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HW6_sol

# HW6_sol - Homework#6 1(a 2 G p z =(1 z 1 Z 2 s s 2 1 1...

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Homework #6 1. (a) ( ) ( ) ( ) ( )( ) ( )( ) 1 2 1 1 2 1 1 1 1 1 2 ( ) 1 2 0.00937 1 0.936 0.00937 0.00876 1.819 0.819 1 1 0.819 Dead beat controlller: 1 0.819 1 ( ) ( ) ( ) 1 ( ) 0.00937 0.00876 1 p d d p d G z z Z s s z z z z z z z T z z z T z z D z G z T z z z = + + + = = + = = = + 106.78( 0.819) = 0.936 z z + (b) ( ) ( ) ( ) ( )( ) ( ) -1 -2 -1 -1 1 2 1 -1 -2 -1 -1 1 1 1 -1 -2 1 1 1 1 1 1 1 1 1 0.936 1- 1- - 0.936 1- 1 1 -1 - 1- 0.936 0.517 0.48 T z z z z z T z z z z n z n z n z n T n n α α = + = + Τ = Τ Τ = + = + = Τ = ∴Τ = = ( )( ) ( )( ) ( ) ( ) ( )( ) 1 2 -1 -2 -1 -2 2 2 3 0.517 0.483 -1 -0.819 0.517 0.483 ( ) 0.00937 0.0876 1- 0.517 - 0.483 -1 - 0.819 0.517 0.936 0.00937 0.936 0.517 0.483 55 1 0.819 55 = 0.517 0.483 a a z z z z D z z z z z z z z z z z z z z = = + = + + = + = ( ) z 1 0.819 1 0.483 z +

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2. D(z) Z.O.H. 2 5 0.00002 0.012 1 s s + + 0.1 s 0.5 ( ) ( ) ( ) ( ) p 2 p 1 p 1 2 1 1 2 3 1 d 1 5 a) G (s)= 0.0002s 0.12 10 G ( ) G (z)= 1 0.0001 1.5757 3.672 4.748 = 1 1.806 0.896 0.091 For first order response 1 T = 1 s s s z Z s z z z z z z z z δ δ + + + + + Κ ( ) 0.004 T 0.06 1 1 1 2 3 1 2 1 =e e 0.936 0.064 = 1 0.936 1 1.806 0.896 0.091 D(z)= 0.0001 1.5757 3.672 4.748 z z z z z z z z τ δ = = + + + 1 0.064 z ( ) ( ) 1 1 2 3 1 2 3 p p 1 p 2 1 1 1 0.968 1 1.806 0.896 0.091 =411 1 1.389 1.977 0.295

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HW6_sol - Homework#6 1(a 2 G p z =(1 z 1 Z 2 s s 2 1 1...

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