controlled resistive heating of carbon fiber composites · 2020. 9. 25. · each sample consisted...

Chapter 2

Controlled Resistive Heating of

Carbon Fiber Composites

Temperature control is the key to effective resistive heating for composite rigidization. The

ability to monitor and even control the temperature provides an active control strategy in

prescribing and predicting the stiffness of the hardened composite. Further, understanding

how the material responds to an electrical input determines both the type of control to be

used as well as the level of control that can be attained.

This chapter investigates how temperature control of carbon-fiber reinforced polymer

composites is implemented. The material was investigated experimentally and modeled

analytically for use in the final control scheme. A PID feedback controller was applied to

the resistive heating process and the control gains were then experimentally tuned. Infrared

imaging of the composite during heating was also performed as a method for visualizing the

heating process.

2.1 Introduction to Resistive Heating

When Georg S. Ohm (1787-1854) published Die galvanische Kette mathematisch bearbeitet

in 1827, he described the theory and applications of electric current. For his achievements,

the German scientist’s name has been forever attributed to electrical science terminology:

Ohm’s Law (2.1) states the proportionality of current and voltage in a resistor and the SI

18

unit of resistance is the Ohm (Ω) [32].

V = IR. (2.1)

Ohm’s work provides a direct correlation between the potential voltage drop, V , across a

resistive (or Ohmic) material, R, and the electric current, I, flowing through the medium.

In doing so, Ohm’s Law is a fundamental concept that helped establish the basis of modern

electrical theory. James Joule (1818-1889) coupled Ohm’s Law with his own endeavors

in relating heat to mechanical work. Joule worked with Lord Kelvin in developing the

absolute temperature scale (Kelvin, K) and was also acknowledged for his contributions

that eventually led to the First Law of Thermodynamics. His experiments initiated the

concept of the mechanical equivalence of heat, which relates the energy required to raise

the temperature of water 1F. Accordingly, the SI unit of work was named the Joule (J).

However, Joule might be best remembered for his discovery of the relationship, appropriately

named Joule’s Law, between current flow and heat dissapation in a resistive element (2.2).

Specifically, Joule found that the rate of thermal energy generated, E, within a resistive

material,

E = I2R, (2.2)

is proportional to the square of the current, I, and directly proportional to the resistance,

R [33, 34].

Together, Georg Ohm’s and James Joule’s accomplishments close the gap between

electrical energy input (either as a voltage potential or an electric current) and thermal

energy output. As a result, resistive heating can provide both undesired and desired heat

generation. Because of Joule’s Law, resistive heating occurs whenever an electric current

passes through a resistive material. The design of electronic circuitry must account for this

phenomena or the risk of overheating, even melting, the hardware becomes a reality. On the

other hand, Joule’s law sets forth the notion that the amount of thermal energy generated

can be controlled by the inherent resistance of the heating element as well as the applied

electric current. The selection of the input, i.e. current, voltage, or even resistance, to obtain

a desired temperature rise is the most common use for resistive heating. Appliances like

electric stove tops, hairdryers, curling irons, and electric blankets employ resistive heating

to raise the temperature of heating elements.

Internal resistive heating of carbon-fiber reinforced materials provides a way to a

19

new method of rigidization. If current passing through the fibers can generate sufficient

heat, then it is thought that the localized temperature increase can be used to cure the

adjacent thermosetting resin. As Joule demonstrated, this process is an active one; the

temperature of the composite can be controlled via the supplied electrical input. Therefore,

the requirement for a given temperature to be obtained during the rigidization process is

merely a function of the electrical energy supplied to the material.

2.1.1 The Resistive Nature of CFRP Materials

In order for carbon fiber reinforced polymers to be rigidized by resistive heating, the com-

posite must have the appropriate electrical properties. When an electric field is applied

to a material, the motion of electric charges within the material generates current flow.

However, all materials exhibit some resistance, R, to this charge motion. Resistance, then,

depends on both the resistive nature of a given material, called electrical resistivity, and

the geometry of the material

R = ρl

A. (2.3)

Equation 2.3 shows that the resistance of a heating element is proportional to its length, l,

and inversely proportional to its cross-sectional area, A. Further, the electrical resistivity,

ρ, for a given material is a function of temperature. The electrical conductivity, σe, is a

measure of the material’s ability to allow electrical current to flow and is defined as the

reciprocal of resistivity [3]

σe =1

ρ. (2.4)

Table 2.1: Room Temperature Electrical Conductivities of Common Engineer-ing Materials [3]Metals and Alloys σe, (Ω· m)−1 Nonmetals σe, (Ω· m)−1

Silver 6.3 x 107 Graphite 105 (average)Copper, commercial purity 5.8 x 107 Germanium 2.2Gold 4.2 x 107 Silicon 4.3 x 10−4

Aluminum, commercial purity 3.4 x 107 Polyethylene (PE) 10−14

Polystyrene (PS) 10−14

Diamond 10−14

Quantified as Ω-m−1, electrical conductivity (and thus resisivity) is an inherent ma-

terial property that does not depend on geometry. Both conductivity and resistivity are

functions are temperature, however. The difference in conductivity varies greatly between

20

materials and helps categorize materials as conductors, insulators, and semiconductors. Ta-

ble 2.1 illustrates that pure metals have the highest conductivities, which explains their use

as electrical wiring materials. On the opposite end of the spectrum, the electrical insulators

such as polyethylene (PE), polystyrene (PS), and diamond have very small conductivity

values. Between these extremes, semiconductors such as graphite, germanium, and silicon

have conductivities less than metals but much greater than insulators. An in-depth look at

the physical properties of both the carbon fiber tow and thermosetting resin is discussed in

Chapter 3. For now, the primary focus is kept on the method of applying internal resistive

heating to resistive materials.

2.1.2 Resistive Heating Experimental Goals

The application of resistive heating to the carbon-fiber reinforce polymeric materials of

interest required an understanding of how the material heats as well as the electrical power

requirements needed to reach curing temperatures. Thermal control was implemented on

these materials through a two-step process. First, the material was subjected to open-loop

heating tests, in which a constant voltage was applied to the material for a given amount

of time. In doing so, techniques for measuring the temperature were established and the

power requirements to achieve certain temperatures was recorded. The heating and cooling

time constants were also measured as a way of experimentally modeling the heated material.

Closed-loop, or feedback, control was then applied to the heating process. In this strategy,

a measured temperature was compared to a desired temperature and the input voltage

(or current) was regulated in order to reduce the error between the two. Selected for its

effectiveness and simplicity, a proportional-integral-derivative (PID) was chosen as the type

of control strategy to use. The goals, and resulting success, of this testing were chosen in

order to produce an effective, repeatable resistive heating rigidization method for CFRP

materials. The prescribed stiffening that this method can produce, then, is very much

dependent on the ability to control the temperature of the material. The specific detailed

objectives and goals for this testing are summarized:

• Establish temperature measurement of CFRP samples during resistive heating.

• Measure temperatures achieved for selected input voltages during open-loop testing.

• Record heating and cooling time constants for use in system identification.

21

• Apply feedback control, by way of a PID controller, to the resistive heating process.

• Tune the controller to achieve accurate and precise temperature control.

2.2 Thermal Control Experimental Setup

To perform temperature observation during resistive heating, the samples were first fixed on

each end. Each sample consisted of a 15−20cm length of polymer resin-coated carbon fiber

tow. An applied voltage (generated in Simulink and dSpace and then amplified by a ±20V,

±2A HP 6825A Bipolar Power Supply/Amplifier) across the sample resulted in current flow

between the voltage leads. Omega J-type (Iron-Constantan) thermocouples were placed at

three positions along the sample to measure temperature. An additional thermocouple was

also used to record the ambient air temperature. Temperatures from the thermocouples

were then measured and recorded by an Omega OMK-DAQ-56 data acquisition module

and Personal DAQView software. Then, data from this device was transmitted via USB to

a personal computer.

dSpace Controller

Power Supply/Amp

iV+ V-

Th1 Th4 Th6

ThambData

OMK-DAQ-56

Simulink

V(t)Personal Computer

dSpace ControllerdSpace

Controller

Power Supply/Amp

Power Supply/Amp

iV+ V-

Th1 Th4 Th6

ThambData

OMK-DAQ-56

Simulink

V(t)Personal ComputerPersonal Computer

Figure 2.1: Test setup schematic for open-loop resistive heating with tempera-ture monitoring.

The temperature was measured at multiple positions in order to detect possible

temperature differences, or gradients, along the length of the material. Since the tow

consisted of such fine fibers, the placing of the thermocouples (much larger in contrast)

required multiple iterations. At first, untwisted fiber tow was position into the fixture

(2.3). However, the fibers were easily separated, allowing the thermocouple to pass through

the thickness of the material. Poorly placed thermocouples not only lead to imprecise

22

8 ¼”

Th1 Th2 Th3

Composite SampleV+ V-

8 ¼”

Th1 Th2 Th3

Composite SampleV+ V-

Figure 2.2: Resistive heating with temperature monitoring experimental setup.

temperature measurements, but in the presence of a feedback control algorithm can cause

incorrect amounts of energy to be supplied, resulting in an inaccurate heating method. One

solution to this problem was twisting the fiber tow samples. This technique kept the fibers

in a “tighter knit” configuration and in turn, caused the sample to have a more consistent

cross-sectional area.

Figure 2.3: Thermocouple positioning without twisting (left) and with twisting(right). Notice how the tip of the thermocouple protrudes through the tow inthe first picture. Twisting the samples helped to hold the thermocouple in aposition to better measured internal temperature.

This experimental setup was also designed to measured the amount of current flowing

through the material. Knowing how much current flows allows for the electrical power to

be calculated as well as the resistance of the material to be monitored during heating.

To perform these tasks, a current-measuring circuit was designed and built (Figure 2.4).

Modeling the sample as a resistor with unknown resistance, Rstrands, the output voltage,

Vout, was measured directly during the tests. Knowing the voltage drop across a known

23

+ ∆V -

+

Vout

-

R1

Rstrands

R2

R3

+

-

OP177

V-

V+i

+

Vin

-

+ ∆V -

+

Vout

-

R1

Rstrands

R2

R3

+

-

OP177

V-

V+i

+

Vin

-

Figure 2.4: Current sensing circuit used to measure current flow and materialresistance.

resistance, R3, allowed the current flowing through R3 (and also the sample, Rstrands) to

be determined. Likewise, the voltage drop, ∆V , across the strands was measured and from

that, the resistance of the sample was obtained. Figure 2.5 illustrates a flow-chart type

representation of how each unknown value was computed.

R2/R1

( )( ) ( )

( )

3

33

1

2

1

2

3

1

2

1

11

1

R

Vi

VVV

VVV

RV

VRR

VV

in

RR

out

RR

out

inst

RR

RR

inout st

+

+

−+

=

−=∆

+==

−

+=⇒+

+=Vin

Vout

R3 i

∆V

V+

Rst

R2/R1

( )( ) ( )

( )

3

33

1

2

1

2

3

1

2

1

11

1

R

Vi

VVV

VVV

RV

VRR

VV

in

RR

out

RR

out

inst

RR

RR

inout st

+

+

−+

=

−=∆

+==

−

+=⇒+

+=Vin

Vout

R3 i

∆V

V+

Rst( )

( ) ( )

( )

3

33

1

2

1

2

3

1

2

1

11

1

R

Vi

VVV

VVV

RV

VRR

VV

in

RR

out

RR

out

inst

RR

RR

inout st

+

+

−+

=

−=∆

+==

−

+=⇒+

+=Vin

Vout

R3 i

∆V

V+

Rst

Figure 2.5: Post-processing circuit and associated equations for indirect currentmeasurement.

This testing apparatus (Figure 2.1) was then used to perform open-loop resistive

heating on samples of the CFRP tow. However, when closed-loop control was performed

the experimental setup was changed to accomodate temperature as a feedback control signal.

Specifically, four signal conditioners (Omega #CCT-22-0/400C) with a range of 0− 400oC

were used to provide the cold-junction reference point for the thermocouples and then

output 0 − 10V voltage signals proportional to the measured temperatures. These sig-

nal conditioners replaced the OMK-DAQ-56 temperature data acquisition module, which

could not output temperature signals. When incorporated into the previous experimental

24

Thermocouple Signal ConditionersThermocouple Signal Conditioners

Figure 2.6: Signal conditioners used to measure and output temperature signalsrequired for feedback control.

setup (Figure 2.1), the new experimental setup sends measured temperatures back into

Simulink/dSpace, where the control algorithm could process them.

dSpace Controller

Power Amplifier

iV+ V-

Th1 Th2 Th3 Thamb

Simulink

(Lab PC)

SC1 SC2 SC3 SCamb

OUT

IN

*Temperature Feedback

*Control Signal

*PID Controller Algorithm

Low-Pass RC Filtering

dSpace ControllerdSpace

Controller

Power AmplifierPower

Amplifier

iV+ V-

Th1 Th2 Th3 Thamb

Simulink

(Lab PC)

Simulink

(Lab PC)

SC1SC1 SC2SC2 SC3SC3 SCambSCamb

OUT

IN

*Temperature Feedback

*Control Signal

*PID Controller Algorithm



Figure 2.7: Experimental schematic used for feedback temperature control.

In order to visualize the procedure of applying a PID control to this system, the

Simulink Block diagrams used to control temperature are shown Figures 2.8. In these

diagrams, the conversion of measured temperature to control voltage is traced.

Using dSpace to accept thermocouple voltages, the input signals were then converted

to temperature and the average temperature was computed. The error between the mea-

sured temperature and the temperature set point was then scaled by the PID control gains,

which generated a control effort power value. Taking into account changes in the ambient

temperature (an external disturbance) and using a constant initial resistance value for the

25

M

Tset Data

V1

V2

V3

V4

T1

T2

T3

Tav g

Tamb

TemperatureConversion

10

Ro

Ro

Tset

Tav g

Tamb

V

PID Control

Current Voltage Current

Current Monitoring

1

V(t)

Channel Outputsfrom D-Space

Channel 1 Voltage

Channel 2 Voltage

Channel 3 Voltage

Channel 4 Voltage

Channel 5 Voltage

Channel Inputsto D-Space

f(t)=(V^2)/R+hAsT_inf

1

V

0.083

hAs

error PID Control

PID Loopsqrt

4

Tamb

3

Tavg

2

Tset

1

Ro

1

PID Control

0.4

Kp

0.04

Ki

0

Kd

1s

du/dt

1

error

Figure 2.8: a. Simulink model created to house the temperature control al-gorithm (top). b. Temperature feedback control loop used to compute thecorrective control voltage (middle). c. PID controller (bottom) located withinthe temperature feedback loop (b).

sample, a corrective control voltage was calculated. This signal was then sent out of dSpace,

through the power supply/amplifier, and into the material.

2.3 Open-Loop Heating Results and Discussion

The resistive heating process was initially examined by inputting a single voltage pulse and

recording the temperature response along the strands. The pulse length was selected to

allow the material to reach a final, or steady-state, value. Then the voltage was turned off

and the temperature was observed as the material cooled down. Figure 2.9 shows the tem-

perature responses measured at the three locations along the samples for an input voltage of

10V with 3 minutes of heating and 3 minutes of cooling. The measured responses illustrate

26

0 50 100 150 200 250 300 350 4000

50

100

150

Tem

pera

ture

- C

t2sample52.mat

Th1

Th4

Th6

0 50 100 150 200 250 300 350 400-10

-5

0

5

10

15

Time - s

Vol

tage

Max Power = 16.458 WMax Current = 1.6172 A

Vin

Vout

Figure 2.9: Typical temperature and voltage responses measured for an inputvoltage of 10V.

some important aspects of the heating and cooling properties of this type of composite ma-

terial. First and foremost, the material experiences an exponential temperature rise (when

voltage is turned ON) from an initial temperature, Ti, up to a higher final temperature, Tf .

Cooling is denoted by an exponential decay (when voltage is OFF) from an initially high

temperature, Ti, to cooler final temperature, Tf . Each of these responses are approximated

by the following equation

T (t) = Ae−ct + B (2.5)

where,

A = Ti − Tf (2.6)

B = Ti (2.7)

and c represents the exponential growth (heating) or decay (cooling) rate. The correspond-

ing heating and cooling time constants,

τ =1

c, (2.8)

which refer to how quickly the material responds to a given input, can also be measured

from these plots. Values of the heating constants are then later used to refine the predicted

response model developed for controlled, open-loop heating.

The voltage plot in Figure 2.9 gives additional insight into the power requirements

of the sample. Shown as a blue, dotted line, the input voltage, Vin, represents the voltage

27

applied across the strands. In addition, a red, dotted line plots the values of an output

voltage, Vout, measured from the post-processing circuit during the experiment. Recall that

two additional goals of this test were to measure the current flowing through the material

and, from that measurement, track changes in the electrical resistance of the material.

Returning to Figure 2.9, it is noticed that Vout remains “flat” during the heating process.

Examining the top equation in Figure 2.5 further clarifies how the resistance of the strands

changes for a given change in the output voltage,

Rst = R3

(

Vin

Vout

(

R2

R1

+ 1

))

− R3 ⇒ Rst =G

Vout

− R3, (2.9)

where G is a constant if all other resistances and the input voltage remain fixed. Taking

the partial derivative of Equation 2.9 with respect to the measured output voltage yields

the following∂Rst

∂Vout

= −G

V 2out

⇒ ∂Rst = −G

V 2out

∂Vout. (2.10)

As derived, a change in resistance of the sample, Rst, is proportional to a change in the

output voltage, Vout. Since Figure 2.9 shows a relatively unchanging measurement of Vout

over the length of the heating cycle, we can infer that the resistance of the strands also

remains steady. However, a steady resistance is also dependent on the material having

a resistivity that does not vary with temperature. The amount of resistance change per

temperature increase, then, will also be considered during this test. As it will be shown

later, a fixed value of resistance greatly simplifies the both the simulation of the temperature

response as well as the eventual temperature control of the process.

Previously mentioned in the goals for this experiment, it was desired to record the

maximum temperature (an average of the three thermocouple measurements along the

sample) achieved for varying amounts of applied voltage. For each sample, the input voltage

was varied (from 0.5V to 10V in 0.5V increments) and the corresponding temperature

response was measured (Figure 2.10). It was observed that the temperature of the tow

sample was proportional to the square of the applied voltage.

Further, by measuring the current with the sensing circuit shown in Figure 2.4, the

amount of current to obtain these temperatures was also examined. Again, the temperature

was proportional to the square of the current. A second-order polynomial trend-line verifies

this relationship graphically.

The quadratic relationships between temperature and voltage (and current) shown

28

0 50 100 150 200 250 300 350 40020

30

40

50

60

70

80

90

100

110Plot of all Thavg Responses

Time - s

Tem

pera

ture

- C

Run1Run2

Run3

Run4

Run5Run6

Run7

Run8Run9

Run10

Run11

Run12Run13

Run14

Run15Run16

Run17

Run18

Run19Run20

Figure 2.10: Average temperature response of the sample for various inputvoltages (Run1=0.5V and Run20=10.0V).

in Figure 2.11 are consistent with Equation 2.2, which states that the heat produced by an

electrical signal in a resistive element is proportional to the square of the current. Further,

if Equation 2.1 is substituted into Equation 2.2, the heat generated is equally proportional

to the square of the applied voltage

E =

(

V

R

)2

R =V 2

R. (2.11)

As it will be further shown in later sections, the temperature of the material is directly

proportional to the amount of heat generated within it. In addition, the heat generated

within the material is proportional to the power supplied to the material. This relation,

then, states that the temperature attained is also linearly proportional to the power supplied

(Figure 2.12)

P = V I = I2R =V 2

R. (2.12)

Heating and cooling time constants for each sample test were also computed from the

average temperature response and were later used to help model the heating process. This

knowledge of the “system’s” response to a known input was also valuable when applying

29

y = 0.6253x2 + 2.1939x + 18.666

R2 = 0.9968

0

20

40

60

80

100

120

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Voltage - V

Tem

pera

ture

- C

y = 20.508x2 + 23.985x + 17.329

R2 = 0.9972

0

20

40

60

80

100

120

0 0.5 1 1.5 2

Current - A

Tem

pera

ture

- C

y = 0.6253x2 + 2.1939x + 18.666

R2 = 0.9968

0

20

40

60

80

100

120

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Voltage - V

Tem

pera

ture

- C

y = 20.508x2 + 23.985x + 17.329

R2 = 0.9972

0

20

40

60

80

100

120

0 0.5 1 1.5 2

Current - A

Tem

pera

ture

- C

Figure 2.11: Measured average maximum temperature per input voltage (a)and current (b) applied.

y = 5.3283x + 23.903

R2 = 0.9908

0

20

40

60

80

100

120

0 5 10 15 20

Power - W

Tem

pera

ture

- C

Figure 2.12: Material temperature exhibits a linear relation to electrical power.

feedback control to the heating procedure. From this round of tests, an average heating time

constant, τh and an average cooling time constant, τc, were extracted from the measured

data. These values represent the time for the response to reach 1−e−1 (63.2%) of its steady-

state value [35]. The time constants measured demonstrate no significant dependence on

the applied voltage (and thus, the temperature attained) and were roughly the same for

heating (19.2 ± 1.8 seconds) and cooling (20.8 ± 2.6 seconds). A discussion of how these

time constants are modeled is later addressed and shows that these values are primarily

dependent on the material itself.

The resistance of the sample was also mapped versus the temperature reached for

each level of applied voltage. It was desired to observe if this property changed greatly or

if it could be assumed to remain constant during the heating process. A constant heating

process translates into a time-invariant system model for use in feedback control. Other-

wise, the control strategy must continually update the resistance value as the temperature

30

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Input Voltage - V

Tim

e C

on

sta

nts

- s

Heating

Cooling

Figure 2.13: Measured heating and cooling time constants for open-loop resis-tive heating tests.

changed. Through the circuit described previously, the resistance of the strands were mea-

sured indirectly and tracked relative to an initial resistance value (Figure 2.14). Resistance

4

6

8

10

12

14

16

0 20 40 60 80 100 120

Temperature - C

Res

ista

nce

- W

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

∆∆ ∆∆R

esis

tanc

e -

ΩΩ ΩΩRo = 10 Ω

Figure 2.14: Sample resistance as a function of temperature.

does decrease with increasing temperature, but only slightly. At 100oC, the sample resis-

tance has only decreased by 5.25% to 9.48Ω. The change in resistance might be more of

a factor at higher temperatures, though in the temperature range presented, it remained

stable.

While the temperature of the material has yet to be controlled, resistive heating with

temperature monitoring was established and a method of positioning the thermocouples was

achieved. Further, the steady-state temperature attained was measured as a function of the

voltage, current, and power supplied to the sample. It was also observed that the resistance

of the material did not change significantly during these heating tests. Short of feedback

control, curing temperatures for UnyteSet resin (160oC-170oC) have yet to be achieved

even in open-loop resistive heating. In order for these higher temperatures to be generated,

31

greater amounts of power must be supplied. The resulting experimental setup takes into

account the need for increased power supply and in doing so uncovers a better way to

measure current flow.

2.3.1 High-Temperature Open-loop Resistive Heating

Expanding the results from the low temperature experiments, it was desired to track the

final temperatures attained for larger input voltages. In thought, the quadratic trend-line

shown in Figure 2.11 would be stretched to higher voltages and temperatures. This step

required a change of hardware to safely accommodate higher voltages (and currents). Using

a Xantrex XHR 300V-3.5A DC Power Supply, the output voltage was triggered via remote

signaling. Simulink and dSpace were still used to generate the signal shape and the new

power supply then scaled the signal to desired voltage levels. Another benefit of using

this hardware was that both the output voltage (equivalent to the voltage potential across

the sample) and current from the power supply can be directly monitored and recorded as

scaled voltage signals. Simply, by using this power supply, higher power can be sourced to

the composite sample and the post-processing circuit was eliminated from the picture. A

new round of temperature response testing on samples of G40-800 carbon fiber coated with

Unyte201 polymer resin was conducted for voltages varying from 1 to 18V.

y = 0.9898x2 + 0.4696x + 23.232

R2 = 0.9985

0

50

100

150

200

250

300

350

400

0 5 10 15 20

Voltage - V

Tem

pe

ratu

re -

C

y = 6.2951x + 30.64

R2 = 0.9945

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60

Power - W

Tem

pera

ture

- C

y = 0.9898x2 + 0.4696x + 23.232

R2 = 0.9985

0

50

100

150

200

250

300

350

400

0 5 10 15 20

Voltage - V

Tem

pe

ratu

re -

C

y = 6.2951x + 30.64

R2 = 0.9945

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60

Power - W

Tem

pera

ture

- C

Figure 2.15: Power requirements measured during high-temperature, open-loopresistive heating tests.

Again, the voltage and power were monitored for high temperature resistive heating.

This process only further verified that temperature is dependent on the square of the volt-

age applied or directly proportional to the applied power. Temperatures near 350oC were

achieved, but at the cost of more than 50W of power. With such a large power requirement,

32

the ability to store and then supply high peak power will be crucial for in-space rigidization

via this method. However, the total electrical energy may offset high power requirements if

the material can be cured in a short amount of time. The novel thermoset resin, UnyteSet

201, used in this study also helps to diminish the power needed for high temperature cure.

This material cures at temperatures in the range of 150 − 200oC, whereas a resin such as

PETU cures at more than 250oC. If the temperature-power relationship shown in Figure

2.15 is referenced, the power to reach the cure temperature can be reduced by more than

37% by using the UnyteSet resin (≈ 22W) instead of the PETU thermoset (≈ 35W).

2.4 Active Temperature Control of Resistive Heating

Open-loop resistive heating, which has been addressed up until now, applied a given voltage

to a resistive material and the resulting temperature increase was measured. However, in

order to achieve a desired temperature through voltage selection, a model for the system

must be well-defined. This type of control, called open-loop control, applies a controller,

independent of the output, to the “plant.” In effect, the appropriate control signal is first

computed based on a desired reference temperature. The control signal, which is then

applied to the actual system, generates the desired temperature response. The possibility

of open-loop control as an effective control strategy is investigated for this system.

ControllerSystem

(Controlled Object)

Reference Input

Controlled Output

Disturbance Input

Control Input

ControllerSystem

(Controlled Object)

Reference Input

Controlled Output

Disturbance Input

Control Input

Figure 2.16: Open-loop control scheme [9].

2.4.1 Model Formulation

For open-loop control to be effective, an accurate model of the controlled object must be

known. In resistive heating, a model for a known length of the CFRP material can be

developed as a function of applied voltage.

33

y x

z

i

ρρρρ, m, Cp

qg

qc

L

+V

-V

Ac

y x

z

i

ρρρρ, m, Cp

qg

qc

L

+V

-V

Ac

Figure 2.17: Theoretical heating element used in developing a system model.

The resistive element (Figure 2.17) of known dimensions (length, L, and cross-

sectional area, Ac) and material parameters (resistivity, ρ, and specific heat, Cp) is subjected

to an applied voltage, ∆V which results in a current, i, flowing through the sample. This

model accounts for the heat generated, qg, by Joule-effect heating and the heat given off

due to free-convection, qc. Further, it is assumed that heat conduction in the radial direc-

tion and thermal radiation from the sample are negligible. In doing so, we apply a lumped

capacitance simplification, which assumes that the “the temperature of the solid is spatially

uniform at any instant during the transient process” [33]. Simply, the lumped capacitance

method negates conduction by assuming that temperature gradients within the solid are

negligible. The Biot number, Bi, provides a measure of the temperature drop within a solid

relative to the temperature difference between the solid and its environment. It can be

calculated to validate this assumption [33]

Bi =hLc

k< 0.1, (2.13)

where, h is the convection coefficient between the solid and the surrounding air, Lc is

the characteristic length (Lc is half of the radius for long cylinders [33]), and k is the

thermal conductivity of the material. For carbon-fiber, axial thermal conductivity can

range anywhere from 5 − 200 W/m·K [2]. However, the convection coefficient, h, depends

on temperature, fluid properties (density, viscosity, thermal conductivity, and specific heat),

surface geometry, and flow conditions and is more difficult to approximate. So, for now,

let us assume that lumped capacitance can be applied to this system. The first law of

thermodynamics, which demands conservation of energy, is then applied to the resistive

34

element

Ein − Eout = ∆E. (2.14)

For this process, the heat generated, qg, comes from the applied electrical signal, the energy

given off is due to convection, qc, and the change in energy of the sample results in a

temperature increase

qg − qc = mcpdT

dt. (2.15)

Applying Joule’s law, and substituting in the expression for convection heat transfer, we

obtain an expression for the heat balance of this system,

V (t)2

R− hAs (T (t) − T∞) = mcp

dT

dt, (2.16)

where V (t) is the voltage potential across the length of the sample, R is the effective

resistance of the sample, As is the surface area, T∞ is the ambient (or film) temperature of

the surrounding air, m is the mass of the sample, cp is the material’s specific heat, and T is

the temperature of the sample at any point along the length. Re-arranging this expression

yields the following first-order, linear, ordinary differential equation:

mcpdT

dt+ hAsT =

V (t)2

R+ hAsT∞. (2.17)

Written in standard form [36], Equation 2.17 is simplified to

dT

dt+ pT (t) = f(t), (2.18)

where

p =hAs

mcp

(2.19)

and

f(t) =

[

V (t)2

R+ hAsT∞

] (

1

mcp

)

. (2.20)

The solution to the above differential equation can be solved via many techniques, varia-

tion of parameters, undetermined coefficients, etc. [36]. More importantly, it provides a

relationship between the sample temperature, T , the material parameters, and the input

voltage, V ,

T (t) = e−pt

[

C

pept +

(

T∞ −C

p

)]

, (2.21)

where again,

p =hAs

mcp

(2.22)

35

and

C =

[

V (t)2

R+ hAsT∞

] (

1

mcp

)

. (2.23)

Comparing Equation 2.5 to Equations 2.21 and 2.22, and recalling Equation 2.8, the time

constant for the temperature response,

τ =1

p=

mcp

hAs

, (2.24)

is a function of the material properties of the sample (m and cp), the sample dimensions

(As), and the convection coefficient, h.

Having a relationship between temperature and applied voltage allows for an open-

loop controller to calculate the exact voltage input based on a desired temperature. How-

ever, when an exact understanding of the system breaks down and accurate material pa-

rameters are not known, open-loop control suffers. For the sake of seeing how closely the

current model can control temperature, we can model the input power required to cause

a desired temperature increase. It is important to note that the applied signal, V (t), is

modeled as a unit step function multiplied by the magnitude of the voltage. The Laplace

transform of this term can be written as

L

[

V (t)2

R

]

=V 2

RL [u(t)] =

V 2

R

1

s(2.25)

where u(t) is a unit step input. For the entire solution, we start with the original differential

equation (Equation 2.17) and apply a Laplace Transformation

(mcp) [sT (s) − T (0)] + (hAs)T (s) =V 2

R

1

s+ (hAs)T∞. (2.26)

Grouping like terms and re-arranging yields an expression for the input power,

V 2

R= s [mcps + hAs] T (s) − mcpT (0) − hAsT∞, (2.27)

as a function of instantaneous temperature, T , initial temperature, T0, and ambient tem-

perature, T∞. This expression can then be written in block form and defines the open-loop

controller applied to the system in Figure 2.16. Notice that both the ambient temperature,

T∞, and initial temperature, T0, are factors in the performance of this controller (Figure

2.18). If these values are the same and the temperature, T (s), is defined as the increase in

temperature from its initial value,

T (s) = ∆ (T (s) − T (0)) , (2.28)

36

hAs

mcps+hAs

mcp

mcps+hAs

mcps+hAs+

-

-

V(s)2/R

T(s)

T (s)

T0(s)

CONTROLLER

hAs

mcps+hAs

hAs

mcps+hAs

mcp

mcps+hAs

mcp

mcps+hAs

mcps+hAsmcps+hAs+

-

-

+

-

-

V(s)2/R

T(s)

T (s)

T0(s)

CONTROLLER

Figure 2.18: Block diagram representation of the open-loop temperature con-troller.

then the transfer function, G(s), between temperature increase and applied power can be

written

G(s) =1

mcps + hAs

. (2.29)

Equation 2.29 states that an increase in temperature for a step input voltage is first order,

represented by an exponential growth. The general shape of this first-order model conforms

to the measured exponential growth temperature responses (Figure 2.10).

A change in ambient temperature, which can affect the system during resistive heat-

ing, can also be thought of as an external disturbance (Figure 2.19).

ControllerSystem

(Controlled Object)

Desired Temperature

Sample Temperature

Ambient Temperature

Input Power

Initial Temperature

ControllerSystem

(Controlled Object)

Desired Temperature

Sample Temperature

Ambient Temperature

Input Power

Initial Temperature

Figure 2.19: Block diagram of temperature control, via an open-loop controller.

If the ambient temperature is fed into the controller, as shown in the block diagram,

then the controller can account for this instantaneous value when it computes the control

signal. The controller, on the other hand, is completely independent from the actual sam-

ple temperature (controlled variable) and thus, in general, it cannot account for external

disturbances to the system. An underlying concern with this technique, then, is whether

37

or not the designer has an accurate system model. In this case, our inability to accurately

measure or calculate the convection coefficient and various material properties (ρ, m, cp, As,

etc.) weakens the effectiveness of an open-loop controller. Nonetheless, predictive open-loop

heating was attempted on CFRP samples.

2.4.2 Predictive Joule Heating Results

Using Equation 2.21, the temperature response was simulated for both the heating (V 6= 0)

cooling regions (V = 0). Matlab was used to generate the predicted response for various

voltage signals. Specifically, the code allowed the user to specify the initial heating and

final cooling time periods as well as define the input voltage value. The user also specifies

a temperature window in which the sample was allowed to heat and cool for a selected

number of cycles at the same voltage level. The code then computed when to turn on and

off the voltage in order to mimic these temperature swings and used these times to generate

the voltage signal pattern automatically. This signal was read directly into Simulink and

an exact replica was sent out of dSpace into the material. In this manner, the predicted

response to a unique voltage signal was directly compared with the measured response

from the same input. By using a combination of estimated material parameters and the

experimentally measured time constants, the terms “mcp” and “hAs” (shown in Figure 2.18

and Equation 2.27) were approximated for this system and implemented into the predictive

response simulation.

0 100 200 300 400 500 600 70020

25

30

35

40

45

50

55

60

65

Time - s

Tem

pera

ture

- C

Heating (V is ON)

Cooling (V is OFF)

0 100 200 300 400 500 600 700

-4

-2

0

2

4

6

8

Time - s

Vol

tage

- V

During cycles:Voltage is OFF for: 4.9357s.

Voltage is ON for: 98.5982s.

Figure 2.20: Simulated temperature response for an input of 6V and a temper-ature window of 10oC (left). Corresponding voltage signal generated to causethe presribed heating (right).

Attempts to model and simulate the temperature response of the system proved

38

0 100 200 300 400 500 60020

25

30

35

40

45

50

55

60

Time - s

Tem

pera

ture

- C

olsample31.mat

Th1

Th4Th6

Ambient Temp

0 100 200 300 400 500 600 70020

25

30

35

40

45

50

55

60

65

Time - s

Tem

pera

ture

- C

Open Loop Sample 31 (3-24-05)

Heating (V is ON)

Cooling (V is OFF)

Measured Response

0 100 200 300 400 500 60020

25

30

35

40

45

50

55

60

Time - s

Tem

pera

ture

- C

olsample31.mat

Th1

Th4Th6

Ambient Temp

0 100 200 300 400 500 600 70020

25

30

35

40

45

50

55

60

65

Time - s

Tem

pera

ture

- C

Open Loop Sample 31 (3-24-05)

Heating (V is ON)

Cooling (V is OFF)

Measured Response

Figure 2.21: Measured temperature response induced by the presribed volt-age signal (left). Comparison of the simulated temperature and the averagemeasured temperature (right).

inaccurate. While the general shapes of the curves matched, the nominal temperature

values differed significantly (Figure 2.21). As a result, temperature control via an open-loop

control does not provide accurate temperature response within the material. The inability

to effectively model the material and correct for external disturbances further negates this

approach.

2.4.3 Feedback Temperature Control

Feedback control, on the other hand, updates the control input based on discrepancies

between a measured controlled variable and the desired reference input. This technique

still requires a controller but does not require the system to be completely known. What

feedback control does require is a way to compare a measured value (say, temperature) with

a desired value throughout the controlled process. It is this step that typically introduces

sensors into the picture. The experimental setup, described in Section 2.2, demonstrates

ControllerSystem

(Controlled Object)

Reference Input

Controlled Output

Disturbance Input

Control Input+

-

Error

Sensor

ControllerSystem

(Controlled Object)

Reference Input

Controlled Output

Disturbance Input

Control Input+

-

Error

Sensor

Figure 2.22: Typical feedback control structure [9].

39

how temperature was fed back into Simulink/dSpace such that the control algorithm could

compare desired and measured temperatures.

For the application of resistive heating temperature control, a PID controller was

selected. The basis for this control strategy stems from the success of proportional-integral-

derivative (PID) controllers as being robust, yet simple. The performance of the controlled

+

++

1/s

sKd

Ki

Kp

e u

+

++

1/s

sKd

Ki

Kp

e u

Figure 2.23: Transfer function for a PID controller.

system depends on the selection of three control gains: proportional gain (Kp), integral

gain (Ki), and derivative gain (Kd). The process of determining the “best” values for the

respective gains has been addressed by many and described by VanDoren as “often more of

an art than a science” [37]. Notably, Ziegler and Nichols developed techniques for “tuning”

these control gains in order to match desired performance [38, 39].

An understanding of the three control gains and their functions determines how they

may be adjusted to achieve the desired level of control. Proportional control, with gain Kp,

outputs a control effort,

u(t) = Kpe(t), (2.30)

directly proportional to the measured error, e(t), between the controlled variable and the

set point [37, 40]. With greater error, the larger the control effort becomes to diminish this

difference in temperature. However, proportional controllers tend to settle on the wrong

corrective error, leaving an offset between the process variable and the set point. Integral

control, adjusted through the gain Ki, generates a control effort proportional to the the

sum of all previous errors [37, 40]

u(t) = Ki

tf∫

t0

e(t)dt. (2.31)

External disturbance cancellation is another benefit of using integral control. The addition

of the integral controller provides assurance against steady-state errors, but is not always

40

the end-all for corrective control. Many PI (proportional-integral) controllers respond quite

slowly without the use derivative control, Kd. This type of control generates a control

action proportional to the time derivative of the error signal,

u(t) = Kd

d

dt(e(t)) , (2.32)

and is used to generate a large corrective effort immediately after a load change in order to

eliminate the error as soon as possible [37]. A full PID controller, then, combines the three

types of control and requires selection for all three gains. The corresponding control signal

for this controller is then written as:

u(t) = Kpe(t) + Ki

tf∫

t0

e(t)dt + Kd

d

dt(e(t)) . (2.33)

If the ratio of control effort, u(t), to the measured error, e(t), is defined as the control

sensitivity, G(t), then the Laplace Transformation of this equation can be taken to achieve

the transfer function for the controller [41]

G(s) = Kp +Ki

s+ Kds. (2.34)

Shown in Figure 2.23, the block diagram form of this transfer function demonstrates

that the summation of these control gains provides the overall control signal. Using PID,

temperature control was applied to the resistive heating process. Specifically, the three

gains, Kp, Ki, and Kd, were varied and their effects on the system were experimentally

observed.

2.4.4 Feedback Control Experimental Results

Using Simulink to construct and provide the control algorithm processing, and dSpace

to record temperature measurements and output the control effort, feedback control was

applied to the resistive heating process. The basic feedback structure shown in Figure

2.22 assumes that the dynamics of the plant include the material itself as well as the

thermocouples and that the material temperature is consistent along the length of the

sample. In effect, feedback sensor dynamics from the thermocouples were neglected and an

average measured temperature was used as the controlled variable.

The first round of temperature control experiments involved applying a “step” input

as the desired temperature signal. The ability for the measured temperature to then match

41

this set point was recorded. A typical response measured during these tests is shown and

its defining characteristics are labeled.

0 50 100 150

18

20

22

24

26

28

30

32

34

36

Time - s

Tem

pera

ture

- C

Proportional Gain, Kp: 0.5Integral Gain, Ki: 0.1Derivative Gain, Kd: 0

Avg. Final Temperature, Tf: 30.02 C

Percent Overshoot, P.O.: 16.83%Settling Time, ts: 22.20 sec.

Damping Ratio, zeta: 0.493

ts

Figure 2.24: Representative temperature response taken during the implemen-tation and tuning of a PID controller.

Several aspects of this figure were used to evaluate the effects of the selected control

gains, which are shown within the plotting area in Figure 2.24. First, the average final

temperature, or steady-state temperature, was recorded as a measure of accuracy. Also,

the percent overshoot, a measure of how much the measured temperature (blue line) “over-

shoots” or goes beyond the desired temperature signal (red line), was recorded. The ability

for the control system to reach a desired temperature without severely overshooting it is

important when prescribing a desired temperature-versus-time curing profile. Lastly, the

settling time, ts, of the measured response was calculated as the time that it took the

measured (actual) temperature to reach and maintain a temperature within ±5% (green

boundary lines) of the desired temperature. In evaluating each of the controller gain set-

tings, these pieces of information were reported and helped to establish the final level of

control. The results of this section are organized so as to reflect the gain selection process

that was performed. The effects of each gain are evaluated for step, ramp, and tracking

desired temeperatures.

The plots in Figure 2.25 demonstrate that the average temperature can be driven

to match the desired temperature. However, temperature overshoot (43% and 15%, respec-

42

0 50 100 150

18

20

22

24

26

28

30

32

34

36

38

Time - s

Tem

pera

ture

- C


Avg. Final Temperature, Tf: 29.97 CPercent Overshoot, P.O.: 43.16%Settling Time, ts: 81.60 sec.


ts

0 50 100 150

18

20

22

24

26

28

30

32

34

36

Time - s

Tem

pera

ture

- C

Proportional Gain, Kp: 0.5Integral Gain, Ki: 0.1

Derivative Gain, Kd: 0.1




ts

0 50 100 150

18

20

22

24

26

28

30

32

34

36

38

Time - s

Tem

pera

ture

- C


Avg. Final Temperature, Tf: 29.97 CPercent Overshoot, P.O.: 43.16%Settling Time, ts: 81.60 sec.


ts

0 50 100 150

18

20

22

24

26

28

30

32

34

36

Time - s

Tem

pera

ture

- C

Proportional Gain, Kp: 0.5Integral Gain, Ki: 0.1

Derivative Gain, Kd: 0.1




ts

Figure 2.25: The first few attempts at selecting gains resulted in marginalcontrol.

tively) proves to be quite significant. The first plot shows that for a desired temperature of

30oC, the actual measured temperature reached 34oC at its maximum point. The measured

temperature in the first plot also experiences significant oscillation and as a result takes

almost 82 seconds to steady out.

0 50 100 150

18

20

22

24

26

28

30

32

34

Time - s

Tem

pera

ture

- C

Proportional Gain, Kp: 0.4Integral Gain, K

i: 0.04

Derivative Gain, Kd: 0




ts

0 50 100 150

20

25

30

35

40

45

Time - s

Tem

pera

ture

- C


i: 0.04





ts

0 50 100 150

18

20

22

24

26

28

30

32

34

Time - s

Tem

pera

ture

- C


i: 0.04





ts

0 50 100 150

20

25

30

35

40

45

Time - s

Tem

pera

ture

- C


i: 0.04





ts

Figure 2.26: Through a trial-and-error process, control gains that decreased theovershoot (left) were chosen. Some temperature nonlinearities appear when thesame gains are used for a higher desired temperature (right).

The process of selecting the gains that drive the measured temperature to the desired

temperature set point with minimal overshoot explored many gain values. Figure 2.26

demonstrates that with control gains of 0.4, 0.04, and 0 for Kp, Ki, and Kd respectively,

causes the actual temperature to reach and maintain the desired temperature. Overshoot

for this setting was diminished greatly and the average steady-state temperature accurately

43

matched a desired temperature of 30oC. These same control gains, when used to match a

step input of 40oC, were not as effective. Temperature nonlinearities in the plant resulted in

greater overshoot and longer settling time even though the final temperature matched the

desired temperature. In order to further verify this nonlinearity, the set temperature was

increased even further and the temperature responses were measured for constant control

gains. The controlled temperatures show higher amounts of percent overshoot of increased

desired temperature values.

0 20 40 60 80 100 12020

30

40

50

60

70

80

Time - s

Tem

pera

ture

- C Tset=35C

Tset=45C

Tset=55CTset=65C

Tset=75C

* Kp = 0.40, Ki = 0.04, Kd = 0.04

PO = 0%

PO = 0.57%

PO = 2.91%

PO = 3.56%

PO = 4.31%

Figure 2.27: Temperature dependent nonlinearities within the “plant” result indifferent responses.

A second study investigated the individual effects of each control gain on the resulting

temperature response. For these tests, all but one variable were left constant. First, the

proportional gain, Kp, was varied from 0.5 to 1.0 and Ki and Kd were held at 0 for a desired

temperature of 30oC. Proportional gain, Kp, is a control term that scales the output control

effort proportionally to the measured temperature error. As a result, this control gain sets

the initial slope of the temperature response. For higher desired temperatures and thus

larger initial errors, the proportional gain results in a steeper temperature increase (heating

rate). Since Ki was held at zero throughout this study, each temperature response exhibited

steady-state error and none matched the temperature set point of 30oC.

With the proportional gain affecting the initial temperature rate increase, the inte-

gral gain was now varied from 0.025 to 0.100 while holding Kp, Kd, and the set temperature

constant. As discussed before, integral gain is used to minimize the steady-state error of

a controlled variable. Figure 2.29 demonstrates this concept for the temperature response

controlled with a non-zero Ki value (red line). The observed effect that Ki had on the

44

0 50 100 15021

22

23

24

25

26

27

28

29

Time - sT

empe

ratu

re -

C

Kp=0.5

Kp=0.6

Kp=0.7Kp=0.8

Kp=1.0

Set Temperature: 30 CKi = Kd = 0

Figure 2.28: Temperature response versus a varied proporional gain, Kp.

temperature response was reflected in terms of the controlled system’s damping. This con-

trol gain, when relatively larger (≈ 0.1), caused the measured temperature to overshoot

the desired temperature and then oscillate before steadying out. As the integral gain was

reduced to smaller values, the controlled temperature experienced less overshoot, exhibit-

ing more of a “damped” response. So, in order to minimize overshoot, which is a goal for

matching the prescribed temperature response, the integral gain was selected to be relative

small compared to the proportional gain (Kp = 0.5).

Lastly, the derivative gain, Kd was varied for a constant temperature step input at

fixed values of proportional and integral gains. The derivative gain, according to literature

[37], is designed to speed up the response (or reduce its settling time). However, the

measured temperature response was not noticeably affected by the derivative gain at low

levels. The selection of the Kp and Ki values from previous analysis have produced an

accurate, highly damped temperature response. Adding derivative gain to the PI controller

did not quicken the temperature response for the system. Even more, in attempts to reduce

the power required to control the temperature, eliminating one control gain potentially

lessens the magnitude of the control signal and thus reduces power applied to the material.

For step response, it was discovered that a proportional-integral (PI) controller re-

sulted in a temperature response that matched the desired temperature and minimized

overshoot. However, this type of desired signal is not practical when it comes to prescribing

a temperature versus time cure schedule [42]. In this case, it is more common to ramp (in-

crease linearly) the temperature up to the curing temperature, hold it there, and then allow

45

0 50 100 15020

22

24

26

28

30

32

Time - s

Tem

pera

ture

- C

Ki = 0

Ki = 0.1

Set Temperature: 30 CKd = 0, Kp = 0.5

Nearly identical slopes!

0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.5

1

1.5

2

2.5

PID Proportional Gain, Kp

Initi

al S

lope

- C

/s

0 50 100 15020

22

24

26

28

30

32

Time - s

Tem

pera

ture

- C

Ki = 0

Ki = 0.1



0 50 100 15020

22

24

26

28

30

32

Time - s

Tem

pera

ture

- C

Ki = 0

Ki = 0.1



0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.5

1

1.5

2

2.5

PID Proportional Gain, Kp

Initi

al S

lope

- C

/s

Figure 2.29: By increasing Ki to a value of 0.05, the steady-state error disap-pears, but the initial slope remains (left). Calculated initial slopes as a functionof increasing proportional gain solidifies its effect on the temperature response(right).

0 10 20 30 40 50 60 70 80 90 10020

25

30

35

40

45

50

Time - s

Tem

pera

ture

- C

Proportional Gain, Kp: 0.4


Set Temperature: 40 C

Ki=0.040

Ki=0.035

Ki=0.030

Ki=0.025

Ki=0.100

Figure 2.30: Integral gain effects on controlled temperature response.

it to cool. With that said, the ability to track the desired temperature becomes important

for evaluating the effectiveness of this controller. By applying a ramping desired temper-

ature, the effects of Kp and Ki on the ability to track a changing reference temperature

were examined. For these tests, Kd was held at 0 since it provided no additional control

advantage during the step tests.

The plots in Figure 2.32 provide several insights into the tracking ability of a PI

controller. First, it is observed that the proportional gain had little effect on the controller’s

tracking ability. For each gain value, the controller “lagged” the desired temperature signal.

Secondly, varying the integral gain resulted in a more noticeable effect. As the value of

46

0 50 100 15020

25

30

35

40

45

Time - sT

empe

ratu

re -

C

Kd=0

Kd=0.02Kd=0.04

Set Temperature: 40 CProportional Gain: 0.4Integral Gain: 0.03

Figure 2.31: The measured temperature response demonstrated a weaker de-pendence on the value of the derivative gain at low levels of Kd.

0 50 100 150 200 250 30020

22

24

26

28

30

32

34

36

38

40

Time - s

Tem

pera

ture

- C

TsetKp=0.4

Kp=0.5

Kp=0.6

Kp=0.8Kp=1.0

Ki = 0.03Kd = 0

0 50 100 150 200 250 30022

24

26

28

30

32

34

36

Time - s

Tem

pera

ture

- C

TsetKi=0.05

Ki=0.09

Ki=0.13

Ki=0.17Ki=0.20

Kp = 0.5Kd = 0

0 50 100 150 200 250 30020

22

24

26

28

30

32

34

36

38

40

Time - s

Tem

pera

ture

- C

TsetKp=0.4

Kp=0.5

Kp=0.6

Kp=0.8Kp=1.0

Ki = 0.03Kd = 0

0 50 100 150 200 250 30022

24

26

28

30

32

34

36

Time - s

Tem

pera

ture

- C

TsetKi=0.05

Ki=0.09

Ki=0.13

Ki=0.17Ki=0.20

Kp = 0.5Kd = 0

Figure 2.32: Ramping temperature responses measured for varying proportionalgains (left) and integral gains (right).

Ki increased, the controlled temperature overshot the desired signal at the end of the

ramping section and exhibited more oscillation during the final zero-order temperature

hold. The values of Ki tested, which were larger than the integral gain (0.03) used in the

first plot, demonstrated that increased integral gain also decreased the lag error during

the temperature ramp. Overall, selecting Ki for a tracking signal reveals the trade-off

between first-order accuracy for larger values of integral gain and zero-order accuracy for

smaller values of Ki. This decision is simplified since some error can be tolerated during

the heating (temperature ramping) phase of a cure schedule. More important, though,

is minimizing the overshoot of the measured temperature and providing accurate steady-

state temperature holding. By selecting an integral gain to be “small,” but non-zero, these

47

stipulations were met and the control signal, u(t) was kept to a minimum for given values

of Kp and Kd.

Using the selected values to mimic a full-cure schedule, the effectiveness of the con-

troller is shown. The gain values used during this last demonstration were again varied

to see the effect on a desired temperature profile that combines step, ramp, and hold pat-

terns. The error between the desired temperature and the feedback temperature was also

examined. Each combination provided a controlled temperature within a few degrees of the

0 50 100 150 200 250 300 350 40020

25

30

35

40

45

50

Time - s

Tem

pera

ture

- C

Tset

Kp=0.5,Ki=0.1,Kd=0.04Kp=0.5,Ki=0.08,Kd=0.04

Kp=0.5,Ki=0.1,Kd=0

50 100 150 200 250 300 350 400 450-1

-0.5

0

0.5

1

1.5

Maximum: 1.025CMinimum: -0.671C

Average: 0.030C

Err

or -

C

50 100 150 200 250 300 350 400 450-4

-2

0

2

4

6

Time - s

Err

or -

%

Maximum: 4.102%Minimum: -2.331%

Average: 0.091%

0 50 100 150 200 250 300 350 40020

25

30

35

40

45

50

Time - s

Tem

pera

ture

- C

Tset

Kp=0.5,Ki=0.1,Kd=0.04Kp=0.5,Ki=0.08,Kd=0.04

Kp=0.5,Ki=0.1,Kd=0

50 100 150 200 250 300 350 400 450-1

-0.5

0

0.5

1

1.5

Maximum: 1.025CMinimum: -0.671C

Average: 0.030C

Err

or -

C

50 100 150 200 250 300 350 400 450-4

-2

0

2

4

6

Time - s

Err

or -

%

Maximum: 4.102%Minimum: -2.331%

Average: 0.091%

Figure 2.33: PI controller used to control temperature through a full, curing-schedule-type profile (left). The associated error for the third combination ofcontroller gains as a function of time (right).

desired temperature throughout the test. Using the third combination, which employs only

proportional and integral gains (PI), it was shown that the controller was accurate to ±1oC

(ignoring the initial temperature step). So, through an extensive experimental parametric

study of the control gains, the final Kp, Ki, and Kd values chosen are 0.4, 0.04, and 0,

respectively. Without derivative control, but stemming from a PID control strategy basis,

the resulting feedback controller is simply a proportional-integral (PI) controller.

Results from the feedback controller experiments were expanded to higher temper-

atures by using the Xantrex XHR 300V-3.5A DC Power Supply/Amplifier. Specifically,

it was desired to see if temperature dependent non-linearities in the system affected the

PI controller’s performance at more-realistic curing temperatures. Again, both step and

tracking desired temperature signals were used as references. Looking at the tempera-

ture response for the desired temperature step input (Figure 2.34), it is evident that the

overshoot increased slightly for higher set points. In addition to the average measured tem-

48

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Time - s

Tem

pera

ture

- C

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

Time - s

Pow

er -

W

Energy values for each run:

Run 1: E = 0.075452 W-hrRun 2: E = 0.14892 W-hrRun 3: E = 0.23058 W-hr

Run 1: Tset=45C

Run 2: Tset=65CRun 3: Tset=85C

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Time - s

Tem

pera

ture

- C

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

Time - s

Pow

er -

W

Energy values for each run:

Run 1: E = 0.075452 W-hrRun 2: E = 0.14892 W-hrRun 3: E = 0.23058 W-hr

Run 1: Tset=45C

Run 2: Tset=65CRun 3: Tset=85C

Figure 2.34: Temperature response measured for higher temperatures (left).Associated electrical power and energy for each test (right).

peratures (black lines), the maximum and minimum temperatures are plotted. These values

represent the variation in temperature measured by each thermocouple. Also, the electrical

power and energy (the area under the power versus time curve) supplied to the samples

were measured. For a step input of 85oC, the maximum power supplied was over 50W,

though the total energy during the test was less than 0.24W-hr. This plot demonstrates

that rigidization through resistive heating demands large amounts of power, but if cured

quickly, uses only moderate amounts of energy.

Again, the average measured temperature was used as the feedback control signal,

and temperature difference band between the maximum and minimum recorded tempera-

tures is shown. While the average temperature was controlled to precisely match the desired

0 50 100 150 200 250 300 350 4000

50

100

150

200

Time - s

Tem

pera

ture

- C

Meas. Temp. Band

Desired Temp.

Average Temp.

0 50 100 150 200 250 300 350 4000

10

20

30

Time - s

Pow

er -

W

Energy Consumed (area): 1.6301 W-hr

Figure 2.35: Tracking ability of the PI controller for a high temperature “curing-type” schedule.

49

temperature signal, the gap between maximum and minimum temperature widened as a

function of temperature. Further, the electrical power data collected shows that power

levels decreased by ramping the desired temperature. Intuitively, this makes sense. For a

large step input, the controller must output a large corrective signal to make up for a great

initial error measurement. In terms of the chosen PI controller gains, these values provided

accurate control even at the much higher curing temperatures.

Discussed later in Chapter 3, the controlled resistive heating of carbon-fiber rein-

forced polymers is used to induce thermoset resin curing and matrix consolidation, which

rigidizes the material. As an example of a heating schedule used to rigidize the samples,

Figures 2.36 and 2.37 look at the temperature profile, the electrical energy required, and the

error in the controlled temperature. This test forecasts the ability of temperature-controlled

resistive heating to match a desired temperature schedule. This sample was heated up 160oC

0 50 100 150 200 250 300 350 4000

5

10

15

20

Time - s

Pow

er -

W

Energy Consumed: 1.27 W-hr

0 50 100 150 200 250 300 350 400 45020

40

60

80

100

120

140

160

180

Time - s

Tem

pera

ture

- C

Desired

Actual

0 50 100 150 200 250 300 350 4000

5

10

15

20

Time - s

Pow

er -

W

Energy Consumed: 1.27 W-hr

0 50 100 150 200 250 300 350 400 45020

40

60

80

100

120

140

160

180

Time - s

Tem

pera

ture

- C

Desired

Actual

Figure 2.36: Controlled temperature (left) and resulting electrical power (right)measured for the cure of CFRP sample.

at a constant heating rate of 60oC/min and held at the curing temperature for 2 minutes.

The heating process required 1.27W-hr of electrical energy over a total time of 6 minutes

and 40 seconds, with a peak power of roughly 20W. During this controlled heating process,

the material’s temperature was kept within ±8oC of the desired temperature at all times.

Even more, during the dwell time at the curing temperature, the controlled temperature

was within ±2oC of the desired 160oC.

50

0 50 100 150 200 250 300 350 400 450-12

-10

-8

-6

-4

-2

0

2

4

6

8

Time - s

Err

or -

C

0 50 100 150 200 250 300 350 400 45020

40

60

80

100

120

140

160

180

Time - s

Tem

pera

ture

- C

Desired

Actual

0 50 100 150 200 250 300 350 400 450-12

-10

-8

-6

-4

-2

0

2

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8

Time - s

Err

or -

C

0 50 100 150 200 250 300 350 400 45020

40

60

80

100

120

140

160

180

Time - s

Tem

pera

ture

- C

Desired

Actual

Figure 2.37: Temperature profile (left) and dynamic error (right) measuredduring an actual curing schedule.

2.5 Infrared Thermography: A Visual Approach

In establishing the temperature measurement technique used to monitor sample tempera-

ture during the resistive heating process, it was noticed that each of the three thermocouples

measured different values (Figures 2.9 and Figures 2.34 and 2.35). Were the thermocouples

poorly placed (Figure 2.3), or does a real temperature gradient exist along the length of the

material? Up until now, the three thermocouple temperatures were averaged at every point

in time during the tests. This technique was chosen merely to simplify the data through the

assumption that the temperature along the length of the carbon-fiber samples was constant.

After all, current flowing through a uniformly resistive element should produce the same

temperature at each point. In efforts to validate the “evenness” of the sample temperature,

infrared (IR) imaging was performed. By being able to visualize how the material heats, it

was hoped to better understand if and how temperature gradients are introduced into the

samples.

2.5.1 Introduction to Infrared Imaging

Infrared waves, produced as thermal radiation from heated bodies, are electromagnetic

waves whose wavelengths are beyond the visible wavelength spectrum [3]. The emission

of thermal radiation occurs when the oscillations or transitions of the many electrons that

constitute matter release energy. The temperature of the matter, a form of internal energy,

sustains the electron oscillations and is thus related to the emission of thermal radiation

51

[33]. Infrared (IR) cameras detect thermal radiation by columnating the thermal radiation

and focusing it onto a detector of known material.

Figure 2.38: Infrared detection scheme as found in an Inframetrics 760 IRCamera [10].

Infrared imaging, or thermography, is not new to the study of carbon-fiber and other

composites. Much work as been performed on using IR imaging to detect inhomogeneities

that affect the performance of a composite. Specifically, factors such as constituent concen-

trations (fiber-resin ratio), orientation and distribution of reinforcement, voids, and matrix-

reinforcement bonding can be identified through IR. Further, this technique can also locate

foreign material, fiber breakage, and degradation [43]. A form of non-destructive evaluation

or testing (NDE or NDT), thermography can also be used to quickly analyze composites

without further damaging, or even contacting, the material. Jones and Berger performed

thermographic inspection on glass-reinforce composite marine vessel hulls [44]. Favro, et al

used high power photographic flash lamps to generate a heat pulse on the surface of fiber-

reinforced polymers and ceramics. Their work also included the study of crack propagation

as identified through thermography [45]. Further, Sakagami and Ogura, of Osaka Univer-

sity, investigated the transient temperature distribution result from through-thickness and

surface cracks in steel plates as well as delaminated CFRP composite samples [46]. In their

study, they used Joule effect heating, through the application of an electric current, to in-

duce thermal radiation emission from the samples. In the area of spacecraft, Tretout, et

al researched the feasibility of applying thermographic NDT to the evaluation of satellite

structures during assembly. The authors establish an experimental procedure for acquiring

the thermal scans and present a method for processing the data.

52

In contrast to previous work [43, 44, 45, 46], the work performed in this document

applies thermography in a different manner. Instead of using temperature distributions to

detect inhomogeneities within the CFRP samples, the temperature distributions themselves

will be used to quantifiy the “evenness” of the heating process. Particularly, this study

investigated the temperature distribution within the samples during resistive heating and

included sample length, sample twist, and temperature as possible deterrents from uniform

heating. Thermographic imaging was also used to confirm temperature values measured

using thermocouples.

2.5.2 Thermographic Imaging Results and Discussion

An Inframetrics 760 Model IR Imaging Radiometer was used to capture still images of

the sample’s temperature map during resistive heating. The application of power and

measurement of temperature remain as they were used before, with the only additions to

the setup being the IR camera and a television (for real-time viewing). It should be noted

that the images obtained during this test were used qualitatively to investigate temperature

distribution, and not quantitatively to look at nominal temperature values.

Additional infrared thermography images of the resistive heating process were ob-

tained using a Flir ThermaCAM EX320 infrared camera. This instrument provided in-

creased accuracy in not only visualizing temperature gradients but also in measuring nom-

inal temperature values. With this capability, it was desired to verify the temperatures

measured by the thermocouples as well as detect if the thermocouples were affecting the

temperature of the sample.

The tests consisted of prescribing a temperature-time profile for the control system

to match (using an average measured temperature as the feedback signal). During the

heating process, the camera was focused on to the heated sample and still images were

taken. The matrix of test conditions evaluated through IR imaging included sample length

(and thus resistance), sample twist, and also temperature. If these factors contribute to

non-uniform heating, it was hoped to notice this effect in the IR images. While this in-

strument can display infrared images in both black and white and color modes, the images

will be presented in color. The black and white mode, while difficult to distinguish small

temperature differences in gray scale, was used to focus the camera on the object. Then,

with the camera in color mode, the temperature gradient was monitored and recorded. Two

53

iV+ V-

Th1 Th4 Th6

IR Camera

Television

Hot

Cold

iV+ V-

Th1 Th4 Th6

IR Camera

Television

iV+ V-

Th1 Th4 Th6

iV+ V-

Th1 Th4 Th6

IR Camera

Television

Hot

Cold

Figure 2.39: Experimental setup for thermographic imaging of CFRP samplesduring resistive heating.

drawbacks of this device were its rather poor resolution in color mode and its inability to

record real-time videos.

First, the effect that sample length had on the resistive heating process was ex-

amined. The measured temperatures were plotted versus the desired temperature and the

electrical power and energy were also recorded. Increasing the length of the sample increases

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 3"

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 4"

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 5"

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 6"

0 20 40 60 80 100 120 140 160 180 2000

2

4

6

Time - s

Pow

er -

W

Electric Power Consumed

Length=3"

Length=4"Length=5"

Length=6"

2 3 4 5 6 7 8 90

0.05

0.1

0.15

Length - in

Ene

rgy

- W

-hr

Electrical Energy Consumed

Linear Trendline: E = 0.020L + 0.019 W-hr

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 3"

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 4"

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 5"

0 50 100 150 2000

20

40

60

Time - s

Tem

pera

ture

- C

Sample Length = 6"

0 20 40 60 80 100 120 140 160 180 2000

2

4

6

Time - s

Pow

er -

W

Electric Power Consumed

Length=3"

Length=4"Length=5"

Length=6"

2 3 4 5 6 7 8 90

0.05

0.1

0.15

Length - in

Ene

rgy

- W

-hr

Electrical Energy Consumed

Linear Trendline: E = 0.020L + 0.019 W-hr

Figure 2.40: Measured temperature responses (left) and associated electricalpower supply (right).

its resistance and mass. As a result, more power was required to achieve the same temper-

ature and thus more energy was used during the heating process (Figure 2.40). However,

infrared stills captured for these samples demonstrate even heating. As shown, the samples

have a hot (dark red) core region running the length of the sample and the temperature

54

Sample Length: L = 3" Sample Length: L = 4"

Sample Length: L = 5" Sample Length: L = 6"

Figure 2.41: Still images captured for various lengths at a temperature of 60oC.

cools radially outward.

Secondly, the maximum temperature attained was thought to possibly induce and/or

widen a temperature gradient. Four different maximum temperatures were used to obtain

IR still images of the heating process. Again, the samples heated evenly along their lengths,

with the only noticeably temperature gradient in the radial direction. Focusing in on a

0 50 100 1500

50

100

150

Time - s

Tem

pera

ture

- C

Maximum Temperature: Tmax = 60 C

0 50 100 1500

50

100

150

Time - s

Tem

pera

ture

- C


0 50 100 1500

50

100

150

Time - s

Tem

pera

ture

- C


0 50 100 1500

50

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Time - s

Tem

pera

ture

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Maximum Temperature: Tmax = 60 C Maximum Temperature: Tmax = 80 C


0 50 100 1500

50

100

150

Time - s

Tem

pera

ture

- C


0 50 100 1500

50

100

150

Time - s

Tem

pera

ture

- C


0 50 100 1500

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100

150

Time - s

Tem

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ture

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0 50 100 1500

50

100

150

Time - s

Tem

pera

ture

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Figure 2.42: Controlled temperatures (left) and temperature gradients (right)via IR imaging of samples heated to different temperatures.

segment of one of the samples allows for the radial temperature gradient to be seen more

clearly. Heating of the thermocouples during this process was also noticed through the IR

imaging. In addition, it was observed (Figure 2.43) during the “cool down” phase of the

heating tests that the samples reach room temperature much sooner than the thermocouples.

As a result, data collected during this phase was skewed by an artificially high thermocouple

55

Figure 2.43: Up-close thermographic image of the CFRP material (horizontal)and thermocouple (vertical) during a controlled resistive heat.

temperatures. This effect is not significant since during the cooling phase, the material has

already under-gone its “curing” process and is merely being brought back to a cooled state.

The effect of sample twist on the temperature distribution was also studied. The

initial resistance for the twisted samples was recorded prior to each heating test.

Table 2.2: Sample resistance measured as a function of the number of axialtwists.

Trial # of Twists Initial R Image # filename1 0 12.7 15 irtwist12 5 10.9 16 irtwist23 10 8.7 17 irtwist34 20 8.4 18 irtwist4

Increasing the number of twists did have a noticeable effect on the resistance of

the sample (Table 2.2), which in turn reduced the amount of power required to heat the

sample. The temperature along the length of the sample, though, was not affected by the

twisting. This find ensured that twisting can be used to help secure the thermocouples in

place without introducing new thermal gradients. Further, as Figure 2.43 demonstrates, the

hottest region of the sample was centered in the cross-section with a slight thermal gradient

noticed in the radial direction.

In general, thermographic imaging through the use of an IR camera has shown

that the temperature is fairly constant along the length of the samples. The ability to

measure the hottest core region of the sample at any point along its length determines

how well the thermocouple measurements agree. Since poor thermocouple placement can

56

0 20 40 60 80 100 120 140 160 1800

2

4

6

8

Pow

er -

W

Time - s

Electrical Power Consumed

0 Twists

5 Twists10 Twists

20 Twists

0 5 10 15 20 250

5

10

15

Twists - #

Res

ista

nce

- O

hms

Sample Resistance

Number of Twists: 0 Number of Twists: 5

Number of Twists: 20

0 20 40 60 80 100 120 140 160 1800

2

4

6

8

Pow

er -

W

Time - s

Electrical Power Consumed

0 Twists

5 Twists10 Twists

20 Twists

0 5 10 15 20 250

5

10

15

Twists - #

Res

ista

nce

- O

hms

Sample Resistance

Number of Twists: 0 Number of Twists: 5

Number of Twists: 20

Figure 2.44: Electrical power and sample resistance (left) and thermographicimaging (right) of twisted samples. As the number of twists increased, the re-sistance and electrical power decreased, but temperature distribution remained“even.”

result in false temperature readings being counted, an average measured value is not a good

choice for the feedback control signal. When an averaged temperature is used, and one

or more thermocouples is not accurately measuring the sample temperature, the average

value is lowered. This results in the control signal increasing its output in order to correct

for a low temperature and in turn, actually raising the true sample temperature above

the desired value. Instead, using the maximum measured temperature (from any of the

three thermocouples) more accurately represents the true core temperature and reduces the

chance of incorporating false temperatures into the control algorithm. The net effect of

using the maximum temperature as the feedback signal is to better represent the actual

temperature within the sample, eliminate the risk of accidentally overshooting the setpoint,

and minimize the control effort required to drive it.

The actual temperature of a coated, carbon fiber tow sample was validated during

resistive heating using an Flir ThermaCAM EX320 IR camera. While this device technically

measures heat flux, temperature values can be obtained for objects of known emissivity in

a defined environment (i.e. ambient temperature). The emissivity of carbon fiber, which

was experimentally measured by Eto, et al [47], ranges between 0.90 and 1.00.

The increased resolution of the images obtained with this IR camera provide clear

evidence that the thermocouples are affecting the sample temperature. While the sample

reaches an nearly constant temperature along its length between the two thermocouples, it

57

20.6°C

359.7°C

SP01*: 357.5SP02*: 171.5 SP03*: 165.2

Figure 2.45: Temperature gradient obtained on a sample during resistive heat-ing

is drastically lower near the thermocouples. For the resistive heating schedule prescribed in

Figure 2.45, the image was taken at a point when the thermocouples measured a maximum

temperature of 160oC. The IR image verifies that the temperatures measured through ther-

mography are also near this value when in the vicinity of the thermocouples. However, away

from the thermocouples the sample reaches a maximum temperature of roughly 360oC.

The size of the thermocouples (20-gauge thermocouple wire is 0.81mm in diameter)

in relation to the twisted tow size ( 1− 2mm in diameter). The thermocouples, in efforts to

place them securely and measure the maximum internal temperature of the tow, are lodged

into the twisted fibers. Because of their size, slight misplacements of the thermocouples

result in drastically different temperatures through the thickness of the sample. Further, the

“large” thermocouples disrupt the fiber alignment and tow orientation in the near vicinity.

This effect, which may cause changes in the flow of electrical current and/or introduce more

surface area subject to convective cooling, results in decreased sample temperature at the

location of the thermocouples. It is seen that for a temperature of 160oC measured by the

thermocouples, IR thermography records a maximum temperature closer to 360oC.

Selecting smaller, 36-gauge (0.13mm wire diameter) thermocouples provides a less-

intrusive temperature measurement technique. Placing the thermocouples becomes easier

and fiber orientation in the tow is preserved.

A resistive heating schedule that prescribes a maximum temperature of 160oC and

58

0 50 100 150 200 250 300 350 4000

50

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200

250

300

350

400

450

500

Time - s

Tem

pera

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- C

Desired

36 ga. J-type20 ga. J-type

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Time - s

Tem

pera

ture

- C

Desired

36 ga. J-type20 ga. J-type

Figure 2.46: Temperatures measured by small and large thermocouples on thesame sample differed drastically.

feeds back the temperature measured by the original thermocouple accurately tracks the

desired temperature. However, the smaller thermocouple measures a much higher sample

temperature during this process. This smaller profile of this thermocouple is less intrusive

on the sample and measures a maximum temperature of nearly 400oC. Comparing the

two thermocouple readings and the IR image obtained for the same heating profile shows

that the smaller thermocouple more accurately measures the maximum temperature of the

sample. In both cases, the large thermocouple affected the sample temperature locally,

significantly underestimating the true temperature and causing the sample to overheat.

2.6 Conclusions

Through the use of feedback control, via an experimentally-tuned PI controller, temperature

control of CFRP materials during resistive heating has been established. First, uncontrolled,

open-loop heating tests were performed in order to observe the heating behavior of these

materials as well as initiate a method for implementing resistive heating and temperature

measurement. Temperature control, both in open-loop and closed-loop configurations were

then addressed. Using a lumped-capacitance heating model of the composite sample, pre-

dictive Joule heating was performed with minimal success. In its place, a feedback control

algorithm was effectively implemented; the controller stemming from PID control theory.

In this structure, a feedback controller compares a measured temperature to a desired set

point and adjusts its corrective control effort to minimize the difference. Through many

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experimental variations of PID control gains, proportional and integral gains of 0.4 and 0.04

were chosen, respectively. The tests revealed that the derivative control did not noticeably

improve the controlled temperature response and was thus eliminated (Kd = 0). Further,

the selected PI control was shown to accurately mimic a desired temperature profile for step,

ramp, and arbitrary tracking patterns. Lastly, thermographic images from an infrared (IR)

camera were used to visually observe the heating process and confirmed that the samples

exhibit consistent temperatures along their length. The accuracy of measuring temperature

with thermocouples was also observed through thermography, and it was determined that

smaller thermocouples provided more accurate readings.

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controlled resistive heating of carbon fiber composites · 2020. 9. 25. · each sample consisted...

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