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Team GreenTeam GreenJohn BarkerJohn BarkerJohn BeverlyJohn BeverlyKeith SkilesKeith Skiles
UTC ENGR329-001UTC ENGR329-0012-15-062-15-06
Steady State and Step Response Steady State and Step Response PerformancePerformance
Speed Control SystemSpeed Control System
OutlineOutline
System BackgroundSystem Background– Description, SSOC, Step ResponseDescription, SSOC, Step Response
FOPDT ModelFOPDT Model Model TheoryModel Theory ResultsResults ConclusionsConclusions
Steady State Operating Curve
0
200
400
600
800
1000
1200
1400
1600
1800
0 20 40 60 80 100
Motor Input (%)
Sp
eed
Ou
tpu
t (R
PM
)
Slope = 17.4
Steady State Operating Curve
0
200
400
600
800
1000
1200
1400
1600
1800
0 20 40 60 80 100
Motor Input (%)
Sp
eed
Ou
tpu
t (R
PM
)
Low
High
Mid
Time Response (Gain)Time Response (Gain)
Gain
17
17.1
17.2
17.3
17.4
17.5
Low Up Mid Up High Up Low Down Mid Down High Down
System Gain (RPM/%)
Time Response (Dead Time)Time Response (Dead Time)Dead Time (s)
0.08
0.09
0.1
0.11
0.12
Low Up Mid Up High Up Low Down Mid Down High Down
Time Response (Time Constant)Time Response (Time Constant)
Time Constant (s)
0
0.05
0.1
0.15
0.2
0.25
0.3
Low Up Mid Up High Up Low Down Mid Down High Down
Step Response Values and ErrorsStep Response Values and Errors
K (RPM/%) t0 (s) τ (s)
Average 17.4 0.11 0.25
Std. Dev 0.05 0.006 0.017
Laplace Domain FOPDT ModelLaplace Domain FOPDT Model
System Transfer FunctionSystem Transfer Function G(s) = G(s) = Ke /Ke /ττs+1s+1
– ParametersParameters
tt00=Dead Time=Dead Time
K = System GainK = System Gain
ττ = Time Constant = Time Constant
-t0s
FOPDT ModelFOPDT Model
Model Equation in Time DomainModel Equation in Time Domain– C(t) = A*u(t-tC(t) = A*u(t-tdd-t-t00)*K*(1-e ))*K*(1-e )-(t-td-t0)
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10
Time (s)
Ou
tpu
t (R
PM
)
0
6
12
18
24
30
36
42
48
Inp
ut
(%)
Model Output
Real Output
Model Input
Real Input
ResultsResults
0
100
200
300
400
500
600
700
800
4.5 5 5.5 6 6.5
Time (s)
Ou
tpu
t (R
PM
)
0
6
12
18
24
30
36
42
48
Inp
ut
(%)
Model Output
Real Output
Model Input
Real Input
Time Response (Dead Time)Time Response (Dead Time)
Dead Time (s)
0
0.02
0.04
0.06
0.08
0.1
0.12
Low Mid High
Time Response (Time Constant)Time Response (Time Constant)
Time Constant (s)
0
0.05
0.1
0.15
0.2
0.25
Low Mid High
Overall ResultsOverall ResultsExperimental Results:Experimental Results:
Steady State Gain : K= 17.1RPM/% ± 0.10Steady State Gain : K= 17.1RPM/% ± 0.10
Dead Time : tDead Time : t00= 0.06s ± 0.012= 0.06s ± 0.012
Time Constant : Time Constant : τ τ = 0.19s ± 0.034= 0.19s ± 0.034
Model Results:Model Results:
Steady State Gain : K= 17.4RPM/%Steady State Gain : K= 17.4RPM/%
Dead Time : tDead Time : t00= 0.1s= 0.1s
Time Constant : Time Constant : τ τ = 0.23s= 0.23s
ConclusionsConclusions
Operating Range 150-1700RPMOperating Range 150-1700RPM K = 17.4 RPM/%K = 17.4 RPM/% tt00= 0.1s= 0.1s ττ = 0.23s= 0.23s
Red Team -Pressure-Steady State Operating And Step Response
Dennis ToCory RichardsonJamison Linden
04/21/23, UTC, ENGR-329
SSOC
Steady State Operating Curve
0
2
4
6
8
10
12
0 10 20 30 40 50 60 70 80 90 100
m, Input Blower Pressure (%)
c, Output Pressure (cm-H20)
Operating Range for Output
Operating Range for Input
Transfer FunctionTransfer
Function
m(s)
Input
c(s)
Output
1
0
s
Ke st
K=Gain=∆c/∆m=(cm-H2O)/%to=Dead Timeτ=Time Constant (use 0.632∆c)Uncertainties (max-min)*(t/n)
Parameters
Steady State Operating Curve
0
2
4
6
8
10
12
0 10 20 30 40 50 60 70 80 90 100
m, Input Blower Pressure (%)
c, Output Pressure (cm-H20)
Lower Upper
Middle
Results
Experimental (Step-up, Step-down) Time Response (Gain) Time Response (Dead Time) Time Response (Time Constant)
Experimental (Step-up)
Step Response Inputs and Outputs
80
82
84
86
88
90
92
13 15 17 19 21 23
Time (sec)
Inp
ut
m(t
) (%
)
0
2
4
6
8
10
12
Ou
tpu
t c
(t)
(cm
-H2
O)
Input Value(%)
Output(cm-H20)
Experimental (Step-down)
Step Response Inputs and Outputs
74767880828486889092
13 15 17 19 21 23
Time (sec)
Inp
ut
m(t
) (%
)
0
2
4
6
8
10
12
Ou
tpu
t c
(t)
(cm
-H2
O)
Input Value(%)
Output(cm-H20)
Time Response (Gain)
Step Response
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Lower-up
Lower-down
Mid-up
Mid-down
Upper-up
Upper-down
Gain (cm-H2O/%)
`
Time Response (Dead Time)
Step Response
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Lower-up
Lower-down
Mid-up
Mid-down
Upper-up
Upper-down
Dead Time (sec)
Time Response (Time Constant)
Step Response
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0Tau (sec)
Lower-up
Lower-down
MId-up Mid-down
Upper-up
Upper-down
FOPDT Model
Model Equation C(t) = A*u(t-td-t0)*K*(1-e-((t-td-t0)/tau))
Parameters td = 15 sec. A = 15 % K = .21 cm-H2O /% t0 = 0.52 sec. tau = 1.8 sec. inbl= 60% outbl=2 cm-H2O
Step Up Input and Ouput vs. TimeExperimental and Model Results
1
2
3
4
5
6
13 14 15 16 17 18 19 20 21 22 23
Time (s)
Out
put (
cm-H
2O)
55
60
65
70
75
80
Inpu
t (%
)
Output(cm-H20)
Output
Input
Step Down Input and Ouput vs. TimeExperimental and Model Results
1
2
3
4
5
6
13 14 15 16 17 18 19 20 21 22 23Time (s)
Out
put (
cm-H
2O)
55
60
65
70
75
80
Inpu
t (%
)
Output(cm-H20)
Output
Input
Model Time Response (Gain)
Model Time Response (Gain)
0.0
0.1
0.2
0.3
0.4
Gain (cm-H2O)
Lower Up
Lower Down
Middle Up
MiddleDown
Upper Up
UpperDown
Model Time Response (Dead Time)
Step Response
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Lower-up
Lower-down
Mid-up Mid-down
Upper-up Upper-down
Dead Time (min)
Model Time Response (Time Constant)Step Response
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0Tau (min)
Lower-up
Lower-down
MId-up Mid-up Upper-up
Upper-up
Results
EXPERIMENTAL PARAMETERS INCREASING
STEADY STATE GAIN K 0.1-0.35 cm-H2O/% DEAD TIME to 0.5 s
TIME CONSTANT t 1.7 s
EXPERIMENTAL PARAMETERS DECREASING
STEADY STATE GAIN K 0.1-0.35 cm-H2O /% DEAD TIME to 0.5 s TIME CONSTANT t 1.7 s
Conclusions
Input operating range Output operating range (K) goes up as the input % is
increased (0.1-0.35cm-H2O/%) (to) stays constant (0.5sec) ( ) stays constant (1.7sec)
Outline
System Background Description, SSOC, Step Response
FOPDT Theory Model Theory Results Conclusions
Steady 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
SSOC
TEAM 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
FOPDT Model
Model Equation
Excel Parameters td = Time step occurs A = Height of Step inbl = Initial Input outbl = Initial Steady Value
0
1)( 0
ttt
d
d
eKtttuAtC
Experimental and Model Results
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 Results…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
Results
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 … 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… 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
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