Embed Size (px)
DESCRIPTION
Observable Canonical Form Fri, Sept 11 EE 460 Advanced Control and System Integration Transfer Function Block Diagram State-Space Model Slide 3 of 5
Citation preview
EE 460 Advanced Control and Sys IntegrationState-Space Realizations
Fri, Sept 11 EE 460 Advanced Control and System Integration Slide 1 of 5
Controllable Canonical Form
Fri, Sept 11 EE 460 Advanced Control and System Integration
Transfer Function
Block Diagram
State-Space Model
Slide 2 of 5
1 1
2 2
3 3
0 1 2 34 4
0 1 0 0 00 0 1 0 00 0 0 1 0
1
x xx x
ux x
a a a ax x
x Ax bu
1
20 1 2 3
3
4
xx
y b b b b C xxx
3 23 2 1 0
4 3 23 2 1 0
( )( )
b s b s b s bY sU s s a s a s a s a
14 3 2
3 2 1 0
3 23 2 1 0
1
( ) 1( )
( )( ) 1
X sU s s a s a s a s a
b s b s b s bY sX s
Observable Canonical Form
Fri, Sept 11 EE 460 Advanced Control and System Integration
Transfer Function
Block DiagramState-Space Model
3 3 2 2 1 1 0 0( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0s s s sY s a Y s bU s a Y s b U s a Y s bU s a Y s b U s
Slide 3 of 5
3 31 1
2 22 2
1 13 3
0 04 4
1 0 00 1 00 0 10 0 0
a bx xa bx x
ua bx xa bx x
x Ax bu
1
2
3
4
1 0 0 0
xx
y C xxx
3 2 1 2 3 43 2 1 0 3 2 1 0
4 3 2 1 2 3 43 2 1 0 3 2 1 0
( )( ) 1
b s b s b s b b s b s b s b sY sU s s a s a s a s a a s a s a s a s
Cascade Form
Fri, Sept 11 EE 460 Advanced Control and System Integration
Transfer Function Block Diagram
1 2 3 4
( )( )Y s KU s s p s p s p s p
State-Space Model
1𝑠+𝑝1
1𝑠+𝑝2
1𝑠+𝑝3
1𝑠+𝑝4
K( )U s ( )Y s
1( )X s2 ( )X s3( )X s4 ( )X s
1( )X s
-
+
2 ( )X s
-
+
3( )X s
-
+
4 ( )X s
-
+ ( )Y sK
( )U s
1
2
3
4
1 0 0 00 1 0 00 0 1 00 0 0
pp
x x up
p K
x Ax bu
1 0 0 0y x C x
Slide 4 of 5
Parallel Form
Fri, Sept 11 EE 460 Advanced Control and System Integration
Transfer Function Block Diagram
1 2 3 4
31 2 4
1 2 3 4
( )( )Y s KU s s p s p s p s p
KK K Ks p s p s p s p
State-Space Model
1 1
2 2
3 3
4 4
0 0 00 0 00 0 00 0 0
p Kp K
x x up K
p K
x Ax bu
1 1 1 1y x C x
( )U s
1𝑠
4 ( )X s
𝑝4
-
+
𝐾4
1𝑠
1( )X s
𝑝1
-
+
𝐾1
......
...
( )Y s
Slide 5 of 5
