Solution of Tutorial 5 Drive dynamics & control

Transcription

1 ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm D 0.73Nm / rd / s 5.3 J kgm D/J s - L s R RJ m 0.5 s KEK D n 38. rd/s m J D n 69.5 J.8 Motor 750 rev/mn = 83 rd/s rted.3nm 83 D/J 0.6s - L s R Soluton of utorl 4 Controllers for drves F. Rhmn/ October 06

2 ELEC463 RJ m s KEK D n 4.45 rd/s m J D n 6.84 J 0.47 Note tht the motor s over-dmped whle the motor s under-dmped. he nturl frequences re lrgely determned by the mechncl nd electrcl tme constnts. Queston V (s) + E (s) / R s I (s) K (s) L (s) J s D m (s) K E m s K V s sl R J sd K K E / KE J R s s KKE / K / K s s s s E E m m m () For D = 0, () G(s) / K E m m s s (3) n m 45. rd/s (4) Soluton of utorl 4 Controllers for drves F. Rhmn/ October 06

3 ELEC463 nd mn 0.85 (5) RJ where m = mechncl tme constnt of the drve. (6) K K E / K / G(s) s s s 0.07s s 49s 76 E m m Poles fter solvng s 49s 76 0 re s s 4.5 j , 0 () Drw Bode plot n log-log grph pper. 0 Bode Dgrm Mgntude (db) Phse (deg) Frequency (rd/sec) Soluton of utorl 4 Controllers for drves 3 F. Rhmn/ October 06

4 ELEC463 Queston 3 d m dm Lm J D K dt dt = lod ngulr poston = motor shft ngulr poston = N m = lod ngulr speed m = motor shft ngulr speed = N d d J N DN K dt dt Lm K K GK e K GK ( NK ) c c ref g DN K GK NK JN d c g d Lm ref c dt c c K GK K GK dt K GK Comprng the coeffcent to the nturl response, d d 0 dt n dt n KGK c n 5 rd/sec J N DN K GK NK n K GK c g For crtcl dmpng, c Kg v/rd/sec t motor shft () Followng error t 70 rd/sec, DN K GK NK d K GK dt K GK c g Lm ref c c ref DN KGKcNKg d Lm K GK dt K GK c c 8.8 mechncl rdns t the lod. Soluton of utorl 4 Controllers for drves 4 F. Rhmn/ October 06

5 ELEC463 Queston 4 he current controlled system s 00A / R s 0A 0A t = 4t t R = L = 0.03 H L 0.03 sec. R On pplcton of 00V to the stlled motor (E = 0V), wll tend to V /R = 00A. rses to 0A n tme t gven by R V t t L e e R 0 00 e 33.33t t At the hghest nput frequency to the current controller, the rmture current wveform should be the roughly trngulr wveform of fgure bove, wth the pek current just rechng 0A. he perod of the nput frequency s for ths condton s 4t. he correspondng bndwdth s f BW 79 4 t Hz Clerly, wth V hgher or lower thn 00V, the mx BW wll be hgher or lower thn 79 Hz, respectvely. For the desred condton of operton wth V = 00V, the current controller bndwdth must be lmted to 79Hz. Soluton of utorl 4 Controllers for drves 5 F. Rhmn/ October 06

6 ELEC463 Queston 5 he PI controller wthout flter wll hve trnsfer chrcterstc: s s he totl OLF s: s / R s s () Wth controller zero cncellng the rmture pole,.e., =, the totl OLF s: where R s s Gven, rd/sec R L R 0.5 he PI controller s thus G c s 0.s 0.055s Becuse the domnnt current rpple s t 600Hz, ts flter cutoff frequency s two octves below ths frequency ( thumb rule). hus the flter cut-off frequency s f f 600 / 4 50 Hz. he flter trnsfer chrcterstc s f he PI controller wth flter s thus: G c s 0.s s 0.055s 0.006s s 006s Note tht converter voltge gn ws not ncluded n eqn (). If the converter gn s 5, the G c (s) becomes G c s 39. / 5 0.s.6 0.s s 006s s 0.006s Soluton of utorl 4 Controllers for drves 6 F. Rhmn/ October 06

7 ELEC463 Queston 6 he current controller s s where 50 so tht he torque constnt of K of the motor s K 0.V / rev / mn 0. / 60.9V / rd / sec.9 Nm / A he torque controller s m s K.9.9 s s 0.003s. he speed response of the drve to current nput s gven by s K.9 0. J s 0.003s 9.55s 0.003s s 0.003s For the desred BW of Hz (=.54 rd/sec), gn of the bove trnsfer functon s.9 0 log db. he PI controller gn t.56 rd/sec s thus db (equl to the defct gn t.54 rd/sec). hus, the gn of the speed controller s K log he zero nd pole (flter pole) of the speed controller re t octves below nd bove the desred bndwdth. hus, s.56 / fs / hus, the requred speed controller trnsfer functon s s s 0.0s Soluton of utorl 4 Controllers for drves 7 F. Rhmn/ October 06

8 ELEC463 s K s s K K s J s s s K J s s Bode dgrm for Q6 Soluton of utorl 4 Controllers for drves 8 F. Rhmn/ October 06

9 ELEC463 Queston 7 Soluton of utorl 4 Controllers for drves 9 F. Rhmn/ October 06

10 ELEC463 Soluton of utorl 4 Controllers for drves 0 F. Rhmn/ October 06

11 ELEC463 Queston 8 () p = E 00 t fo rd / sec (mech) Ê 00 fo f o p 57 p 0.9 V/rd/sec (b) becuse the rotor flux lnkge d f t ll tme, therefore, d = 0. 0 Nm 3 p (c) f qs qs 0 0 qs f A (d) q 7.4 A ˆq v qs v n v bn 0 d v ds v cn ˆd ˆre dq bc s bs cs ˆre Soluton of utorl 4 Controllers for drves F. Rhmn/ October 06

12 ELEC463 Queston 9 () he rted rotor flux lnkge s V.08 Wb-t ph, pek 45 3 r dr e 50 he reference current ds for ths s.9 A dr.08 ds Lm (b) 0 Nm e L A r qs e 3pLm dr (c) For I = I rted = 5.8 =.6 A qs mx s mx ds A emx 3p Lm qsmx / Nm L dr r (d) Lm R r sl e re qs L dr r e L r m dr 3pL q ˆq v qs v n v bn dr d v ds v cn ˆd ˆe dq bc s bs cs ˆe sl RL t r m Lr d 0 e dr ˆre e ˆrm Soluton of utorl 4 Controllers for drves F. Rhmn/ October 06