KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-sol-hw-3

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-sol-hw-3

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Unformatted text preview: a} m}: {3H1} = 5 _fl+q3 3'(.3+1} 3 .3 3' (5:536. :6 (11:0 5‘ = Y{s}u=fifi 3. YES): (.5+2){.5+3) 2 DE] DEEP (.5'+4}{3+5)(5+I5) 5+4 3+3 '1 _{.3+2}{3+3} 1_{5+5}(s+5}___=4_ ‘1 HFW =_5 ' (S+43I|:.5'+|5:I:=_5 fl3={£+'2}[5+3) =6 {S+4}[S+5:l:=_é HS}: 1 _ I5 + 6 3+4 3+5 3+6 5+6 j 2 a} Its): w 5(r+_) = 6{.r+ } {3" +95+2fl)(3+ 4-} (5 +4)(.r+ 5H5 +4} T? 3cm} =1i m3—+—)1 = {p H“ (5+ 5}(5 +4)‘ 6 + 2 11m): 1s = o HE' (S + 5H3 + 4) ' mi!) is converging {or bounded} because [SKIS] does not have a limit at .5 = and .3 = —5 only, i.e.__ it has a limit for all real values of 3 E II}. It?) is smooth because the denominator of [33(3)] is a product of real factors only. See Fig. 53.9a. b) Inc‘s): 1 1U3'—:I = IMF—.1 I (3' — 65+10}{3+2) (5 — 3+ 2;) {.3—3— 2;}{3 +2) 105—3 its} =1i # :10 H“ (5‘ —fi.r+l|l}]l(5 + 2) Application of final value theorem is not valid because [5X(.r}] does not have a limit for some real .3 2 ll}, i.e.__ at .r = 34:2}. For the same reason, rm is diverging {unbounded}. rd?) is oscillator}? because the denominator of [3115)] includes complex factors. See Fig. sash. XEE}=1I|5.5+5 _ 163+] (53+9)_(s+3;){s—3;) 3 s :am=1a lELiii=ns He (5‘ +9} Application of final value theorem is not valid because [5X[.r}] does 1 have a limit for real 3 = 0. This implies that ruff) i5 not diverging, eii divergence occurs only if [3115)] does not have a limit for some real ta: ofsiet}. :03} i5 oscillator}; because the denominator of [5X[.r}] ia a product complex factora. Since nit} is oscillatory, it is not converging either. E Fig. 53.9c 2H U1!- 2‘!- U1!- 2". J‘ 2' "1!- :H "C!- 41:!- C I]: I '2 2 L!- .' 35 1 4: 5 "1|! Figure 533:1. Simulation ofo3J_foi‘ case a) ELI.” 4H." ritl dull £I.I.I.I I\EI.I.I.I -'CI.I.I.I I: U!- 'I '2 I I: ‘llT'E Figure 53.91). Simulation qur‘sjfor case 33,? 1!- 13' MM I.I -13I -1l- I: I]: ' I: I I!- 3- J!- I 4: 3 In! Figure 5.19:3. Simulating” qt'Xf'rjfm' care C} The Simulin block diagram i5 Shown below. An impulee input should be used to nhtain the function‘s behavior. In this case note that the impulse input in simulated by a rectangular pulse input of very short duration. [At time I = fl and t =i'l.i'lt'll with changes nt~ magnitude mm and 400D respectively i. The MATLAB enmmand impulse might also he used. 3.9 a] Transfer Fen? Trurfifcr Fla-I3 SW”? Giver-1|! 3 g Soup nil Tra nslel Fan-'1- Ehlp'l'l 3 g Sieplfl Figure 533:1. Emmfimi'bfncfi: diagmmfm' cases a}, bl and c}. ...
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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-sol-hw-3

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