Docslide.us Answer for Tutorial 5

UNIVERSITI MALAYSIA MALAYSIA PERLIS Pusat Pengajian Kejuruteraan Bioproses ERT 210! Pro"ess #$na%i"s an& 'ontro( Tutoria( )* #$na%i" Be+a,ior o- .irst/or&er an& Se"on&/or&er Pro"esses

5.1 In addition to the standard standard inputs discussed discussed in Section Section 5.1, other input functions functions occasionally occasionally are useful for special purposes. One, the so-called doublet pulse, is shown in Fig. E5.1.

.igure E)1

(a (a Find Find the the !apl !aplace ace tran transf sfor or" " of this this func functi tion on by firs firstt e#pre e#press ssin ing g it as a co"po co"posi site te of  functions whose transfor"s you already $now. Anser*

(b %hat would be the response response of a process process ha&ing a first-order first-order transfer transfer function function K   K '( '(τ  s1  s1 to this input) Of the integrating process K  process  K ' s)  s) Anser*

(c Fro" these results, can you deter"ine what special property this input offers) Anser*

5.* +wo liuid storage syste"s are shown in Fig.E5.*.Each tan$ is  feet in dia"eter. For syste" I, the &al&e acts as a linear resistance with the flow-head relation q  /.00 h, where q is in gal'"in and h is in feet. For Syste" II, &ariations in liuid le&el h do not affect e#it flow rate q. Suppose that each syste" is initially at steady-state with h 1 ft and q i = 52 gal'"in and that at ti"e t    2 the inlet flow rate suddenly changes fro" 52 to 32 gal'"in. For each of the syste", deter"ine the following infor"ation4 =

.igure E)

(a +he transfer function  H  ( s  = Q i ( s  where the pri"es denote de&iation &ariables. Anser*

(b +he transient response h(t . Anser*

(c +he new steady-state le&els) Anser*

(d If each tan$ is / ft tall, which tan$ o&erflows first) when) Anser*

5.12 +he dyna"ic beha&ior of the liuid le&el in each leg of a "ano"eter tube, responding to a change in pressure, is gi&en by 6

d  h 6

dt 

+

1 µ  dh 6  R  ρ  dt 

+

0  g  6  L

h =

0 - ρ  L

 p (t 

where h' (t  is the le&el of liuid "easured with respect to the initial steady-state &alue,  p' (t  is the pressure change, and R, L, q,  ρ , and  µ  are constants. (a 7earrange this euation into standard gain-ti"e constant for" and find e#pression for K , τ , ζ  in ter"s of the physical constants. Anser*

(b For what &alues of the physical constants does the "ano"eter response oscillate) Anser*

(c %ould changing the "ano"eter fluid so that ρ (density is larger "a$e its response "ore or  less oscillatory) 7epeat the analysis for an increase in  µ  (&iscosity. Anser*

5.18 step change fro" 15 to 01 psi in actual pressure results in the "easured response fro" a  pressure indicating ele"ent shown in Fig. E5.1.

.igure E)1!

(a 8ssu"ing second-order dyna"ics, calculate all i"portant para"eters and write and appro#i"ate transfer function in the for"  R 5 ( s 

 K  =

τ  6 s 6 + 6ζτ  s + 1 where R'  is the instru"ent output de&iation ("", P'  is the actual pressure de&iation (psi. Anser*  P 5 ( s 

(b %rite an eui&alent differential euation "odel in ter"s of actual (not de&iation &ariables. Anser*