TEORI KONTROL OPTIMUM

Transkripsi

1 EO KONOL OPMUM UG Oleh N PY NM : 6 Pogm td Mtemt NU EKNOLOG NDUNG 9

2 .-5 Como of Dffeet Dete Cotolle, 8. Fd the oe-loo otol, to dve the tl tte to whle mmzg the ot Che yo we y mlto (.e., ly yo, to the lt to vefy tht ). Peyele : Pem tte :, dm : ; Hmlto: H, dm: Pem Cotte: H ttoy: H ehgg: N N N, m : ehgg :

3 , G M : , 6 8 G Ce /ml :

4 . Fd ott tte vle feed to t omoet oe of the fom K whee tjetoy. Peyele : Ml : K M :, to yeld dedet otol (ll oed-loo ole t the og). Fd the oed-loo tte 8 K 8...() K (), 59 d,7. m d () d () deoleh d, K,59,7

5 5. Let, wth t. olve the tt eto to deteme the otml otol,. Fd the otml ot. Peyele:, et : ; Q ; Pem tt: Q M : Kotol Otml : M: 6,5,

6 ,76, Otml Cot 9,98 5,8,76 7,9 7,7,9,8,9,5, 9,98 5,8,,96 6,5,76,8,9,9,,96 6,5,99 5,89,9,99 7,876 8,785,76,8 d. Come the tte tjetoe of t,, d. Peyele : Ut fed fl tte deoleh: 8 ; ; 6 Ut fee fl tte deoleh : 8 9,98,9 ; ; 5,8, Pedg tjetoy t fed d fee fl tte, dt dlht d gm et : 6

7 7 e. Now oe. How mt the otol of t,, d e modfed? Peyele: g : K oe loo otol (fed-fl tte) deg,, d m log deg g : ehgg : , G M : , G

8 8 8 Ce /ml : g : K oed loo otol (fee-fl tte) deg, m log deg g : Kotol Otml : ehgg:,7, >

9 9,7, ,9, ,, Dgtl Cotol of Hmo Ollto hmo ollto deed y (.). Detze the lt g mlg eod of. Peyele: tem (.) dt dtl : ) ( ) ( ) ( t t t dm : d Dt d tem dt deg eode mlg dlh: dm :! e

10 5 6 5!!!! o!! 5!! 5!! o!! d, o o d d e o o d o o o Deg dem, deoleh t tem dt: o o o (.). Wth the detzed lt, ote efome de of ) ( ) ( ) ( ) ( N N N whee the tte. Wte l eto fo dgtl otml otolle. Peyele: Deth tem :

11 dm : o o ; o d N N Oleh e met t et, m ml : o o o o o m: / K o o o o o o o o o Mt lt oed-loo dlh:

12 K o o o o Ml eljty, o ehgg deoleh :, m deoleh em-em l: o o Q ; ; o o o o o o o o Otml otol de oleh em : K o ;. Wte ML ote to mlte the lt dym, d e the tme eoe ogm lm.m to ot zeo-t tte tjetoe. d. Wte ML ote to omte, toe the otml otol g, d to dte the otol tte. Wte ML dve ogm to ot tm eoe lot fo the otml otolle. gve the et Peyele: % Pogm Dgtl Cotol of Hmo Ollto = :.5:5; U = zeo(,); =[ ;w^ ]; = [;] ; = eye(); d= zeo(,); = [ ];

13 lm(,,,du,,); ( [ 5 6] ); Fto =m(_d,_d,,,,n,,,c,) % te t Cot Kel d Feed G Fo =N:-: C=o(w*); = (w*); w=w^; Dv= + (((-C*())/w + *()/w)*(-c)/w) + ((-C*())/w + *()/w)*/w)) ; % Feed G K(,) = (((-C*())/w + *()/w)*c - ((-C*())/w + *()/w)*w*)/dv; K(,) = (((-C*())/w + *()/w)*/w) +((-C*())/w + *()/w)*c)/dv; % Cloed loo Plt Mt (,) = C-(-C*K(,)/w); (,) = /w-(-c*k(,)/w); (,) = -w*-(*k(,))/w; (,) = C-(*K(,))/w; % Cot Keel Udte () = (*()/w + C*())*(,)+ (*()/w+c*())*(,)+(); tem=(); () = (C*()-w**tem)*(,) + (C*tem-w**())*(,); () = (C*()-w**tem)*(,) + (C*tem-w**())*(,)+(); % Otml Cotol (:,)= fo =:N % Meghtg Otml Cotol U() = -K(,:)*(:, ); % Plt tte (:, +) = _d* (:, ) + _d*(); ed

14 .- tedy-tte ehvo. th olem we ode the elt dete ytem ee t mle eogh to llow lyt tetmet. h, let the lt (.) hve efome de of N N N...(.). Fd the otml tedy-tte (.e., N ) tt olto d how tht t otve defte. Fd the otml tedy-tte g K d deteme whe t ozeo. Peyele: Deth lt :, deg ; N m, ehgg de efom dt dmodf mejd: Q deg Q Pem tt : Q Oleh e N d ml ovege, m. Ml, m : Q

15 5 d, (.) Ke, et :

16 6 Oleh e: Q dlh mt deft otf, et, d ) det( Q. Deg dem, ) det( d dlh mt deft otf. K K et K j, yt j.. Fd the otml tedy-tte oed-loo lt d demotte t tlty. Peyele: Ml dlh tedy-tte oed loo lt mt, m: K K. Now the otml ott feed K led to the lt. Fd l dte fo the omoet of the otml ot eel. Fd the otml tedy-tte ot eel d demotte tht =.

17 Peyele: Ml : K, m mt lt oed-loo dlh: K Ml, m deoleh em-em l: ; ; Udted ot eel dlh: Q Ml dlh -otml tedy tte ot eel m : Q D em (.), et 7