lec_0312 - g Mike-Fem st m fasW s m 6mm#4;me MI W...

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Unformatted text preview: g: Mike-Fem st m fasW s» m 6mm #4;me MI! W MJR‘a-k rfimkm __ @ pig-H fl "hi-i .1: Lad # "22E L 1‘- (”at % " [mat-'21 2 imrt‘mle dry), \ 44m 1..., 51.. MW ouwafi aimixh. Fax 11““ A v» w " 1m! 1 m;- AHA EWLm+ fie) (MB #- Example 13.4%. We desire to change the flux density in a uuciear .1- ; If fl!" reactor from some value at. to a vaiue of such that the energy required to drive i the control rodsis minimizes. We therefore wish to minimize the cost function ' which approximates this desire 1 J a sf: {p3 + a: m age} 52?. We wilt assume that the reactor can be adequately represented by the point- kinetics equations with one group of delayed: neutrons fiepgfig-t—ta mime/ta The foitowing parameter values are assumed: ,3 =2: 0.0068, A w 10"3 sec, .3. an {31.1 sec“, no u 5 am e... we 6%.... a: w 5 K i0"'5, to m 0, if m 1 sec. The TPBVP is obtained as v. «m n3 fin an‘anFlcwrlAmri: emufiumfie 1" n ~ :1#ME{”“HI} 4'11”?” i “' §]* ref: rsmmflrlmra} with the boun'iary conditions refit...) m 5.r em.) w 6411., w 3.20 K.W., and. F39!) 1“ refit} “ '3- Titc quasilineariaed equations take theforutjr w A]! + u, where the initial and finaicouditions areyifli) m 5,y2{{]) w 320-.y'3iiiw ysifi m: 0, and where “if Emmett!) .. we) a “if“ ““" m ' ’1 [W] 0 3 Air) a “a": “‘1“ 0 0 ii?) i3 Erwttlei’ir) “-13 . 9‘ ‘1‘ [“i‘f" ] 0 “s" i“ We: ”“2 “a“ i} 0 “.1 +3. I 4...... are} e [2Fi{r)tn”(t)1=i.0.wu 4- WHEN“)? ‘7‘] We start the quasitineariaation solution by assuming thatfag} m e... and age} w- Jig: : SHE m eggs for the eeroth iteration. Figure 10 4 1 indicates the quasi“ linearised flue {tensity solution at each stage in the iteration. CGM?UTATIDHAL Merrroos m Orrrstosr Srsrssts Conrnor. CH. to 50 fro” .-., tst trlot by ooosilineoriaotionwx * ' f 40 I I I j v 2nd triol lay ooosilrneorrzotronw 1’ :m r’_ . in?" 50 I III; if r - ifit 2“ it / . eff 2o x «a a i it If x x” .- . 4 th and 5th if it) . f triotliterottoa} ..-- c” ‘ by ouositinecrisotioo A 4' I i I D 0.2 0.61 0.6 0.8 LO time. seconds Fig. met Power level versus time. Sotit'rtott or ssaottttc oprtstat. oott'rnot. Paoatssrs a? oussrmtaaamm Iri a nonlinear control system, it is not generally possible to express ptimfal control law as a product of the state vector and a time-varying In fact, a soiation of the nonlinear, partial differential eqaations rela- he optimal control to the optimum trajectory, Mr) to 5&6), is normally sasitil’e. Furthermore, the optimal control is highly dependent, in a teargmanner, on the initial state vector 3:0,). This means that, for most rearicontrol systems, only opendoop control laws are available even h(,_____.osed-ioop control laws are more desirable. The desirability of l—loop control lasts has led to the development ofspecific optima! control. is specific optimal control (3.0.0.) problem is defined in the following sr. We are given a plant with a state equation of the form “MEI—mm—rl—iP-Iu'—I ...
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