lecture_2_3

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Mechanical Engineering Department Automatic Control Dr. Talal Mandourah 1 Lecture 2 & 3 Automatic Control Laplace Inverse Theorem To solve linear ODE: 1- Laplace transform ODE to s-domain 2- Solve output variable. 3- partial fraction expansion. 4- Inverse Laplace transform. Example 1: . . ,.. 2 ) 0 ( ,.. 1 ) 0 ( 5 2 3 C I y y U y y y s 1) Laplace transform: s s Y y s sY y sy s Y s 5 ) ( 2 )] 0 ( 3 ) ( 3 [ )] 0 ( ) 0 ( ) ( [ 2 U s =step function 2- Solve for output ) 2 )( 1 ( 5 ) ( 5 ) ( ) 2 3 ( 5 1 ) ( ) 2 3 ( 5 1 ) ( 2 ) ( 3 ) ( 5 ) ( 2 ) ( 3 2 ) ( 2 2 2 2 2 2 s s s s s s Y s s s Y s s s s s s Y s s s s s Y s sY s Y s s s Y s s sY s s Y s

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Automatic Control

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Senior Project Guidelines2- Solve output variable.
3- partial fraction expansion.
4- Inverse Laplace transform.
Mechanical Engineering Department
[r,p,k]=residue(num,den)
[r,p,k]=residue(num,den)
Printsys(num,den,’s’)
r = -6.0000
Find zeros and poles of:
num=[0 0 4 16 12];
den=[1 12 44 48 0];
[z,p,k]=tf2zp(num,den)
z = -3