thermal rise 3

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


2/43


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


4/43

perature above room temperature

0

Temp.


5/43


6/43


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=




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


8/43


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


10/43


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


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


13/43


14/43


15/43


16/43


17/43

mp.


18/43


19/43


20/43


21/43


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


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=


Time

step=

Coefficient

of Heating=

Coefficient

of Cooling=

MaximumPower

Dissipation=

Integral

Coefficient=

Heating(power)

Netheating=

Errorsummation


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


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


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


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.


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


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


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=




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


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


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


31/43

proportional to temperature above room temperature

FIXED

0

Temp.


32/43


33/43


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


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=


Timestep=




IntegralCoefficient=

Heating(power)

Netheating=

Errorsummation


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


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


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


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


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


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


40/43


41/43


42/43


43/43

thermal rise 3

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