Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden

Transcription

1 Poton nd Speed Control Lund Unverty, Seden

2 Generc Structure R poer Reference Sh tte Voltge Current Control ytem M Speed Poton

3 Ccde Control * θ Poton * Speed * control control - - he ytem contn to ntegrton. h gve hnt bout to properte of the ytem: h out for the tblty mrgn; ntegrtor my help to elmnte remnng error. θ

4 he mechncl ytem d dt d dt el l d dt d dt el l

5 Poton Control th P-controller θ θ p p * Poton control Speed control θ * θ * * - - pole p ± 4 Lmt for oclltory pole: p p 4 0 4

6 Poton Control Wthout Speed Control * θ - θ * θ Poton control p p p Speed control * ± Only oclltory pole! p θ

7 Speed Control Idel torque ource nd peed enng Lod orque Cloed ytem: Root: Speed ref * orque ref Speed Ctrl orque Source Speed. Inert.e. ny bnddth poble,... but then no longer true...

8 Exmple >> 0.00; >> 0.038; Select 00; h the orque Source model. It repreent the fnte reponce tme of the torque loop 't order tme contnt nd lmtton. Step Ref h the PI-controller. Exmne the content of t by openng t. Rght-clc nd elect "Look under mk". Out Act PI Controller hee to block mke up the mechncl lod, th nert nd lod torque.. orque Source Wth thee he you cn elect f the orque Source model nd / or the Speed Flter hould be engged. h the lod torque model. It behve lke contnt lod torque or lod torque tht lerly or qudrtclly proportonl to peed ccordng to the uer electon. Speed flter f. Lod orque l l h the peed flter. It reduce the dynmc performnce of the meured peed gnl. Inert 0.0; ; f0.0; p00; nf; SpeedScope

9 Concluon Idel condton led to too ft peed controller. he torque ource not ft n relty t eem n the multon. Ho to model the torque ource? Smplet: - t order tme contnt!

10 Speed Control orque dynmc frt order lo p flter Speed ref Cloed ytem: Root: Non oc. root -> orque ref Speed Ctrl * ± 4. orque Source 4 Lod orque. Inert Speed Lmted gve ttonry error th P-control!!

11 Exmple >> 0.00; >> 0.034; Select /4/ 8.5; h the orque Source model. It repreent the fnte reponce tme of the torque loop 't order tme contnt nd lmtton. Step Ref h the PI-controller. Exmne the content of t by openng t. Rght-clc nd elect "Look under mk". Out Act PI Controller hee to block mke up the mechncl lod, th nert nd lod torque.. orque Source Wth thee he you cn elect f the orque Source model nd / or the Speed Flter hould be engged. h the lod torque model. It behve lke contnt lod torque or lod torque tht lerly or qudrtclly proportonl to peed ccordng to the uer electon. Speed flter f. Lod orque l l h the peed flter. It reduce the dynmc performnce of the meured peed gnl. Inert 0.0; ; f0.0; p00; nf; SpeedScope

12 Concluon Dynmc reltc nd the control ytem tble. Wht bout ttonry error?

13 Lod torque cn be: Contnt Lner to peed Qudrtc to peed. ry th contnt 5 Nm Wht hppen? Sttonry error!!

14 Soluton : PI-control * t y t y e Control error dt e t e t t u p τ e u p τ τ

15 Dgtl PI controller k n n p n y n y k y k y k u 0 * * * nt 0 k u n y n y k n n p * nt k u k y k y k u p

16 he torque ource lmted Often peed dependent, e.g. feld ekenng orque, Flux Voltge, Poer Speed

17 Exmple 3 Ho doe the ntegrtor rect to the torque ource lmtton? Oclltory, non-tble! he problem clled ndup of the ntegrtor. he oluton clled Ant Wndup h the orque Source model. It repreent the fnte reponce tme of the torque loop 't order tme contnt nd lmtton. Step Ref h the PI-controller. Exmne the content of t by openng t. Rght-clc nd elect "Look under mk". Out Act PI Controller hee to block mke up the mechncl lod, th nert nd lod torque.. orque Source Wth thee he you cn elect f the orque Source model nd / or the Speed Flter hould be engged. h the lod torque model. It behve lke contnt lod torque or lod torque tht lerly or qudrtclly proportonl to peed ccordng to the uer electon. Speed flter f. Lod orque l l h the peed flter. It reduce the dynmc performnce of the meured peed gnl. Inert 0.0; ; f0.0; p00; nf; SpeedScope

18 Anlog nt ndup e

19 Dgtl Ant-Wndup u nt k u k end u p p f u k > u u k nt n n k 0 y * n y n y * k y k u k mx u k mx u or u k < nt k u or u k mn u nt then mn

20 Exmple 4 he controller tble nd behve ell th nt-ndup, but ho do e et the prmeter?

21 Speed Control Wth PI peed controller nd t order torque ource Lod orque Step * 3 Proportonl.. Integrtng orque ref. orque Source 3 rd order, ho do e olve for the root??. Inert Speed

22 Symmetrc optmum: Open loop trnfer functon Phe deg Mgntude db G Bode Dgrm Frequency rd/ec Select to mxmze phe mrgn

23 Symmetrc optmum: 0 here, > 0 0 j j j j j G

24 Symmetrc optmum:3 Cloe loop chrctertc equton: 0 3 One root: 0 0 Polynoml dvon gve: Other root: ζ Exmple ζ,.e. no complex pole: ± 0,3 ξ ξ

25 Exmple 5 ry out oclltory root ± 0 ξ,3 ξ ζ ξ 4 0.5

26 Noy peed gnl... A flter on the peed gnl gve 4 th order ytem. - Ho to degn?? he engneerng oluton:. Note, t not the peed, but the fltered peed tht controlled!. he flter tme contnt uully much longer thn! 3. Replce the ft torque dynmc th the lo flter dynmc nd degn th ymmetrc optmum on 3 rd order ytem.

27 Exmple

28 ht ll folk...