模式匹配法則於分布參數控制系統設計之研究

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(3) Model Matching Controller Design and Experimental Study of One-dimensional Active Attenuation Systems in Ducts NSC 87-2218-E-009-027 86 8 1

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(7) /"0123456,(789: $;<=>?@AB:CDE F(+,:GH-.BI2JKLMNC =OPQR STU6 VWXY<=Z[( L\U]L^_F2 (Keywords: Active noise control, Parameter adaptive algorithm, Digital signal processor) In this project, an active controller design study is proposed for a one-dimensional noise attenuation system in ducts. A general model matching technique is constructed to characterize the active controller structure by block diagram framework. However, the performance of this controller degenerates due to the aging or uncertainty of sensor’s dynamics. To alleviate this influence, a parameter adaptive algorithm is designed. Finally, Experimental results realized by high-speed DSP show that PAA control is feasible in this project and effectively remedies these uncertainties.

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(26) (87)')*+,DÏü·( closed-form ÈÉÊÂ Ý x<a ÖýHþ. [G. + U. P( x, s) =. Ý x>a Ö P (x , s) =. [G. ( x, a, s) + GU− ( x, a, s). 1− θ 0 (s)θ 1 ( s)e. + D. λ2 − λ1. ( x, a, s) + GD− ( x, a, s). 1 − θ 0 (s)θ 1 (s)e λ2− λ1. ]Q. a. ( s). ] Q ( s) . a. d¶ +. GD ( x, a, s) = G−D( x, a, s) = +. GU (x , a, s) = −. GU (x , a, s) =. 1 λ ( x −a) λ x −λ a [ −e 2 + θ0 ( s)e 2 1 ] (λ1 − λ 2 )∆ 1 [θ 1(s)e λ2 (1−a) −λ1(1−x ) − θ 0 (s)θ1( s)eλ2 −λ1(1+a− x )] (λ1 − λ2 )∆. 1 λ x −λ a λ (1+ x − a)− λ 1 [θ0( s)e 2 1 − θ0 (s)θ1( s)e 2 ] ( λ1 − λ2 )∆ 1 − λ (a− x ) λ (1− a)− λ1 (1− x ) [−e 1 + θ1( s)e 2 ] ( λ1 − λ2) ∆. θ 0( s) θ1( s)

(27) !" #" + D. − D. G ( y,d , s) + G ( y, d, s) X (s) + G ( y , a, s) + G D− ( y , a , s) T2 ( s) = D X ( s) T1 (s) =.  G + ( x ,d , s) + G −D ( x1 ,d , s)   M1 ( s)   D 1  v X ( s)     = ( ) ≡ M s   G + ( x ,d , s) + G − ( x ,d , s)  D D 2 2  M 2 ( s)   X ( s)  .  F1 ( s)  v = F ( s) ≡     F2 ( s) .  GU+ ( x1 , a, s) + GU− ( x 1, a, s)    X ( s)   + −  GU ( x 2 , a, s) + GU ( x 2 , a, s)    X ( s)  . X (s ) = 1 − θ 0 ( s)θ 1 (s)e λ2 − λ1. C1(s) C2(s)

(28) e (Model Matching) !"# v v T2CT M v v =0 T1 + 1 − CT F. $%&'() *+, -.. . Ls Ls Ls Ls − (a − x1 )  . c  − c ( x2 −a ) − c ( a − x2)  c  − c ( x1−a ) e C1 + e C2 = 1 −e c −e     2Ls  2Ls   . (1).. . 3.2 /0 123 . 4(1), 5 !67. 89:;3 <= ! >?@AB (Boundary condition)9C1D EF3GH I"# Ls c. C1 (s ) =. C 2 (s ) =. −. e. Ls ( a− x1 ) c. 1−e. Ls c. e. −. −. 2 Ls (a − x1 ) c. (1 + 2Q) .. (2).. (1− 2Q) .. (3).. Ls (a − x2 ) c. 1− e. −. 2 Ls ( a− x2 ) c. JK-LM Q NOP(Causal)=>? @AB9C QRSTF3UNOP =>?@AB9CV 3.2.1 123W (2)(3)X Y Q = 2Ls C1 ( s) = c. e. −. 1− e. Ls (a− x1 ) c −. 2Ls ( a−x1 ) c. 1 Z [. 2. .. (4).. C2 ( s) = 0 .. (5). \]()[^L8W_àbcdVS _ ef \>ghijklmn op[4]V. . 3.2.2 123q YQ =. 1− e 1 −e. −. 2Ls (a −x1) c. 2 Ls − ( x −x ) c 2 1. 2 Ls C1 ( s) = c. e. −. 1− e. −. 1 Z [. 2. Ls ( a− x1) c. −. −. 2 Ls ( x2 − x1 ) c. Ls. .. (a − 2x1 + x2 ). 2 Ls e c . C 2 ( s) = − 2Ls − ( x2 − x1 ) c 1− e c. (6).. (7).. rsSt 8EuvKw xygh W r ` a b z {|}(Noise Source)| E~tps Swinbank Type tp.

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(36) . v 3.2#$ ¬Î(8) ¹. 1.Bodson,. M.,. “Emerging. Technologies. in.

(37) Control Engineering,” IEEE Control System Magazine, pp.6-8, Dec. 1995 2.Balas, M.J., 1982, "Trends in Large Space Structure Control Theory:Fondest Hopes, Wildest Dreams",IEEE Trans. Automatic Control, AC-27, pp.15-33. 3.Munjal, M.L. and Eriksson, L.J.,”Analysis of a Linear One-dimensional Active Noise Control System by Means of Block Diagrams and Transfer Functions,” Journal of Sound and Vibration, Vol. 129, No. 3, pp.443-455, 1989 4.Tichy, J., Warnaka, G.E. and Poole, L.A., 1984,” Active Noise Reduction Systems In Ducts,” ASME Journal, Nov., pp.1-7 5.Widrow, B. and Walach, E., Adaptive Inverse Control, Prentice-Hall, Inc, 1996 6.Widrow, B and Plett, G.L., “Adaptive Inverse Control based on Linear and Nonlinear Adaptive Filtering”, Proceeding of International Workshop on Neural Networks for Identification, Control, Robotics and Signal/Image Processing, Venice, Italy, pp.30-38, 1996.

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