Chapter4 - MILLING PROCESS. FIG. 1 Typical parts and shapes produced by various cutting processes.
CHAPTER 5 : TYPICAL PROCESS...
Transcript of CHAPTER 5 : TYPICAL PROCESS...
CHAPTER 5 : TYPICAL PROCESS SYSTEMS
When I complete this chapter, I want to be able to do the following.
• Predict output for typical inputs for common dynamic systems
• Derive the dynamics for important structures of simple dynamic systems
• Recognize the strong effects on process dynamics caused by process structures
Outline of the lesson.
• Common simple dynamic systems- First order -Second order - Dead time - (Non) Self-regulatory
• Important structures of simple systems- Series - Parallel- Recycle - Staged
• Workshop
CHAPTER 5 : TYPICAL PROCESS SYSTEMS
SIMPLE PROCESS SYSTEMS: 1st ORDER
The basic equation is:
)t(X K)t(Ydt
)t(dY=+τ
0 20 40 60 80 100 120
0.8
1
1.2
1.4
1.6
1.8
time
tank
con
cent
ratio
n
0 20 40 60 80 100 1200.5
1
1.5
2
time
inle
t con
cent
ratio
n
Maximumslope at“t=0”
Output changes immediately
Output is smooth, monotonic curve
At steady state
∆Y = K ∆X
τ
≈ 63% of steady-state ∆CA
∆X = Step in inlet variable
Would this be easy/difficult to
control?
K = s-s gain
τ = time constant
SIMPLE PROCESS SYSTEMS: 1st ORDER
These are simplefirst order systems
from severalengineeringdisciplines.
SIMPLE PROCESS SYSTEMS: 2nd ORDERThe basic equation is:
)()()(2)(2
22 tXKtY
dttdY
dttYd =++ ξττ
K = s-s gain , τ = time constant , ξ = damping factor
0 10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
Time
Con
trolle
d V
aria
ble
0 10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
Time
Man
ipul
ated
Var
iabl
e
0 20 40 60 80 100 120 140 160 180 2000
0.5
1
1.5
Time
Con
trolle
d V
aria
ble
0 20 40 60 80 100 120 140 160 180 2000
0.2
0.4
0.6
0.8
1
Time
Man
ipul
ated
Var
iabl
e
overdamped underdamped
Would this be easy/difficult to
control?
SIMPLE PROCESS SYSTEMS: 2nd ORDER
These are simplesecond
order systemsfrom severalengineeringdisciplines.
SIMPLE PROCESS SYSTEMS: DEAD TIME
time
Xin
Xout
θ = dead time
θ
Would this be easy/difficult to
control?
)()(
)()( sXesX
tXtX
ins
out
inoutθ
θ−=
−=
SIMPLE PROCESS SYSTEMS: INTEGRATOR
pump valve
Level sensorLevel sensor
Liquid-filledtank
Plants have many inventories whose flows in and out do not depend on the inventory (when we apply no control or manual correction).
These systems are often termed “pure integrators” because they integrate the difference between in and out flows.
outin F F dtdLA
dtdV ρρρρ −==
)()()()(LftFLftF
out
in
≠
≠
SIMPLE PROCESS SYSTEMS: INTEGRATOR
pump valve
Level sensorLevel sensor
Liquid-filledtank
outin FFdtdLA
dtdV ρρρρ −==
Fout
Fin
Plot the level for this scenario
time
SIMPLE PROCESS SYSTEMS: INTEGRATOR
pump valve
Level sensorLevel sensor
Liquid-filledtank
outin FFdtdLA
dtdV ρρρρ −==
Fout
Fin
time
Level
SIMPLE PROCESS SYSTEMS: INTEGRATOR
pump valve
Level sensorLevel sensor
Liquid-filledtank
• Non-self-regulatory variables tend to “drift” far from desired values.
• We must control these variables.
Let’s look aheadto when we apply control.
STRUCTURES OF PROCESS SYSTEMS
T
NON-INTERACTING SERIES
• The output from an element does not influence the input to the same element
• Common example is tanks in series with pumped flow between
• Block diagram as shown
STRUCTURES OF PROCESS SYSTEMS
T
NON-INTERACTING SERIES
• The output from an element does not influence the input to the same element
• Common example is tanks in series with pumped flow between
• Block diagram as shown
Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
STRUCTURES OF PROCESS SYSTEMS
NON-INTERACTING SERIES
Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
STRUCTURES OF PROCESS SYSTEMS
NON-INTERACTING SERIES
Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
)()()( sGsXsY
i
n
iΠ==1
In general:
STRUCTURES OF PROCESS SYSTEMS
NON-INTERACTING SERIES
Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
)()()( sGsXsY
i
n
iΠ==1
In general:
With each element a first order system: )()(
)(11 +
Π== s
KsXsY
i
in
i τ
STRUCTURES OF PROCESS SYSTEMS
NON-INTERACTING SERIES
Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
)()()( sGsXsY
i
n
iΠ==1
In general:
With each element a first order system: )()(
)(11 +
Π== s
KsXsY
i
in
i τ
• overall gain is product of gains
• no longer first order system
• slower than any single element
0 10 20 30 40 50 60 70-5
-4
-3
-2
-1
0
Time
Con
trolle
d Va
riabl
e
0 10 20 30 40 50 60 700
2
4
6
8
10
Time
Man
ipul
ated
Var
iabl
e
Step Response
• Looks as though some dead time occurs
• Smooth, monotonic, not first order
• Slower than any element
• K = Π (Ki)
STRUCTURES OF PROCESS SYSTEMSNON-INTERACTING SERIES
0.10/(5s+1) 1/(5s+1)-1.2/(5s+1) 3.5/(5s+1)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
STRUCTURES OF PROCESS SYSTEMS
NON-INTERACTING SERIES
Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)
v(s) F0(s) T1(s) T2(s) Tmeas(s)
With each element a first order system with dead time:
)()()( i
11 +Π=
−
= seK
sXsY
i
sin
i τ
θ
Guidelines on step response
• Sigmoidal (“S”) shaped
• t63% ≈Σ (θi + τi) [not rigorous!]
• K = Π (Ki) [rigorous!]
• Usually, some “apparent dead time” occurs
STRUCTURES OF PROCESS SYSTEMS
Class Exercise: Sketch the step response for the system below.
τ = 2θ = 2
?
STRUCTURES OF PROCESS SYSTEMS
Class Exercise: Sketch the step response for the system below.
0 5 10 15 20 250
1
2
3
4
5DYNAMIC SIMULATION
Time
Con
trolle
d Va
riabl
e
0 5 10 15 20 250
1
2
3
4
5
Time
Man
ipul
ated
Var
iabl
e
STRUCTURES OF PROCESS SYSTEMS
Class Exercise: Sketch the step response for each of the systems below and compare the results.
Case 1
τ = 2 θ = 2 τ = 2 θ = 2
τ = 2 θ = 1 θ = 1τ = 2 & θ = 2
Case 2
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
time
case
1 re
spon
ses
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
time
case
2 re
spon
ses
Two plants can have different intermediate variables and have the same input-output behavior!
Step
Case1
Case2
STRUCTURES OF PROCESS SYSTEMS
PARALLEL STRUCTURES result from more than one causal path between the input and output. This can be a flow split, but it can be from other process relationships.
G1(s)
G2(s)
X(s) Y(s)
A → B → C
Example process systems Block diagram
STRUCTURES OF PROCESS SYSTEMS
PARALLEL STRUCTURES
G1(s)
G2(s)
X(s) Y(s)
))(()(
)()(
111
21
3
++
+=
sssK
sXsY p
τττ
If both elements are first order, the overall model is
Class exercise: Derive this transfer function
STRUCTURES OF PROCESS SYSTEMS
PARALLEL STRUCTURES can experience complex dynamics. Parameter is the “zero” in the transfer function.
G1(s)
G2(s)
X(s) Y(s)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5
1
1.5
time
outp
ut v
aria
ble,
Y’(t
)
0
-2
1
2
3
4
-1
Which wouldbe difficult/easy
to control?
Sample step response at t=0
STRUCTURES OF PROCESS SYSTEMS
PARALLEL STRUCTURE
Class exercise: Explain the dynamics of the outlet temperature after a change to the flow ratio, with the total flow rate constant.
T
STRUCTURES OF PROCESS SYSTEMS
0 5 10 15 20 2589
90
91
92
93
time
mix
ing
tem
pera
ture
0 5 10 15 20 250.4
0.5
0.6
0.7
time
fract
ion
by-p
ass
0 5 10 15 20 2589
90
91
92
93
time
seno
r out
put
T
Why an overshoot?
PARALLEL STRUCTURES: Explain the dynamics of the outlet temperature after a step change to the flow ratio.
STRUCTURES OF PROCESS SYSTEMS
PARALLEL STRUCTURE
Class exercise: Explain the dynamics of the outlet concentration after a step change to the solvent flow rate.
FA
CA0
V1CA1
V2CA2FS
CAS=0
reactant
solvent
STRUCTURES OF PROCESS SYSTEMS
0 10 20 30 40 50 600.05
0.06
0.07
0.08
0.09
0.1
time
solv
ent f
low
0 10 20 30 40 50 600.39
0.4
0.41
0.42
0.43
tank
2 c
once
ntra
tion
Why an inverse response?
PARALLEL STRUCTURE
Class exercise: Explain the dynamics of the outlet concentration after a step change to the solvent flow rate.
STRUCTURES OF PROCESS SYSTEMS
RECYCLE STRUCTURES result from recovery of material and energy. They are essential for profitable operation, but they strongly affect dynamics.
T0
T3T4
Process example Block diagram
STRUCTURES OF PROCESS SYSTEMS
RECYCLE STRUCTURES
GH1(s) GR(s)
GH2(s)
T0(s)
T1(s) T3(s)
T4(s)
T2(s)
)()()()(
)()(
sGsGsGsG
sTsT
HR
HR
2
1
104
−=
STRUCTURES OF PROCESS SYSTEMS
RECYCLE STRUCTURES
Class exercise: Determine the effect of recycle on the dynamics of a chemical reactor (faster or slower?).
T0
T3T4
• Exothermic reaction
• feed/effluent preheater
)/()(/ .)(/ .)(
1103300400
2
1
+==
=
ssGKKsGKKsG
R
H
H
STRUCTURES OF PROCESS SYSTEMS
Class exercise: Determine the effect of recycle on the dynamics of a chemical reactor (faster or slower?).
0 5 10 15 20 25 30 35 40 45 500
0.5
1
1.5
2
2.5
time
T4 w
ithou
t rec
ycle
T4 is a deviation variable
0 50 100 150 200 250 300 350 400 450 5000
5
10
15
20
25
time
T4 w
ith re
cycl
e
Without recycle, faster and smaller effect
With recycle, slower and larger effect
Different scales!
STRUCTURES OF PROCESS SYSTEMS
STAGED STRUCTURES
FR
FV
xB
xD
Tray n
Liquid
Liquid Vapor
Vapor
STRUCTURES OF PROCESS SYSTEMSSTAGED STRUCTURES
0 10 20 30 40 500.965
0.97
0.975
0.98
0.985
0.99
Time (min)
XD (m
olfra
c)
0 10 20 30 40 500.005
0.01
0.015
0.02
0.025
Time (min)
XB (m
olfra
c)
0 10 20 30 40 508530
8530.5
8531
8531.5
8532
8532.5
Time (min)
R (m
ol/m
in)
0 10 20 30 40 501.35
1.355
1.36
1.365
1.37x 104
Time (min)
V (m
ol/m
in)
Complex structure,smooth dynamics
“Steps” because analyzer provides new measurement only every 2 mintes.
OVERVIEW OF PROCESS SYSTEMS
Even simple elements can yield complex dynamics when combined in typical process structures.
We can
• Estimate the dynamicresponse based on elements and structure
• Recognize range of effects possible
• Apply analysismethods to yielddynamic model
CHAPTER 5: PROCESS SYSTEMS WORKSHOP 1
Four systems experienced an impulse input at t=2. Explain what you can learn about each system (dynamic model) from the figures below.
0 5 10 15 20 25 300
1
2
3
outp
ut
(a)
0 5 10 15 20 25 30-1
0
1
2
3
outp
ut
(b)
0 5 10 15 20 25 30-1
0
1
2
3
time
outp
ut
(c)
0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
time
outp
ut
(d)
CHAPTER 5: PROCESS SYSTEMS WORKSHOP 2
Using the guidelines in this chapter, sketch the response of the measured temperature below to a +5% step to the valve.
T
% openmin/m .
)s(v)s(F
)s(G valve30 10==
125021 3
0
1
+−
==s
min)/m/(K .)s(F)s(T)s(Gtank1
130001
1
2
+==
sKK
sTsTsG / .)()()(tank2 110
012
+=
=
sKK
sTsTsG measured
sensor
/ .
)()()(
(Time in seconds)
CHAPTER 5: PROCESS SYSTEMS WORKSHOP 3
Sensors provide an estimate of the true process variable because the measurement is corrupted by errors.
• Discuss sources of noise in a measurement.
• Define the following terms for a sensor- Accuracy- Reproducibility
• Explain some process measurements needing (a) good accuracy and (b) good reproducibility
• Suggest an approach for operating a process when a key material property (composition, etc.) cannot be measured using an onstream analyzer.
CHAPTER 5: PROCESS SYSTEMS WORKSHOP 4
We are designing the following reactor with recycle. We have two choices for the conversion in the reactor. Will the plant dynamics be affected by the selection?
Fresh feed flow is constant
Pure, unreacted feed
Pure product
X = 50%
X = 95%
CHAPTER 5 : TYPICAL PROCESS SYSTEMS
When I complete this chapter, I want to be able to do the following.
• Predict output for typical inputs for common dynamic systems
• Derive the dynamics for important structures of simple dynamic systems
• Recognize the strong effects on process dynamics caused by process structures
Lot’s of improvement, but we need some more study!• Read the textbook• Review the notes, especially learning goals and workshop• Try out the self-study suggestions• Naturally, we’ll have an assignment!
CHAPTER 5: LEARNING RESOURCES
• SITE PC-EDUCATION WEB - Instrumentation Notes- Interactive Learning Module (Chapter 5)- Tutorials (Chapter 5)
• Software Laboratory- S_LOOP program
• Textbook- Chapter 18 on level modelling and control- Appendix I on parallel structures
CHAPTER 5: SUGGESTIONS FOR SELF-STUDY
1. Extend textbook Figure 5.1 for new input functions (additional rows): impulse and ramp.
2. Determine which of the systems in textbook Figure 5.3 can be underdamped.
3. Explain the shape of the amplitude ratio as frequency increases for each system in textbook Figure 5.1.
4. Discuss the similarity/dissimilarity between self regulation and feedback.
5. Explain textbook Figure 5.5.
6. Discuss the similarity between recycle and feedback.
CHAPTER 5: SUGGESTIONS FOR SELF-STUDY
7. Discuss how the dynamics of the typical process elements and structures would affect our ability to control a process. Think about driving an automobile with each of the dynamics between the steering wheel and the direction that the auto travels.
8. Formulate one question in each of three categories (T/F, multiple choice, and modelling) with solution and exchange them with friends in your study group.