ballbot mw Tài liệu nghiên cứ về Ballbot dành cho Học viên cao học ngành Tự động hóa

restart : with(LinearAlgebra) :

uN

\ Mb, Ro, Ib /

—N

xO = (0,(t)-n-,(t)) -R,

xB := xO + L-sin(@,(t) )

zB = R, + L-cos(8,(¢) )

xd = xO — (L,) :cos(6 (7) )

zA = R, + (L,)-sin(0,(¢) )

T:= + 'b-4I(8,(0)~n-ð,(0), t) tư ‹m, 'djƒ(xO, £) + ly „'4//(9.0); t) + Fg: (diff xB, t)?

+ diff(2B, 1)°) + > Tpy-diff( 01) +0,(1),1)” + mg: (difflxd, 1)? + difftzA, 1)”)

tu (8 90))+3((($ S0 =n(# 49))4

+ L cos(8,(¢) ) lấp 6/2) +2 sin(6,(7) } < Q(t 9Ì) + > iy ($s Ò (7)

+ < 8/9) + > m4 ((( < 9 () — "(ấy 60 }) R, +L, sin (6 () ) lấp s/2))

2

+12eos(8,(0)ˆ | < ot }

C:= M- (0,6) ) -mi'g8g'zA- m„:g-zB

Mo (t) —m,g ere _) — Mpg (R, +L cos(6 (7) ) ) (7)

thel = F 0,(4) =O, © O,(1) =a, 6 (2) =6, 6/(9 =0,|

the? = |“; 0,(4), =< (1), 4,=4,(0, 8 ,=9/(0]

ptl := collect combine simpli diff (subs (the2, diff (subs (thel, T), ©, ) ): t) — subs ( the2,

diff ( subs (thel, T), ,.) ) = subs ( the2, diff (subs (thel, C), ,.) ) ); trig), Lộ È (7), & 0 (7) |

2

(m, Rn +1,n° + m,n’ Ry +14, + myn’ R) l5 00) + (-Ln +l, —mgn R (10)

2

—m,nR,L, sin(6.(2) ) —m, Rn — mgn R,L cos(®,(t) ) —m,nR;) F 8/9]

d 0 (t ] —m,nR,L, cos(8,(t) ) lấn d 0 (t ] =M

pt2 = collect combine( simpli diff (subs the2, diff (subs (thel, T), ®, | ): t) — subs ( the2,

ăw: đˆ

diff (subs (thel, T), 9.) ) = subs ( the2, diff ( subs thel, C), 9.) ) ); trig), E Ò (7), ae 0 (t) l

(-I,n +1, —mgnR, — m,n R,L, sin(,(0)) — mụ Rộ n — mạ n Rụ L cos(6,(0) ) — mụn (11)

&) (Sa 0} + (tn +m,L +2 m,R, L cos(0,(t)) +m, Ry + mp L° +m,R, +I,

đ

df 8/9] — mz L sin(@,(t) ) lá 9 0) R,

2

2 +m, L, cos(6 (7) ) < 0 (t ] R,=-m,gL, cos(6 (7) ) + mg gL sin(@,(t) )

a (0 t); My = 5—5- 2 (600 9

#dsys:= { vl , pt2, dkd}

#dsol(15)

#with( plots)

#odeplot( dsol, l|* o,(t) › E

#odeplot( dsol, I|d¿0) D(@,) (

#odeplot( dsol, [xC, yC], t=0 15

ơ o,) (2) ||, t=0 15)

) | t=0 15, numpoints = 3000 )

Ì t=0 15)

(