Modeling and Control of SRM in Electromechanic Brake System

Transcription

1 Modelng and Control of SRM n Electromechanc Brake System Wenzhe u, Ph.D. student Al Keyhan, Advsor Mechatroncs aboratory Department of Electrcal and Computer Engneerng The Oho State Unversty

2 Agenda I. Proect Goal and Obectves II. Publcatons III. Modelng and Parameters Identfcaton of Swtched Reluctance Motor (SRM IV. Sensorless Control of SRM V. Four-quadrant Torque and Force Control 2

3 I. Proect Goal and Obectve ( Overall proect goal: Develop and mplement a low-cost drve system consstng of a sensorless swtched reluctance motor (SRM wth power converter and controller. Ths drve system shall be operated as part of an electro-mechancal brake system for the purpose of convertng a clampng force command nto a physcal clampng force. 3

4 Proect Goal and Obectve (2 Obectves:. Four-quadrant operaton 2. Desred clampng force response 3. Torque rpple mnmzaton 4. Elmnaton of rotor poston sensor 5. Elmnaton of clampng force sensor 6. Hgh performance, low cost 7. Fault tolerance 4

5 II. Publcatons. Wenzhe u, Al Keyhan, Abbas Fardoun, Neural Network Based Modelng and Parameter Identfcaton of Swtched Reluctance Motors, IEEE Transactons on Energy Converson, Vol. 8, No. 2, June, Wenzhe u, Al Keyhan, Harald Klode, Amulu Bogdan Proca, Modelng and Parameter Identfcaton of Swtched Reluctance Motors From Operatng Data Usng Neural Networks, Internatonal Electrc Machnes and Drves Conference, Madson, Wsconsn, June -4, Wenzhe u, Al Keyhan, "Sensorless Control of Swtched Reluctance Motors Usng Sldng Mode Observers ", Internatonal Electrc Machnes and Drves Conference, Cambrdge, Massachusetts, June 7-2, 2 5

6 III. Modelng and Parameters Identfcaton of SRM Inductance Model of SRM Parameter Identfcaton from Standstll Test Data Parameter Identfcaton from Operatng Data 6

7 Standstll SRM Model R R( ( θ, 7

8 Flux nkage As a Functon of Phase Current and Rotor Poston 8

9 Phase Inductance of SRM ( Usng Fourer seres to represent phase nductance (θ, a θ k θ ( n a n θ, n u ( θ, m k θ ( cosk k N r θ θ 9

10 Phase Inductance of SRM (2 Three-term Inductance Model (8/6 SRM θ θ+ + θ 2 cos ( cos6 ( (, ( cos(2*3 cos(6*3 cos(2*5 cos(6* / 2 / 4 / 2 / 2 / 4 / 2 / 4 / So where ( o o ( 5 5 o o const o 3

11 Phase Inductance of SRM (3 Four-term Inductance Model (8/6 SRM θ θ+ θ+ + θ 8 cos ( cos2 ( cos6 ( (, ( cos(8 *3 cos(2 *3 cos(6 *3 cos(8* 2 cos(2 * 2 cos(6 * 2 cos(8* cos(2 * cos(6 * So / 3 / 3 / 6 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 6 / 3 / 3 / 6 /

12 2 Voltage Equaton ( ( dt d dt d R dt d dt d R dt d R V ω θ where θ m k r k kn cos ( θ θ m k r r k kn kn sn (

13 3 Torque Computaton } ] ( [ sn( { } ] cos( ( [ { } ], ( [ {, ( θ θ θ θ θ θ θ m k k r r m k r k c d kn kn d kn d W T

14 Identfcaton of Inductance from Standstll Test Data ( Obtanng θ Fnte element analyss Standstll test Onlne test Basc dea of standstll test Move the rotor to a specfc poston (θ and block t Inect a voltage pulse to the phase wndng Measure the current generated n the phase wndng Select a model structure and use maxmum lkelhood estmaton (ME to estmate phase parameters 4

15 Identfcaton of Inductance from Standstll Test Data (2 System Model Structures X(k & Y(k + + A( θ C( θ s s X(k + B( θ X(k + + v(k s u(k + w(k X[ ] Y[] u[v] θ s [R, ] w: process nose v: measurement nose 5

16 Identfcaton of Inductance from Standstll Test Data (3 Maxmum kelhood Estmaton nput u phase wndng to be estmated output y estmated parameter R, phase wndng model estmated output _ + error maxmum lkelhood estmaton 6

17 Expermental Setup wth dspace DS3 7

18 Pctures of Test-bed ( Complete Expermental System 8

19 Pctures of Test-bed (2 8/6 SR motor wth ROC 42 Sngle-turn Rotary Encoder 9

20 Pctures of Test-bed (3 Flexble Power Converters 2

21 Pctures of Test-bed (4 PC runnng dspace ControlDesk and Matlab 2

22 Standstll Test Results ( Standstll Test Voltage and Current Waveforms 3 I (A 2 estmated actual Voltage (V x tme (s x -3 22

23 Standstll Test Results (2 Inductance at algned poston 6 x -3 5 nductance at theta deg test data curve-fttng

24 Standstll Test Results (3 Inductance at unalgned poston x -3 nductance at theta 3 deg test data curve-fttng

25 Standstll Test Results (4 Inductance at mdway poston 2.8 x nductance at theta 5 deg test data curve-fttng

26 Standstll Test Results (5 Inductance under dfferent currents at dfferent rotor postons 26

27 Standstll Test Results (6 Flux lnkage 27

28 28 SRM Model for Onlne Operaton ( Model Structure V R R R R d d d d & &

29 29 SRM Model for Onlne Operaton (2 State Space Representaton DU CX Y BU AX X + + & [ 2] X 2 Y + U [V ] d d d d R R R R A d d B D ] C [

30 3 SRM Model for Onlne Operaton (3 Torque Computaton } ] ( [ sn( { } ] cos( ( [ { } ], ( [ {, ( θ θ θ θ θ θ θ m k k r r m k r k c d kn kn d kn d W T

31 SRM Model for Onlne Operaton (4 2-ayer Recurrent Neural Network 3

32 SRM Model for Onlne Operaton (5 Applcaton of Neural Network to Estmate Rd and d After the neural network s traned wth smulaton data (usng parameters obtaned from standstll test. It can be used to estmate exctng current durng on-lne operaton. When s estmated, the damper current can be computed as 2 and the damper voltage can be computed as V 2 V R then the damper resstance R d and nductance d can be dentfed usng output error or maxmum lkelhood estmaton. 32

33 Model Valdaton ( Model valdaton wth operatng data Current Response n Phase A - cov me a sure d curre nt (A e stma te d curre nt (A measured voltage (V tme (s Curre nt Re s ponse n P ha se C - cov me a sure d curre nt (A e stma te d curre nt (A measured voltage (V tme (s Current Response n Phase B - cov measured current (A e s tma te d curre nt (A measured voltage (V tme (s Current Response n Phase D - cov measured current (A e s tma te d curre nt (A measured voltage (V tme (s 33

34 Model Valdaton (2 Model valdaton wth operatng data 25 Current Response n Phase A measured current (A estmated current (A measures voltage (V tme (s 34

35 IV. Sensorless Control of SRM Drves Inductance-based analytcal model of SRM Sldng mode observer based sensorless controller Sensorless control at near zero speeds Sensorless control at standstll Conclusons 35

36 Sensorless Control System of SRM Why Sensorless To enhance relablty, and reduce sze and cost of the system To cope wth harsh ambent condtons dctated by the applcaton What s an optmal Sensorless scheme No extra hardware/sensors Good resoluton/accuracy over the entre speed rang 4-Q capablty n Motorng/generatng operaton What are typcal problems facng Sensorless technology n SRM drves Poor dynamcs durng startup, Startng hestaton mted speed range Falure at super hgh speeds 36

37 Sldng Mode Observer ( Sldng mode observer based controller Controller V SRM SRM model + _ I Î Observer θˆ ωˆ Note: The controller uses estmated θˆ and ωˆ n ths case 37

38 38 Sldng Mode Observer (2 System dfferental equatons (I dt d ( dt d R dt d R V ω θ λ + R V dt d ω θ V g f dt d,, (,, ( ω θ ω θ + ( Or, to smplfy,,, g( + ω θ R,, ( f + ω θ ω θ where

39 Sldng Mode Observer (3 System dfferental equatons (II dθ ω dt dω dt J [ T T ] f ( X, θ, l 2 ω (2 (3 m where f2( X,, ω [ T Tl ] T Tl θ and [,,...] J J X 2 Equatons (~(3 form the system dfferental equatons. 39

40 Sldng Mode Observer (4 Defnton of sldng mode observer dˆ f ˆ ˆ + g ˆ ˆ ( ˆ, θ, ω ( ˆ, θ, ω V dt dθˆ m ˆ ω + sgn( ( î dt m d ˆ ω f ( ˆ, ˆ, ˆ ( ( ˆ 2 X θ ω + 2sgn dt ˆ where θ,î, ˆ ω are the estmatons of θ,, ω. (4 (5 (6 4

41 Sldng Mode Observer (7 Smulaton results of sldng mode observer based controller RPM, e θ <2 o e ω <.5RPM actual rotor poston estmated rotor poston theta (o speed (RPM actual rotor speed estmated rotor speed tme (sec 4

42 Sldng Mode Observer (8 Smulaton results of sldng mode observer based controller 2RPM, e θ <2 o e ω <2RPM actual rotor poston estmated rotor poston theta (o speed (RPM 5 actual rotor speed estmated rotor speed tme (sec When speed s below 2 RPM, the error becomes sgnfcant. 42

43 Sensorless Control at Near Zero Speeds ( Inductance model based sensorless method V R + ( + d dt + ω θ The last tem n above equaton can be omtted at near zero speeds. So we get (V R + d (7 dt 43

44 Sensorless Control at Near Zero Speeds (2 Determnaton of turn-on and turn-off poston When a phase s on, compute the value of left sde of equaton (7 at two specal angles: f(θ on +π/2n r and f(θ off At any tme, compute the rght sde of Eqn(2 approxmately by: g (V R t If g matches f(θ on +π/2n r, then turn on next phase; If g matches f(θ off, then turn off current phase. 44

45 Sensorless Control at Near Zero Speeds (4 Smulaton results (3 RPM swtchng sgnal Angle Desred (o Actual(o Error A B C D theta (o θ ona θ offa θ onb θ offb θ onc.5.5 θ offc θ ond θ offd When speed s below 2 RPM, the error s acceptable. 45

46 Sensorless Control at Standstll ( Determne rotor poston at standstll by applyng short voltage pulse to each phase. Apply a short voltage pulse to phases sequentally. Measure the peak current value generated n each phase. Determne the swtchng sgnals by comparng peak current values. 46

47 Sensorless Control at Standstll (2 Current waveform at dfferent rotor poston At dfferent rotor postons, the phase currents have dfferent peak values when excted by a voltage pulse θ o Ia Ib Ic Id θ o Ia Ib Ic Id θ2 o Ia Ib Ic Id x x x θ3 o Ia Ib Ic Id θ4 o Ia Ib Ic Id θ5 o Ia Ib Ic Id x x x -4 47

48 Sensorless Control at Standstll (3 Peak currents at dfferent rotor postons By comparng the peak values of phase currents, a specfc rotor poston regon can be determned. peak current when excted by 6µs pulse nput B,C C C,D D D,A A A,B B phase A phase B phase C phase D

49 Sensorless Control at Standstll (4 Determne swtchng sgnals by comparng peak values of phase currents: Peak Currents I c >I d >I b >I a I d >I c >I a >I b I d >I a >I c >I b I a >I d >I b >I c I a >I b >I d >I c I b >I a >I c >I d I b >I c >I a >I d I c >I b >I d >I a Rotor Poston [ o, 7.5 o ] [7.5 o, 5 o ] [5 o, 22.5 o ] [22.5 o, 3 o ] [3 o, 37.5 o ] [37.5 o, 45 o ] [45 o, 52.5 o ] [52.5 o, 6 o ] Phases to be excted B, C C C, D D D, A A A, B B 49

50 Sensorless Control - Conclusons An nductance model of SRM can be used to desgn sensorless controller for full speed range. When speed s above 2RPM, a sldng mode observer based sensorless controller can yeld satsfactory results. At near zero speeds s, the turn-on poston for next phase and the turn-off poston for current phase can be determned by matchng nductances. At standstll, rotor poston can be estmated by applyng voltage pulses and comparng peak current values. 5

51 V. Four Quadrant Torque and Force Control of SRM for EMB 5

52 4-Q Torque and Force Control n EMB System Usng SRM ( System structure F cmd Controller swtchng sgnal Inverter V,I SRM T,θ Plant F θ, ω Observer Four-quadrant operaton Force control and torque rpple mnmzaton Sensorless operaton (no rotor poston sensors 52

53 4-Q Torque and Force Control n EMB System Usng SRM (2 Two control loops + torque control Outer loop: force control (PID Inner loop: current control (Hysteress Fcmd Force control (PID Tcmd Torque control Icmd Fcl SRM and Brake system V I Current control (Hysteress θ, ω Observer 53

54 4-Q Torque and Force Control n EMB System Usng SRM (3 Smulnk Model of the EMB System 54

55 4-Q Torque and Force Control n EMB System Usng SRM (4 Torque Control and Torque Rpple Mnmzaton Because the phase torque n SRM s dscontnuous, to generate a rpple-free resultant torque, there must be overlap between phases. It s mportant to determne how the torque s dstrbuted n phases durng phase overlap. Torque factor f(, θ s defned here to represent the torque dstrbuton among phases: T N T N f ( θ T ref 55

56 4-Q Torque and Force Control n EMB System Usng SRM (8 Choce of Torque Factor for 8/6 SRM:.2 Torque Fa c tor.8 A B C D theta

57 4-Q Torque and Force Control n EMB System Usng SRM (9 Steps to determne reference current for each phase:. Compute the torque factors for all phases accordng to current rotor poston and turnngon/turnng-off angles ; 2. Compute the desred torque T for each phase by multplyng the T ref wth correspondng torque factor; 3. Compute reference current I for each phase to generate desred torque. 57

58 4-Q Torque and Force Control n EMB System Usng SRM (3 Smulaton result clampng force response 25 Force (N tme (s

59 4-Q Torque and Force Control n EMB System Usng SRM (4 Smulaton result torque-speed curve 6 4 w (rad/s T (Nm

60 4-Q Torque and Force Control - Conclusons SRM n EMB needs 4-quadrant operaton. Inductance model and pre-defned torque factor can be used for torque control and torque rpple mnmzaton. Desred clampng force response can be obtaned by applyng force control + torque control + current control n EMB system. 6