0-1 Intro Control

7/25/2019 0-1 Intro Control

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0 0.2 0.4 0.6 0.8 10

50

100

posicion

posicion[rad]

0 0.2 0.4 0.6 0.8 10

50

100

velocidad

velocidad[rad/s]

0 0.2 0.4 0.6 0.8 10

1

2

3

4

corriente de armadura

corriente[A]

tiempo [s]

0 0.2 0.4 0.6 0.8 10

50

100

posicion

posicion[rad]

0 0.2 0.4 0.6 0.8 10

50

100

velocidad

velocidad[rad/s]

0 0.2 0.4 0.6 0.8 10

1

2

3

4

corriente de armadura

corriente[A]

tiempo [s]

(a) (b)


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0 0.5 1 1.5 2140

160

180

200

220

240

260

280

300

320

340

posicin xdvs x

r

posicinx

[mm]

tiempo [s]

xd(x deseada)

xr(x real)

0 0.5 1 1.5 260

80

100

120

140

160

180

200

220

240

260

posiciny

[mm]

tiempo [s]

posicin ydvs y

r

yd(y deseada)

yr(y real)

x y

140 160 180 200 220 240 260 280 300 320 34060

80

100

120

140

160

180

200

220

240

260

posicin x [mm]

posiciny[mm]

trayectoria deseada vs real

trayectoria deseada

trayectoria real


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100

150

200

250

300

350

0

50

100

150

200

80

70

60

50

40

30

20

x [mm]

Seguimiento de trayectoria en el espacio de trabajo de un robotRobot SCARA 3GDL

y [mm]

z[mm]

trayectoria del robot

trayectoria deseada

x y

z


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0 1 2 3 4 50

0.02

0.04

0.06

0.08

0.1

0.12type of road disturbance

time [s]

profile[m]


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0 1 2 3 4 5

10

5

0

5

10

body aceleration

aceleration[m/s2]

0 1 2 3 4 50.05

0.0150

0.015

0.05

0.08

body position

position[m]

0 1 2 3 4 5

0.1

0.05

0

0.05

0.1suspension deflection

deflection[m]

0 1 2 3 4 5

0.02

0.01

0

0.01

0.02

wheel deflection

deflection[m]

0 1 2 3 4 52000

1500

1000

0

500

1000actuator force

time [s]

force[N]

0 1 2 3 4 50.02

0

0.05

0.1

0.12

wheel position

time [s]

position

[m]

active

pasive

active

pasive

active

pasive

active

pasive

active

pasive


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f(t)

L[f(t)] =F(s) =

0est dt [f(t)]

= lm+

0

f(t) est dt

f(t) : f(t) = 0, t 0

+


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f(t)

Af(t)

A

L[A f(t)] =AL[f(t)]

f1(t) f2(t)

f1(

t) +

f2(

t)

L[f1(t) +f2(t)] = L[f1(t)] + L[f2(t)]


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f(t) =t t 0

L[t] =

0est t dt= lm

+

0

est t dt

= lm+

1

s2est(st+ 1)

t=t=0

= lm+

s+ 1

s2est

+

1

s2es0

(s 0 + 1)= lm

+

ss3es

+

1

s2= 0 +

1

s2

= 1

s2, s >0

s + 1

s2es

+

s >0

udv =uv vdu

xeaxdx

u = x

du = dx

dv = eaxdx

dv= e

ax

a

xeaxdx = xeax

a

eax

a dx=

xeax

a e

ax

a2 + c

= eax

a

x 1

a

+ c


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f(t) =eat

L[eat] =

0est eat dt= lm

+

0

e(as)t dt

= lm+

1

a s e(as)tt=

t=0

= lm+

1

a s e(as)

1

a s e(as)0

= 0 + 1

s a= 1

s a , s > a s > a

F(s)

s

s

s0


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u(t)

v(t)

a t

b ba

u(t)v(t)dt=

u(t)v(t)t=b

t=a b

au(t)v(t)dt

v(t) u(t)

d(uv) =udv+ vdu udv = d(uv) vdu udv = uv

vdu


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d2

dt2f(t) =

d

dt

ddt

f(t)

Ld2

dt2f(t)

= L

ddt

ddt

f(t)

=sLd

dtf(t)

d

dtf(0)

= s{sF(s) f(0)} ddt

f(0)

= s2

F(s) sf(0) f(0)

f(0) = ddtf(0) f(t) = ddtf(t)

t= 0

n

f(t)

Ldn

dtnf(t)

= snF(s) sn1f(0) sn2f(0) . . .

. . . sfn2(0) fn1(0)


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f(t) = cos at, sen at

f(t) =

cos at

L[cos at] = ss2 +a2

f(t) =

sen at

L[sen at] = as2 +a2


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f(t)

F(s)

L1

F(s)

L1[F(s)] =f(t) = 12j

c+jcj

F(s)estds, para t >0

c

F(s)

j

c

f(t)

f(t)


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1

s( s + 1) =

A

s+

B

( s + 1)

1

s2( s + 1) =

A

s +

B

s2+

C

( s + 1)

1

s2( s + s + 1) =

A

s+

Bs +C

( s + s+ 1)

A B C


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x=Cest


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mx+ kx = 0

m

k


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x(t) =A1 cos nt+ A2 sen nt,

A1 A2

x0 x0 t= 0

x(0) = A1=x0,

x(0) = nA2= x0.

A1=x0 A2= x0/n

x(t) =x0 cos nt +x0

n

sen nt,

x(t) =xm sen(nt ),

xm = x20+ ( x0x0n

) Amplitud [m, in, ft]

= tan1( x0

x0n) Angulo de Fase

n = 2

nPeriodo [s]

f = 1

n=

n

2 F recuencia [Hz]


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mx+kx = 0,

L{mx} + L{kx} = 0,

m[s

2

X(s) sx0 x0] +kX(s) = 0,(ms2 + k)X(s) = msx0+mx0,

X(s) = msx0+mx0

ms2 + k ,

X(s) = sx0

s2 + km+

x0

s2 + km

L1{

X(s)}

= L

1{

sx0

s2 + km}+L1{

x0

s2 + km},

= x0L1{ s

s2 +2n} + x0

nL1{ n

s2 +2n

x(t) = x0 cos nt +x0n

sen nt.


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x, x

0,001 ms

x(0) = 0,1 [m]

m= 2,5 [kg] k= 300 [Nm]

0 1 2 30.1

0.05

0

0.05

0.1Posicion de la masa [x]

tiempo [s]

po

sicion[m]

0 1 2 32

1

0

1

2Velocidad de la masa [dx]

tiempo [s]

velo

cidad[m/s]

0.1 0.05 0 0.05 0.12

1

0

1

2Plano de fase

[x]

[dx]

x(t) x(t)


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F(t) =F0 cos nt

mx+kx=F0 cos t.

xh

xp

xh(t) =C1 cos nt +C2 sen nt,

n = (k/m)1/2

F(t)

xp(t)

xp(t) =Xcos t,


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X

xp(t)

X

X= F0

k m 2.

x(t) =C1 cos nt+C2 sen nt + F0

k m 2 cos t.

C1 C2

x(t = 0) = x0 x(t = 0) =

x0

C1=x0 F0

k m 2 , C2=x0n

,

x(t) =

x0 F0

k m 2

cos nt +x0

n

sen nt

+ F0

k m 2

cos nt


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x(t) =Cest,

C s

ms2 +cs +k = 0,

s1,2 = c

c2 4mk

2m

=

c

2m c

2m

2

k

m

.

x1(t) =C1es1t y x2(t) =C2e

s2t


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1

c > cc c/2m >

k/m

x(t) =C1e{+

21}nt +C2e{

21}nt


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x(t= 0) =x0 x(t=

0) = x0 C1 C2

C1 = x0n(+

2 1 + x0)

2n2 1

,

C2 = x0n(

2 1 x0)2n

2 1


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F(t) =F0 cos t

mx+cx+ kx =F0 cos t

xh

xp

xp(t) =Xcos(t )

X


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X[(km2) cos(t) c sen(t)] =F0 cos t

cos(t ) = cos t cos + sen t sen ,

sen(t ) = sen t cos cos t sen .

cos t

sen t

X[(k m2)cos + c sen ] = F0,X[(k m2)sen c cos ] = 0

X

X = F0

[(k m2)2 +c22]1/2

= tan1

c

k m2


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Date post:	25-Feb-2018
Category:	Documents
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