A Robust RF-MRAS based Speed Estimator using Neural Network as a Reference Model for Sensor-less Vector Controlled IM Drives

Transcription

1 Control Theory and Inforatic Vol, No.3, 0.iite.org A Robut RF-MRAS baed Speed Etiator uing Neural Netork a a Reference Model for Senor-le Vector Controlled IM Drive A. Venkadean, Reearch Scholar Departent of Electrical and Electronic Engineering Pondicherry Engineering College, Pondicherry, India E-ail: a_venkyeee@pec.edu S. Hiavathi, Profeor Departent of Electrical and Electronic Engineering Pondicherry Engineering College, Pondicherry, India A. Muthuraalinga, Profeor and Head Departent of Electrical and Electronic Engineering Pondicherry Engineering College, Pondicherry, India The author acknoledge the financial upport of the Departent of Science and Technology, Delhi for the grant of Junior Reearch Fellohip (JRF)-Profeional to the firt author for puruing thi reearch ork. The reearch project titled AI technique for Electrical Drive i upported by the grant fro the All India Council for Technical Education (AICTE), a tatutory body of Governent of India. File Nuber: No 803/BOR/RID/RPS- 79/ and 800/RID/TAPTEC-3/00-0. Abtract Thi paper propoe a robut MRAS baed peed etiator for enorle vector controlled IM ive. Rotor Flux baed MRAS Model Reference Adaptive Syte (RF-MRAS) for rotor peed etiation i gaining popularity for it iplicity in enorle vector controlled IM ive. In thi chee, the voltage odel equation are ued a the reference odel. The voltage odel equation in turn depend on tator reitance hich varie ith teperature during otor operation and ore predoinant at lo frequencie/peed. Hence eparate on-line etiator i required to track the tator reitance variation. The nely developed MRAS technique ue a robut Single Neuron Cacaded Neural Netork (SNC-NN) baed rotor flux etiator trained fro input/output data a reference odel in the place of the conventional voltage odel in RF-MRAS to for a robut RF-MRAS baed peed etiator. Thi ake the reference odel robut to tator reitance variation ithout the need for eparate R etiator. The perforance of the propoed peed etiator i invetigated extenively for variou operating condition. The perforance of propoed MRAS i hon to ork for ide range of operating condition including zero peed operation. The robutne of the propoed RF-MRAS baed peed etiator i deontrated through MATLAB iulation and copared ith the conventional RF-MRAS. Keyord: Robut Rotor Flux-Model Reference Adaptive Syte, Rotor flux etiator, neural netork, SNC-NN odel, Senor-le operation, vector-controlled IM ive.. Introduction Advance in digital technology have ade the vector control realizable by indutrie for high perforance variable peed control application. Variou vector controlled technique for induction otor ive have been propoed in the literature. In particular, enor-le vector control i an eerging area. The peed enor hich i expenive, fragile, require extra attention fro failure under hotile environent and need pecial encloure and cabling i not needed for enor-le cloed loop control of Induction Motor (IM) ive. Thi lead to cheaper and ore reliable control. The perforance of enor-le vector controlled IM ive depend to a large extent on the knoledge of otor peed. Variou technique for peed etiation have been uggeted uch a Model Reference Adaptive Syte (MRAS), Luenberger and Kalan filter Oberver, Sliding Mode Oberver. MRAS chee offer ipler ipleentation and require le coputational effort copared to other ethod and therefore the ot popular

2 Control Theory and Inforatic Vol, No.3, 0.iite.org trategie ued for enor-le control (Shady et al., 009). Variou MRAS chee have been introduced in the literature baed on rotor flux, back electrootive force, and reactive poer (S.Maiti et al., 008, 00; P.Va, 998). Hoever, rotor flux MRAS, firt introduced by Schauder et al. (99) i the ot popular MRAS trategy. In thi MRAS chee, the conventional voltage odel equation are ued a the reference odel. Conventional voltage odel uffer fro the proble of pure integrator and variation of tator reitance epecially at lo frequencie/peed (B.K.Boe, 005; J.Holtz et al., 003). Several technique are propoed in the literature to overcoe the proble of pure integrator (B.K. Boe et al., 997; J.Hu et al., 998). Stator reitance varie ith teperature during otor operation and ore predoinant at lo frequencie/peed. Nuerou ethod for on-line R etiation are propoed in the literature (B. Karanayil et al., 007, 005; N. Jaala et al., 0). But the additional R etiator ould increae the coplexity of the ive yte. Neural Netork (NN) baed etiator provide an alternate olution for flux etiation. It dipene the direct ue of coplex atheatical odel of the achine and hence overcoe the proble of integrator. The nonlinear dynaic yte apping capability of neural netork a ell proven in the literature (K.S. Narena et al., 990). They can be trained to be adaptive for paraeter variation. Several Neural Netork ethod are reported for flux etiation. Prograable-cacaded lo pa filter a realized a a recurrent NN hoe eight are obtained through a polynoial-nn (L.E.B. da Silva et al., 999). Single Layer Feed-forard Neural Netork (SLFF-NN) trained uing input/output data i propoed for rotor flux etiation (Shady et al., 009). It i hon to iprove the perforance of the ive at very lo and near zero peed, provide iunity to otor paraeter variation, reove lo-pa filter/ integrator and reduce the error. The Heuritic Deign ethodology for Multilayer Feed-Forard NN baed flux etiator i propoed (A.Venkadean et al. 00). A copact NN odel ith deired accuracy aue iportance in real ipleentation of on-line flux etiator to enure fater etiation for effective control. Single Neuron Cacaded (SNC) NN odel i identified and hon to provide ditinctly copact NN odel for on-line flux etiation (A.Muthuraalinga et al., 00). In thi paper, SNC-NN baed flux etiator trained ith data including R change i propoed to eliinate the need eparate for on-line R etiator. The deigned robut SNC-NN odel i propoed to replace the conventional voltage odel in the RF-MRAS to for robut RF-MRAS baed peed etiator. The perforance of the robut RF- MRAS i invetigated extenively for variou operating condition. The perforance of propoed MRAS i hon to ork for ide operating range of operating condition including zero peed. The robutne of the propoed RF- MRAS baed peed etiator i deontrated through MATLAB iulation and copared ith the conventional RF-MRAS. The paper i organized a follo. Section II detail the enor-le IM ive, RF-MRAS and it iue. Section III decribe the SNC-NN baed flux etiator. The perforance tudy of the propoed robut RF-MRAS baed peed etiator i carried out and iulation reult are preented in ection IV. The perforance tudy of the propoed and conventional MRAS baed peed etiation chee for paraeter variation are carried out and iulation reult are preented in ection V. Section VI conclude the paper.. Speed Senor-le Vector Controlled IM Drive The peed enor-le vector control of induction otor ive preented i indirect rotor flux field oriented control. Figure ho the overall block diagra of the peed-enor-le ive yte of an induction otor. Generally through a PI controller, the peed error ignal i proceed and the torque coand i generated. It i cobined ith the flux coand correponding to the flux error to generate the coon reference to control the otor current. The reference i ued to produce the PWM pule to trigger the voltage ource inverter and control the current and frequency applied to the IM ive. The perforance of enor-le vector controlled IM ive to a large extent depend on the accuracy of peed etiation. There are any peed etiation chee available in the literature. Out of hich, Rotor Flux Model Reference Adaptive Syte (RF-MRAS) i the ot popular MRAS trategy. The general block diagra of MRAS chee for peed etiation i hon in Figure. The MRAS chee conit of a reference odel hich deterine the deired tate and adaptive (adjutable) odel hich generate the etiated value of the tate. The error beteen thee tate i fed to an adaptation echani to generate an etiated value of the rotor peed hich i ued to adjut the adaptive odel. Thi proce continue till the error beteen to output tend to zero. A. RF-MRAS

3 Control Theory and Inforatic Vol, No.3, 0.iite.org In RF-MRAS, the tate variable ued i the rotor flux. Conventional voltage odel equation for rotor flux etiation are ued a the reference odel becaue it i independent of the rotor peed. The voltage odel equation are given in (). d di v d dt L d i r R d σ L dt d = L v q i di () qr q q dt dt The current odel equation for rotor flux etiation are ued a the adaptive odel becaue it i dependent on the rotor peed. The current odel equation are given in (). Where, d ω T r L i dt r d d = + T i qr ω qr r q r T dt r v ( d vq) - Stator voltage d axi (q axi) i ( d iq) - Stator current d axi (q axi) ( d q ) - Stator flux d axi (q axi) ( qr ) - Rotor flux d axi (q axi) R( Rr ) - Stator reitance (rotor) L( Lr ) - Stator inductance (rotor) L - Magnetization inductance σ = - L -Leakage Co-Efficient Lr L Lr T r = -Rotor Tie Contant Rr () With correct peed ignal, ideally, the fluxe calculated fro the reference odel and thoe calculated fro the adaptive odel ill atch, that i, = ' and = ', here and are reference odel output and ' and ' qr qr qr are the adaptive odel output. An adaptation algorith ith PI controller, a indicated, can be ued to tune the peed ( ω ) o that the error ξ = 0. r, et In deigning the adaptation algorith for the MRAS, it i iportant to take account of the overall tability of the yte and enure that the etiated peed ill converge to the deired value ith atifactory dynaic characteritic. Uing popov criteria for a globally ayptotically table yte, the folloing relation for peed etiation can be derived. In teady tate, ξ = 0 balancing the fluxe; in other ord, ω = ξ Ki r, et K p+ S (3) ξ = ' ' qr qr (4) = ' and qr = ' qr qr (5) Fro the equation (), it i inferred that the voltage odel ued a the reference odel in RF-MRAS are dependent on reitance R and inductance L, L, L r. The variation of thee paraeter tend to reduce the accuracy of the flux etiation. Particularly, teperature variation of R becoe ore doinant epecially at lo frequencie/peed. At higher frequencie, the influence of R variation on the etiator i negligible. A all iatch in R beteen the otor and the etiator ould caue the flux etiated fro the voltage odel baed 3

4 Control Theory and Inforatic Vol, No.3, 0.iite.org etiator to get ift fro the actual. Thi lead to large error in the peed etiation hich ould affect the overall enorle operation of IM ive. A eparate additional on-line R etiator ay overcoe thi proble but it ould increae the coplexity of the ive yte. Hence to overcoe thee proble, a Single Neuron Cacaded Neural Netork (SNC-NN) baed flux etiator trained ith data including R change i propoed to eliinate the need for eparate on-line R etiator. The propoed Single Neuron Cacaded Neural Netork baed flux etiator i ued to replace the conventional voltage odel baed flux etiator in RF-MRAS to for robut RF-MRAS. 3. Robut SNC-NN baed Flux Etiator ued a a Reference Model in RF-MRAS The data baed flux etiator i deigned uing SNC-NN odel. The Single Neuron Cacaded (SNC) architecture (A.Muthuraalinga et al., 00) ith ultiple input/ingle output i hon in Figure 3. SNC-NN architecture conit of an input layer, hidden layer and an output layer. The firt hidden layer receive only external ignal a input. Other layer (M) receive external input and output fro all previou (M-) ayer. To create ultilayer tructure hidden layer are added one by one and the hole netork trained repeatedly uing the concept of oving eight o a to obtain copact netork (A.Muthuraalinga et al., 00). Thi proce continue, till the perforance index i reached. Cacading ingle neuron in every hidden layer in the Single Neuron Cacaded (SNC) architecture greatly iplifie the deign proce and can be elf-organized hich aid deign autoation iilar to SLFF-NN. Thu SNC-NN cobine the advantage of elf organizing feature of SLFF-NN and poer ultilayer apping capability of MLFF-NN. Alo SNC-NN odel i identified and hon to provide ditinctly copact NN odel for on-line flux etiation (A.Muthuraalinga et al., 00). Hence in thi paper, SNC-NN odel i choen to odel the on-line Flux Etiator. The indirect field oriented controlled (IFOC) IM ive yte ith inuoidal pule idth odulation i built uing MATLAB ith itching frequency of 0 KHz. The preent and pat aple of the d-q coponent of the tator voltage { v d ( k), v d ( k ), vq ( k), vq( k ) } and tator current { i d ( k), i d ( k ), iq ( k), ( k ) }are ued a the input to the SNC-NN Model. The output are the direct and quaature axi rotor fluxe { ( k), qr( k) }. The block diagra of SNC-NN baed flux etiator i hon in Figure 4. The vector controlled IM ive i the variable frequency ive. Hence, equal nuber of data et for all operating condition i ued to train the netork. Around,66 data et are obtained fro the IFOC Syte for variou operating condition. In the literature, it i reported that the change in R ay go upto 50% (B. Karanayil et al., 007, 005). Hence, to ake SNC-NN robut to paraeter variation, axiu of 50% change in R variation i incorporated in the training data et. The activation function for hidden layer and output layer i choen a tan-igoid and pure linear function repectively. The SNC-NN i trained ith input/output data uing LM algorith for the required Mean Square Error (MSE) of The obtained SNC-NN odel for flux etiation ha the tructure 8-3(h)- (h-hidden layer ith one neuron). The obtained SNC-NN odel for flux etiation replace the conventional voltage odel in the RF-MRAS to for robut RF-MRAS. 4. Perforance of Propoed Robut RF-MRAS baed Speed Etiator The perforance of propoed robut RF-MRAS chee i teted for peed etiation for variou operating condition extenively through MATLAB iulation. Saple reult for the ajor tet condition are preented in the folloing ection. ) Tet - Stair Cae Speed Tranient fro 48 to 0 to 48 rad/ec at No Load: In thi tet, the IM ive i ubjected to a tair cae peed coand fro 48 rad/ec to zero peed in a erie of five 40 rad/ec tep continuing to 48 rad/ec, at no load. The perforance of robut RF-MRAS i hon in Figure 5. The rotor fluxe etiated fro the propoed flux etiator track the actual ith negligible error for all the peed coand including the zero peed. The peed etiated fro the propoed MRAS chee i alo found to cloely track ith the actual. The reult depict Stable operation of the propoed MRAS chee, particularly around zero peed. ) Tet - Load Torque Change fro 0% to 00% at 48rad/ec: The tet exaine the load torque diturbance capability of the propoed MRAS baed peed etiation chee. The ive i operated ith reference peed of 48rad/ec. 00% tep change in load torque i applied at.5ec. The propoed robut MRAS ho better teady tate and dynaic perforance ith negligible error beteen the actual iq 4

5 Control Theory and Inforatic Vol, No.3, 0.iite.org and etiated peed, a hon in Figure 6. The etiated rotor peed underhoot iilar to actual peed and ettle fater ith the actual a oon a the tep change in load torque i applied. 3) Tet 3- Load Torque Change fro 00% to 50% at 48rad/ec: The tet 3 alo exaine the load torque change capability of the robut RF-MRAS. The ive i initially operated ith the peed coand of 48rad/ec ith 00% load condition and uddenly the load torque i reduced to 50% at.5ec. In thi cae alo, the peed etiated fro the propoed robut RF-MRAS i found to cloely atch ith the actual ith negligible error. The etiated peed overhoot iilar to the actual peed and ettle fater ith the actual a oon a the load torque i uddenly reduced to 50%, a preented in Figure 7. 4) Tet 4- ±48 rad/ec Speed at No Load: The tet 4 exaine the peed reveral capability of propoed peed etiation chee. Initially, the ive i operated ith the peed coand of 48rad/ec. The lo peed reveral i taking place during.5- ec. The coand peed i fixed to -48rad/ec after ec. The perforance of propoed peed etiation chee i hon in Figure 8. The propoed peed etiation chee ho better perforance. The peed etiated i found to cloely atch ith the actual ith negligible error. The propoed MRAS chee ork for ide range of operating condition fro 48 (rad/ec) to -48 (rad/ec) including zero peed operation. The error beteen the actual and the etiated peed fro the propoed RF-MRAS for variou operating condition are conolidated and preented in Table I. The error in the peed etiated fro the propoed MRAS chee i found to be ithin ±0.4% for noral operating peed. At very lo operating peed, the error i found to be ithin ±.4%. 4. Perforance Coparion of Propoed robut RF-MRAS and Conventional RF-MRAS baed peed Etiator for Stator Reitance Variation The perforance of propoed robut RF-MRAS and conventional RF-MRAS i teted for tep change in tator reitance variation. Of coure, in a real ive, the tator reitance never undergoe abrupt variation in repone to teperature change due to the large theral tie contant. The tep variation repreent an extree cae and i ued to ho the robutne of the propoed MRAS. The effect of R variation i invetigated at very lo peed of rad/ec ith 50% load condition. To different cae for tator reitance detuning are conidered. (a) Slight R detuning: The actual R of the induction otor are lightly detuned ith repect to the noinal one, a follo: R = 5% (6) R In thi cae, 5% tep change in R i effected at ec. The locu diagra of rotor fluxe for the robut SNC-NN odel and voltage odel are preented in Figure 9(a) and repectively. It i undertood that the locu diagra of rotor fluxe of robut SNC-NN odel cloely track the locu of the actual flux and it i centered on the origin iilar to the actual flux. The radiu of the locu of the propoed flux etiator i alo found to be iilar to the actual flux. In the cae of voltage odel baed flux etiator, the locu of rotor fluxe i not centered on the origin and it i hifted aay fro the origin approxiately b. The radiu of the locu of the voltage odel baed flux etiator i alo oberved to get increaed approxiately by 4.777%. Hence, the propoed robut SNC-NN baed flux etiator i found to etiate the flux coponent ith good accuracy even hen there i change in the R ith d and q-axi rotor flux MSE of and repectively. The peed etiated fro the robut RF-MRAS and conventional RF-MRAS i preented in Figure 0(a) and repectively. Fro the reult obtained, it i obviou that the peed etiated fro the robut RF-MRAS track cloely the actual peed even hen there i a change in the R and the error in the peed etiation i alot negligible. But, the peed etiated fro the RF-MRAS fluctuate beteen (rad/ec) to.0873 (rad/ec). 5

6 Control Theory and Inforatic Vol, No.3, 0.iite.org 4. Large R detuning: In any real application, the R ay vary on range hich are larger than thoe conidered in previou ection. In order to check the robutne of the propoed peed etiator in the preence of larger detuning, the actual R of the induction otor are largely detuned ith repect to the noinal one, a follo: R = 50% (7) R 50% tep change in R i effected at ec. The locu diagra of rotor fluxe for the propoed robut SNC-NN odel and voltage odel are preented in Figure (a) and repectively. Fro the reult obtained, it i oberved that even in the cae of large paraeter detuning, the locu of the robut SNC-NN odel track the actual flux locu very ell. But the centre of the locu of flux etiated fro the voltage odel i hifted largely aay fro the origin approxiately 0.374b hich i % tie larger than the previou one. The radiu i alo oberved to get increaed approxiately by 56.87% hich i uch larger than the previou one. The robut peed etiation i oberved fro the propoed peed etiator even in the cae of large paraeter detuning hich i preented in Figure. The peed etiated uing RF-MRAS ocillate beteen (rad/ec) to (rad/ec) hich i evident fro Figure (a). Thu the centre and radiu of the locu of flux etiated fro the voltage odel keep on increae ith increae in R. Thi lead to increae of ocillation in the etiated peed uing voltage odel. The conventional RF-MRAS can alo be ade robut to R variation ith an additional on-line R etiator hich ould increae the coplexity of the ive yte. Thu the NN baed etiator, trained ith paraeter variation reult in the robut NN baed flux etiator. The robut NN baed etiator ued a the reference odel in RF-MRAS hich reult in the robut RF-MARS. Thi in turn reult in robut peed etiation even in the preence of R variation. 5. Concluion Thi paper propoe a robut RF-MRAS for peed etiation over ide operating range in enorle IM ive. The robut data baed flux etiator i deigned uing SNC-NN odel ith data including R variation to avoid the requireent of eparate need for on-line R etiator. The deigned robut NN baed flux etiator i propoed to replace the conventional voltage odel in RF-MRAS to fro a robut RF-MRAS. The perforance of propoed MRAS i extenively invetigated for variou operating condition. The propoed MRAS i hon to ork for ide range of operating condition including zero peed. The error in the peed etiated fro the propoed MRAS chee i found to be ithin ±0.4% for noral operating peed. At very lo operating peed, the error i found to be ithin ±.4%.The robutne of propoed MRAS chee i illutrated for paraeter variation and found to outperfor the conventional RF-MRAS chee. The advantage of the Propoed MRAS chee are: independent of tator reitance, the reference odel in propoed robut RF-MRAS i free fro the integrator related proble, and the reference odel in the propoed MRAS i coputationally le rigorou a copared to the integral equation a involved in the reference odel of conventional RF-MRAS. Thu the propoed robut RF-MRAS baed peed etiation chee i hon to perfor ell under all operating condition including R variation. Hence it i concluded that a robut RF-MRAS baed peed etiator i a proiing technique for peed etiation in enor-le vector controlled IM ive. APPENDIX The paraeter of the induction achine ued for iulation are given in the table hon belo. INDUCTION MOTOR PARAMETERS Paraeter Value Paraeter Value Rated Poer Rated voltage Rated current Type Frequency Nuber of pole Rated Speed.kW 45V.77A 3 Ph 50Hz 4 45RPM Stator Reitance (R ) Rotor Reitance (R r) Magnetizing Inductance (L ) Stator Inductance (L ) Rotor Inductance (L r) Total Inertia (J T) Friction Coefficient (B) 6.03Ω 6.085Ω H 0.59H 0.59H Kg 0.007Kg / 6

7 Control Theory and Inforatic Vol, No.3, 0.iite.org Reference Shady M.Gadoue, Daian Giaouri, John W.Finch (009) Senorle Control of Induction Motor Drive at very Lo and Zero Speed Uing Neural Netork Flux Oberver. IEEE Tranaction on Indutrial Electronic 56(8): doi: 0.09/TIE S.Maiti, C. Chakraborty, Y.Hori and M.C. Ta (008) Model reference adaptive controller-baed rotor reitance and peed etiation technique for vector controlled induction otor ive utilizing reactive poer. IEEE Tranaction on Indutrial Electronic 55(): doi: 0.09/TIE S.Maiti and C. Chakraborty (00) A ne intantaneou reactive poer baed MRAS for enorle induction otor ive. Siulation Modelling Practice and Theory 8: doi: 0.06/j.ipat P. Va (998), Senorle Vector and Direct Torque Control, NeYork:Oxford Univ. Pre Colin Schauder (99) Adaptive Speed Identification for Vector Control of Induction Motor ithout Rotational Tranducer. IEEE Tranaction on Indutry Application 8(5) Bial K. Boe (005) Modern Poer Electronic and AC Drive. Prentice-Hall. India J.Holtz, J.Quan (003) Drift- and Paraeter-Copenated Flux Etiator for Peritent Zero-Stator- Frequency Operation of Senorle-Controlled Induction Motor. IEEE Tranaction on Indutry Application 39(4): doi: 0.09/TIA B.K.Boe, N.R.Patel (997) A Prograable Cacaded Lo-Pa Filter-Baed Flux Synthei for a Stator Flux-Oriented Vector-Controlled Induction Motor Drive. IEEE Tranaction on Indutrial Electronic 44(): J.Hu, B.Wu (998) Ne Integration Algorith for Etiating Motor Flux over a Wide Speed Range. IEEE Tranaction on Poer Electronic 3(5): B. Karanayil, M.F.Rahan and C.Grantha (007) Online Stator and Rotor Reitance Etiation Schee Uing Artificial Neural Netork for Vector Controlled Speed Senorle Induction Motor Drive. IEEE Tranaction on Indutrial Electronic 54(): doi: 0.09/TIE B. Karanayil, M.F.Rahan and C.Grantha (005) Stator and Rotor Reitance Oberver for Induction Motor Drive Uing Fuzzy Logic and Artificial Neural Netork. IEEE Tranaction on Energy Converion 0(4): doi: 0.09/TEC N. Jaala, A.M.A.Haidar, N.L.Rali, N.L.Iail and A.S.M.Sulaian (0) A Neuro-fuzzy Approach for Stator Reitance Etiation of Induction Motor. International Conference on Electrical, Control and Coputer Engineering K.S.Narena, K.Parthaarathy (990) Identification and Control of Dynaical Syte Uing Neural Netork. IEEE Tranaction on Neural Netork ():4-7 Luiz.E.B.daSilva,B.K.Boe,Joao.o.p.Pinto (999) Recurrent-Neural-Netork-Baed Ipleentation of a Prograable Cacaded Lo-Pa Filter Ued in Stator Flux Synthei of Vector-Controlled Induction Motor Drive. IEEE Tranaction on Indutrial Electronic 46(3): A.Venkadean, S.Hiavathi, and A.Muthuraalinga (00) Deign of Feed-Forard Neural Netork Baed On-line Flux Etiator for Senor-le Vector Controlled Induction Motor Drive. International Journal of Recent Trend in Engineering and Technology 4(3):0-4 A.Muthuraalinga, A.Venkadean and S.Hiavathi (00) On-Line Flux Etiator uing Single Neuron Cacaded Neural Netork Model for Senor-le Vector Controlled Induction Motor Drive. (ICSDC-00), Manipal Inititute of Technology, Manipal, India:

8 Control Theory and Inforatic Vol, No.3, 0.iite.org Input Supply Solid State IM Drive Syte v a C PWM Inverter v c i a i c IM ω r ψ ref ω r,ref ψ ψ qr Rotor Flux Oriented Controller PWM-a PWM-b PWM-c ω r,et ω r,et Speed Etiator Figure. Senor-le Vector Controlled IM Drive hoing the requireent of Speed Etiator vdq idq Reference Model qr ' ξ Adaptive Model ' qr ω r, et Adaptive Mechani (PI-Controller) Figure. RF-MRAS baed Speed Etiator 8

9 Control Theory and Inforatic Vol, No.3, 0.iite.org p p p R,,R b n Layer f a,, Layer,,,,R,, R b n f a,, b Layer n f a Figure 3. SNC-NN ith ultiple input/ingle output here, p - Input vector, p = [,,... R], k Link eight of neuron i of layer for input i, - j fro neuron j of layer k. Input eight of neuron i of layer for i, R - external input R. b i - bia for neuron i of layer. f - Activation function of all neuron in a layer. a i - Output of neuron i of layer v d ( k) v d ( k ) vq( k) vq( k ) i d ( k) i d ( k ) iq( k) iq( k ) SNC-NN Baed Flux Etiator ( k) qr( k) Figure 4. The Input and Output of SNC-NN baed Flux Etiator 9

10 Control Theory and Inforatic Vol, No.3, 0.iite.org (a) Figure 5. Perforance Curve for Tet Condition- : (a) Rotor Fluxe Rotor Speed (a) Figure 6. Perforance Curve for Tet Condition- : (a) Rotor Fluxe Rotor Speed (a) Figure 7. Perforance Curve for Tet Condition-3 : (a) Rotor Fluxe Rotor Speed (a) Figure 8. Perforance Curve for Tet Condition-4 : (a) Rotor Fluxe Rotor Speed 0

11 Control Theory and Inforatic Vol, No.3, 0.iite.org Figure 9. Locu of Rotor Fluxe ith Slight R Detuning: (a) Voltage Model Robut SNC-NN Model Figure 0. Rotor Speed ith Slight R Detuning: (a) RF-MRAS Robut RF-MRAS Figure. Locu of Rotor Fluxe ith Large R Detuning: (a) Voltage Model Robut SNC-NN Model (c) Figure. Rotor Speed ith Large R Detuning: (a) RF-MRAS Robut RF-MRAS

12 Control Theory and Inforatic Vol, No.3, 0.iite.org TABLE I PERFORMANCE OF THE PROPOSED RF-MRAS BASED SPEED ESTIMATOR FOR VARIOUS SPEED COMMANDS Coand Speed (rad/ec) Actual Speed (rad/ec) Etiated Speed uing Robut RF-MRAS (rad/ec) %Error

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