dynamic process modeling - apmonitorapmonitor.com/che436/uploads/main/lecture4_notes.pdfmodeling...
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![Page 1: Dynamic Process Modeling - APMonitorapmonitor.com/che436/uploads/Main/Lecture4_notes.pdfModeling Dynamic Process Behavior •The best way to understand process data is through modeling](https://reader034.vdocuments.us/reader034/viewer/2022051511/602874cb6e1bab50b51eeaf5/html5/thumbnails/1.jpg)
Dynamic Process Modeling
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Understanding Dynamic Process Behavior
• To learn about the dynamic behavior of a process, analyze measured process variable test data
• Process variable test data can be generated by suddenly changing the controller output signal
• Be sure to move the controller output far enough and fast enough so that the dynamic behavior of the process is clearly revealed as the process responds
• The dynamic behavior of a process is different as operating level changes (nonlinear behavior) so collect process data at normal operating levels (design level of operation)
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Modeling Dynamic Process Behavior• The best way to understand process data is through modeling
• Modeling means fitting a first order plus dead time (FOPDT) dynamic process model to the data set:
where:
y(t) is the measured process variable
u(t) is the controller output signal
• The FOPDT model is low order and linear so it can only approximate the behavior of real processes
)()()(
PPP tuKtydt
tdy
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Modeling Dynamic Process Behavior
• When a first order plus dead time (FOPDT) model is fit to dynamic process data
• The important parameters that result are:
• Steady State Process Gain, KP
• Overall Process Time Constant, P
• Apparent Dead Time, P
)()()(
PPP tuKtydt
tdy
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• Tuning of controller means selecting the parameters for “best” operation
• FOPDT model of dynamics of the process are used• Kp
• p
• p
• See correlations
• This “Tuning Guide” is located near the end of the pdf file for the Practical Process Control book
• This is a place to start (close but not best)
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The FOPDT Model
• model parameters (KP, P and P) are used in correlations to compute initial controller tuning values
• sign of KP indicates the action of the controller
(+KP reverse acting; KP direct acting)
• size of P indicates the maximum desirable loop sample time (be sure sample time T 0.1P)
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Step Test Data and Dynamic Process Modeling
• Process starts at steady state
• Controller output signal is stepped to new value
• Measured process variable allowed to complete response
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O pe n L oop S t e p T e s tP r o c e s s : C u s t o m P r o c e s s C o n t r o l l e r : M a n u a l M o d e
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Step Test
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O pe n L oop S t e p T e s tP r o c e s s : C u s t o m P r o c e s s C o n t r o l l e r : M a n u a l M o d e
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Process Gain From Step Test Data
• KP describes how much the measured process variable, y(t), changes in response to changes in the controller output, u(t)
• A step test starts and ends at steady state, so KP can be computed from plot axes
where u(t) and y(t) represent the total change from initial to final steady state
• A large process gain means the process will show a big response to each control action
)( Output, Controller in the Change StateSteady
)(Variable, Process Measured in the Change StateSteady
tu
tyKP
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KP for Gravity Drained Tanks
Steady state process gain has a: size (0.095), sign (+0.095), and units (m/%)
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y = (2.88 - 1.93) m
u = (60 - 50) %
%
m095.0
%5060
m 93.188.2
u
yK P
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Overall Time Constant From Step Test Data
Time Constant P describes how fast the measured process variable, y(t), responds to changes in the controller output, u(t)
P is how long it takes for the process variable to reach 63.2% of its total change, starting from when the response first begins
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Step Test
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O pe n L oop S t e p T e s tP r o c e s s : C u s t o m P r o c e s s C o n t r o l l e r : M a n u a l M o d e
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P for Gravity Drained Tanks
1) Locate where the measured process variable first shows a clear initial response to the step change – call this time tYstart
From plot, tYstart = 9.6 min
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G ra v i t y D ra i n e d T a n k s - O p e n L o o p S t e p T e s tP r o c e s s : G r a v i t y D r a i n e d T a n k C o n t r o l l e r : M a n u a l M o d e
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P for Gravity Drained Tanks2) Locate where the measured process variable reaches y63.2, or
where y(t) reaches 63.2% of its total final change
Label time t63.2 as the point in time where y63.2 occurs
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Why is tau = 63.2% to steady-state?
equation FOPDT fromdelay - time thedropKuyt
y
Book) PDC of 42 (pg. Transform LaPlace)()()0()( sKUsYyssY
FunctionTransfer obtain to0y(0) with Rearrange1)(
)(
s
K
sU
sY
function) (step 1/sU(s)1
1)(
s
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ssY
Book) PDC of (pg.42 Transform LaPlace Inverse1)(
t
eKty
At t632.01)( 1 KeKty
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P for Gravity Drained Tanks
• y(t) starts at 1.93 m and shows a total change y = 0.95 m
• y63.2 = 1.93 m + 0.632(y)
= 1.93 m + 0.632(0.95 m) = 2.53 m
• y(t) passes through 2.53 m at t63.2 = 11.2 min
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y = 0.95 m
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y63.2 = 2.53 m
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P for Gravity Drained Tanks- The time constant is the time difference between tYstart and t63.2
- Time constant must be positive and have units of time
From the plot: P = t63.2 tYstart = 11.2 min 9.6 min = 1.6 min
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y = 0.95 m
tYstart t63.2
P = 1.6 minutes
y63.2 = 2.53 m
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Apparent Dead Time From Step Test Data
• P is the time from when the controller output step is made until when the measured process variable first responds
• Apparent dead time, P, is the sum of these effects:• transportation lag, or the time it takes for material to travel from one point
to another
• sample or instrument lag, or the time it takes to collect analyze or process a measured variable sample
• higher order processes naturally appear slow to respond
• Notes:• Dead time must be positive and have units of time
• Tight control in increasingly difficult as P 0.7P
• For important loops, work to avoid unnecessary dead time
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P for Gravity Drained Tanks
P = tYstart tUstep
= 9.6 min 9.2 min = 0.4 min
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Processes Have Time-Varying Behaviors
• The predictions of a FOPDT model are constant over time
• But real processes change every day because• surfaces foul or corrode
• mechanical elements like seals or bearings wear
• feedstock quality varies and catalyst activity drifts
• environmental conditions like heat and humidity change
• So the values of KP, P, P that best describe the dynamic behavior of a process today may not be best tomorrow
• As a result, controller performance will degrade with time and periodic retuning may be required
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Processes Have Nonlinear Behaviors
• The predictions of a FOPDT model are constant as operating level changes
• The response of a real process varies with operating level
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E x a m p l e N o n l i n e a r B e h a v i o r P r o c e s s : C u s t o m P r o c e s s C o n t r o l l e r : M a n u a l M o d e
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response shape is different
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even though controller
output steps are the same
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Gravity Drained Tanks is Nonlinear
A controller should be designed for
a specific level of operation!
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N o n l i n e a r B e h a v i o r o f G ra v i t y D ra i n e d T a n k sM o d e l : F i r s t O r d e r P l u s D e a d T i m e ( F O P D T ) F i l e N a m e : T E S T .D A T
G a i n ( K ) = 0 .0 7 5 , T i m e C o n s t a n t ( T 1 ) = 1 .1 5 , D e a d T i m e ( T D ) = 0 .5 3 S S E : 2 0 6 .0
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variable response
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Manual Fitting (FOPDT) - Practice
1. Find Kp = y/ u
2. Find p
3. Find y0.632
4. Find t0.632
5. Find p
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Find Kp
• Kp = ymax / u = -2.06 m/-15%
= 0.137 m/%
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Find p
p = 0.505
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Find yFind ymax
y = 1.94
y0 = 4
ymax = 1.94 – 4 = -2.06
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Find y0.632
Find t0.632
Find p
0.632 ymax = (0.632) (2.06) = 1.30 m
y0.632 = 4 - 1.30 = 2.70 m
t0.632 = 4.5 min
p = 4.5 – 3.05 = 1.45 min
Caution: Account for dead time when calculating p!