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Transcription:

Chpte EEE8- Chpte # EEE8- Stte Spce Al d Cotolle Deg Itodcto to tte pce Obevblt/Cotollblt Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8-. Itodcto Ae tht we hve th ode te: f, ', '',.... Ve dffclt to td t eve f t le te we t olve th ode polol eqto. Theoetcll we c e geoetc d/o ltcl ethod bt th c be ppled ol oe pecfc ce. Copte c be ed to tckle th poble d the e bette wth t ode ODE we bek the th ode ODE to te of t ode ODE. Alo b g tce we c e powefl tool fo le lgeb. The gol of th chpte to todce ew ppoch the odellg of dcl te, the ethod clled tte pce l d t f oe vetle th the well-kow Tfe Fcto. Moe pecfcll, the clcl cotol te deg techqe (ch oot loc d feqec epoe ethod) e geell pplcble to: ) Sgle Ipt Sgle Otpt (SISO) te b) Ste tht e le d te vt (hve pete tht do ot chge wth te) The tte pce ppoch geelzed te do ethod fo odellg, lg d degg cotol te d ptcll well ted to dgtl pleetto. The tte pce ppoch c del wth: ) Mlt Ipt Mlt Otpt te b) No-le d te vt te c) Altetve cotolle deg ppoche Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- Eple: Ae the ple -pg te: F(t) k (t) Fcto, Ug Newto echc we get: d d F k F k choog, we hve: k F F k O k F A The vble d defe the tte vecto, whch t defe the tte ( coplete /decpto) of the te. owg the cet tte d the fte pt we c pedct the fte tte,.e. the fte behvo of the te. I the foeetoed ce, kowg the vle/decto of the foce F, the cet dplceet d peed of the object we c fll defe t fte dplceet d peed. Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- I oe geel ce whe we hve tte d pt we hve: d d... b b... b,,,,,,,... b b... b,,,,,,, d,,,..., b, b,... b, Th c be wtte vecto fo : A whee:,..., b,...... b,,......,, A,,............,............ b,...... b,,......, Now, ode to oto the te we eed eo to ee vo vble lke the dplceet d veloct of the. et e tht we c b eo fo both vble (the peed d the dplceet), the we defe the otpt of the te to be: C et e tht we c b ol oe eo, tht ee the dplceet, the the otpt : C et e tht we c b ol oe eo, tht ee the veloct, the C the otpt : Modle ede: D D Go - d.go@cl.c.k 4/4

Chpte EEE8- et e tht we hve ol oe eo tht ee le cobto C of the dplceet d veloct: Hece, the ot geel ce: c, c, c, c, c, c, c, c, c, c, c, c, C p c c p, cp, c p p, cp, c p, Fll let e tht ( the tfcl ce) tht the pt c dectl flece the otpt, the we hve: C D, Fo oe t D. So the te decbed b A C D : A C D p O vecto fo: A C D Modle ede: D D Go - d.go@cl.c.k 5/4

Chpte EEE8- Whee: I geel:, p ( t) A t ( t) ( t) ( t) ( t) C( t) ( t) D( t) ( t) Whee tte vecto,.e. pt vecto,.e. p otpt vecto,.e. p A tte t,.e. A pt t,.e. C p otpt t,.e. C p D p feed fowd t (ll zeo),.e. D p If the te e Te Ivt (TI): ( t) A( t) ( t) ( t) C( t) D( t) D + - + d/ C + A The tte of te coplete of the te t ptcl pot te. If the cet tte of the te d the fte pt gl e kow the t poble to defe the fte tte d otpt of the te. Modle ede: D D Go - d.go@cl.c.k 6/4

Chpte EEE8- The tte of te be defed the et of vble (tte vble) whch t oe tl te t o, togethe wth the pt vble, copletel detee the behvo of the te fo te t t o. The tte vble e the llet be of vble tht c decbe the dc te of te d t ot ece cott tht the e eble. The e whch tte vble chge wth te c be thoght of tjecto deol pce clled tte pce. Two deol tte pce oete efeed to the phe ple whe oe tte the devtve of the othe. The choce of the tte pce vble fee log oe le e followed: The t be lel depedet. The t pecf copletel the dc behvo of the te. Fll the t ot be pt of the te. Eple.: Fd the tte pce odel of the followg te: t t t t 4t 4 4 4, A C 4 Modle ede: D D Go - d.go@cl.c.k 7/4

Chpte EEE8- Eple.: Fd the tte pce odel of the followg te: t t t t t 6 t 5 5 t t t t t t t t Hece: 6 6 6 5 t t 5 t t t t t t 5 t 5 5 5 Eple of tte pce odel (NOT ASSESSED MATEIA) Eple. Ae the followg ple electoechcl tht cot of electoget d v(t) f The foce of the getc feld dectl elted to the cet the etwok. The foce tht eeted o the object f ka, whee k A Modle ede: D D Go - d.go@cl.c.k 8/4

Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k 9/4 potve cott. To plf the l we e tht the dplceet ve ll d tht ll e the cet h le eltohp wth the foce: k f A Ug cct theo: v d Ug Newto d lw: k k k f A Now, we c defe, d. Th: v v k k k k A A Hece the tte pce odel : A v k k A Now let e tht we hve ol oe eo tht wll et the dplceet : Th the tte pce odel : v k k A

Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k /4 Eple.4 Aothe eple how the et fge. The hft of the eptel ected DC oto coected to the lod J thogh ge bo. d v d v J T T T T J T T T T, T T T T J J d d v v I defe, : v J J v J J v J v(t) EMF T,θ N N θ o J T,θ T o,θ o

Chpte EEE8- Eple.5: It c be poved tht odel of the Idcto Mche : d D D D d Q Q Q D d D Q D Q D d Q Q D Q D Q D D Q Q D D D Q Q Q O: Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k /4 Q D q d Q D q d Q D Q q d Q D q D q d Q D d Q q d Q D Q D q d Q D D d d d d d d d d

Chpte EEE8- Stte pce The te tte c be wtte vecto fo :,, T,,,, T,,,,, T, => A tdd othogol b (ce the e le depedet) fo - deol vecto pce clled tte pce. Eple of tte pce e the tte ple (=) d tte D pce (=), Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- elto of tte pce d TF If we hve TI tte pce () te, how c we fd t TF? T ( t) A( t) ( t) X ( ) () AX ( ) U ( ) I A X ( ) U ( ) () X ( ) I A U ( ) I A () Ad fo the d eqto of the te: Y( ) CX ( ) DU ( ) => Y( ) C I A U ( ) I A () DU ( ) Y( ) C I A D U( ) C I A () defto TF: CI A D d CI A () IC. the epoe to the Alo: ( ) ( ) () IT X I A U I A X ( t) I A U ( ) I A () If = => X ( t) I A X () Modle ede: D D Go - d.go@cl.c.k 4/4

Chpte EEE8- So G C I A D the TF. Fo le lgeb: G, j I A Cj D I A, whee the th col of the t d C j the j th ow of C. Hece I A the CE of the TF!!! So: G ( ) G ( ) G q( ) G( ) G( ) Gq ( ) G () Gp( ) Gp( ) Gpq( ) Y U Y Y Y, G, G,... U U U G G Eple.6: Fd the TF of the followg te:. d 5 I A.5.5 G.5.5 Modle ede: D D Go - d.go@cl.c.k 5/4

Chpte EEE8- Eple.7: Fd the TF of the followg te:. d 5 I A.5.5 G,.5.5 I A.5.5 G,.5.5 O: G C I A D.5.5.5.5.5.5 G G.5.5.5.5 Modle ede: D D Go - d.go@cl.c.k 6/4

Chpte EEE8- Eple.8: Fd the TF of the followg te:. d 5 I A.5.5.5 G,.5.5.5 I A.5.5 G,.5.5 I A.5.5 / G,.5.5 / I A.5.5 G,.5.5 O: Modle ede: D D Go - d.go@cl.c.k 7/4

Chpte EEE8- G C I A D.5.5.5.5.5.5 G G G.5.5.5.5.5.5.5 Obevblt Ae tht we hve the followg te:. Notce tht the odel copled d ce C t poble to ee how behve (o poble f A w ot dgol o C w I ). Th ple tht we cot oto, fo eple t c dvege to ft wth cttophc elt fo o te. Ae tht we hve othe te: Modle ede: D D Go - d.go@cl.c.k 8/4

Chpte EEE8- Clel thee two odel e dffeet. I tht ce t c be poved tht the te hve the e tfe fcto thee pole-zeo ccelto: I A C D 6 G I A I A C D G I A 6 6 whch ectl the e the TF of the ft te, wht wog? Thee pole zeo ccellto t the ecod odel Cotollblt Ae tht we hve the followg te: I th ce we c ee how both tte behve bt we cot chge w o tht we c flece de to the fo of. If A w ot dgol we wold be ble to cotol thogh. Sll we hve pole-zeo ccellto : Modle ede: D D Go - d.go@cl.c.k 9/4

Chpte EEE8- I A C D G I A 6 6 Hece the ft ce b popel defg we c cotol both tte bt we cot ee the ecod tte, whle the ecod ce we c ee both tte bt we cot cotol the ecod tte. The ft te clled obevble d the ecod cotollble. The lo of the cotollblt d/o obevblt de to pole/zeo ccellto. Thee te e cceptble d the olto to tht poble to e-odel the te. The te tht e both cotollble d obevble e clled l elto. We eed to develop tet to detee the cotollblt d obevblt popete of the te. Dffclt tk f the te ole. I o ce we pl hve to fd the k (the be of e Idepedet (I) ow o col) of two tce. Fo obevblt: MO C CA CA CA. If the k of th t le th T the the te obevble. Fo cotollblt: MC A A A the the te cotollble.. If the k of th t le th Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- Eple.9: Detee the Obevblt of the followg te: CA 6 M O 6 Ad obvol thee ol oe I col/ow Eple.: Detee the Obevblt of the followg te: CA 6 M O 6 Ad obvol thee e I col/ow Eple.: Detee the Obevblt of the followg te: 4 A 4 M C Ad obvol thee ol oe I col/ow Eple.: Detee the Obevblt of the followg te: 4 A 4 M C Ad obvol thee e I col/ow. Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- Ttol Eece II. Deve tte pce epeetto of the pg te g tht the te h otpt: the dplceet d the veloct.. epet Qeto g tht the dplceet the ol te otpt.. Fd the tte pce odel of the followg te: 6 5 ( t) 4 4. A tte pce odel gve b 4 5... 6 7 8 9.4.5.6 A 4 5,.7.9, 6 7 8 9... 4 5.4.5.6 C 5, D () Wht the ode of the te? (b) How pt/ otpt do we hve th te? (c) Wht e the deo of the t D? 5. Fd the tte pce odel of: () 4 4'' ' 4.' 5 Modle ede: D D Go - d.go@cl.c.k /4

Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k 4/4 (b) 4 4 I ech ce fd: The ode of the te? How pt/ otpt do we hve th te? 6. Fd the tfe fcto of te wth:,,, 4 D C A. 7. Fd the tfe fcto of te wth:,,, 4 D C A. 8. Fd the tfe fcto of te wth:,,, 4 D C A. 9. Wht the chctetc eqto Q.6-8? Wht the te ode? I tht te tble? Wh? Ae thee te obevble/cotollble?

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