Homework 1 Automatic control System
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Homework 1 1 Homework 1 Problem 1 Known the differential equations of a system () rt denotes input. () ct denotes output. 1 () x t , 2 () x t and 3 () x t are intermediate variables . 1 K , 2 K , 3 K , 1 T , 2 T are all constants . All initial conditions are zero. Draw the block diagram and find transfer function of the system. Problem 2 Find the transfer function of the system shown in Fig.problem2 (block diagram reduction) Fig.problem2 1 2 1 2 1 1 3 2 3 2 2 3 () () () () () () () () () () () () xt rt ct dx t T x t Kxt dt x t x t Kct dc t T ct Kx t dt G 1 G 2 G 3 G 4 R C
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Automatic control System
Transcript of Homework 1 Automatic control System
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Homework 1
1
Homework 1
Problem 1
Known the differential equations of a system
( )r t denotes input. ( )c t denotes output.
1( )x t , 2 ( )x t and 3( )x t are intermediate variables .
1K , 2K , 3K , 1T , 2T are all constants .
All initial conditions are zero.
Draw the block diagram and find transfer function of the system.
Problem 2
Find the transfer function of the system shown in Fig.problem2 (block
diagram reduction)
Fig.problem2
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21 2 1 1
3 2 3
2 2 3
( ) ( ) ( )
( )( ) ( )
( ) ( ) ( )
( )( ) ( )
x t r t c t
dx tT x t K x t
dt
x t x t K c t
dc tT c t K x t
dt
G1 G2 G3 G4
R C