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

1

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