ME 322: Instrumentation
Lecture 36
April 20, 2015
Professor Miles Greiner
Proportional Control
Announcements/Reminders
• HW 12 Due Friday
• This week: Lab 11 Unsteady Karmon Vortex Speed
• One-hour periods with your partner
• Schedule on WebCampus
– Please be on time and come prepared!
• Lab Practicum Final
– Guidelines, Schedule
• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Tests/Index.htm
– Schedule
• On WebCampus
• Please let me know if there are conflicts with other finals
– Practice Periods
• May 2-3, 2014
Lab 12 Setup
• Measure beaker water temperature using a
thermocouple/conditioner/myDAQ/VI
• Use myDAQ analog output (AO) to operate a digital
relay that turns heater on/off to control the water
temperature
Full on/off Control
• LabVIEW VI “logic”
– Measure thermocouple temperature for 1 sec
• Average, T, display
– Compare to TSP (compare and select icons)
– Turn 200 W heater on/off if T is below/above TSP
– Waveform Chart
• T and TSP versus time
• e = T-TSP versus time
– Repeat
• Constructed last lecture
– http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation
/Labs/Lab%2012%20Thermal%20Control/Lab%20Index.htm
Full On/Off Temperature Control
Front Panel
On/Off Control Temperature Response
• Full On/off control
–
–
–
–
Reaches TSP after ~3 minutes
Gives oscillatory response
Average temperature TAvg > TSP
Maximum error is roughly 2.5°C
• Want heater power to be high to reach TSP quickly
• Would oscillations decrease if power decreased near T ~ TSP?
How to reduce heater power using a relay?
FTO = 0.1
FTO = 0.5
FTO = 0.9
• Reduce the Fraction of Time the heater is On (FTO)
– Maximum heater power QMax = V2/R
• Reduce FTO to decrease heater power
– Heater Q = (FTO)(QMax)
• How to implement this in LabVIEW?
Strobe Light VI
• Stacked sequence loop
• Milliseconds to Wait
• Vary cycle time and FTO
Proportional Control
• Reduce heater power (FTO) when T is within a small increment DT of TSP
– Define 𝑓 𝑇 =
𝑇𝑆𝑃 −𝑇
(=
𝐷𝑇
1 𝑎𝑡 𝑇 = 𝑇𝑆𝑃 − 𝐷𝑇; = 0 𝑎𝑡 𝑇 = 𝑇𝑆𝑃 )
• Three temperature zones:
– For T < 𝑇𝑆𝑃 − 𝐷𝑇 ,
– For 𝑇𝑆𝑃 − 𝐷𝑇 < 𝑇 < 𝑇𝑆𝑃 ,
– For 𝑇 > 𝑇𝑆𝑃 ,
f> 1
FTO = 1
1 > f >0
f <0
𝐹𝑇𝑂 = 𝑓
FTO = 0
• For DT = 0, Proportional is same as full power On/Off
• What is Q when T = 𝑇𝑆𝑃 ?
– Why isn’t that good?
How to construct a Proportional-Control VI
Current
Temperature
• Calculate FTO
– Indicate FTP using a bar, dial and/or numeric indicator
• Use stacked sequence loop to turn heater on and off
• Write to a Measurement File VI
– Segment Headings (No Headers)
– X value (time) Column (one column only)
• Starting Point
Proportional Control
Proportional-Control Temp versus Time
90
On/Off
80
T
Temperature, T [C]
70
TSP
Proportional
60
TSP - DT
50
Proportional
40
30
20
0
10
20
30
40
50
60
70
80
90
Time, t [minutes]
• TSP = 65°C and TSP = 85°C
• As DT is increases (control becomes more proportional)
– Oscillatory amplitude decreases
• Temperature eventually becomes steady
– The “steady-state” average temperature 𝑇𝐴𝑉𝐺 decreases
• Error magnitude 𝑒 = 𝑇𝐴𝑉𝐺 − 𝑇𝑆𝑃 increases with DT and 𝑇𝑆𝑃
Average Temperature Error and Unsteadiness
versus DT and TSP
2.0
1.4
1.5
1.2
1.0
1.0
0.0
TRMS [C]
TA - TSP [°C]
0.5
TSP = 65°C
-0.5
0.8
TSP = 85°C
0.6
-1.0
-1.5
0.4
TSP = 85°C
TSP = 65°C
-2.0
0.2
-2.5
0
1
2
3
4
5
DT [°C]
6
7
8
9
10
0.0
0
1
2
3
4
5
6
7
8
9
10
DT [C]
• The average temperature error 𝑒 = 𝑇𝐴𝑉𝐺 − 𝑇𝑆𝑃
– Is positive for DT = 0, but decreases and becomes negative as
DT increases.
– Decreases as TSP increases
• TRMS (same as standard deviation) is and indication of
thermocouple temperature unsteadiness
– Unsteadiness decreases as DT increases, and as TSP decreases.
Proportional-Control Questions
• Why is the steady temperature below the set-point
(desired) value?
• Why do temperature oscillations disappear as DT
gets larger?
• Is there another control technique that eliminates
the steady state error?
Steady State Temperature Error
• 𝑄 − 𝑊 = 𝑄𝐼𝑛 − 𝑄𝑂𝑢𝑡 =
𝑇𝑆𝑃 −𝑇
𝐷𝑇
• 𝑄𝑀𝑎𝑥
𝑑𝑈
𝑑𝑡
=
𝑑𝑇
𝜌𝑐𝑉
𝑑𝑡
− ℎ𝐴 𝑇 − 𝑇𝐸𝑛𝑣 = 𝜌𝑐𝑉
𝑑𝑇
𝑑𝑡
• Let 𝑇𝑆𝑆 be the temperature under steady state conditions
–
•
𝑑𝑇𝑆𝑆
𝑑𝑡
=0
𝑇𝑆𝑃 −𝑇𝑆𝑆
𝑄𝑀𝑎𝑥
𝐷𝑇
= ℎ𝐴 𝑇𝑆𝑆 − 𝑇𝐸𝑛𝑣
– 𝑄𝑀𝑎𝑥 𝑇𝑆𝑃 − 𝑇𝑆𝑆 = ℎ𝐴 𝐷𝑇 𝑇𝑆𝑆 − 𝑇𝐸𝑛𝑣
– 𝑄𝑀𝑎𝑥 𝑇𝑆𝑃 + ℎ𝐴 𝐷𝑇 𝑇𝐸𝑛𝑣 = 𝑇𝑆𝑆 ℎ𝐴 𝐷𝑇 + 𝑄𝑀𝑎𝑥
• 𝑇𝑆𝑆 =
𝑄𝑀𝑎𝑥
𝑇𝑆𝑃 +ℎ𝐴𝑇𝐸𝑁𝑉
𝐷𝑇
𝑄𝑀𝑎𝑥 𝐷𝑇+ℎ𝐴
• 𝑒𝑆𝑆 = 𝑇𝑆𝑆 − 𝑇𝑆𝑃 = −
𝑇𝑆𝑃 −𝑇𝐸𝑁𝑉
𝑄
𝑀𝑎𝑥
1+ℎ𝐴
𝐷𝑇
– Magnitude increases with 𝑇𝑆𝑃 − 𝑇𝐸𝑁𝑉 and
ℎ𝐴 𝐷𝑇
𝑄𝑀𝑎𝑥