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

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Homework #6 1. (a) () ( ) ( ) 1 2 11 2 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 pd Gz z Z ss zz z Tz z Dz z z −− ⎡⎤ =− ⎢⎥ + ⎣⎦ + + == −+ = 106.78( 0.819) = 0.936 z z + (b) ( ) -1 -2 -1 -1 12 1 -1 -2 -1 -1 1 -1 -2 1 0.936 1- - 0.936 1 1 -1 - 0.936 0.517 0.48 z z z z z z z n z nz n z n Tn n αα =+ = + Τ Τ = + = ∴Τ = = ( ) ( ) ( ) -1 -2 -1 -2 2 2 3 0.517 0.483 -0.819 0.517 0.483 0.00937 0.0876 1- 0.517 - 0.483 - 0.819 0.517 0.936 0.00937 0.936 0.517 0.483 55 1 0.819 55 = 0.517 0.483 aa 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 ss + + 0.1 s 0.5 () p 2 p 1 p 12 1 123 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 zZ s zz z zzz z z δ −− −−− ++ ⎡⎤ ⎢⎥ ⎣⎦ −+− Κ− 0.004 T 0.06 1 1 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 τ == 1 0.064 z 1 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 1T ( ) D(z)= G (z) 1 0.5 0.5 b) G ( ) 0.5 G ( ) 1 0.002 = 1 z z z s s Z s z z +−− ⎛⎞ ⎜⎟ −Τ ⎝⎠ = =− 11 1 1 1 0.064 D 0.002 1 0.968 1 32 1 0.968 z z Ζ =⋅ =
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3.
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This document was uploaded on 12/28/2011.

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

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