ME 322: InstrumentationLecture 37

April 22, 2015

Professor Miles Greiner

Proportional control characteristics, Shift register and integral control program

Announcements/Reminders• HW 12 Due Friday

• X2 (write a Proportional Control VI)

• HW 13 Due Monday• L12PP (on/off, proportional and integral control)

• HW 14 Due Wednesday• X3

• Review for final (Next Wed. & Fri.)• Open Lab Practice (Next Saturday and Sunday)• Lab Practicum Finals (Schedule on WebCampus)

– Guidelines• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Tests/Index.htm

• This week: Lab 11 Unsteady Karmon Vortex Speed• One-hour periods with your partner• How is it going?

Lab 12 Setup

• Measure the beaker water temperature using a thermocouple/conditioner/myDAQ/VI

• Use myDAQ analog output (AO) to turn heater on/off to control the water temperature– Use Fraction of Time On (FTO) to control heater power

Proportional Control

• Fraction of time on (FTO) when T is within a small increment DT of TSP – Define

• Three temperature zones:– For , f > 1 FTO = 1– For , 1 > f >0– For , f < 0 FTO = 0

• For DT = 0, Proportional control is the same as full power On/Off control• Corrective Heat input:

– Q = QMAX*FTO = – QMAX= V2/R

CurrentTemperature

Proportional Control• VI construction (start at midpoint)

Set-Point, Lower-Control, and Measured Temperatures vs Time

• Two set point temperatures (65°C and 85°C), • Increasing DT = 0, 5, 10°C decreases unsteadiness but reduces the average steady

state temperature TA below TSP

• (same as standard deviation) measures unsteadiness• eSS = TAVG-TSP measures steady-state error

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90

Tem

pera

ture

, T [C

]

Time, t [minutes]

T TSP

TSP - DT

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10

T RM

S[C

]

DT [C]

TSP = 65°C

TSP = 85°C

Unsteadiness and Error versus DT

• Unsteadiness TRMS decreases as DT increases

– And as TSP decreases

– Want this to be zero

• The average steady-state error e = TSS-TSP – Is positive for DT = 0, but decreases as DT increases– Magnitude increases as DT increases– Want this to be zero

𝑇 𝑅𝑀𝑆

Proportional Control is Flawed• Proportional control is able to eliminate

unsteadiness.• But, we found that if DT is large enough to make the

temperature steady, then the steady-state temperature is below the desired set-point value

• What should Q (and FTO) be?

Energy Balance

• So far we haven’t done much quantitative analysis• Proportional Control

– Q = QMAX*FTO = – At , Q = 0,

• The steady state temperature will always be below TSP (so that QIN balances QOUT)

• Under steady-state conditions, QIN = QOUT, we want T = TSP

– FTO*QMAX = hA(TSP-TENV)

• But we don’t (want to) know h or and they may be changing

• What is another scheme to find FTP?–

TQIN = FTO(QMAX) QOUT = hA(T-TENV)

TENV

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90

0 10 20 30 40 50 60 70 80 90

Te

mp

era

tu

re

, T

[C

]

Time, t [minutes]

T TSP

TSP - DT

Integrate Error

• Integrate error–

• Corrective Action from integration (integral fraction of time on)–

• FTOi will – Increase with time when )– Decrease with time when )– Stay constant when

• How to choose DTi?– Q will be too responsive if DTi is small (or not responsive enough if DTi is too

large). In ME 410 Control, you will learn how to choose DTi. – Wait for temperature to be steady before turning on integral control (Decreasing

DTi)

If T-TSP > 0, thenDecrease FTO

If T-TSP < 0, thenIncrease FTO

How to implement this in LabVIEW

• Need to calculate at each time step– Then sum at each step

• Within While Loop– Use Shift Register to pass data from one step to the next

• Modify Proportional Controller to include integration

Figure 2 VI Block Diagram

Write To Measurement File File Format: Microsoft Excel (.xlsx) File Path:C:\Users\Miles Greiner\Documents\LabVIEW Data\test.xlsx Mode: Save to one file Ask user to choose file: False If a file already exists: Use next available filename X value(time) columns: One column only Description:

Figure 1 VI Front Panel

• Plots help the user monitor the measure and set-point temperatures T and TSP, temperature error T–TSP, and control parameters

Figure 3 Measured, Set-Point, Lower-Control Temperatures and DTi versus Time

• Data was acquired for 40 minutes with a set-point temperature of 85°C.• The time-dependent water temperature is shown with different values of the

control parameters DT and DTi. • Proportional control is off when DT = 0 • Integral control is effectively off when DTi = 107 (10log(DTI) = 70)