Section 7 - Controllers for drive systems

Transcription

1 Secton 7 - Controllers for drve systems

2 Structure of a typcal drve control system Controllers Power Input Power Converter T,, Motor Load 2

3 Sensors n Electrc Drve Systems Current sensors: Resstve shunt, Hall probes, GMR and AMR sensors Speed sensors: DC tacho generators, optcal and magnetc encoders (ncremental and absolute types), synchro resolvers Poston sensors: Resstve sensors, optcal and magnetc encoders (ncremental and absolute types), synchro resolvers Torque and rotor flux sensors: Sensors based on sgnal processng of voltage and current waveforms. 3

4 Resstve shunt current sensors Man dsadvantages of resstve shunt sensng: lack of solaton from power lnes; the shunt may float at lne potental, temperature senstvty (for resstve flament), nductance of the flament (for wre wound element), need for dfferental amplfers wth hgh common mode rejecton rato (CMRR). 4

5 Hall Current sensors Open loop These sensors are solated from supply lnes. Closed loop The closed loop verson regulates the Hall voltage to zero by closed loop control. The current through a col s contnuously regulated for ths to occur. Ths sensor s easly scalable and requres lttle compensaton for temperature. 5

6 Speed and poston sensors Analogue tacho generators: these speed sensors are small commutator DC or AC machnes wth PM exctaton. Suffers from nose whch requre flterng. Dgtal speed and poston sensors: Synchro Resolvers, optcal and magnetc encoders. Sensors based on sgnal processng of voltage and current waveforms. 6

7 Magnetc Resolver Speed and poston sensors V V snt R m HF sgnal suppled to rotor va a rotary transformer. s m s2 m 2 V V K sn sn t V V K cos sn t Identcal stator wndngs, 90 dsplaced. K and K 2 are equal. Magnetc resolvers are more robust Angle s arbtrary. mechancally than optcal sensors 7

8 Synchro resolver to dgtal converter R 2 S 3 S 24 Speed Count Clockout Drecton 8

9 Incremental encoders 9

10 Up to 4x encoder pulse frequency can be counted n a up-down counter. Two-complement addton over a samplng duraton gves the speed. The z-pulse synchronzes the count to absolute poston readng. Codng of the count s mportant. Incremental Encoder nterface 0

11 Absolute encoders MSB track 4 bt Absolute encoder dsc 0 bt Absolute encoder dsc There are as many LED+recever dode channels as the number of bts/tracks. Each channel must have collmated lght sources. Incremental encoders are thus cheaper. Top frequency lmted to about 300kHz. Magnetc encoders are becomng avalable. LSB track

12 An elementary poston control system + a e K c e G I F m GB J L e o N: + Assume that the motor s drven by a current source; no speed loop. T em K T a a Ge ' e K e e K c o c 2 d m dm T 2 T em J J T dt dt 2 d 2 dt K T a J N d d dt n n 2 2 n dt T KTGe J N T 2

13 2 ' KGK T c n fn n JT N Stay awake questons:. Why can t the drve settle at the desred poston? 2. Whch parameters of the motor, load and controller determne the undamped natural frequency? 3. How to damp the oscllatons? 3

14 Vscous dampng Underdamped Motor + GB Good Vscous Couplng, D L 2 d m dm ' em T 2 T c + T J D K GK dt dt J 2 ' d d KGK T c D dt dt N T 2 2 d D d n T n Overdamped dt J dt t The requred vscous dampng D may prove costly, bulky and neffcent. 4

15 Error due to load torque T L and vscous dampng D L T N L T Lm ; 2 ' d d T K GK J D K dt dt N N Lm T c e ; T 2 e K GK N ' K T c ; 2 d e d e TLm 2 e JT D K dt dt N d dt d 2 2 e 2 2 dt d ; dt d dt e In the steady-state when transents have ded down, TLm Ke N T T T Lm L L e 2 ' ' NK N KTGK c / N NKTGKc 5

16 Poston loop dampng va speed feedback + e e o K c e G e 3 = K 3 m I F a m, m T GB N: J L + ' c 3m m ' e K K ; 2 d d JT K 2 K K ; dt dt 2 d ' T T c 2 T c 3m J K GK K GK K dt ' KTGKc K ; N K ' KGKK T c 3 Thus, the tacho-generator feedback serves the same role as dampng D! An nner speed control loop provdes dampng to the outer loop wthout requrng any mechancal dampng element. 6

17 Error n poston followng Wth vscous frcton D and fxed load torque T L, d d T Dd TLm dt dt N K dt NK 2 Lm JT D K 2 e; e D K e TLm NK Wth tacho-gen feedback D K T Lm o K NK Note: '. K can be arbtrarly selected va K c. K can be modfed by K When the poston reference does not move, the steady-state error s T LM /NK. wthout tacho-gen feedback e e t 7

18 Speed control + e K c e G I F a m T GB J L e 3 = K 3 m N: 2 ' d d TLm KcGKT T 2 e J D K dt dt N N e ; K GK N ' K c T ; In the steady-state, de TLm JT De Ke D ; dt N d dt de ; dt e TLm N D D K 8

19 Herarchcal cascaded drve control structure ref d/dt m T CONV M E Poston Controller Speed Controller Torque and Flux Controller Torque produces acceleraton, so a torque controller s also an acceleraton controller, whch should provde dampng to the speed controller, when t acts as the mnor loop for the speed controller. The flux controller s also a part of the torque control loop because flux affects torque drectly. 9

20 A. Proportonal Controller R Typcal controllers - R R K p e KR e K B. Transent velocty feedback controller R e e o K 3 C R R R K c e E K c K 3 scr scr 20

21 C. Phase advance or error rate feedback (lag lead)controller C R e = K e o = K R C R 2 K c R R e R R 2 RCs RCs D. Integral Controller R e = K R e o = K R K c C e E K c R sc R 2

22 Role of the nner current (torque) loop * * Converter Speed Controller Current ampltude & rate lmts Current Controller The nner loop enables torque to be controlled drectly. It smplfes the speed controller desgn. A contnuous current controller, beng an acceleraton controller, provdes dampng for the speed loop. Current lmts (both n ampltude and rate) can be exercsed easly through the current controller, thus also lmtng the maxmum current that flows through the motor armature for all condtons of operaton, ncludng stallng. 22

23 Converter delays Swtchng delay t s manly determned by the converter swtchng frequency. 0 msec for -phase, fully controlled thyrstor brdge converter (50 Hz supply) 3.3 msec for 3-phase, brdge converter (50 Hz supply) 00 sec for a bpolar swtched PWM converter wth swtchng frequency of 0 khz. e c2 e c T OFF T ON T OFF T s 23

24 Representaton of swtchng delay T d T e 2 s c d Ke Ts v dc Ts d Ke K T s d K T s d e c K V a / K E T st a st d s m 24

25 Current controlled DC motor drve For a very hgh gan current controller, I a = I aref /a, overcomng the speed dependent dsturbance, E a. Wth what penalty? Bandwdth lmtaton s desrable. 25

26 Current controller desgn for a DC machne I aref + Current Controller + Power Supply Conv + sta I a E a V a / R a I a E a 0,.e., stalled condton, s used for desgnng the current controller. Why? What s voltage compensaton? Voltage compensaton based on speed offers fast (more precse or accurate) current response durng the transent case. Current controller desgn for SM and IM? What replaces T a? 26

27 Current loop desgn va transfer characterstc (Bode dagram) Assumng operaton n the stalled condton, Controller+converter Ia ; I st aref ; T T s / Ra Ts st Ts 2 a Stalled armature /(R a T 2 ) = /T ; T = T a results n closed-loop control bandwdth of. I aref + Current Controller + Converter V a / Ra st a I a I a I aref + Ts I a I aref I a G GH st I a 27

28 Current controller desgn va Bode dagram Gan db 0 TF wthout current controller / Ra st a 0 Current controller, G(c) (PI wth a flter) G c ( s ) o st s st F OLTF of the current control loop 0-20db/dec CLTF of the current control loop /T a /T F = /T rad/sec = 628 rad/sec - 40db/dec 2 f s rad/sec =2π 300 log Current controller desgn wth desred BW = 00Hz (628 rad/sec) 28

29 Other desgn ssues The flter cut-off frequency /T F swtchng frequency. should be 4 tmes below the For PWM converter drven motor, the current sensng should be PWM synchronsed n order to avod the converter delay of /2T s. Feedforward of estmated back-emf (voltage compensaton) s often used for mprovng dynamc response; t has some stablty ssues though, because of the postve feedback. 29

30 Example: PI controller wth ant wnd-up V = KS * ERROR + I U = IF ABS(V) > IMAX THEN IMAX * SIGN(V) ELSE V NI = I + KS * ERROR * H / TIS + U - V TS = T + H R t f v t e t e t dt c rr rr R 0 CfR 30

31 Speed reference Wthout wnd up Wth wnd up 3

32 Current controllers for machnes contd. Feld current controller desgn for a DC machne s smlar for a control, except that there s no back-emf as dsturbance n the feld crcut. For AC machnes: Smlar desgn rules for q, as for a control for DC machnes. The back-emfs n d-and q-axes are taken as dsturbances, so desgn s for stalled or zero back-emf condton, as for a DC machne. Under the condton for RFOC, there s no back-emf n the rotor d- axs (see eqns and ). 32

33 Speed controller desgn va Bode dagram The purpose of the speed controller s to regulate the speed of the drve close to the speed reference. to follow a specfed speed profle closely. Assume that a current controllers exsts wth I a Iref Ts I ref wthn the speed control bandwdth. ref G s (s) Ts I a T em K T Js T fb Speed Controller K g 33

34 Speed controller desgn Assumng I a = I ref,.e., for operaton wthn the speed control BW, ref + G s (s) Ts Ts T s 2 Fs I aref Ts I a K T T em J s T fb K g G(s) K /J s G (s) K K / J s fb s T T ref s T g T 34

35 Example: Speed controller desgn example va Bode dagram Gan db 0 TF wthout speed controller = /T KK T g J s Ts T 0 40 db/dec Speed controller, G s (s) OLTF of speed control loop G c st ( s ) s st o F 0 CLTF of the speed control loop s Desred Speed Control BW /T Fs log 35

36 Smplfed representaton and control of a drve wth nner torque/current loop Assumpton: The nner current loop overcomes the dsturbance of back emf and delvers regulated current(s) to the motor. Ths loop s assumedtohaveabandwdth/t whch s much hgher than the electro-mechancal system. I I Ts ref + Z C (s) - T Lm (s) R R f G A (s) (converter + motor) T G L (s) (Load) Controller H F (s) (Flter) H T (s) (Sensor) 36

37 E (s) + R f /R - /R f Z C (s) G A (s) G L (s) H F (s) H T (s) E (s) + R f /R - G C (s) G A (s) G L (s) H T (s) H F (s) G (s) fb G ( s ) G(s) st st st st K 2 K st st st 3 2 s 4 where T s = T 3 + T

38 DC motor drve wth nerta and frcton (T 2 = J T /D, /T = current loop bandwdth); and neglgble fxed load torque G c ( s ) s o s s 2 s s F F 2 PI controller wth flter Usng Kessler s crteron: T, 2 T 2 and o 2KT s G(s) G(s)G (s) c (s) G 2sT st fb * 2 (s) G 2sTs 2s Ts s s *(t) (t) fb 2T t s (t) 2 e sn 2T 4 t s 4.7T s t 38

39 DC motor drve wth neglgble frcton and fxed load torque. (/T 2 s the current loop bandwdth) G ( s ) st K st st 2 s G c ( s ) s o s s 2 s s F F 2 Usng Kessler s crteron: 4 T, T, s 2 2 o 8KT T s () s 4sT s * () s 4sTs 8s Ts 8s Ts 39

40 Poston controller To move the load to the desred poston wth specfed dynamcs. To follow a movng reference wth specfed followng error. To hold the reference poston wth a specfed T- characterstc (the so-called stcton characterstc, or the S curve). The nner speed control loop provdes dampng for the poston control loop. 40

41 Desgn of a poston controller Ts J s T s 4

42 OLTF G ( s ) (s) (s) ref p K H(s)G(s) p H(s) s Kp H(s)G(s) s s A. Va G(s) compensaton n the poston feedback path G s T (s) T T (s) >> T 2 for lead-lag 2 The controller parameters must be chosen such that the poston loop has suffcent phase-lead (margn) for stablty. 42

43 B. Va H(s) compensaton wth flter n the speed feedback path Wth a hgh-gan speed controller H(s) K F(s) g T s K g F s T s Thezero(+T s),whchsactuallythepolenf(s), provdes for the desred level of phase-lead (margn) for the poston controller. However, the addtonal flter lag n the speed controller may lead to stablty problem wthn the speed controlled system. The End 43