. - INSANANEOUS SPEED OBSERVER Since extremely low-reolution rotary encoder are intalled in railway vehicle, the interval between two conecutive pule

Transcription

1 HIGH PERFORMANCE PARAE ORQUE CONRO OF INDUCION MOORS IN OW SPEED RANGE FOR PURE EECRIC BRAKING SYSEMS IN RAIWAY RACION ilit Kovudhikulrungri, Daiuke ateihi, akafumi Koeki he Univerity of okyo 7-3- Hongo, Bunkyo-ku, okyo , Japan el , Fax Abtract he aim of thi paper i to realize a high performance parallel torque control of traction motor in low peed range for pure electric brake in railway application. o do thi, the author introduced intantaneou peed oberver to a ingle-invertermultiple-motor ytem to etimate the peed in low peed range. Variou imulation and experiment poitively how the accurate peed and load torque etimation, which i neceary for realization of pure electric braking ytem... - INRODUCION he combination of air- and electric brake play a major role in braking ytem of electric railway vehicle. hi combination, however, often caue evere riding comfort and inaccuracy of topping poition becaue of the low and fluctuated repone of the brake mechanical part. Moreover, the phyical characteritic of the mechanical part, i.e., brake hoe, alway vary with peed, temperature and urface condition. o eliminate thee problem, it i neceary to operate the electric brake a the main braking cheme. hi lead to the propoal of pure electric braking ytem []. However, peed detection at low peed cannot be implemented effectively becaue coare encoder are intalled in Japanee railway vehicle. For intance, encoder ued in ordinary Japanee railway vehicle have an extremely low reolution of 6 pule per revolution (ppr). When the peed drop below 5 km/h, the peed information i not available. A a reult, the cloed-loop control i witched to the open loop control by the driver. An eddy current brake or the friction brake i operated intead of the regenerative brake. Fig. ummarize thi problem. Fig.. Summary of the problem page /6

2 . - INSANANEOUS SPEED OBSERVER Since extremely low-reolution rotary encoder are intalled in railway vehicle, the interval between two conecutive pule become longer and longer at low peed a hown in Fig.. It i obviouly een that the interval between the pule,, i longer than the DSP clock ampling time,. We define a the ampling frame. If we ue the normal peed calculation from the encoder, we will loe the accuracy and thi lead to intability at low peed. o olve thi problem, it i neceary to etimate accurate peed information at every ampling intant. For thi purpoe an intantaneou peed oberver i introduced to the ytem. he block diagram of the intantaneou peed oberver i hown in Fig. 3. he oberver i derived from a peed oberver in dicrete-time domain with diturbance dynamic conideration. [ k ] = ( A C) xˆ[ k] + Bu[ k] Cy[ k] x ˆ + + () where ˆ = [ ˆ ω ˆ θ ] x ˆ, u = em, y = θ, i the oberver gain matrix [ l ] l l 3, ω i the motor peed in rad/, θ i the haft angle in radian, i the diturbance torque, em i the produced torque, J i the motor moment of inertia and i the ampling time. Matrice A, B and C are derived from their continuou time domain matrice A c, B c and C c, repectively, by the following relation Fig.. Comparion between a rotary encoder and an intantaneou peed oberver em B J Fig.3. Block diagram of an intantaneou peed oberver k = u xˆ y [m-] [ z A ω Fig.4. Expanded dicrete-time ignal C θ [m+] A = exp( A ) I + () c A c B = exp( A c ( τ )) Bcdτ = ( I + exp( A c )) Bc (3) where / J A c =, C = C c (4) B, = [ ] c / J = C c. Subtituting the continuou time matrice into (), (3) and (4), finally the following dicrete-time matrice are obtained a follow / J A =, / J = / J B, = [ ] C, he problem i which ampling time, or, hould be ued. Since the output can be detected only when there i an encoder pule, pole placement and tability of the ytem depend on the interval between the pule,. If i ued a the ampling time, it i neceary to extend the matrix A, B and C due to the number of ampling intant in that interval and thi i difficult to implement []. On the other hand, we can ue a the ampling time of the ytem by uing the etimated haft angle when the detected pule are not available a page /6

3 illutrated in Fig.4. Note that thick arrow repreent actual value while thin arrow repreent etimated value. hi lead to the aumption that y, k =, K; K = / y =, (5) yˆ otherwie where k i the ampling index in each ampling frame. Hence, the oberver equation can be expreed a follow k =, K ; x ˆ = Axˆ + Bu + ( y yˆ ) (6) k + k k k, K ; x ˆ k = Axk + Buk (7) + ˆ hee imply that the oberver correct the error when pule are detected and act a a imulator when pule are unavailable. Due to thi fact, the lat ampling intant in each ampling frame decide the dynamic of the next ampling frame. Dynamic of each frame can be expreed by xˆ k = A ( A ) k C x ˆ + A + + A Bu k k k Bu + A k k + A y k Bu (8) o place the oberver pole, let rearrange (8) to obtain X ˆ [ m + ] = AXˆ [ + BU[ + y [ (9) where B AB B = M K A B A = M M K A B M B O O A ( A C) ( C) A A K, M B M, ( A C) A = M K A. Pole of the oberver are obtained by olving the following equation eig( A) = z I A =. () Solving (), we found that there are 3K pole on z-plane. Among thee, there are only 3 pole that do not locate at the origin. Auming that thee 3 pole are placed at z = p, we obtain the oberver gain a follow ( p) ( + p) + ( p) K l = () K 3 ( p) 3 J l 3 = (3) K All pole in () have been fixed by the aid of multirate ampling theory. he number of pole depend on the interval between encoder pule,. hi confirm the fact that the dynamic of the ytem i dependent on. We can find the pole on z-plane when only i ued a the ampling time by olving (). In thi cae the matrix A i imply ( A C), i and i calculated from (), () and (3). he pole on z-plane when i ued a the ampling time and the correponding oberver ettling time veru the ratio of to i hown in Fig. 5 and 6, repectively. he oberver ettling time i linearly dependent on the pule interval π π Fig.5. Pole on z-plane when i ued a the ampling time. Fig.6. Oberver ettling time veru the ratio of interval of the pule and DSP Clock 3 ( p) ( ) ( p) ( p + ) 3 l = + p + () K K page 3/6

4 * ω * i d * i q ωˆ i q i d ωˆ ˆ em Fig.7. he ytem ued to verified the oberver reference peed etimated peed without diturbance compenation Fig.8. Simulation reult i w i u etimated peed with diturbance compenation θ (a) direct calculation from encoder (b) etimation by the oberver Fig.. Comparion of the peed from the encoder and the oberver when the encoder pule interval i. econd (a) inverter (b) MG et Fig.9. Experimental apparatu he validity of application of the intantaneou peed oberver to an induction motor i verified by the ytem illutrated in Fig. 7. Fig.8 how the imulation reult. It i obviouly een that the etimated peed converge to the reference peed. It can etimate the peed correctly until peed drop below 5 rpm, which correpond to the vehicle peed of.9 km/h. he vehicle can be topped eaily by locking the wheel. he oberver wa alo examined through a imple induction motor drive experiment. he apparatu are hown in Fig. 9. Since the dc generator i ued a a load, the ytem become no load at low peed. he no load operation i very evere becaue of the exitence of undeired pace harmonic of the magnetic flux ditribution in the IM itelf, which caue the rickety rotation. hi doe not occur in traction where the moment of inertia i much larger. Even though the experiment at low peed cannot be realized the operating condition of the oberver at low peed can be teted by reducing the reolution of the encoder o that the correponding interval between the pule can be obtained. For intance, if we want to examine the operation at rpm by a 6-ppr encoder, we mut reduce the reolution to 6 ppr and operate the motor at rpm. Fig. how the peed calculated directly from a 6-ppr encoder and the etimated peed from the oberver, repectively, when the motor run at rpm. It i obviouly een that the application of the oberver improve the peed information. hi alo confirm that the oberver work effectively even at the condition where the encoder pule cannot be detected frequently PARAE ORQUE CONRO In railway traction drive, an inverter i normally ued to drive everal motor connected in parallel a hown in Fig.. In thi cae it i neceary to concentrate on the difference in wheel radii becaue it caue difference in rotational peed. A a reult, the lip velocity change and thi affect the amount of current in each motor [3]. page 4/6

5 * i d * i q i q i d J J ωˆ ˆem i u i w Fig.. he propoed parallel torque control Fig.. Parallel motor control Since the motor are connected in parallel, it i impoible to control each motor current. Only the total amount of the current can be controlled. For implicity, we examined thi by a one-inverter-twomotor car model. It block diagram i hown in Fig.. Wheel radii are.47 and.43 meter. wo intantaneou peed oberver are ued to etimate the peed of each motor. hen the average etimated peed i ued for vector rotation. Note that only torque control i implemented to emulate normal train control. Due to the difference of the wheel radii, the amount of the current flowing into each motor are not identical. It i impoible, however, to ue the exact amount for calculation of the oberver. In thi cae, the average value of the current detected from current enor i ued. he imulation reult in Fig. 3 how that application of the intantaneou peed oberver i poible although there i only one et of current enor. encoder actual peed oberver (a) wheel radiu of.47 m encoder actual peed oberver (b) wheel radiu of.43 m Fig.3. Etimated peed of each motor 4. - ESIMAION OF OAD ORQUE Another intereting feature of the intantaneou peed oberver i that it i able to etimate the diturbance or load torque. hi i very ueful for calculation of adheion force, which will be ued for anti-lip control. Since there i only a et of current enor, the etimated page 5/6

6 load torque become the average value. o olve thi problem, it i neceary to calculate the value of torque current, i Sq of each motor from lip. i Sq = i ω (4) R mr where R i the rotor circuit time contant, i mr i the magnetizing current and S ω S i the lip. he value of the magnetizing current i roughly the ame a the flux current or d-axi current, which i kept contant. Simulation reult in Fig. 4 how the improvement of load torque etimation. he etimated load torque can accurately track the actual value. (a) deviation of load torque etimation (b) etimation by uing lip velocity Fig.. Correction of load torque etimation 5. - CONCUSIONS hi paper ha decribed a poibility to maintain a precie control in low peed range of an ac traction motor. o do thi, intantaneou peed oberver have been introduced to the ytem to etimate the peed when the information from rotary encoder i not available. We alo examined the behavior of the oberver when they are applied to a ingle-inverter-multiple-motor ytem, where the amount of the current can be meaured at the inverter terminal. he oberver, not only etimated precie peed information, but alo yielded accurate load torque etimation, which i neceary in anti-lip control. he application of the intantaneou peed oberver to ac traction ytem will be an effective technique for realizing pure electric braking of electric railway vehicle. REFERENCES [] Sone, S.: Power electronic technologie for low cot and energy conervation on world railway vehicle. Proc. of IPEC-okyo, vol., pp, , Japan, Apr. [] Kovudhikulrungri,.; Koeki,.: Stability analyi of an intantaneou peed oberver for an induction motor with a low-reolution encoder. Proc. of J-RAI, pp , Japan, Dec. [3] ateihi, D.; Kovudhikulrungri,.; Koeki,.: Application of an intantaneou peed oberver for the control of braking torque for multiple-motor-ingleinverter ytem. Proc. of J-RAI, pp , Japan, Dec. page 6/6

7 Precie orque and Speed Control In Pure Electric Braking Operation of AC raction in ow Speed Range ilit Kovudhikulrungri he Univerity of okyo Faculty of Engineering Department of Electrical Engineering akafumi Koeki he Univerity of okyo Faculty of Science Department of Information and Communication Abtract: hi paper decribe a method to achieve precie torque and peed control of AC traction in low peed range. he author apply an intantaneou peed oberver to improve the peed information and propoe a new pole aignment by analyi in multirate-dicrete-time domain. Validity of thi method i verified though variou imulation. Introduction he combination of air- and electric brake play a major role in braking ytem of electric railway vehicle. hi combination, however, often caue evere riding comfort and inaccuracy of topping poition becaue of the low and fluctuated repone of the brake mechanical part. Moreover, the phyical characteritic of the mechanical part, i.e., brake hoe, alway vary with peed, temperature and urface condition. o eliminate thee problem, it i neceary to operate the electric brake a the main braking cheme. hi lead to the propoal of pure electric braking ytem []. However, peed detection at low peed cannot be implemented effectively becaue coare encoder are intalled in Japanee railway vehicle. For intance, encoder ued in ordinary Japanee railway vehicle have an extremely low reolution of 6 pule per revolution (ppr). When the peed drop below 5 km/h, the peed information i not available. A a reult, the cloed-loop control i witched to the open loop control by the driver. An eddy current brake or the friction brake i operated intead of the regenerative brake. Fig. ummarize thi problem. Intantaneou peed oberver Since extremely low-reolution rotary encoder are intalled in railway vehicle, the interval between two conecutive pule become longer and longer at low peed a hown in Fig.. It i obviouly een that the interval between the pule,, i longer than the DSP clock ampling time,. We define a the ampling frame. If we ue the normal peed calculation from the encoder, we will loe the accuracy and thi lead to intability at low peed. o overcome thee problem, it i neceary to etimate the Fig.: Summary of the problem θ [ m ] [ k = K θ θ[ m +] Fig.: Encoder pule at low peed

8 intantaneou peed when the information from the encoder i not available. hi etimation cheme i called intantaneou peed oberver [].. Principle of the Intantaneou Speed Oberver According to the timing diagram in Fig. the ampling intant [m,k] i defined by ( ) + k [ m, ] t = m θ, () [ k where θ [ i haft angle. By thi definition, it i poible to etimate the rotor peed at any ampling intant [m,k], tarting from it value etimated in the previou ampling intant [m,k-], if we know the value of the produced torque, em, and the diturbance, : ˆ[ ω m, k] = ˆ[ ω m, k ] em [ m, k] + [ + em[ m, k ] + [ + J, () where ω i the motor peed in rad/, J i the moment of inertia and ^ mean etimated value he error of etimation caue by two factor the deviation of poition detection from the encoder, θ, and the diturbance,. Hence, the update law have been propoed by γ θ[ m + ] ˆ[ ω m + ] =, (3) Jγ θ[ m + ] [ m + ] =. (4) he coefficient γ and γ allow u to aign the deired etimation error dynamic. he oberver i rearranged into tate pace variable where x ˆ[ m + ] = Axˆ[ + Bu[ (5) x ˆ[ m ] = [ ˆ ω ˆ ], u[ = [ em ω ], γ γ ( γ γ ) A = J Jγ, γ ( γ γ ) γ + γ B = J Jγ. (6) γ Pole of the oberver can be found from the eigenvalue of matrix A: ( = z + γ + 3γ ) z γ γ +. (7) We can adjut the dynamic of the oberver by fixing the pole by olving (7). Note that z i the Z-tranform variable that ha the relation z = exp( ) (8) By thi fact, we can conclude that the period between the pule,, i an important factor deciding the oberver dynamic. Since change dependently to peed, a imple way to decide the dynamic of the oberver i to fix the pole at nominal peed. hi method work effectively when there i no wide-range of peed variation. In railway application, however, we deal with a wide range of peed variation. Placing the pole at the nominal peed reult in noie problem at high peed and intability at low peed.. Generalization of the Intantaneou Speed Oberver o examine the behavior of the intantaneou peed oberver at every ampling intant, it i generalized by the aid of multirate ampling theory [3,4] Fig.3 how the block diagram of the intantaneou peed oberver. he oberver i derived from a peed oberver in dicrete-time domain with diturbance dynamic conideration. [ k ] = ( A C) xˆ[ k] + Bu[ k] Cy[ k] x ˆ + + (9) where ˆ = [ ˆ ω ˆ θ ] x ˆ, u = em, y = θ, i the oberver gain matrix [ l l ] l 3 and i the ampling time. Matrice A, B and C are derived from their continuou time domain matrice A c, B c and C c, repectively, by the following relation A = exp( A ) I +, () c A c

9 em J ω θ k = u B z C xˆ A y Fig.3: Block diagram of an intantaneou peed oberver B = exp( A c ( τ )) Bcdτ = ( I + exp( A c )) Bc, () where / J A c =, C = C c, () B, = [ ] c / J = C c. Subtituting the continuou time matrice into (), () and (), finally the following dicrete-time matrice are obtained a follow / J A =, / J = / J B, = [ ] C. (3) he problem i which ampling time, or, hould be ued. Since the output can be detected only when there i an encoder pule, pole placement and tability of the ytem depend on the interval between the pule,. If i ued a the ampling time, it i neceary to extend the matrice A, B and C due to the number of ampling intant in that interval and thi i difficult to implement [3]. On the other hand, we can ue a the ampling time of the ytem by uing the etimated haft angle when the detected pule are not available a illutrated in Fig.4. Note that thick arrow repreent actual value while thin arrow repreent etimated value. hi lead to the aumption that y, k =, K; K = / y =, (4) yˆ otherwie where k i the ampling index in each ampling frame, K i the lat ampling intant in each frame Hence, the oberver equation can be expreed a follow k =, K ; x ˆ = Axˆ + Bu + ( y yˆ ) (5) k + k k k, K ; x ˆ k = Axk + Buk (6) + ˆ hee imply that the oberver correct the error when pule are detected and act a a imulator when pule are unavailable. Due to thi fact, the lat ampling intant in each ampling frame decide the dynamic of the next ampling frame. Dynamic of each frame can be expreed by xˆ k = A ( A ) k C x ˆ + A + + A Bu k k Bu + A k k + A y k k Bu o place the oberver pole, let rearrange (7) to obtain where B AB B = M K A B Xˆ [ (7) X ˆ [ m + ] = AXˆ [ + BU[ + y [ (8) A = M M K A [ m,] [ m,] xˆ xˆ = M xˆ Fig.4: Expanded dicrete-time ignal [ m, K ] B M B O O A and [ ( A C) ( C) A A K M B M, ( A C), [ m,] [ m,] = u u U =. M u[ m, k ] A M K A Pole of the oberver are obtained by olving the following,

10 equation eig( A) = z I A =. (9) where z i the Z-tranform variable due to ampling time. z = exp( ) () π π Solving (9), we found that there are 3K pole on z -plane. Among thee, there are only 3 pole that do not locate at the origin. Auming that thee 3 pole are placed at z = p, we obtain the oberver gain a follow ( p) ( + p) + ( p) K l =, () K 3 ( p) ( ) ( p) ( p + ) 3 l = + p +, () K K ( p) 3 J l 3 =. (3) K he oberver gain in (), () and (3) alway change due to the number of ampling intant, K, which i the ratio of interval between the pule,, to the DSP clock ampling period,. hi confirm the fact that the dynamic of the ytem i dependent on. We can alo find the pole on z -plane when only i ued a the ampling time by olving (9). In thi cae the matrix A i imply ( A C), i and i calculated from (), () and (3). he pole on z -plane, z -plane and the correponding oberver ettling time veru the ratio of to are hown in Fig. 5, 6 and 7, repectively. he oberver pole are fixed at origin and.7 on z -plane. It i obviouly een that the pole on z -plane move within the unit circle. hi guarantee the tability of the oberver. he oberver ettling time i, moreover, linearly dependent on the pule interval. he validity of application of the intantaneou peed oberver to an induction motor i verified by the ytem illutrated in Fig. 8. Fig.9 how the imulation reult. It i obviouly een that the etimated peed converge to the reference peed. he repone of the whole ytem i alo table even at low peed. he oberver etimate the peed correctly until peed drop below 5 rpm, which correpond to the vehicle peed of.9 km/h. he 3 π π π π Fig.5: Pole on z -plane π π π π π π π π π π π π π vehicle can be topped eaily by locking the wheel. On the other hand, we can alo ee the behavior of pole on z -plane when the pole on z -plane are fixed at a nominal peed. In thi cae, the nominal peed i et to 3 rpm. he pule interval from a 6-ppr encoder i.33 econd. he pole are fixed at.7 on z -plane, a hown in Fig., reulting in oberver ettling time of.8 econd. Movement of the pole on z -plane when the peed i higher and lower than the nominal peed are hown in Fig. (a) and (b), repectively. here are 3K pole but only three pole move. When the motor rotate π Fig.6: Pole on z -plane π π Fig.7: Oberver ettling time

11 fater than the nominal peed, the pole move within the unit circle o the intability doe not occur. On the other hand, when the peed drop below the nominal peed, one of the pole move toward outide of the unit circle and thi lead to the intability at low peed. he imulation reult by thi pole aignment i hown in Fig.. It i obviouly een that the etimated peed ocillate. Stability of thi pole aignment, however, can be improved by uing a lower peed a a nominal peed. Fig. how the repone of the ytem when the oberver i deigned at the nominal peed of rpm and the pole are fixed at.7 on z -plane. here i no big ocillation at low peed but the diturbance rejection i lower. * ω * i d * ωˆ i q i q i d ωˆ ˆ em Fig.: he ytem ued to verified the oberver i w i u Fig.: Simulation reult when pole on z -plane are fixed π π π π π π π π π π π π π π π π π π π π Fig.3: Pole on z -plane θ π π π π π π π π π π π π π π π π π π π π (a) peed higher than the nominal peed π π π π π π π π π π π π π π π π π π π π (b) peed lower than the nominal peed Fig.8: Pole on z -plane Fig.9: Simulation reult when pole on z -plane (nominal peed of 3 rpm). Fig.: Simulation reult when pole on z -plane (nominal peed of rpm).

12 3 Simulation Reult According to orque or Current Command In the preent traction control, the acceleration and braking operation are achieved by notch command, which are the level of the torque-producing current. he appropriated notch command are determined by the driver. Only the current, i.e., torque control loop are enough for manual operation ince the driver act a a peed controller. Precie peed information i, however, till neceary in manual operation ince it i ued for vector rotation. Fig. 3(a) and 3(b) how the torque repone without and with the oberver, repectively. It i found that the torque repone without the oberver ocillate at low peed. A a reult the electric brake cannot be implemented. On the other hand, the torque repone with the oberver ha le ocillation. Fig. 3(c) how the imulation reult due to the torque repone in Fig. 3(b). It i obviouly een that the ocillation doe not occur at low peed and the propoed ytem give much better braking force repone alo in the preent manual peed control than a conventional ytem. 4 Concluion hi paper ha mentioned about the advantage of the application of the intantaneou peed oberver to traction control. he oberver can etimate intantaneou peed between the encoder pule, yielding the precie peed information. We propoed a new pole aignment method by generalizing the oberver in multirate-dicrete-time domain and fixing them. hi method alway maintain the tability of the oberver but it i difficult to calculate the gain in cae of high order ytem. On the other hand, for ingle rate pole aignment method, i.e. fixing on z -plane, the tability depend on the nominal peed ued in deign. he lower nominal peed yield the more table repone but lower diturbance rejection. hi method may be a good olution when we face with a high order ytem. We alo applied the oberver to torque control, which i the normal control cheme of railway vehicle and obtained a deirable reult comparing with the conventional control cheme. Reference [] S. Sone, Power Electronic echnologie for ow Cot and Energy Conervation on World Railway Vehicle, Proc. IPEC-okyo, vol., pp , (a) orque repone without the oberver (b) orque repone with the oberver (c) Speed according to torque in (b) Fig.4: Simulation reult of torque control. [] Y. Hori, Robut Motion Control Baed on a wo-degree of-freedom Servoytem, Advanced Robotic, vol.7, No.6, pp , 993 [3] M. Araki, K. Yamamoto, Multivariable Multirate Sampled-Data Sytem: State-Space Decription, ranfer Characteritic and Nyquit Criterion, IEEE ran. Automatic Control, vol. AC-3, pp.45-54,986. [4]. Kovudhikulrungri,. Koeki, Stability Analyi of an Intantaneou Speed Oberver for an Induction Motor with a ow-reolution Encoder, Proc. J-RAI, Kawaaki, Dec.,

13 ilit Kovudhikulrungri*, Control of a raction Motor at ow Speed with Conideration of Vehicle Dynamic ilit Kovudhikulrungri*, and akafumi Koeki (he univerity of okyo) Abtract he objective of thi paper i to realize a precie control of a traction motor in low peed range with conideration of vehicle dynamic. o do thi, an intantaneou peed oberver i introduced to the ytem to olve the problem due to a low-reolution encoder. he ytem i generalized by multirate ampling theory o that vehicle dynamic can be included in the oberver model. he effectivene of the propoed ytem i verified through variou imulation. Keyword: traction motor, low peed range, intantaneou peed oberver, multirate ampling theory Introduction Uing regenerative braking a a main braking cheme from top peed to zero peed or pure electric brake yield variou merit to electric train, for intance, in the apect of energy aving, riding comfort, maintenance cot, and o on (). However, main obtacle in realization are the inefficient braking force of electric brake at high peed and electric braking control at low peed due to encoder problem. hi paper will focu on the latter problem. Since the encoder intalled in Japanee train normally have reolution only 6 pule per revolution, ppr. he peed information calculated from thee pule largely deviate from the actual value at low peed, epecially in braking operation, where peed drop abruptly. hi reult in failure of electric braking control and air brake i ued to compenate it. he evere riding comfort occur due to the hocked at the tranition tate. In thi paper, the author introduce an etimation cheme called intantaneou peed oberver to etimate the peed between the pule. Since there are ome low frequency mechanical reonance in bogie ytem, the propoed control ytem i developed from a two-bogie train, which i compoed of a motor car (M-car) and a trailer (-car). he oberver i generalized by the aid of multirate ampling theory o that the vehicle dynamic i fixed in the oberver. Variou imulation reult verify the effectivene of the propoed ytem. Plant Model In order to conider the effect of bogie ytem dynamic, the plant model i implified to a -bogie vehicle, compoed of a motor car and a trailer a hown in Fig.. Note that the motor car i driven by only one motor and model of analyi i developed under the aumption that no lip and lide occur during the operation. he block diagram of the plant i hown in Fig.. Equation of motion in tate pace are decribe a follow x & = A cx + B c u, y = C c x, () b k brg krg M + M J M + M J r( M + M J ) r( M + M J ) A =, c br kr b k R M g RgM M M x v x B( x) M M Fig.. Plant model k b v /6

14 R g r ( M + M J ) B c = u = em, y = θ m., = [ ] C c, ω θ x =, v x Decription and value of the parameter are lited in able. 3 Intantaneou peed oberver Since extremely low-reolution rotary encoder are intalled in railway vehicle, interval between two conecutive pule become longer and longer at low peed a hown in Fig. 3. It i obviouly een that the interval between the pule,, i longer than the DSP clock ampling time,. We define a the ampling frame. If we ue the normal peed calculation from the encoder, we will loe the accuracy. hi lead to intability at low peed. 3. Principle of the intantaneou peed oberver he principle of the intantaneou peed oberver i to etimate the peed between the pule. he etimated value will be corrected when the next pule i detected. According to the timing diagram in Fig.3, the ampling intant [m,n] i defined by () able : Decription and value of parameter Symbol Decription Value B( x) Coupler backlah cm b F D, F D k Damping contant Diturbance force on each car Spring contant M Ma of the M-car 5 kg M Ma of the -Car 5 kg M J m N n Equivalent ma of motor moment of inertia Number of pule at ampling intant in each frame Number of ampling intant kg R g Gear ratio 5.64 r Wheel radiu.43 m em Motor torque oad torque Interval between encoder pule DSP clock ampling time. m v, v x, x θ ω Velocity of each car Ditance of each car Motor haft angle Motor peed ( ) + n [ m, ] t = m θ [ n, () em R g r F D - F D k +b M M x x + v v - x Fig.. Block diagram of the plant R g r n = N θ [ m ] θ [ θ [ m +] θ where θ [ i haft angle. By thi definition, it i poible to etimate the rotor peed at any ampling intant [m,n], tarting from it value etimated in the previou ampling intant [m,n-], if we know the value of the produced torque, em, and the diturbance,. By thi principle, the oberver i decribed by the following equation ˆ[ ω m, n] = ˆ[ ω m, n ] em [ m, n] + [ + em[ m, n ] + [ + J, (3) where ω i the motor peed in rad/, J i the moment of inertia and ^ mean etimated value. he error of etimation, which can be corrected when an encoder pule i detected, i caued by two factor the deviation of poition detection from the encoder, θ, and the diturbance,. Hence, the update law have been propoed by γ θ[ m + ] ˆ[ ω m + ] =, (4) Fig. 3. Encoder pule at low peed Jγ θ[ m + ] [ m + ] =. (5) /6

15 u B c C c θ and C are derived from their continuou time domain matrice with diturbance conideration A cd, B cd and C cd, A c repectively, where u xˆ y he coefficient γ and γ allow u to aign the deired etimation error dynamic. 3. Generalization of the Intantaneou Speed Oberver he intantaneou peed oberver mentioned in the previou ection i a partial oberver. In cae of a complicated ytem, it doe not include the dynamic of the plant. Moreover, It wa derived by a particular method. herefore it i difficult to extend the oberver in cae that a higher order i required. hi ection deal with generalization of the intantaneou peed oberver in tate pace by uing multirate ampling theory (3) o that the dynamic of the plant can be fixed in the oberver. Fig.4 how the block diagram of the intantaneou peed oberver. he oberver i derived from a peed oberver in dicrete-time domain with diturbance dynamic conideration. where ( A C ) xˆ[ n] + B u[ n] y[ n] x ˆ[ n + ] = + C, (6) x ˆ = [ ˆ ω ˆ θ v ˆ xˆ F D ], em the oberver gain matrix B C z A n=,n Fig. 4. Block diagram of the intantaneou peed oberver n = u =, y = θ, i [ l l l 3 l 4 l 5 ]. Note that ubcript indicate that the contant DSP clock i Fig. 5. Dicrete time ignal b M + MJ A = br cd R M g k M + MJ kr RgM Rg r ( M + M J = cd ) brg / r ( M + MJ ) b M krg / r ( M + MJ ) k M B, = [ ] C cd. Rg / r ( M + MJ ), Fig. 5 how a diagram of dicrete time ignal. hick arrow repreent actual value and thin arrow tand for etimated value. From the diagram, the actual output y or the haft angle can be obtained only when an encoder pule i detected. At thi moment, the error of etimation i corrected. On the other hand, when pule are not detected, the oberver principally work a a imulator. hi condition can be achieved by uing the etimated haft angle when the detected pule are not available a illutrated in the diagram. hi method i practical in imulation and experiment ince it can be program eaily. hi lead to the aumption that y, n =, N; N = / y =, (7) yˆ otherwie where n i the ampling index in each ampling frame, N i the lat ampling intant in each frame. Hence, the oberver equation can be expreed a follow n =, N ; x ˆ = A xˆ + B u + ( y yˆ ), (8) n+ n n n, N ; x ˆ n+ = A xˆ n + B un. (9) Due to thi fact, the lat ampling intant in each ampling frame decide the dynamic of the next ampling frame. Dynamic of each frame can be expreed by xˆ n = A ( A C ) n ˆ n n x + A B u + A B n + + A B un + A y o place the oberver pole, let rearrange (7) to obtain n n u.(7) X ˆ [ m + ] = AXˆ [ + BU[ + y [, (8) ued a the ampling time of the ytem. Matrice A, B 3/6

16 where A = M M O B A B B B = M M N N A B A B xˆ[ m,] ˆ xˆ[ m,] X[ = and M xˆ[ m. N] ( A C ) ( A C ) A, M N A ( ) A C O M B u[ m,] u[ m,] U [ =. M u[ m, N ], A = M N A Pole of the oberver are obtained by olving the following equation N eig( A) = eig( A ( A C )) = zi A =, (9) where z i the Z-tranform variable due to the contant ampling time, i.e. z -domain. z = exp( ). () Solving (9), we found that there are 5K pole on z -plane. Among thee, there are only 5 pole that do not locate at the origin. Hence, we can place thee 5 pole to adjut the dynamic of the oberver. 3.3 Relationhip between the contant ampling time, Subtituting the value of in (9) and uing the fact that C equal to C, we obtain ( ) eig A = (4) C Hence, the pole on z -plane that are not located at the origin are equivalent to the pole on z -plane. By thi fact, we can calculate the oberver gain for the intantaneou peed oberver in z -domain by (4) and convert to z -domain by (3). (3) i remarkably important for the tability of the oberver. It i neceary to conider the effect of the interval between the pule. he author experienced the problem of intability when placing the pole by uing only (4) (4). 4 Simulation Reult Validity of the propoed method i verified through variou imulation. Fig. 6 how the block diagram of the ytem. Stroke of pring and damper between the bogie when the natural frequency i 5 rad/ and the damping factor of the bogie ytem i varied are hown in Fig. 7. he controller are eparated into current controller and mechanical ytem controller. Pole placement i achieved by Keler canonical form. he oberver ettling time i et to be three-time fater than the controller at the nominal peed of 3 rpm. he effect of backlah when the damping factor of the coupler i et to.5 i hown in Fig. 8. he reference peed i et to the motor peed of 3 rpm. he train i aumed to run on an uphill gradient of 5 degree at the 8 th econd. It i obviouly een that the backlah caue ocillation. hi and the variable ampling time i defined a the period between two conecutive pule, o it alway varie dependently on motor peed. When dealing with a variable-ampling-time ytem, a controller and an oberver are conventionally deigned at a nominal peed or nominal operating point by fixing the pole of z-plane. hi method work effectively at nominal peed but the repone of the ytem deteriorate at relatively different peed. Oberver equation i decribed by x ˆ[ m ] = A xˆ[ + B u[ + ( y[ yˆ[ ). () + Note that ubcript indicate that i ued a a ampling time, i.e. z -domain. o find the relationhip between both domain, let aume that the input ignal in each ampling frame in z -domain are contant. (7) can be rearranged a follow * ω em i a ˆ ω, ˆ, θ vˆ, xˆ, ˆ θ Fig. 6. Block diagram of the propoed control ytem ζ = ˆ N x [ m + ] = Axˆ[ + Bu[ + A ( y[ yˆ[ ). () Comparing () and () lead to the following relation N = A N or = ( A ). (3) Fig. 7. Stroke of the coupler when it natural frequency i fixed at 5 rad/ and the damping factor i varied 4/6

17 (a) Motor peed Fig. 8. Effect of backlah in the coupler and compenation ζ Fig. 9. Motor peed due to each damping factor (b) Velocity of -car Fig.. Comparion of the repone of the ytem when extended and conventional intantaneou peed oberver are applied when the damping factor of the pring and damper i et to.5 ocillation can be uppreed by uing the etimated diturbance to compenate it. Fig. 9 how the repone of the ytem when the damping factor of the bogie ytem i varied. Decrement of the damping factor reult in a large ocillation. However, when the damping factor become.7, the ytem ocillate with large amplitude again. It need careful invetigation furthermore. Comparion of the performance of thi propoed oberver and a conventional intantaneou peed oberver are hown in Fig. and. Note that the conventional oberver ha motor peed, haft angle and load torque a tate variable. herefore, the vehicle dynamic, coupling force, backlah, gradient force and other diturbance are etimated in term of load torque. From the figure, they are obviouly een that the conventional one can etimate the motor peed more accurately than the extended one when the diturbance i injected to the ytem. However, the peed of the velocity of the -car i robut to the diturbance in cae of the extended oberver ince the vehicle dynamic i modeled in the oberver and the etimated velocity i ued for controller deign. Fig. how the braking repone. Note that the damping factor i.5. At the 5 th econd, a braking command i injected to the ytem and peed gradually drop. he ytem (a) Motor peed (b) Velocity of -car Fig.. Comparion when the damping factor of the pring and damper i.3 5/6

18 can operate tably even at a very low peed of 5 rpm. Note that, at 5 rpm the interval between the pule i. econd, which i very long when compared to the -microecond clock ampling time. 5 Concluion and Future Development Fig.. Repone when braking hi paper ha decribed a method for peed etimation for an electric train in which a coare peed encoder i intalled. he main problem of the ytem i realization of a precie control at low peed, where the information from the encoder i not available. o olve thi problem, we introduce an intantaneou peed oberver to etimate the peed between the encoder pule. Since there are ome low frequency mechanical reonance and nonlinearity in bogie ytem, the oberver i generalized baed on multirate ampling theory o that it can be extended to fix the dynamic of the bogie ytem in the oberver. he oberver gain cannot be calculated directly from the conventional method. It i neceary to conider the effect of the interval between the pule a indicated in (3). We verified the effectivene of the oberver through variou imulation. Note that the coupler ued in imulation ha a backlah, which caue a evere ocillation when there i an abrupt diturbance. hi problem can be olved by uing the etimated diturbance to compenate it. We alo compared the performance of the propoed oberver and the conventional intantaneou peed oberver. he propoed oberver improved the repone of the -car becaue the vehicle dynamic i modeled in the oberver. he propoed oberver alo reduced the number of unknown component in the etimated diturbance. hi i eential for accurate etimation of adheion force. For future development, we plan to extend the frame work to etimate the adheion force in order to examine the lip-lide phenomena. hi i very important for realization of re-adheion control. Finally, we plan to verify the ytem by experiment. Reference () S. Sone, Power Electronic echnologie for ow Cot and Energy Conervation on World Railway Vehicle, Proc. IPEC-okyo, vol., pp ,. () Y. Hori, Robut Motion Control Baed on a wo-degree of-freedom Servoytem, Advanced Robotic, vol.7, No.6, pp , 993 (3) M. Araki, K. Yamamoto, Multivariable Multirate Sampled-Data Sytem: State-Space Decription, ranfer Characteritic and Nyquit Criterion, IEEE ran. Automatic Control, vol. AC-3, pp.45-54,986. (4). Kovudhikulrungri,. Koeki, Precie orque and Speed Control In Pure Electric Braking Operation of AC raction in ow Speed Range, AMC the 7 th International Workhop on Advance Motion Control, Maribor, Slovenia, (to be preented) 6/6

19 Paper Precie Speed and orque Control for AC raction Pure Electric Braking Sytem in ow Speed Range Student Member ilit Kovudhikulrungri (he Univerity of okyo) Member akafumi Koeki (he Univerity of okyo) hi paper decribe a poibility to increae the operation range of railway' pure electric braking ytem at low peed range. Since low-reolution peed encoder are normally intalled, precie peed information i unavailable at low peed. An etimation cheme called intantaneou peed oberver i introduced to etimate the peed for precie torque and peed control. he tability of the ytem i analyzed by multirate ampling theory and digital control theory. Several imulation reult and experiment poitively how the improvement of peed etimation and the poibility to extend the operation of the pure electric brake. Keyword: Pure electric brake, induction motor, low-reolution encoder, low peed, intantaneou peed oberver, tability.. Introduction he combination of air brake and electric brake play a major role in braking ytem of electric railway vehicle. hi combination, however, often caue evere riding comfort and inaccuracy of top poition becaue of the low repone of the brake' mechanical part. Moreover, the phyical characteritic of the mechanical part, i.e. brake hoe, alway vary with velocity, temperature and urface condition. o eliminate thee problem, it i neceary to operate the electric brake a the main braking cheme. hi lead to the propoal of pure electric brake (). he pure electric brake can improve regenerative energy and riding comfort, ince the repone of the electric ytem i fater. If we can control the top poition preciely, the train automatic topping control (ASC) can be realized. One of the difficultie in realization i the preciion of the peed information, which i neceary for a cloed loop control. Since encoder intalled in a vehicle have only 6 pule per revolution (ppr), it i difficult to obtain peed information at every ampling time, epecially at low peed. hi reult in the failure of the cloed loop control. Conequently, the open loop control i applied when the vehicle peed drop below 5 km/h and a friction brake i normally applied. here are normally ome hock due to the tranition of the witching of braking cheme and variation of braking force due to the manual operation. hi finally reult in a evere riding comfort. he ue of the friction dependent mechanical brake alo, moreover, deteriorate the accuracy of topping poition. he dynamic of the railway vehicle i relatively imple, compared to robotic or other indutrial drive although it drive technique cannot alway be imple becaue there are ome low frequency mechanical reonance in bogie ytem. Epecially, motor control for traction i traightforward ince torque control i implemented. he vector control ha been recently introduced to the vehicle. If ome peed etimation cheme are applied, it i poible to achieve an effective motor drive or braking control. Regarding to the problem of encoder, the application of peed enorle drive technique to traction are being tudied. However, the peed etimation at low peed i difficult to achieve due to parameter variation. Due to the exitence of the peed encoder and the difficultie of the enorle drive technique, in thi paper, we introduce an intantaneou peed oberver, which can etimate the peed at every ampling when the peed ignal from the encoder i not directly ueful (). Since thi paper deal with operation at low peed, the tability of the ytem i analyzed by multirate ampling and digital control theory. he propoed control ytem i verified through everal imulation and experiment.. Intantaneou peed oberver In order to etimate the peed when the information from the encoder i unable to obtain frequently, an intantaneou peed oberver i introduced to the ytem. It timing diagram i hown in Fig.. he ampling intant [m,k] i defined by t = ( θ [ m ]) + k [ m, k ], () where and are the variable period between the encoder pule and DSP (digital ignal proceor) ampling period, repectively.

20 k= K θ [ m ] θ[ θ[ m + ] motor torque, em average peed, ω * ω Speed Controller (I-P) ωˆ * i d * i q Current Controller (I) & EMF Compenator i q i d dq uvw IM Model AC V Rectifier and Inverter i w i u IM RE θ etimated peed, ωˆ etimated diturbance, ˆ ωˆ ˆ em Intantaneou Speed Oberver Fig.. he propoed control ytem Fig.. iming diagram of an intantaneaou peed oberver By thi definition, it i poible to etimate the rotor peed at any ampling intant [m,k], tarting from it value etimated in the previou ampling intant [m,k-], if we know the value of the produced torque, em and the mechanical diturbance torque, ˆ[ ω m, k] = ˆ[ ω m, k ] em [ m, k] + [ + em[ m, k ] + [ +, () J where J i the moment of inertia, ^ mean etimated value and the definition of the ymbol i given in Fig.. he error of etimation i caued by two factor - the deviation of poition detection from the encoder, θ, and the diturbance torque,. Hence, the update law have been propoed by γ θ[ m + ] ˆ[ ω m + ] =, (3) he coefficient γ and γ allow u to aign the deired etimation error dynamic. he oberver i rearranged into tate pace variable where Jγ θ[ m + ] [ m + ] =. x ˆ[ m + ] = Axˆ[ + Bu[, x ˆ[ m ] = [ ˆ ω ˆ ], u[ = [ ω ], em ( ) γ γ γ γ A = J, Jγ γ (4) (5) ( γ ) γ γ + γ B = J Jγ. γ Note that ω i the average peed calculated from the encoder pule. Pole of the oberver are identical to the eigenvalue of matrix A: z + γ + 3γ ) z γ γ + =. ( 3. Propoed control ytem Fig. how the block diagram of the propoed control ytem. In order to obtain the fat dynamic, vector control trategy i applied to the traction motor. he current and peed controller are deigned baed on coefficeint coordination in characteritic polynomial (3). he intantaneou peed oberver i introduced to the ytem to improve the peed information. he deired dynamic of the intantaneou peed oberver i obtained by aigning the location of the pole according to (7). In order to obtain the deired time repone, the pole of the oberver are placed on -plane by the relation, ln z =. Auming that the oberver pole on -plane are located at p φ and p φ, we can correct the etimation error by the following equation (4), 3 p coφ p coφ γ = e + e co( p inφ), he model of imulation, which i a implified vehicle drive ytem i hown in Fig. 3. Note that the motor peed (6) (7) (8) (9) p coφ p coφ γ = + e e co( pinφ). ()

21 of rpm correpond to the vehicle peed of cm/ or.4 km/h. he motor parameter are lited in able. he pole of control ytem on -plane are found at 6.97 ± 5. herefore, the oberver pole are placed at 8 on -plane. he DSP ampling time,, i et to. m. Fig. 4 how the imulation reult. It i obviouly een that the etimated peed converge to the command. After 6 econd, a braking command i introduced to the ytem and the peed drop. he etimated peed tart to ocillate at low peed range. able Motor rating at 5 Hz and parameter rated voltage rated current rated power rated peed V 3.6 A.5 kw 4 rpm number of pole 4 Stator reitance.54 Rotor reitance Stator leakage inductance Rotor leakage inductance Magnetizing inductance IM 6 ppr RE Gear ratio 4.56: Fig. 3. Simplified drive ytem 6.6 mh.55 mh mh 86mm 4. Stability Analyi In the previou ection, the validity of the application of the intantaneou peed oberver ha been examined. It wa found that the ytem ocillated at low peed. In order to extend the operation range of the electric brake, it i neceary to analyze the tability of the oberver. Since the oberver etimate the value of the peed between the pule at every ampling time of the DSP clock, it deal with two ampling time. One i the contant DSP clock ampling time. he other i the period between the pule, which alway varie, epecially in braking operation. From thi reaon, the oberver ha been analyzed baed on multirate ampling theory (5). Fig. 5 how the block diagram of the oberver. Note that the oberver i modified to full-order for implicity in analyi and to ee the behavior of the etimated poition that will be ued for error correction. he gain matrice and the variable vector are decribed by Ac = he tate equation of the oberver i rearranged o that it i written in the form of where k J J, Bc =, Cc =, K = k, k3 ( ω θ ) and y = θ uc = em, xc = c. A = x& = A x + Bu k k k 3 k J, B = k k 3 J, ( θ ) and = ( ˆ ω ˆ θ ˆ ) u = em x. he ytem i converted to dicrete-time domain by the multirate ampling theory. Fig. 6 how the expanded dicrete-time ignal. he produced torque,, i read and em () () (3) peed (rpm) 3 peed command etimated peed em + + B c J ω C c θ + - A c time(ec) Fig. 4. Simulation reult Fig. 5. Block diagram of a peed oberver K

22 the peed i etimated at every DSP ampling time,, wherea the motor poition i corrected when the next pule i detected at the ampling time. hi i alo defined a the ampling frame. he pole placement i analyzed by uing multirate ampling theory. It i found that the lat ampling intant of each ampling frame contain enough information to detemine the behavior of the ytem (6). We can adjut the dynamic of the oberver by tuning the oberver gain by the following equation, ( p )( p ) + ( p )( p ) + ( p )( p ) 3 3 k =,(4) p p p3 k3 = J, (6) 3 where p,p and p 3 are pole of the oberver on -plane. Fig. 7 and 8 how the etimated peed when the peed command are fixed at 3 rpm and 5 rpm, repectively. he oberver pole are placed at 8 on -plane. here i no relative ocillation at 3 rpm but the ocillation occur within a contant band of rpm at 5 rpm. o improve the tability and the performance of the oberver, it i neceary to conider the relationhip between the Nyquit frequency and the location of the pole. he Nyquit angular frequency i found from π Ω =. (7) Fig. 9 how the pole on z-plane according to the cae in Fig. 7 (3 rpm) and Fig. 8 (5 rpm). he pole location in cae of 3 rpm are illutrated by the right cro, while the other cae i indicated by the left one. It i obviouly een that when peed drop, the pole move toward outide of the θ ( p ) + ( p ) + ( p ) 3 k =, ( )( )( ) D D u u u D (k) D un (5) effective region, where the natural frequency, ω n, i le than the Nyquit frequency, Ω (the haded area, i.e., the natural frequency i greater than the Nyquit frequency ). hi reult in ocillation a hown in Fig. 8. o improve the tability of the ytem, it i neceary to place the pole inide the effective region. For aurance of the tability without harmful ocillation of high frequency, we contrain o that the pole are placed inide 5 percent of the Nyquit frequency and the damping ratio of.5. We define thi region a conervative region in thi paper. hi, however, low down the repone of the ytem. o obtain a fater repone, the location of the pole can be placed at a maller value of damping factor. Fig. how the new pole location according to the damping ratio of.7 and percent of the Nyquit frequency. Note that region encloed by the inner contour correpond to 5 percent of the Nyquit frequency and the damping ratio of.5. he imulation according to the new pole location i hown in Fig.. he ocillation ha been effectively removed. We can conclude that at low peed, the oberver pole on -plane hould be placed o that they alway locate within the conervative region, i.e., the pole are fixed on z-plane. peed(rpm) Fig. 7. Simulation reult at the command of 3 rpm peed(rpm) time (ec) time (ec) Fig. 8. Simulation reult at the command of 5 rpm em x D (k) x D ( k +) ωˆ θˆ D x D x D xn imaginary axi ˆ Fig. 6. Expanded dicreted-time ignal real axi Fig. 9. Movement of pole when peed drop

23 torque command torque (N) imaginary axi time (ec) torque repone (a) orque repone without oberver real axi Fig.. New pole location at the command of 5 rpm torque (N) - torque command torque repone peed(rpm) time (ec) (b) orque repone with oberver time (ec) Fig.. Simulation reult at the command of 5 rpm due to the new pole location 3 peed (rpm) actual peed torque current 5-5 current (A) peed (rpm) peed command etimated peed time (ec) Fig.. Simulation reult due to the new pole location able : Pole aignment trategy Rotational peed High ow Oberver pole fix on -plane fix on z-plane ytem pole fix on -plane fix on z-plane Since fixing the oberver pole on z-plane reult in low down of the oberver dynamic, it i neceary to reduce the controller gain o that the oberver repone remain fater. he pole aignment trategy i ummarized in able. he imulation reult i hown in Fig.. After the braking command i input, the peed drop and the location of the oberver pole on z-plane change until it reache the critical peed. he oberver pole on z-plane are then fixed and the controller gain are reduced, reulting in the lower but tabler repone. Due to the imulation reult, it can be time (ec) (c) Actual peed according to the torque current Fig.3. Simulation reult of torque control operated cloe to the motor peed of rpm, correponding to the vehicle peed of.4 km/h. At thi point, the vehicle can be topped by locking the wheel without ware and tear of mechanical component. 5. Simulation reult according to torque or current command In the preent traction control, the acceleration and braking operation are achieved by notch command, which are the level of the torque-producing current. he appropriate notch command are determined by the driver. Only the current, i.e., torque control loop are enough for manual operation ince the driver act a a peed controller. Precie peed information i, however, till neceary in manual operation ince it i ued for vector rotation. Fig. 3(a) and (b) how the torque repone without and with the oberver, repectively. Note that the pole aignment trategy in able i implemented. It i found that the torque repone without the oberver ocillate at low peed. A a reult the electric braking cannot be implemented. On the other hand, the torque repone with the oberver ha le ocillation. Fig. 3(c) how the imulation reult due to the torque repone in Fig. 3(b). It i obviouly een that the ocilla-

24 5 Inverter 4 MG et peed (rpm) 3 (a) MG et, inverter and controlling PC 3 4 time (ec) Fig.6. Speed calculated directly from the encoder when the pule interval i. econd (equivalent to the pule condition of a 6-ppr encoder when the motor rotate at rpm) 5 (b) Encoder Fig.4 Experimental apparatu peed (rpm) 4 3 AC V Rectifier A time (ec) Fig.7. Speed etimated from the oberver when the pule interval i. econd PC Inverter IM RE DC Generator 6 5 Fixed controller gain DSP MS3C3 v&i Fig.5. Experiment etup tion doe not occur at low peed and the propoed ytem give much better braking force repone alo in the preent manual peed control than a conventional ytem. 6. Experimental Reult Variou experiment have been carried out to examine the validity of applying the oberver to the ytem. he apparatu and the experiment etup are hown in Fig. 4 and 5, repectively. Since the DC generator i ued a a load, the mechanical load become zero at low peed. hi doe not correpond to real traction, where the moment of inertia i much larger and effect of lope exit. Even though the experiment at low peed cannot be realized for thi reaon, the operating condition of the oberver at low peed can be teted by reducing the reolution of the encoder o that the correponding interval between the pule can be obtained. For intance, if we want to examine the operation at rpm by a 6-ppr encoder, we mut reduce the reolution to 6 ppr and operate the motor at rpm. For thi condition, the period between the pule i., the peed (rpm) 4 3 varied control -ler gain time (ec) peed command Fig.8. Repone when peed drop when the pule interval i. econd oberver time contant i fixed at.9 and the peed controller equivalent time contant i.68. Fig. 6 and 7 how the peed calculated directly from a 6-ppr encoder and the etimated peed from the oberver, repectively, when the motor run at rpm. It i obviouly een that the application of the oberver improve the peed information. hi alo confirm that the oberver work effectively even at the condition where the encoder pule cannot be detected frequently he experimental reult when the reference peed gradually drop are hown in Fig. 8. he peed overhoot, which will be fatal in real braking operation, can be uppreed by by reducing the controller gain a ummarized in able.

25 7. Concluion hi paper ha propoed to introduce an intantaneou peed oberver to improve the peed information epecially at low peed. Since the oberver can etimate the peed at every ampling time of the DSP, the precie peed control can be realized. he tability analyi baed on multirate ampling theory and digital control theory ha been carried out and it leaded to the concluion that fixing the oberver pole on z-plane can improve the tability at low peed. he imulation reult howed the poibility to extend the electric brake until the motor peed of rpm or.4 km/h, correponding to the vehicle peed. he validity of the oberver in critical condition where the encoder pule cannot be detected frequently wa verified through the experiment with reduced encoder pule. he application of the intantaneou peed oberver to AC traction ytem will be an effective technique olution for realizing pure electric ordinary braking of electric railway vehicle. Reference () S. Sone, Power Electronic echnologie for ow Cot and Energy Conervation on World Railway Vehicle, Proc. IPEC-okyo, vol., pp , () Y. Hori, Robut Motion Control Baed on a wo- Degree of-freedom Servoytem, Advanced Robotic, vol.7, No.6, pp , 993 (3) Y. Hori, K. Ohnihi, Applied Control Engineering, Maruzen, pp (In Japanee) (4). Kovudhikulrungri,. Koeki, Speed Etimation of Induction Motor in ow Speed for Pure Electric Brake, ranportation, Electric Railway and inear Drive Conference, pp.9-4, Sapporo, July, (5) M. Araki, K. Yamamoto, Multivariable Multirate Sampled-Data Sytem: State-Space Decription, ranfer Characteritic and Nyquit Criterion, IEEE ran. Automatic Control, vol. AC-3, pp.45-54,986 (6). Kovudhikulrungri,. Koeki, Stability Analyi of an Intantaneou Speed Oberver for an Induction Motor with a ow-reolution Encoder, J-RAI, Kawaaki, Dec., ilit KOVUDHIKURUNGSRI (Student Member) wa born in Bangkok, hailand on the 7th September 977. He received a mater degree in electrical engineering from the Univerity of okyo in and i preently a Ph.D. tudent in the ame univerity. Hi reearch field are electric drive, control ytem and railway engineering. akafumi KOSEKI (Member) wa born in okyo on the 9th July 963. He received a Ph.D. degree in electrical engineering from the Univerity of okyo in 99 and i preently an aociate profeor at the Department of Information and Communication, the Univerity of okyo. He i tudying application of electrical engineering to public tranport ytem, epecially, to linear drive, and analyi and control of traction ytem.