modeling and digital simulation- pole placement
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MSFanimation
Scope
Mux
B/M
S-Function
Step
K/M
( ) 32 ( )t u t
1
s
Sum
1
s
XY Graph
1/M Integrator2Integrator1
x1x2Displacement
Velocity
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mg
l
T
sinmg T
1
s
1( )x t1
s
B m
1sin ( )g
x tl
2 1( ) ( )x t x t 2 ( )x t
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B/m
1
s
Inte PenAnimation
Theta
Mux
S-Function
Fcn
Sum
1
s
x2 x1
XY Graph
9.81/0.613*sin(u)
Integrator2grator1
omega
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DeltaStep
x1
1 ( )u t
1
s
Sum
1
s
Gain integr 2integ 1
30
35.6*sin(u)
15*sin(u)
Saturation
x'1=x2x'2
0c
t td d
ct td d f
4
mg
l
T
u
x
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x Ax Bu
y Cx Du
Theta
x
Demux
State-SpaceIn 1
Out 1
1
2
Terminator 2
Terminator 1
Demux
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Plant
nK
( )u t
2K
1K
Plant
( )n
x t
1( )x t2( )x t
"
( )y t
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x Ax Bu y Cx Du
theta
Demux
State-Space
In 1
Out 1
1
2
Demux
(4)K
(1)K
(2)K
(3)K
( ) ( )u t Kx t
State feedback
using pole-placement design1K
2K
3K
4K
Sum
x