8/6/2019 Thermal Rise 3
1/43
Temperature C Simple Proportional Model: Heating proportional to Error and Cooling proportional to te
25 Setpoint= 60 5
0.5 1 0.05 5
Time Temp. Error Cooling Temp rise=0 25 35 8.75 0 4.38 4.38
0.5 29.38 30.63 7.66 0.22 3.72 3.72
1 33.09 26.91 6.73 0.4 3.16 3.16
1.5 36.25 23.75 5.94 0.56 2.69 2.69
2 38.94 21.06 5.26 0.7 2.28 2.28
2.5 41.23 18.77 4.69 0.81 1.94 1.94
3 43.17 16.83 4.21 0.91 1.65 1.65
3.5 44.82 15.18 3.8 0.99 1.4 1.4
4 46.22 13.78 3.45 1.06 1.19 1.19
4.5 47.41 12.59 3.15 1.12 1.01 1.015 48.42 11.58 2.89 1.17 0.86 0.86
5.5 49.29 10.71 2.68 1.21 0.73 0.736 50.02 9.98 2.5 1.25 0.62 0.62
6.5 50.64 9.36 2.34 1.28 0.53 0.537 51.17 8.83 2.21 1.31 0.45 0.457.5 51.62 8.38 2.1 1.33 0.38 0.38
8 52 8 2 1.35 0.32 0.328.5 52.33 7.67 1.92 1.37 0.28 0.28
9 52.6 7.4 1.85 1.38 0.23 0.23
9.5 52.84 7.16 1.79 1.39 0.2 0.210 53.04 6.96 1.74 1.4 0.17 0.17
10.5 53.21 6.79 1.7 1.41 0.14 0.14
RoomTemp=
ProportionalFactor=
Timestep=
Coefficientof Heating=
Coefficientof Cooling=
MaximumPowerDissipation=
Heating(power)
Netheating=
01
23
45
67
8910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
3738
3940
4142
4344
4546
4748
49
25
30
35
40
45
50
55
60
65
70
Temp.
Time
Tempera
ture
8/6/2019 Thermal Rise 3
2/43
8/6/2019 Thermal Rise 3
3/43
38 54.17 5.83 1.46 1.46 0 038.5 54.17 5.83 1.46 1.46 0 0
39 54.17 5.83 1.46 1.46 0 0
39.5 54.17 5.83 1.46 1.46 0 040 54.17 5.83 1.46 1.46 0 0
40.5 54.17 5.83 1.46 1.46 0 041 54.17 5.83 1.46 1.46 0 0
41.5 54.17 5.83 1.46 1.46 0 0
42 54.17 5.83 1.46 1.46 0 0
42.5 54.17 5.83 1.46 1.46 0 0
43 54.17 5.83 1.46 1.46 0 0
43.5 54.17 5.83 1.46 1.46 0 0
44 54.17 5.83 1.46 1.46 0 0
44.5 54.17 5.83 1.46 1.46 0 0
45 54.17 5.83 1.46 1.46 0 0
45.5 54.17 5.83 1.46 1.46 0 0
46 54.17 5.83 1.46 1.46 0 0
46.5 54.17 5.83 1.46 1.46 0 0
47 54.17 5.83 1.46 1.46 0 0
47.5 54.17 5.83 1.46 1.46 0 048 54.17 5.83 1.46 1.46 0 0
48.5 54.17 5.83 1.46 1.46 0 0
49 54.17 5.83 1.46 1.46 0 0
49.5 54.17 5.83 1.46 1.46 0 050 54.17 5.83 1.46 1.46 0 0
8/6/2019 Thermal Rise 3
4/43
perature above room temperature
0
Temp.
8/6/2019 Thermal Rise 3
5/43
8/6/2019 Thermal Rise 3
6/43
8/6/2019 Thermal Rise 3
7/43
Temperature CoPI Model: Heating proportional to Error (+ integral of error) and Cooling proportion
25 Setpoint= 60 5
0.5 1 0.05 5
Time Temp. Error Cooling Temp rise=
0 25 35 8.75 0 4.38 4.38 0 0
0.5 29.38 30.63 7.66 0.22 3.82 3.82 35 0.21
1 33.2 26.8 6.7 0.41 3.34 3.34 65.63 0.39
1.5 36.54 23.46 5.86 0.58 2.92 2.92 92.43 0.55
2 39.46 20.54 5.13 0.72 2.55 2.55 115.89 0.7
2.5 42.02 17.98 4.5 0.85 2.23 2.23 136.42 0.82
3 44.25 15.75 3.94 0.96 1.95 1.95 154.41 0.93
3.5 46.2 13.8 3.45 1.06 1.71 1.71 170.16 1.02
4 47.9 12.1 3.02 1.15 1.49 1.49 183.96 1.1
4.5 49.4 10.6 2.65 1.22 1.3 1.3 196.06 1.185 50.7 9.3 2.33 1.28 1.14 1.14 206.66 1.24
5.5 51.84 8.16 2.04 1.34 1 1 215.96 1.3
6 52.84 7.16 1.79 1.39 0.87 0.87 224.12 1.34
6.5 53.71 6.29 1.57 1.44 0.76 0.76 231.29 1.39
7 54.47 5.53 1.38 1.47 0.67 0.67 237.58 1.43
7.5 55.14 4.86 1.22 1.51 0.58 0.58 243.11 1.46
8 55.72 4.28 1.07 1.54 0.51 0.51 247.97 1.49
8.5 56.23 3.77 0.94 1.56 0.45 0.45 252.25 1.51
9 56.68 3.32 0.83 1.58 0.39 0.39 256.02 1.54
9.5 57.07 2.93 0.73 1.6 0.34 0.34 259.34 1.56
10 57.41 2.59 0.65 1.62 0.3 0.3 262.27 1.57
10.5 57.71 2.29 0.57 1.64 0.26 0.26 264.85 1.59
11 57.98 2.02 0.51 1.65 0.23 0.23 267.14 1.611.5 58.21 1.79 0.45 1.66 0.2 0.2 269.17 1.61
RoomTemp=
ProportionalFactor=
IntegralCoefficient(x1000)=
Timestep=
Coefficientof Heating=
Coefficientof Cooling=
MaximumPowerDissipation=
IntegralCoefficient=
Heating(power)
Netheating=
Errorsummation
IntegralHeatingcontribution
1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 94 10 16 22 28 34 40 46 52 58 64 70 76 82 88 94
25
30
35
40
45
50
55
6065
70
Ti
Tempera
ture
8/6/2019 Thermal Rise 3
8/43
8/6/2019 Thermal Rise 3
9/43
41 59.94 0.06 0.01 1.75 0 0 289.19 1.74
41.5 59.94 0.06 0.01 1.75 0 0 289.25 1.74
42 59.94 0.06 0.01 1.75 0 0 289.31 1.74
42.5 59.95 0.05 0.01 1.75 0 0 289.37 1.74
43 59.95 0.05 0.01 1.75 0 0 289.42 1.74
43.5 59.95 0.05 0.01 1.75 0 0 289.48 1.74
44 59.95 0.05 0.01 1.75 0 0 289.53 1.7444.5 59.95 0.05 0.01 1.75 0 0 289.58 1.74
45 59.95 0.05 0.01 1.75 0 0 289.63 1.74
45.5 59.95 0.05 0.01 1.75 0 0 289.68 1.74
46 59.95 0.05 0.01 1.75 0 0 289.72 1.74
46.5 59.95 0.05 0.01 1.75 0 0 289.77 1.74
47 59.96 0.04 0.01 1.75 0 0 289.82 1.74
47.5 59.96 0.04 0.01 1.75 0 0 289.86 1.74
48 59.96 0.04 0.01 1.75 0 0 289.9 1.74
48.5 59.96 0.04 0.01 1.75 0 0 289.94 1.74
49 59.96 0.04 0.01 1.75 0 0 289.99 1.74
49.5 59.96 0.04 0.01 1.75 0 0 290.03 1.74
50 59.96 0.04 0.01 1.75 0 0 290.06 1.74
59.96 0.04 0.01 1.75 0 0 290.1 1.74
59.96 0.04 0.01 1.75 0 0 290.14 1.74
59.96 0.04 0.01 1.75 0 0 290.18 1.74
59.97 0.03 0.01 1.75 0 0 290.21 1.74
59.97 0.03 0.01 1.75 0 0 290.25 1.74
59.97 0.03 0.01 1.75 0 0 290.28 1.74
59.97 0.03 0.01 1.75 0 0 290.31 1.74
59.97 0.03 0.01 1.75 0 0 290.35 1.74
59.97 0.03 0.01 1.75 0 0 290.38 1.74
59.97 0.03 0.01 1.75 0 0 290.41 1.74
59.97 0.03 0.01 1.75 0 0 290.44 1.74
59.97 0.03 0.01 1.75 0 0 290.47 1.74
59.97 0.03 0.01 1.75 0 0 290.5 1.7459.97 0.03 0.01 1.75 0 0 290.52 1.74
59.97 0.03 0.01 1.75 0 0 290.55 1.74
59.97 0.03 0.01 1.75 0 0 290.58 1.74
59.97 0.03 0.01 1.75 0 0 290.6 1.74
59.98 0.02 0.01 1.75 0 0 290.63 1.74
59.98 0.02 0.01 1.75 0 0 290.65 1.74
59.98 0.02 0.01 1.75 0 0 290.68 1.74
59.98 0.02 0.01 1.75 0 0 290.7 1.74
59.98 0.02 0.01 1.75 0 0 290.72 1.74
59.98 0.02 0.01 1.75 0 0 290.75 1.74
59.98 0.02 0.01 1.75 0 0 290.77 1.74
59.98 0.02 0.01 1.75 0 0 290.79 1.7459.98 0.02 0.01 1.75 0 0 290.81 1.74
59.98 0.02 0 1.75 0 0 290.83 1.74
59.98 0.02 0 1.75 0 0 290.85 1.75
59.98 0.02 0 1.75 0 0 290.87 1.75
59.98 0.02 0 1.75 0 0 290.89 1.75
59.98 0.02 0 1.75 0 0 290.91 1.75
59.98 0.02 0 1.75 0 0 290.92 1.75
59.98 0.02 0 1.75 0 0 290.94 1.75
59.98 0.02 0 1.75 0 0 290.96 1.75
59.98 0.02 0 1.75 0 0 290.98 1.75
59.98 0.02 0 1.75 0 0 290.99 1.75
59.98 0.02 0 1.75 0 0 291.01 1.75
59.98 0.02 0 1.75 0 0 291.02 1.7559.99 0.01 0 1.75 0 0 291.04 1.75
8/6/2019 Thermal Rise 3
10/43
8/6/2019 Thermal Rise 3
11/43
60 0 0 1.75 0 0 291.52 1.75
60 0 0 1.75 0 0 291.52 1.75
60 0 0 1.75 0 0 291.52 1.75
8/6/2019 Thermal Rise 3
12/43
l to temperature above room temperature
6
0.01
100103
106109
112115
118121
124127
130133
136139
142145
148151
154157
160163
166169
172175
178181
184187
190193
196199
Temp.
T
me
8/6/2019 Thermal Rise 3
13/43
8/6/2019 Thermal Rise 3
14/43
8/6/2019 Thermal Rise 3
15/43
8/6/2019 Thermal Rise 3
16/43
8/6/2019 Thermal Rise 3
17/43
mp.
8/6/2019 Thermal Rise 3
18/43
8/6/2019 Thermal Rise 3
19/43
8/6/2019 Thermal Rise 3
20/43
8/6/2019 Thermal Rise 3
21/43
8/6/2019 Thermal Rise 3
22/43
Temperature CoPID Model: Heating proportional to Error (+ integral of error + differential of error) a
25 Setpoint= 60 5
0.5 1 0.05 5
Time Temp. Error Cooling Temp rise=
0 25 35 8.75 0 4.38 4.38 0 00.5 29.38 30.63 7.66 0.22 5.43 5.43 35 0.35
1 34.8 25.2 6.3 0.49 5.13 5.13 65.63 0.661.5 39.93 20.07 5.02 0.75 4.39 4.39 90.83 0.91
2 44.32 15.68 3.92 0.97 3.57 3.57 110.89 1.11
2.5 47.88 12.12 3.03 1.14 2.82 2.82 126.58 1.273 50.71 9.29 2.32 1.29 2.2 2.2 138.69 1.39
3.5 52.91 7.09 1.77 1.4 1.7 1.7 147.98 1.48
4 54.61 5.39 1.35 1.48 1.3 1.3 155.08 1.55
4.5 55.91 4.09 1.02 1.55 1 1 160.47 1.65 56.91 3.09 0.77 1.6 0.76 0.76 164.56 1.65
5.5 57.67 2.33 0.58 1.63 0.58 0.58 167.65 1.68
6 58.25 1.75 0.44 1.66 0.44 0.44 169.98 1.7
6.5 58.69 1.31 0.33 1.68 0.33 0.33 171.73 1.72
7 59.02 0.98 0.24 1.7 0.25 0.25 173.04 1.73
7.5 59.28 0.72 0.18 1.71 0.19 0.19 174.02 1.748 59.47 0.53 0.13 1.72 0.15 0.15 174.74 1.75
8.5 59.61 0.39 0.1 1.73 0.11 0.11 175.28 1.75
RoomTemp=
ProportionalFactor=
IntegralCoefficient(x1000)=
Time
step=
Coefficient
of Heating=
Coefficient
of Cooling=
MaximumPower
Dissipation=
Integral
Coefficient=
Heating(power)
Netheating=
Errorsummation
IntegralHeatingcontribution
01
23
45
67
8910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
3738
3940
4142
425
30
35
40
45
50
55
6065
70
Temp.
Time
Tempera
ture
8/6/2019 Thermal Rise 3
23/43
9 59.73 0.27 0.07 1.74 0.08 0.08 175.66 1.769.5 59.81 0.19 0.05 1.74 0.06 0.06 175.94 1.76
10 59.87 0.13 0.03 1.74 0.05 0.05 176.13 1.76
10.5 59.92 0.08 0.02 1.75 0.04 0.04 176.26 1.7611 59.95 0.05 0.01 1.75 0.03 0.03 176.34 1.76
11.5 59.98 0.02 0.01 1.75 0.02 0.02 176.39 1.7612 60 0 0 1.75 0.01 0.01 176.41 1.76
12.5 60.01 -0.01 0 1.75 0.01 0.01 176.41 1.76
13 60.02 -0.02 0 1.75 0.01 0.01 176.4 1.76
13.5 60.03 -0.03 0 1.75 0.01 0.01 176.37 1.76
14 60.04 -0.04 0 1.75 0.01 0.01 176.34 1.76
14.5 60.05 -0.05 0 1.75 0.01 0.01 176.3 1.76
15 60.06 -0.06 0 1.75 0.01 0.01 176.24 1.76
15.5 60.07 -0.07 0 1.75 0.01 0.01 176.18 1.76
16 60.08 -0.08 0 1.75 0.01 0.01 176.11 1.76
16.5 60.08 -0.08 0 1.75 0.01 0.01 176.04 1.76
17 60.09 -0.09 0 1.75 0 0 175.96 1.76
17.5 60.09 -0.09 0 1.75 0 0 175.87 1.76
18 60.1 -0.1 0 1.75 0 0 175.78 1.76
18.5 60.1 -0.1 0 1.75 0 0 175.68 1.7619 60.1 -0.1 0 1.75 0 0 175.58 1.76
19.5 60.1 -0.1 0 1.76 0 0 175.48 1.75
20 60.1 -0.1 0 1.76 0 0 175.38 1.75
20.5 60.1 -0.1 0 1.76 0 0 175.28 1.7521 60.1 -0.1 0 1.75 0 0 175.18 1.75
21.5 60.1 -0.1 0 1.75 0 0 175.08 1.75
22 60.1 -0.1 0 1.75 0 0 174.98 1.75
22.5 60.09 -0.09 0 1.75 0 0 174.89 1.75
23 60.09 -0.09 0 1.75 0 0 174.8 1.75
23.5 60.09 -0.09 0 1.75 0 0 174.7 1.75
24 60.08 -0.08 0 1.75 0 0 174.62 1.75
24.5 60.08 -0.08 0 1.75 0 0 174.53 1.75
25 60.08 -0.08 0 1.75 0 0 174.45 1.7425.5 60.07 -0.07 0 1.75 0 0 174.38 1.74
26 60.07 -0.07 0 1.75 -0.01 -0.01 174.31 1.74
26.5 60.06 -0.06 0 1.75 -0.01 -0.01 174.24 1.74
27 60.06 -0.06 0 1.75 -0.01 -0.01 174.18 1.7427.5 60.05 -0.05 0 1.75 -0.01 -0.01 174.13 1.74
28 60.04 -0.04 0 1.75 -0.01 -0.01 174.08 1.7428.5 60.04 -0.04 0 1.75 -0.01 -0.01 174.03 1.74
29 60.03 -0.03 0 1.75 -0.01 -0.01 173.99 1.74
29.5 60.03 -0.03 0 1.75 -0.01 -0.01 173.96 1.7430 60.02 -0.02 0 1.75 -0.01 -0.01 173.93 1.74
30.5 60.02 -0.02 0 1.75 -0.01 -0.01 173.91 1.74
31 60.01 -0.01 0 1.75 -0.01 -0.01 173.9 1.74
31.5 60 0 0 1.75 -0.01 -0.01 173.89 1.7432 60 0 0 1.75 -0.01 -0.01 173.88 1.74
32.5 59.99 0.01 0 1.75 0 0 173.89 1.74
33 59.99 0.01 0 1.75 0 0 173.89 1.74
33.5 59.98 0.02 0 1.75 0 0 173.91 1.74
34 59.98 0.02 0 1.75 0 0 173.92 1.74
34.5 59.98 0.02 0.01 1.75 0 0 173.94 1.7435 59.98 0.02 0.01 1.75 0 0 173.96 1.74
35.5 59.97 0.03 0.01 1.75 0 0 173.98 1.74
8/6/2019 Thermal Rise 3
24/43
36 59.97 0.03 0.01 1.75 0 0 174.01 1.7436.5 59.97 0.03 0.01 1.75 0 0 174.04 1.74
37 59.97 0.03 0.01 1.75 0 0 174.06 1.74
37.5 59.97 0.03 0.01 1.75 0 0 174.09 1.7438 59.97 0.03 0.01 1.75 0 0 174.12 1.74
38.5 59.97 0.03 0.01 1.75 0 0 174.15 1.7439 59.97 0.03 0.01 1.75 0 0 174.18 1.74
39.5 59.97 0.03 0.01 1.75 0 0 174.21 1.74
40 59.97 0.03 0.01 1.75 0 0 174.24 1.74
40.5 59.97 0.03 0.01 1.75 0 0 174.26 1.74
41 59.97 0.03 0.01 1.75 0 0 174.29 1.74
41.5 59.97 0.03 0.01 1.75 0 0 174.32 1.74
42 59.97 0.03 0.01 1.75 0 0 174.34 1.74
42.5 59.98 0.02 0.01 1.75 0 0 174.37 1.74
43 59.98 0.02 0.01 1.75 0 0 174.39 1.74
43.5 59.98 0.02 0.01 1.75 0 0 174.42 1.74
44 59.98 0.02 0.01 1.75 0 0 174.44 1.74
44.5 59.98 0.02 0.01 1.75 0 0 174.46 1.74
45 59.98 0.02 0.01 1.75 0 0 174.48 1.74
45.5 59.98 0.02 0 1.75 0 0 174.51 1.7546 59.98 0.02 0 1.75 0 0 174.52 1.75
46.5 59.98 0.02 0 1.75 0 0 174.54 1.75
47 59.98 0.02 0 1.75 0 0 174.56 1.75
47.5 59.98 0.02 0 1.75 0 0 174.58 1.7548 59.98 0.02 0 1.75 0 0 174.6 1.75
48.5 59.98 0.02 0 1.75 0 0 174.61 1.75
49 59.99 0.01 0 1.75 0 0 174.63 1.75
49.5 59.99 0.01 0 1.75 0 0 174.64 1.75
50 59.99 0.01 0 1.75 0 0 174.66 1.75
8/6/2019 Thermal Rise 3
25/43
d Cooling proportional to temperature above room temperature
10
0.01 0.7
0 04.38 3.06
5.43 3.85.13 3.59
4.39 3.07
3.57 2.52.82 1.98
2.2 1.54
1.7 1.19
1.3 0.911 0.7
0.76 0.53
0.58 0.41
0.44 0.31
0.33 0.23
0.25 0.180.19 0.13
0.15 0.1
Differential
Coefficient=Rate ofErrorChange
DifferentialHeatingcontribution
344
4546
4748
4950
Temp.
8/6/2019 Thermal Rise 3
26/43
0.11 0.080.08 0.06
0.06 0.04
0.05 0.030.04 0.02
0.03 0.020.02 0.01
0.01 0.01
0.01 0.01
0.01 0.01
0.01 0.01
0.01 0.01
0.01 0.01
0.01 0.01
0.01 0
0.01 0
0.01 0
0 0
0 0
0 00 00 0
0 0
0 00 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 00 00 0
-0.01 0
-0.01 0-0.01 0
-0.01 0-0.01 0
-0.01 0
-0.01 0-0.01 0
-0.01 0
-0.01 0
-0.01 0-0.01 0
-0.01 0
0 0
0 0
0 0
0 00 0
0 0
8/6/2019 Thermal Rise 3
27/43
0 00 0
0 0
0 00 0
0 00 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 00 00 0
0 0
0 00 0
0 0
0 0
0 0
0 0
8/6/2019 Thermal Rise 3
28/43
Temperature C Simple Proportional + Delay Model: Heating proportional to measured Error and Cooling
25 Setpoint= 60 6 2
0.5 1 0.05 5
Time Temp. Error Cooling Temp rise=0 25 35 10.5 0 5.25 5.25
0.5 25 35 10.5 0 5.25 5.25
1 25 35 10.5 0 5.25 5.25
1.5 25 35 10.5 0 5.25 5.25
2 30.25 29.75 8.93 0.26 4.33 4.33
2.5 35.5 24.5 7.35 0.53 3.41 3.41
3 40.75 19.25 5.78 0.79 2.49 2.49
3.5 46 14 4.2 1.05 1.58 1.58
4 50.33 9.67 2.9 1.27 0.82 0.82
4.5 53.74 6.26 1.88 1.44 0.22 0.225 56.24 3.76 1.13 1.56 -0.22 -0.22
5.5 57.81 2.19 0.66 1.64 -0.49 -0.496 58.63 1.37 0.41 1.68 -0.64 -0.64
6.5 58.85 1.15 0.35 1.69 -0.67 -0.677 58.63 1.37 0.41 1.68 -0.64 -0.647.5 58.14 1.86 0.56 1.66 -0.55 -0.55
8 57.51 2.49 0.75 1.63 -0.44 -0.448.5 56.83 3.17 0.95 1.59 -0.32 -0.32
9 56.2 3.8 1.14 1.56 -0.21 -0.21
9.5 55.65 4.35 1.31 1.53 -0.11 -0.1110 55.21 4.79 1.44 1.51 -0.04 -0.04
10.5 54.89 5.11 1.53 1.49 0.02 0.02
RoomTemp=
ProportionalFactor=
Thermaldelay=
Timestep=
Coefficientof Heating=
Coefficientof Cooling=
MaximumPowerDissipation=
Heating(power)
Netheating=
1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 974 10 16 22 28 34 40 46 52 58 64 70 76 82 88 94 1
25
30
35
40
45
50
55
60
65
70
Temp.
Time
Tempera
ture
8/6/2019 Thermal Rise 3
29/43
11 54.68 5.32 1.6 1.48 0.06 0.0611.5 54.56 5.44 1.63 1.48 0.08 0.08
12 54.53 5.47 1.64 1.48 0.08 0.08
12.5 54.55 5.45 1.64 1.48 0.08 0.0813 54.6 5.4 1.62 1.48 0.07 0.07
13.5 54.68 5.32 1.6 1.48 0.06 0.0614 54.76 5.24 1.57 1.49 0.04 0.04
14.5 54.84 5.16 1.55 1.49 0.03 0.03
15 54.91 5.09 1.53 1.5 0.02 0.02
15.5 54.97 5.03 1.51 1.5 0.01 0.01
16 55.01 4.99 1.5 1.5 0 0
16.5 55.04 4.96 1.49 1.5 -0.01 -0.01
17 55.05 4.95 1.48 1.5 -0.01 -0.01
17.5 55.06 4.94 1.48 1.5 -0.01 -0.01
18 55.06 4.94 1.48 1.5 -0.01 -0.01
18.5 55.05 4.95 1.49 1.5 -0.01 -0.01
19 55.04 4.96 1.49 1.5 -0.01 -0.01
19.5 55.03 4.97 1.49 1.5 -0.01 -0.01
20 55.02 4.98 1.49 1.5 0 0
20.5 55.01 4.99 1.5 1.5 0 021 55 5 1.5 1.5 0 0
21.5 55 5 1.5 1.5 0 0
22 55 5 1.5 1.5 0 0
22.5 54.99 5.01 1.5 1.5 0 023 54.99 5.01 1.5 1.5 0 0
23.5 54.99 5.01 1.5 1.5 0 0
24 54.99 5.01 1.5 1.5 0 0
24.5 54.99 5.01 1.5 1.5 0 0
25 55 5 1.5 1.5 0 0
25.5 55 5 1.5 1.5 0 0
26 55 5 1.5 1.5 0 0
26.5 55 5 1.5 1.5 0 0
27 55 5 1.5 1.5 0 027.5 55 5 1.5 1.5 0 0
28 55 5 1.5 1.5 0 0
28.5 55 5 1.5 1.5 0 0
29 55 5 1.5 1.5 0 029.5 55 5 1.5 1.5 0 0
30 55 5 1.5 1.5 0 030.5 55 5 1.5 1.5 0 0
31 55 5 1.5 1.5 0 0
31.5 55 5 1.5 1.5 0 032 55 5 1.5 1.5 0 0
32.5 55 5 1.5 1.5 0 0
33 55 5 1.5 1.5 0 0
33.5 55 5 1.5 1.5 0 034 55 5 1.5 1.5 0 0
34.5 55 5 1.5 1.5 0 0
35 55 5 1.5 1.5 0 0
35.5 55 5 1.5 1.5 0 0
36 55 5 1.5 1.5 0 0
36.5 55 5 1.5 1.5 0 037 55 5 1.5 1.5 0 0
37.5 55 5 1.5 1.5 0 0
8/6/2019 Thermal Rise 3
30/43
38 55 5 1.5 1.5 0 038.5 55 5 1.5 1.5 0 0
39 55 5 1.5 1.5 0 0
39.5 55 5 1.5 1.5 0 040 55 5 1.5 1.5 0 0
40.5 55 5 1.5 1.5 0 041 55 5 1.5 1.5 0 0
41.5 55 5 1.5 1.5 0 0
42 55 5 1.5 1.5 0 0
42.5 55 5 1.5 1.5 0 0
43 55 5 1.5 1.5 0 0
43.5 55 5 1.5 1.5 0 0
44 55 5 1.5 1.5 0 0
44.5 55 5 1.5 1.5 0 0
45 55 5 1.5 1.5 0 0
45.5 55 5 1.5 1.5 0 0
46 55 5 1.5 1.5 0 0
46.5 55 5 1.5 1.5 0 0
47 55 5 1.5 1.5 0 0
47.5 55 5 1.5 1.5 0 048 55 5 1.5 1.5 0 0
48.5 55 5 1.5 1.5 0 0
49 55 5 1.5 1.5 0 0
49.5 55 5 1.5 1.5 0 050 55 5 1.5 1.5 0 0
8/6/2019 Thermal Rise 3
31/43
proportional to temperature above room temperature
FIXED
0
Temp.
8/6/2019 Thermal Rise 3
32/43
8/6/2019 Thermal Rise 3
33/43
8/6/2019 Thermal Rise 3
34/43
Temperature CoPI Model+ delay: Heating proportional to measured Error (+ integral of error) and C
25 Setpoint= 60 4
0.5 1 0.05 5
Time Temp. Error Cooling Temp rise=
0 25 35 7 0 3.5 3.5 0 0
0.5 25 35 7 0 3.59 3.59 35 0.181 25 35 7 0 3.68 3.68 70 0.35
1.5 25 35 7 0 3.76 3.76 105 0.53
2 28.5 31.5 6.3 0.18 3.41 3.41 140 0.72.5 32.09 27.91 5.58 0.35 3.04 3.04 171.5 0.86
3 35.76 24.24 4.85 0.54 2.65 2.65 199.41 13.5 39.53 20.48 4.1 0.73 2.24 2.24 223.65 1.12
4 42.94 17.06 3.41 0.9 1.87 1.87 244.13 1.22
4.5 45.98 14.02 2.8 1.05 1.53 1.53 261.19 1.31
5 48.63 11.37 2.27 1.18 1.23 1.23 275.21 1.385.5 50.88 9.12 1.82 1.29 0.98 0.98 286.57 1.43
6 52.75 7.25 1.45 1.39 0.77 0.77 295.7 1.48
6.5 54.28 5.72 1.14 1.46 0.6 0.6 302.95 1.51
7 55.51 4.49 0.9 1.53 0.46 0.46 308.68 1.54
7.5 56.49 3.51 0.7 1.57 0.35 0.35 313.17 1.57
8 57.26 2.74 0.55 1.61 0.26 0.26 316.68 1.58
8.5 57.86 2.14 0.43 1.64 0.19 0.19 319.41 1.6
9 58.32 1.68 0.34 1.67 0.14 0.14 321.55 1.61
RoomTemp=
ProportionalFactor=
IntegralCoefficient(x1000)=
Timestep=
Coefficientof Heating=
Coefficientof Cooling=
MaximumPowerDissipation=
IntegralCoefficient=
Heating(power)
Netheating=
Errorsummation
IntegralHeatingcontribution
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
51
53
55
57
59
61
63
65
67
69
25
30
35
40
45
50
55
60
65
70
Time
tempera
ture
8/6/2019 Thermal Rise 3
35/43
9.5 58.66 1.34 0.27 1.68 0.1 0.1 323.23 1.6210 58.92 1.08 0.22 1.7 0.07 0.07 324.57 1.62
10.5 59.11 0.89 0.18 1.71 0.05 0.05 325.65 1.63
11 59.25 0.75 0.15 1.71 0.03 0.03 326.53 1.6311.5 59.35 0.65 0.13 1.72 0.02 0.02 327.28 1.64
12 59.42 0.58 0.12 1.72 0.02 0.02 327.92 1.6412.5 59.47 0.53 0.11 1.72 0.01 0.01 328.5 1.64
13 59.51 0.49 0.1 1.73 0.01 0.01 329.02 1.65
13.5 59.53 0.47 0.09 1.73 0.01 0.01 329.52 1.65
14 59.55 0.45 0.09 1.73 0.01 0.01 329.98 1.65
14.5 59.56 0.44 0.09 1.73 0.01 0.01 330.43 1.65
15 59.57 0.43 0.09 1.73 0.01 0.01 330.87 1.65
15.5 59.58 0.42 0.08 1.73 0.01 0.01 331.3 1.66
16 59.58 0.42 0.08 1.73 0.01 0.01 331.72 1.66
16.5 59.59 0.41 0.08 1.73 0.01 0.01 332.14 1.66
17 59.6 0.4 0.08 1.73 0.01 0.01 332.55 1.66
17.5 59.6 0.4 0.08 1.73 0.01 0.01 332.95 1.66
18 59.61 0.39 0.08 1.73 0.01 0.01 333.35 1.67
18.5 59.61 0.39 0.08 1.73 0.01 0.01 333.74 1.67
19 59.62 0.38 0.08 1.73 0.01 0.01 334.13 1.6719.5 59.63 0.37 0.07 1.73 0.01 0.01 334.51 1.67
20 59.64 0.36 0.07 1.73 0.01 0.01 334.88 1.67
20.5 59.64 0.36 0.07 1.73 0.01 0.01 335.24 1.68
21 59.65 0.35 0.07 1.73 0.01 0.01 335.6 1.6821.5 59.66 0.34 0.07 1.73 0.01 0.01 335.95 1.68
22 59.67 0.33 0.07 1.73 0.01 0.01 336.29 1.68
22.5 59.67 0.33 0.07 1.73 0.01 0.01 336.62 1.68
23 59.68 0.32 0.06 1.73 0.01 0.01 336.95 1.68
23.5 59.69 0.31 0.06 1.73 0.01 0.01 337.27 1.69
24 59.7 0.3 0.06 1.73 0.01 0.01 337.58 1.69
24.5 59.7 0.3 0.06 1.74 0.01 0.01 337.88 1.69
25 59.71 0.29 0.06 1.74 0.01 0.01 338.17 1.69
25.5 59.72 0.28 0.06 1.74 0.01 0.01 338.46 1.6926 59.72 0.28 0.06 1.74 0.01 0.01 338.75 1.69
26.5 59.73 0.27 0.05 1.74 0.01 0.01 339.02 1.7
27 59.74 0.26 0.05 1.74 0.01 0.01 339.29 1.7
27.5 59.74 0.26 0.05 1.74 0.01 0.01 339.55 1.728 59.75 0.25 0.05 1.74 0.01 0.01 339.81 1.7
28.5 59.76 0.24 0.05 1.74 0.01 0.01 340.06 1.729 59.76 0.24 0.05 1.74 0.01 0.01 340.3 1.7
29.5 59.77 0.23 0.05 1.74 0.01 0.01 340.54 1.7
30 59.77 0.23 0.05 1.74 0.01 0.01 340.77 1.730.5 59.78 0.22 0.04 1.74 0 0 340.99 1.7
31 59.79 0.21 0.04 1.74 0 0 341.21 1.71
31.5 59.79 0.21 0.04 1.74 0 0 341.43 1.71
32 59.8 0.2 0.04 1.74 0 0 341.64 1.7132.5 59.8 0.2 0.04 1.74 0 0 341.84 1.71
33 59.81 0.19 0.04 1.74 0 0 342.04 1.71
33.5 59.81 0.19 0.04 1.74 0 0 342.24 1.71
34 59.81 0.19 0.04 1.74 0 0 342.42 1.71
34.5 59.82 0.18 0.04 1.74 0 0 342.61 1.71
35 59.82 0.18 0.04 1.74 0 0 342.79 1.7135.5 59.83 0.17 0.03 1.74 0 0 342.97 1.71
36 59.83 0.17 0.03 1.74 0 0 343.14 1.72
8/6/2019 Thermal Rise 3
36/43
36.5 59.84 0.16 0.03 1.74 0 0 343.31 1.7237 59.84 0.16 0.03 1.74 0 0 343.47 1.72
37.5 59.84 0.16 0.03 1.74 0 0 343.63 1.72
38 59.85 0.15 0.03 1.74 0 0 343.78 1.7238.5 59.85 0.15 0.03 1.74 0 0 343.94 1.72
39 59.86 0.14 0.03 1.74 0 0 344.08 1.7239.5 59.86 0.14 0.03 1.74 0 0 344.23 1.72
40 59.86 0.14 0.03 1.74 0 0 344.37 1.72
40.5 59.87 0.13 0.03 1.74 0 0 344.51 1.72
41 59.87 0.13 0.03 1.74 0 0 344.64 1.72
41.5 59.87 0.13 0.03 1.74 0 0 344.77 1.72
42 59.88 0.12 0.02 1.74 0 0 344.9 1.72
42.5 59.88 0.12 0.02 1.74 0 0 345.03 1.73
43 59.88 0.12 0.02 1.74 0 0 345.15 1.73
43.5 59.88 0.12 0.02 1.74 0 0 345.27 1.73
44 59.89 0.11 0.02 1.74 0 0 345.38 1.73
44.5 59.89 0.11 0.02 1.74 0 0 345.49 1.73
45 59.89 0.11 0.02 1.74 0 0 345.6 1.73
45.5 59.9 0.1 0.02 1.74 0 0 345.71 1.73
46 59.9 0.1 0.02 1.74 0 0 345.82 1.7346.5 59.9 0.1 0.02 1.75 0 0 345.92 1.73
47 59.9 0.1 0.02 1.75 0 0 346.02 1.73
47.5 59.91 0.09 0.02 1.75 0 0 346.12 1.73
48 59.91 0.09 0.02 1.75 0 0 346.21 1.7348.5 59.91 0.09 0.02 1.75 0 0 346.3 1.73
49 59.91 0.09 0.02 1.75 0 0 346.39 1.73
49.5 59.91 0.09 0.02 1.75 0 0 346.48 1.73
50 59.92 0.08 0.02 1.75 0 0 346.57 1.73
59.92 0.08 0.02 1.75 0 0 346.65 1.73
59.92 0.08 0.02 1.75 0 0 346.73 1.73
59.92 0.08 0.02 1.75 0 0 346.81 1.73
59.92 0.08 0.02 1.75 0 0 346.89 1.73
59.93 0.07 0.01 1.75 0 0 346.97 1.7359.93 0.07 0.01 1.75 0 0 347.04 1.7459.93 0.07 0.01 1.75 0 0 347.11 1.74
59.93 0.07 0.01 1.75 0 0 347.18 1.74
59.93 0.07 0.01 1.75 0 0 347.25 1.7459.93 0.07 0.01 1.75 0 0 347.32 1.74
59.94 0.06 0.01 1.75 0 0 347.39 1.7459.94 0.06 0.01 1.75 0 0 347.45 1.74
59.94 0.06 0.01 1.75 0 0 347.51 1.74
59.94 0.06 0.01 1.75 0 0 347.57 1.7459.94 0.06 0.01 1.75 0 0 347.63 1.74
59.94 0.06 0.01 1.75 0 0 347.69 1.74
59.94 0.06 0.01 1.75 0 0 347.75 1.74
59.95 0.05 0.01 1.75 0 0 347.8 1.7459.95 0.05 0.01 1.75 0 0 347.85 1.74
59.95 0.05 0.01 1.75 0 0 347.91 1.74
59.95 0.05 0.01 1.75 0 0 347.96 1.74
59.95 0.05 0.01 1.75 0 0 348.01 1.74
59.95 0.05 0.01 1.75 0 0 348.06 1.74
59.95 0.05 0.01 1.75 0 0 348.1 1.7459.95 0.05 0.01 1.75 0 0 348.15 1.74
59.96 0.04 0.01 1.75 0 0 348.2 1.74
8/6/2019 Thermal Rise 3
37/43
59.96 0.04 0.01 1.75 0 0 348.24 1.7459.96 0.04 0.01 1.75 0 0 348.28 1.74
59.96 0.04 0.01 1.75 0 0 348.32 1.74
59.96 0.04 0.01 1.75 0 0 348.37 1.7459.96 0.04 0.01 1.75 0 0 348.41 1.74
59.96 0.04 0.01 1.75 0 0 348.44 1.7459.96 0.04 0.01 1.75 0 0 348.48 1.74
59.96 0.04 0.01 1.75 0 0 348.52 1.74
59.96 0.04 0.01 1.75 0 0 348.56 1.74
59.97 0.03 0.01 1.75 0 0 348.59 1.74
59.97 0.03 0.01 1.75 0 0 348.63 1.74
59.97 0.03 0.01 1.75 0 0 348.66 1.74
59.97 0.03 0.01 1.75 0 0 348.69 1.74
59.97 0.03 0.01 1.75 0 0 348.72 1.74
59.97 0.03 0.01 1.75 0 0 348.76 1.74
59.97 0.03 0.01 1.75 0 0 348.79 1.74
59.97 0.03 0.01 1.75 0 0 348.82 1.74
59.97 0.03 0.01 1.75 0 0 348.84 1.74
59.97 0.03 0.01 1.75 0 0 348.87 1.74
59.97 0.03 0.01 1.75 0 0 348.9 1.7459.97 0.03 0.01 1.75 0 0 348.93 1.7459.97 0.03 0.01 1.75 0 0 348.95 1.74
59.98 0.02 0 1.75 0 0 348.98 1.74
59.98 0.02 0 1.75 0 0 349 1.7559.98 0.02 0 1.75 0 0 349.03 1.75
59.98 0.02 0 1.75 0 0 349.05 1.75
59.98 0.02 0 1.75 0 0 349.07 1.75
59.98 0.02 0 1.75 0 0 349.1 1.75
59.98 0.02 0 1.75 0 0 349.12 1.75
59.98 0.02 0 1.75 0 0 349.14 1.75
59.98 0.02 0 1.75 0 0 349.16 1.75
59.98 0.02 0 1.75 0 0 349.18 1.75
59.98 0.02 0 1.75 0 0 349.2 1.7559.98 0.02 0 1.75 0 0 349.22 1.7559.98 0.02 0 1.75 0 0 349.24 1.75
59.98 0.02 0 1.75 0 0 349.26 1.75
59.98 0.02 0 1.75 0 0 349.28 1.7559.98 0.02 0 1.75 0 0 349.3 1.75
59.98 0.02 0 1.75 0 0 349.31 1.7559.98 0.02 0 1.75 0 0 349.33 1.75
59.98 0.02 0 1.75 0 0 349.35 1.75
59.98 0.02 0 1.75 0 0 349.36 1.7559.98 0.02 0 1.75 0 0 349.38 1.75
59.99 0.01 0 1.75 0 0 349.39 1.75
59.99 0.01 0 1.75 0 0 349.41 1.75
59.99 0.01 0 1.75 0 0 349.42 1.7559.99 0.01 0 1.75 0 0 349.44 1.75
59.99 0.01 0 1.75 0 0 349.45 1.75
59.99 0.01 0 1.75 0 0 349.46 1.75
59.99 0.01 0 1.75 0 0 349.48 1.75
59.99 0.01 0 1.75 0 0 349.49 1.75
59.99 0.01 0 1.75 0 0 349.5 1.7559.99 0.01 0 1.75 0 0 349.51 1.75
59.99 0.01 0 1.75 0 0 349.53 1.75
8/6/2019 Thermal Rise 3
38/43
59.99 0.01 0 1.75 0 0 349.54 1.7559.99 0.01 0 1.75 0 0 349.55 1.75
59.99 0.01 0 1.75 0 0 349.56 1.75
59.99 0.01 0 1.75 0 0 349.57 1.7559.99 0.01 0 1.75 0 0 349.58 1.75
59.99 0.01 0 1.75 0 0 349.59 1.7559.99 0.01 0 1.75 0 0 349.6 1.75
59.99 0.01 0 1.75 0 0 349.61 1.75
59.99 0.01 0 1.75 0 0 349.62 1.75
59.99 0.01 0 1.75 0 0 349.63 1.75
59.99 0.01 0 1.75 0 0 349.64 1.75
59.99 0.01 0 1.75 0 0 349.65 1.75
59.99 0.01 0 1.75 0 0 349.66 1.75
59.99 0.01 0 1.75 0 0 349.66 1.75
59.99 0.01 0 1.75 0 0 349.67 1.75
59.99 0.01 0 1.75 0 0 349.68 1.75
59.99 0.01 0 1.75 0 0 349.69 1.75
59.99 0.01 0 1.75 0 0 349.7 1.75
59.99 0.01 0 1.75 0 0 349.7 1.75
59.99 0.01 0 1.75 0 0 349.71 1.7559.9959.99
59.99
8/6/2019 Thermal Rise 3
39/43
oling proportional to temperature above room temperature
5
0.01
71
73
75
77
79
81
83
85
87
89
91
93
95
Column B
8/6/2019 Thermal Rise 3
40/43
8/6/2019 Thermal Rise 3
41/43
8/6/2019 Thermal Rise 3
42/43
8/6/2019 Thermal Rise 3
43/43