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

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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}. ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online