Observer-based speed estimation method for sensorless vector control of induction motors

Transcription

1 Observer-base spee estimation metho for sensorless vector control of inuction motors C.-M. Lee C.-L.Chen nexing terms: nuction motors, Spee estimation, Vector control Abstract: The metho is base on an aaptive flux observer in the rotor-spee reference frame, in which a secon-orer Kalman filter is employe to moify the estimate rotor flux to improve the performance of spee estimation. The Kalman filter moifies the estimate rotor flux base on the measure stator currents. The estimate spee is use in the spee feeback for vector control an in the co-orinate transformation for current controller. The propose metho has the avantage of saving much computation time in comparison with the reuce-orer extene Kalman filter. Compare with the conventional aaptive observer, the propose metho has the avantage of better accuracy to follow the spee comman uner heavy loas. Experimental results show the effectiveness of the propose metho. 1 ntrouction Vector-controlle inuction motor rives have been wiely use in high-performance applications. Conventional vector control methos [ 1-61 require motor spee as a feeback signal. To obtain the spee information, transucers such as shaft-mounte tachogenerators, resolvers, or igital shaft position encoers are use, which egrae the system's reliability, especially in hostile environments. Sensorless vector control is propose to cope with the spee-sensing problem. Various approaches of sensorless vector control have been presente in the literature. H. Kubota et ul. [7] propose an aaptive flux observer to estimate the rotor flux an spee. The computation process of estimating the rotor spee is simple, an the estimate rotor flux is use to calculate the vector rotation angle. However, experimental results show that large spee errors appear uner heavy loas. Kalman filtering is known for obtaining high-accuracy estimates of state variables uner noisy environments. Y.R. Kim et al. [8] use a fifth-orer extene EE, 1998 EE Pvoceeings onlinc no Paper first receive 1st September 1997 an in rcvise form 27th January 1998 The authors are with the Power Electronics Laboratory, Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan Kalman filter to ientify the spee of an inuction motor. The performance of the spee estimation is excellent but ithe computation process consumes a lot of time. Y.S. Kim et al. [O] employe a reuce thirorer extene Kalman filter to estimate the rotor spee. Accoring to [O, 111, the number of multiplications in the K-alman filter is proportional to the thir power of the state size. Therefore the reuce-orer extene Kalrnan filter saves much computation time in comparison with the fifth-orer extene Kalman filter, but is cjtill time-coiisuming compare with the aaptive flux observer. We propose a new spee estimation metho which is base on an aaptive flux observer in the rotor spee reference frame. A secon-orer Kalman filter is then employe to moify the estimate rotor flux. The moifie estimate rotor flux is substitute into the flux observer to improve 1 he performance of the rotor spee estimation. The estimate spee takes place of the feeback signal for conventional vector control, an thus a sensorless vector control system is establishe. 'The propose metho saves much computation time compare with the reuce-orer extene Kaliman filter an has better performance uner heavy loas than the conventional aaptive observer. 2 Principles of propose approach This Section is ivie into five subsections: part A introuces the basic inuction motor moel, part B escribes the flux observer evelope by Kubota et al. [7], part C examines the etails of implementing the secon-orer Kalman filter to estimate the rotor flux. The estimate rotor flux is to be substitute into the rotor-spee estimation equation evelope in part B to improve the performance of spee estimation. Part D escribes the process of the propose metho by a flow chart. 2. Motor moel The state equations of an inuction motor in the rotorspee reference frame can be expresse as follows: Y = [ is ZJ be Proc -Contuol Theory Appl, Vol 145, No 3, Muy

2 following spee estimation equation: i,\ 1 1 = [i,s iq,jt stator current 4r = [4, 4qrT rotor flux v, = [v~,~ vqslt stator voltage R,s, R, stator an rotor resistance L,s, L, stator an rotor self inuctance L, mutual inuctance CT leakage coefficient, CT = 1 - L,*/(L,L,.) z, rotor time constant, z, = L,/R,.,. motor angular velocity (8) where K,] is a proportional constant. f the observer gain matrix G is chosen so that the first term of eqn. 6 is negative-semiefinite, the aaptive flux observer will be stable accoring to the Lyapunov's irect metho. For ease of implementation, we choose G =. Then the first term of eqn. 6 will be negative-semiefinite since an inuction motor itself is stable. 2.2 Aaptive flux observer The state observer in the rotor-spee reference frame is written as follows [7]: (3) where signifies the estimate quantities an G is the observer gain matrix which is to be etermine so that eqn. 3 can be stable. Note that all the state variables are in the rotor-spee reference frame. The estimation error of the states can be written as where e=x-x AA=A-A --e = (A + GC)e - AAX t (4) awr -Aw, -Awr/k : =[ k = (al,l,)/l,, aw, = 2, - w, Define the following Lyapunov function caniate [7]: V = e T e + (L+ - L+)~/x (5) where h is a positive constant. The time erivative of V is -V = et{(a + GC)T + (A + GC)}e t -wrat L,,, at - 7, L"'& Define the iscrete state-moel an output moel as follows: state moel (lower two rows of eqn. 9): + 2AW,-&/X t (6) where ei, = it(, - ir, e,,,, = i, - iq5. By equating the secon an the thir term of eqn. 6, we obtain the output moel (upper two rows of eqn. 9): (1) 36 EE PvocControl Theory Appl.. Vol. 145, No. 3, May 998

3 Consier this iscrete-state moel an output moel with noises where z(k + 1) = F(k)Z(k) + u(k) + w(k) (12) z(k) = H(k)Z(k) + u(k) (13) 1 vqq (k+l1-[1- (%+* ) at z Y s ( ~ )+wt~sihj-~vqsitj] w(k) v(k) E[wJ = E[v,] = E[WWT] = E[wjwjT = = ranom noise matrix of state moel = ranom noise matrix of output moel i z,j = qsii i = j E[vv7] = R E[vivjT] = i #,j = rsii i =,j E[w,v,7] = E[x(O)] = n() E[(x(O) - x(o))(x(o) - 2())T] = P() P() = estimation error covariance matrix at time t =o 6ii = kroneclcer elta Note that in the efinition of the output moel eqn. 13, the stator currents are actually measure values 191, so is(k + 1) an ijk + 1) represent the measure stator current at the present state, an is(k) an &(k) represent the measure stator current at the previous state. Thus, we can apply the Kalman filtering technique to estimate the rotor flux by the following steps [8]: (i) Preiction of stute:?(k + lk) = F(k)?(k/k) + ~ ( k ) (14) (ii) Estimation qf error covariunce matrix: P(k + lk) = F(k)P(kk)FT(k) + Q(k) (15) (iii) Computution oj Kalwlan jilter gain: K(k + 1) = P(k + lk)ht(k + 1) (iv) Upate of x [H(k + l)p(k + lk)ht(k + 1) + R(k + l)] - the error covariunce mutrix: (16) P(k + 1Jk + 1) = [ - K (k + 1)H(k + l)] P(k + lk) (v) Stute estimation: q k + lk + 1) = q k + 1Jk) + K(k + l)[z(k + 1) (17) -H(k + l)2(k.+ ilk)] (18) EE Proc -Control Theory Appl, Vol. 145, No. 3, Muy 1998 The moifie estimate rol or flux obtaine utilising the secon-orer Kalman filter is then substitute into the spee estimation equation (eqn. 8) to obtain better estimation of the rotor spee. Since there is no change in eqn. 8 except the improve flux estimation, the stability conition state in the previous Section woul not eteriorate. r t state eq.9 to obtain e.9. is iqs br &,r Fig. 1 measure stator currents to obtain icls iqs secon-orer Kalman filter (14)-(18) to obtain moifie $r est. rotor spee estimate : a Flowhuvt of pvopose spee estimation?wth# 2.4 Flowchart of propose metho The overall process of the propose metho can be represente in the flow chart as shown in Fig. 1. First, state equation eqn. 9 is use to obtain the estimate stator currents an rotor flux. Seconly, stator currents are measure. Then the secon-orer Kalman filter eqns is utilise to moify the estimate rotor flux base on the measure stator currents. Finally, eqn. 8 is use to obtain the estimate rotor spee. The estimate rotor spee is upate an the whole process repeats again. 3 Comparison of computation time To compare the computation time of various methos we give a table which shows the require simulation time of each metho for a sensorless vector control system to run for 1 secons an simulation time is lops. There are in total one milllion iterations. The simulation is performe on a Penlium 15OMHz PC. Note that the computation time shown in Table 1 inclues the calculation of the inuction motor moel. From Table 1, it is shown that the propose metho can greatly reuce the computation time compare with reuce-orer extene Kalman filter an full-orer extene Kalman filter. As shown in the experimental results, the propose metho performs much better than the conventional aaptive observer, especially uner heavy loa conitions. Table 1: Comparison of commputation time for various methos Conventional aaptive observer 21.66s Propose metho s Reuce-orer extene Kalman filter 284.7s Full-orer extene Kalman filter s 361

4 Table 2: Parameters of inuction motor R, 2.7Q R, 2.22Q L,.352H L,.352H L,.342H J,.825 kn-m2 4 Experimental implementation 4. Experimental setup The block iagram of the spee-sensorless space vector control system with the propose spee estimation scheme is shown in Fig. 2. The software part is implemente in a Pentium 12MHz PC. The machine uner stuy is a 3-HP, 4-pole squirrel-cage inuction motor, whose parameters are shown in Table 2. The spee estimation scheme replaces the spee signal feeback path of the conventional vector control. The stator currents are measure with Hall-effect sensors an sample through an AD car whose sampling rate is 1kHz. The terminal voltages are calculate by the following equations: loa conitions using the new spee estimation metho. For comparison, Fig. 6 shows the experimental results of the same conitions using the conventional aaptive observer. From Figs. 5 an 6, the new spee estimation metho performs better than the conventional aaptive observer, especially uner heavy loas [1._ f time,s Fig. 4 Experimental results of forwar-reverse operation uner full-loa conition using new spee estimation metho estimate mr spee estimation scheme software harware Fig. 2 Spee-sensorless space vector contvol system with new spee estimation scheme where SA, S, an S, represent the switching states, which can be 1 or, an Vc represents the DC bus voltage of the inverter, which is assume constant. One cycle of the control program takes about 4 9 for ~ the aaptive observer an 84 for the propose metho, i.e. the inverters are switche at about 2 an 12kH2, respectively p,u, Fig. 5 Experimental results of steay-state rotor spee uner various lou conitions using new spee estimation metho (._. E L 2 3 B 3 e Fig. 6 Experimental results of steay-state rotor spee uner various loa conitions using conventional aaptive observer P.U 5 Conclusions time,?, Fig. 3 Experimental results oj forwar-reverse operation uner no -lou conition using new spee estimation metho 4.2 Experimental results Figs. 3 an 4 show experimental results of forwarreverse operation uner no-loa an full-loa conitions, respectively. Fig. 5 shows the experimental results of the steay-state rotor spee uner various 362 We have presente a new spee estimation metho of an inuction motor base on an aaptive observer in the rotor-spee reference frame in which a seconorer Kalman filter was employe to moify the estimate rotor flux. The new spee estimation metho was implemente in a spee-sensorless space vector control system. Experimental results showe that the spee-control performance is goo enough that the propose metho coul be use in most nonservo applications. Experimental comparison uner various EE Proi -Control Theory Appl, Vu1 145, No 3, Muy 1998

5 loa conitions between the conventional aaptive observer an the new spee estimation metho was also mae. The new spee estimation metho performe better than the conventional aaptive observer, especially uner heavy loas. 6 References 1 GABREL, R., LEONHARD, W., an NORDBY, C.J.: Fieloriente control of a stanar AC motor using microprocessors, EEE Truns., 198, A-16, (2), pp KUME, T., an WAKANE, T.: High-performance vector-controlle AC motor rives: applications an new technologies, 3 EEE Tran.Y., 1987, A-23, (5), pp OGASAWARA, S., AKAG, H., an NABAE, A.: The generalize theory of inirect vector control for AC machines, ZEEE Trans., 1988, A-24, (3), pp NLSEN, R., an KAZMERKOWSK, M.P.: Reuce-orer observer with parameter aaption for fast rotor flus estimation in inuction machines, TEE Proc. D, 1989, CTA-136, (l), pp WJESUNDERA, D.S., an JACKSON, R.D.: Observers for fiel-oriente control of inuction motor rives, ZEE Proc. B, 1992, EPA-139, (4), pp KAO, Y.T., an LU, C.H.: A.nalysis an esign of microprocessor-base vector-controlle inuction motor rives, EEE Trans., 1992, E-39, (l), pp KUBOTA, H., MATSUSE, K., an NAKANO, T.: DSP-base spee aaptive flus observer of inuction motor, EEE Trans., 1993; A-29, (2)1, pp KM, Y.R., SUL, S.K., an PARK, M.H.: Spee sensorless vector control of inuction motor using extene Kalman filter, EEE Trans., 1994, A-3, (5), pp KM, Y.S., KM, S.U., an YANG,.W.: mplementation of a spee sensorless vector control of inuction motor by reuceorer extene Kalman filter. Proceeings of EEE-AS annual meeting, 1995, pp TAN, J., an KYRAKOPOJLOS, N.: mplementation of a tracking Kalman filter on a igital signal processor, EEE Trans., 1988, E-35, (l), pp GELB, A.: Applie optimal estimation (Cambrige, MA, MT Press, 1974) EE Proc.-Control Theory Appl, Vol. 145, No 3, Muy