Motion Control Systems Chapter 1

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1 Asf Šboć Kouh Ohsh Moo Cool Syss Chp Elcochcl Syss Dycs Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P

2 Bsc us Mchcl Syss Poso locy Foc wok Mou x F F ( xx ) p p x x W F Fx x x Kc gy Pol gy ol gy xx U ( x) px Fx U ( ) ( ) U ( ) U ( ) ( ) U ( ) ( ) U ( ) E F U Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P

3 Bsc us Elccl Syss Chg cu () Pol gy Elcc pol U ( ) ξ ξ ξ U ( ) Pow P Flux lkg olg φ φ() φ Mgc gy φ ξ ξ ξ 0 0 φ φ 0 φ φ ( φ ) syss C φ Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 3

4 Ful Cocps Pcpl of s Aco fo Cos Syss l bw fx pos Aco log ph gg Γ ( ) ( ) ( ( ) ( ) ) S Γ Γ ( () () ) h cul ph k by h sys s x of S( Γ) h soluo s Eul-gg uo Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 4

5 Ful Cocps Dycs - Expl h soluo s Eul-gg uo (*) oo of boy Pol fl ( x ) U x ( x) (**) Copso of (*) (**) Fo (***) follws x x U x x x x ( x) c x c( x) U x c (***) ( x) U ( x) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 5

6 Ful Cocps Eul-gg uo 0 gg U Mchcl syss x x U ( x) Elcogc syss φ U φ U C Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 6

7 7 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Ful Cocps No-pol Dssp Focs No-pol focs Dssp focs F... F R... R s s s R F b R ; Rlgh fc.

8 Ful Cocps Coss Holoocs coss h (... ) 0 j j... Ico focs gg ulpls h cs j F λ j j... j λ j j... Eul-gg uos R F F cs j... Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 8

9 Ful Cocps Euos of Moo Pl pulo Coos Kc gy I I Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 9

10 0 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Ful Cocps Euos of Moo Pl pulo Coos Vlocs of h C of h ss y x l l 0 cos 0 s y x l l l l l l cos cos cos s s s

11 Ful Cocps Euos of Moo Pl pulo Coos slol oo kc gy ( ) ( ) ( ) ( ) ( )) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P

12 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Ful Cocps Euos of Moo Pl pulo Coos Rool oo kc gy [ ] ; 0 [ ] I I I I I I I

13 3 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Ful Cocps Euos of Moo Pl pulo Coos ol kc gy I I I A A [ ] A

14 Ful Cocps Euos of Moo Pl pulo Coos gg A U s jo U gl cos ( ) g( l cos( ) l cos( )) g ( ) g ( ) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 4

15 Ful Cocps Euos of Moo Pl pulo Coos gg A U jo gl cos( ) g ( ) U g ( ) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 5

16 Ful Cocps Euos of Moo Pl pulo Coos Euos of oo g g ( ) τ ( ) τ b b ( ) ( ) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 6

17 Ful Cocps Euos of Moo Pl pulo Euos of oo b( ) g τ A b ( ) [ b ( ) b ( )] [ g g ] g Ipu focs τ [ τ τ ] Kc gy () x R A Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 7

18 Euos of Moo Pops Kc gy.. I slo locs Rool sps.... y P f k sss.. 4 τ 4 Mo of I τ τ 3 3 τ x Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 8

19 9 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Euos of Moo Pops Kc gy Vlocs R R 3 3 I j j j A R A I A Kc gy x

20 Euos of Moo Pops Copos of uos of oo j j j j j j j j j... j k jk j k j k jk j k... b j k j j j j k b ( ) j k j k j jk ( )... k k j j k k j j k jk j k Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 0

21 Euos of Moo Pops Copos of uos of oo g U U g 0 j j g j 0 col g j... Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P

22 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Euos of Moo cs F τ g b A A A A A A b... R U g h h co R h λ λ h F

23 Euos of Moo Opol Spc Dycs Cofguo x [ x... x ] x f R Vlocy x f f R Kc gy gg x Λ( x)x ( xx ) U ( x) x x F x x Λ x x x Λ ( x)x Λ x Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 3

24 Euos of Moo Opol Spc Dycs Euos of oo x Λ x x ( xx ) U ( x) Λ x x x.. x μ( x x ) p( x) Λ x μ ( x x ) Λ ( x) x xλ... xλ F x x x x x x... Λ Λ x x x x p ( x) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 4

25 Euos of Moo Opol Spc Dycs A x Λ( x)x Kc gy c A x Λ( x) x ( ) Λ ( Λ) ( Λ( x) x μ( x x ) p( x) ) F A b( ) g τ Vlocy Foc loshp x τ F Cofguo spc Opol spc Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 5

26 Elccl Ccus Ccu ycs C R () gg Rlgh fc. Eul-gg c. R * U ( ) R R R C I () () R C Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 6

27 Elccl Ccus C Ccu ycs C C R I R () () () R C C R () Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 7

28 Elcochcl Syss Elcogc o x x x gx ( x) R R x x R x I x () x g x ( x) 0 R I () ( x) R ( ) f x * ( x) ( x) x * ( ( x) ) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 8

29 Elcochcl Syss Elcogc o Euos of oo x g x ( x) x f () R ( ( x) ) * * Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 9

30 Elccl Mch Vbls [ ] s s s... [ ]... [ ] [ ] s s s Iuccs s s cos( ) Iucc x s k ( ) s π cos ± k s s s ( ) s ( ) So xs s Roo xs Mgc cogy * ( ) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 30

31 3 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Elccl Mch gg Rlgh fc. Mchcl sys R B R () () B x τ I R

32 3 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Elccl Mch gg Rlgh fc. R B R () () R I R 0 Elccl sys

33 Elccl Mch gg Rlgh fc. R ( ) ( ) B R Dycs ( ) B ( ) R ( ) () τ x Foc τ ( ) EMF ( ) Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 33

34 34 Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Elccl Mch Dycs () B x R τ τ Foc [ ] s s s s 0 0 τ s f s f s f k k k Φ Φ Φ s ϕ τ

35 Elccl Mch Dycs ( ) B ( ) R ( ) () τ x Foc τ k Φ f s Dycs b τ ( ) τ τ ( ) s K Φ K ( Φ) s x Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P 35

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