Feedback control of temperature in solids with a finite speed of heat propagation is investigated in this work. The emphases are placed on the effect of rapid thermal relaxation in high-rate heating and the possible delay during the short-time operations. Fundamental characteristics and dominating parameters are identified for effective feedback control in proportional heating. Transient instability, including the intrinsic transition from the desirable stability, neutral stability, to the ultimate unstable response are investigated in a wide spectrum of heating rates. Delayed heating is found to have a destabilizing effect during the short-time transient.

1.
Tzou, D. Y., 1997, Macro- to Microscale Heat Transfer: The Lagging Behavior, Taylor & Francis, Washington, D.C.
2.
Tzou, D. Y., 1992, “Thermal Shock Phenomena Under High-Rate Response in Solids,” in Annual Review of Heat Transfer, Chapter 3, pp. 111–185, Tien, C. L. ed., Hemisphere, Washington, D.C.
3.
O¨zisik
,
M. N.
, and
Tzou
,
D. Y.
,
1994
, “
On the Wave Theory in Heat Conduction
,”
ASME J. Heat Transfer
,
116
, pp.
526
535
.
4.
Joseph
,
D. D.
, and
Preziosi
,
L.
,
1989
, “
Heat Waves
,”
Rev. Mod. Phys.
,
61
, pp.
41
73
.
5.
Tien
,
C. L.
, and
Chen
,
G.
,
1994
, “
Challenges in Microscale Conductive and Radiative Heat Transfer
,”
ASME J. Heat Transfer
,
116
, pp.
799
807
.
6.
Taitel
,
Y.
,
1972
, “
On the Parabolic, Hyperbolic and Discrete Formulations of the Heat Conduction Equation
,”
Int. J. Heat Mass Transfer
,
15
, pp.
369
371
.
7.
Tzou
,
D. Y.
, and
Li
,
J.
,
1993
, “
Thermal Waves Emanating from a Fast-Moving Heat Source with a Finite imension
,”
ASME J. Heat Transfer
,
115
, pp.
526
532
.
8.
Tzou
,
D. Y.
,
1992
, “
Damping and Resonance Phenomena of Thermal Waves
,”
ASME J. Appl. Mech.
,
59
, pp.
862
867
.
9.
Goldman, C. H., Norris, P. M., and Tien, C. L., 1995, “Picosecond Energy Transport by Fractons in Amorphous Materials,” ASME/JSME Thermal Engng. Conf., 1, pp. 467–473.
10.
Tzou
,
D. Y.
, and
Chen
,
J. K.
,
1998
, “
Thermal Lagging in Random Media
,”
AIAA J. Thermophysics Heat Transfer
,
12
, pp.
567
574
.
11.
Peterson
,
G. P.
, and
Ma
,
H. B.
,
1999
, “
Temperature Response and Heat Transport in a Micro Heat Pipe
,”
ASME J. Heat Transfer
,
121
, pp.
438
445
.
12.
Tzou, D. Y., 1999, “Ultrafast Heat Transport: The Lagging Behavior,” invited paper, Microscale Heat Transfer and Fluid Flow in Gigahertz to Terahertz Photonics, SPIE’s 44th Annual Meeting, 18–22 July, Denver, Colorado.
13.
Hwu
,
R. J.
,
1993
, “
Recent Development of Millimeter-Wave High-Power Back-to-Back Varactor Diode Frequency Tripler
,”
Microwave J.
,
36
, pp.
240
253
.
14.
Adler
,
M. S.
,
Owyang
,
K. W.
,
Baliga
,
B. J.
, and
Kokosa
,
R. A.
,
1984
, “
The Evolution of Power Device Technology
,”
IEEE Trans. Electron Devices
,
31
, pp.
1570
1591
.
15.
Zhu
,
L.
,
Vafai
,
K.
, and
Xu
,
L.
,
1999
, “
Device Temperature and Heat Generation in Power Metal-Oxide Semiconductor Field Effect Transistors
,”
AIAA J. Thermophysics Heat Transfer
,
13
, pp.
185
194
.
16.
Nulman
,
J.
,
1987
, “
Rapid Thermal Processing of Electronic Materials
,”
Mat. Res. Symp.
,
92
, pp.
141
147
.
17.
Tzou, D. Y., 1997, “Macro- to Microscale Heat Transfer: The Lagging Behavior,” keynote lecture, Brazilian 14th Congress of Mechanical Engineering, December 8–12, 1997, Bauru-SP, Brazil.
18.
Tzou, D. Y., 2000, “Ultrafast Transient Behavior in microscale Heat/Mass Transport,” Advanced Photon Source Millennium Lecture Series, Argonne National Laboratories, March 1, Chicago, Illinois.
19.
Tzou, D. Y., 2000, “Microscale Heat Transfer and Fluid Flow,” Plenary Lecture and Panel of Terahertz and Gigahertz Electronics and Photonics, 2000 (45th) SPIE’s Annual Meeting, 30 July to 4 August, San Diego, California.
20.
Fung
,
R. F.
, and
Tseng
,
C. C.
,
1999
, “
Boundary Control of an Axially Moving String via Lyapunov Method
,”
ASME J. Dyn. Syst., Meas., Control
,
121
, pp.
105
110
.
21.
Fung
,
R. F.
,
Wu
,
J. W.
, and
Wu
,
S. L.
,
1999
, “
Stabilization of an Axially Moving String by Nonlinear Boundary Feedback
,”
ASME J. Dyn. Syst., Meas., Control
,
121
, pp.
117
120
.
22.
Orlov
,
Y. V.
, and
Utkin
,
V. I.
,
1983
, “
Application of Lyapunov Method in Distributed System
,”
Autom. Remote Control (Engl. Transl.)
,
44
, pp.
426
431
.
23.
Habib
,
M. S.
, and
Radcliffe
,
C. J.
,
1991
, “
Active Parametric damping of Distributed Parameter Beam Transverse Vibration
,”
ASME J. Dyn. Syst., Meas., Control
,
113
, pp.
295
299
.
24.
Fattorini, H. O., 1999, Infinite Dimensional Optimization and Control Theory, Cambridge University Press, UK.
25.
Cattaneo
,
C.
,
1958
, “
A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation
,”
Comp. Rend.
,
247
, pp.
431
433
.
26.
Vernotte
,
P.
,
1961
, “
Some Possible Complications in the Phenomena of Thermal Conduction
,”
Comp. Rend.
,
252
, pp.
2190
2191
.
27.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, second edition, Oxford University Press, UK.
28.
Tzou
,
D. Y.
,
1995
, “
A Unified Field Theory for Heat Conduction from Macro- to Micro-Scale
,”
ASME J. Heat Transfer
,
117
, pp.
8
16
.
29.
Tzou
,
D. Y.
,
1995
, “
The Generalized Lagging Response in Small-Scale and High-Rate Heating
,”
Int. J. Heat Mass Transfer
,
38
, pp.
3231
3240
.
30.
Tzou
,
D. Y.
,
1995
, “
Experimental Evidences for the Lagging Behavior in Heat Propagation
,”
AIAA J. Thermophysics Heat Transfer
,
9
, pp.
686
693
.
31.
Chiffelle, R. J., 1994, “On the Wave Behavior and Rate Effect of Thermal and Thermomechanical Waves,” MS Thesis, University of New Mexico, Albuquerque, New Mexico.
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