OrientedControl of Induction Motor with Rotor ResistanceAdaption, IEEE Transactions on Industry Applications,Vol. IA-30,NO.5, 1994.[31 H.Kubota, K.Matsuse, T.Nakano: New Adaptive FluxObserver of Induction Motor or Wide Speed Range MotorDrives, Conf.Rec.IEEE-IECON 90,pp. 92 1-926.[4] G.(;riva, F.Profumo , C.Ilas, R.Magureanu, P.Vranka: AUnitary Approach to Speed Sensorless Induction MotorField Oriented Drives Based on Various Model ReferenceSchemes, Conf.Rec.IEEE-IAS96, San Diego, USA,October 1996, pp. 1594-1599.[51 C.Ilas, R.Magureanu: A General Adaptation Mechanism

and its Applications to Induction Motor Direct FieldOriented Drives, Conf.Rec.IEEE-ISIE96, Warsaw,Poland, June 1996, pp. 923-928.[6] TMS320C240, TMS320F240 DSP Controllers - DataBook, Texas Instruments, 1997.

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High Performance Sensor Less Control of IM Drives for Industry Applications