flow rate control system “step response modeling” february 15, 2006 u.t.c. engineering 329
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Flow Rate Control SystemFlow Rate Control System
““Step Response Modeling”Step Response Modeling”
February 15, 2006February 15, 2006
U.T.C.U.T.C.
Engineering 329Engineering 329
Yellow TeamYellow Team
Jimy GeorgeJimy George Jeff LawrenceJeff LawrenceTaylor MurphyTaylor Murphy Jennifer PotterJennifer Potter
OutlineOutline
System BackgroundSystem Background• Description, SSOC, Step ResponseDescription, SSOC, Step Response
FOPDT TheoryFOPDT Theory Model TheoryModel Theory ResultsResults ConclusionsConclusions
Flow System SetupFlow System Setup
Block DiagramBlock Diagram
Steady State OperationSteady State Operation
Flow Rate Versus Time @ 80% Input
7576777879808182838485
0 10 20 30 40
Time (s)
Po
wer
Inp
ut
(%)
0
5
10
15
20
25
Flo
w R
ate
(lb
/min
)
Input
Output
Steady Operation
SSOCSSOCTEAM STEADY STATE OPERATING CURVE
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80 90 100
m, Input Pump Speed (%)
c, Output Flow Rate (lb/min)
Operating Range for Input
Operating Range for Output
Step Response: 70%-85%Step Response: 70%-85%
FOPDT ModelFOPDT Model
Transfer FunctionTransfer Function
1
0
s
Ke st
FOPDT ModelFOPDT Model
Model EquationModel Equation
Excel ParametersExcel Parameters– ttdd = Time step occurs = Time step occurs– A = Height of StepA = Height of Step– inbl inbl = Initial Input= Initial Input– outbloutbl = Initial Steady Value= Initial Steady Value
0
1)( 0
ttt
d
d
eKtttuAtC
Experimental and Model Experimental and Model ResultsResults
Experimental and Model Results
70
72
74
76
78
80
82
84
86
24 24.5 25 25.5 26 26.5 27 27.5 28
Time (s)
Inp
ut
(%)
14
15
16
17
18
19
20
21
22
Ou
tpu
t (l
b/m
in)
Excel Model of FOPDT
Experimental Values
K (lb/min/%) = 0.26
Tau (sec) = 0.46
t0 (sec) = 0.42
Experimental and Model Experimental and Model Results…contResults…cont
Experimental and Model Results
70
72
74
76
78
80
82
84
86
24 24.5 25 25.5 26 26.5 27 27.5 28
Time (s)
Inp
ut
(%)
14
15
16
17
18
19
20
21
22
Ou
tpu
t (l
b/m
in)
Excel Model of FOPDT
Experimental Data
K (lb/min/%) = 0.27
Tau (sec) = 0.47
t0 (sec) = 0.47
ResultsResults
Week 3 Values of K
Step down
Step Up Step Up
Step Down
Step UpStep Down
Step Up
Step Down
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8
Trial
K (lb
/min
/%)
45%-55% 55%-70% 70%-85% 85%-100%
Week 3 Values of K
Step down
Step Up Step Up
Step Down
Step UpStep Down
Step Up
Step Down
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8
Trial
K (lb
/min
/%)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of K
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8
Trial
K (lb
/min/
%)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of K
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8
Trial
K (lb
/min/
%)
45%-55% 55%-70% 70%-85% 85%-100%
Results … contResults … cont
Week 3 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau
(sec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 3 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau
(sec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau (
sec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau (
sec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau (
sec)
45%-55% 55%-70% 70%-85% 85%-100%
Results… contResults… cont
Week 3 Values of t0
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8
Trial
t 0 (s
ec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 3 Values of t0
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8
Trial
t 0 (s
ec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of t0
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8
Trial
t 0 (s
ec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of t0
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8
Trial
t 0 (s
ec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of t0
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8
Trial
t 0 (s
ec)
45%-55% 55%-70% 70%-85% 85%-100%
MODEL PARAMETERSDECREASING
STEADY STATE GAIN K 2.5 V/%
DEAD TIME to 0 s
TIME CONSTANT 0.6 s / 1.2 s / 2.4 s
EXPERIMENTAL PARAMETERSDECREASING
STEADY STATE GAIN K 2.5 V/%
DEAD TIME to 0 s
TIME CONSTANT 0.2 s
OVERALL RESULTS
MODEL PARAMETERS
STEADY STATE GAIN,K = 0.25 lb/min/%
DEAD TIME, to = 0.45 s
TIME CONSTANT, 0.48 s
EXPERIMENTAL PARAMETERS
STEADY STATE GAIN,K = 0.25 lb/min/%
DEAD TIME, to = 0.39 s
TIME CONSTANT, 0.51 s
OVERALL RESULTS
bbOVERALL RESULTS
Experimental ErrorStandard Deviations
STEADY STATE GAIN,K = ± 0.01(lb/min/%)
DEAD TIME, to = ± 0.08 (sec)
TIME CONSTANT, ± 0.03 (sec)MODEL ErrorStandard Deviation
STEADY STATE GAIN,K = ± 0.01 (lb/min/%)
DEAD TIME, to = ± 0.02 (sec)
TIME CONSTANT, ± 0.04 (sec)