MECH 322 Instrumentation

Feedback Temperature Control

Performed: 04/20/06

Pablo Araya : I believe I performed 100% of this lab

Participation (__/50 points)

ABSTRACT• The goal of this work is to construct a feedback system to

control the temperature of water in a beaker, and evaluate its performance.

• A heater connected to a solid state relay and a thermocouple are placed in a beaker of water. A LabVIEW program is constructed to monitor the water temperature and close/open the relay if the temperature is below/above a user-specified set point value. Three different temperature set points are examined.

• The rate at which the heater/natural convection system increases the steady state temperature is greater than the rate it decreases it.

• The amplitude of the steady state temperature increased as the set point temperature increased, but its oscillatory period decreased.

Fig. 1 Type-J Thermocouple Temperature versus Output Voltage

• A third order polynomial appears to accurately represent the data. • The relation between signal conditioner output and the thermocouple

voltage is VTC = (VOUT/ 0.105143 V/mV) - 4.632 mV• These relations are used to interpret the voltage measured by the

data acquisition system to determine the thermocouple temperature.

Ttc = 1.05E-02Vtc3 - 2.18E-01Vtc

2 + 1.98E+01Vtc - 1.89E-04

0

20

40

60

80

100

120

0 1 2 3 4 5 6

Vtc [mV]

Ttc

[oC

]

Figure 2 VI Front Panel

Figure 3 VI Block Diagram

Formula Formula: Vout/0.105143-4.632

Formula2 Formula: 1.05E-02*Vtc**3 - 2.18E-01*Vtc**2 + 1.98E+01*Vtc - 1.89E-04

Figure 4 Measured Temperature versus Time for Three Set Points

• The steady state error amplitude increases and period decreases as the set point temperature increases.

• The temperature rise rate when the set-point temperature is increased is greater than the settling rate when the set-point is decreased.

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500Time [Sec]

Te

mp

era

ture

, T [

°C]

Measurement

Set Point

Cycle Time = 1 Sec

Table 1 Time to Reach Set Point

• For each set-point change, this table gives data for the temperature change T = TSP-TI, the time to reach the set point P1 = tR–tC,and the average rate of temperature change dT/dt = T/ P1.

• In steps 1 and 2 the 200 W immersion heater is used to increase the temperature.

• In step 3, natural convection to the surroundings is used to lower the set-point temperature.

• The rate of temperature decrease due to convection is slower than the rate of increase from the heater

Initial Temperature

Set Point Temperature

Temperature Change

Set Point Change Time

Time Set Point Reached

Time to Reach Set Point

Average Slew Rate

Step Ti TSPT tC tR P1 dT/dt

°C °C °C sec sec sec °C/s1 28.7 45 16.3 109 336 227 0.0722 45 85 40 904 1426 522 0.0773 85 70 -15 1553 1921 368 -0.041

Figure 5 Temperature vs Time for Tsp=45oC

• The unsteady waveform, period and amplitude are somewhat regular.

• The temperature spends more time above the set point than below it.

• The maximum error is EMAX = 0.7°C

• The oscillatory amplitude and period range from TPP = 0.5-0.9°C and P2 = 61 - 86 s, respectively.

44.6

44.8

45

45.2

45.4

45.6

45.8

46

350 450 550 650 750 850Time [Sec]

Te

mp

era

ture

, T [

°C]

Measurement

Set Point

Figure 6 Temperature vs. Time for Tsp=85oC

• The unsteady waveform is somewhat irregular, but its period and amplitude are roughly constant

• The temperature spends about the same amount of time below and above the set point.

• The maximum error is EMAX = -1.3°C

• The oscillatory amplitude and period range from TPP = 1.5-1.9°C and P2 = 15-26 s.

83.5

84

84.5

85

85.5

86

86.5

1400 1450 1500 1550Time [Sec]

Te

mp

era

ture

, T [

°C]

Measurement

Set Point

Figure 7 Temperature vs. Time for Tsp=70oC

• The unsteady waveform, period and amplitude are not regular

• The temperature spends more time above the set point than below it.

• The maximum error is EMAX = 1.4°C

• The steady state oscillatory amplitude and period vary between TPP = 0.7-1.6°C and P2 = 16-40 s, respectively.

69

69.5

70

70.5

71

71.5

1950 2000 2050 2100 2150 2200 2250 2300

Time [Sec]

Te

mp

era

ture

, T [

°C]

Measurement

Set Point

Table 2 Steady State Behaviors after the Set Point is Reached

• The rate at which the heater increases the temperature is greater than the rate natural convection decreases it.

• The steady state behavior is regular at the first two set points and irregular at the final set point.

• The steady state peak-to-peak temperature variations increase with set-point temperature, but the oscillatory period decreases.

• The convection heat transfer from the beaker to the surroundings is larger at the hotter set points.

TSPT P1 dT/dt TPP P2 Oscilatory

°C °C sec °C/s °C sec Behavior45 16.3 227 0.072 0.5 - 0.9 61 - 86 Regular85 40 522 0.077 1.5 - 1.9 15 - 26 Regular70 -15 368 -0.041 0.7 - 1.6 16 - 40 Irregular