HW5_sol

HW5_sol - ME576 #5 Solution 1.Bollinger3.16. Cn = 4 (1 )(1...

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ME 576 #5 Solution 1. Bollinger 3.16. () ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) nn 1 n n n n 2 2 41 1 0 .5BB C S 1 B 1 B 2 1 B 1 0.5B where =e m 1 0.5B 1B a. r =2S 21 C r 1 B 1 B 2 1 B 1 0.5B 1.264B 1 0.5B 1.264B 0.632B 1 0.104B 0.264B e δ δδ −− = + = ∴= + == 2 234 n 2 1 0.104B 0.264B b. 2.518B(1 0.5B) C 2.518B B 0.561B 0.206B .... 1 0.104B 0.264B + + -4 -3 -2 -1 0 1 2 3 4 0123456 Time Series1
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() ( ) ( ) ( ) ( ) ( ) ( ) ( ) n n n n nn n p nnn 1 c. From part (a) 2 1 1 0.5B B 11 B C 2 1 B 1 0.5B r 1 1B 1 B 2 1 1 0.5B C e1 B 1 B 2 1 1 0.5B B 1 B CC e G( ) m e m 1 B 1 B 1 0.5B 21 B 21 1 B z δ δδ −− = + ∴= == ⋅= 1 T 1 1 t 1 - 1n n - 1 pI p I p Corresponding continuous model. ( ) 2 ( ) where =e e e ( =1) Controller m -m =e -0.5e 1 0.5B or K+KT KB KT PI controller K + T=1 z dc t ct mt dt τ δτ += = p I K +K =0.5 K =0.5 K =0.5
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2. Bollinger 12.1 () 1 p 2 1 1 2 1 1 1 -1 c cp 1 -1 c 1 c -1 cc 1 200 G(z ) 1 200T 1 1 200 1 200 G(z) G (z)G ( ) 1 G( ) 200 1 G( ) 1 1 200 For T=0.5 100 100 ( ) 1 1 100 1 100 Ch zZ s z z z z z Kz z z zK z z z z z z K ⎡⎤ =− ⎢⎥ ⎣⎦ Τ = Τ⋅ == Τ= = +− Τ ΚΚ = −− ⋅ −− 1 c pc 0.5 T 0.4
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HW5_sol - ME576 #5 Solution 1.Bollinger3.16. Cn = 4 (1 )(1...

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