IEEE Systems, Man and Cybernetics Magazine - January 2023 - 62

The parameters used for modeling
are shown in Table 2.
In the calorimeter, when the
internal temperature Tin
and the
temperature of ambient air Tamb
are equal, there is no heat leakage
from the chamber. Therefore,
the amount of the endotherm of
the Peltier element is equal to the
quantity of heat emitted by the
DUT and is expressed as follows
using (1) and the power consumption
of the fan on the cold
side QFc
[9]:
uQ ST I== -cp cp
in
()
-
TT
p
hc
R -- .
2 rI Q
1
pFp
2
c
Table 2. The modeling parameters.
Parameter
Sp
rp
Th
Tc
Tin
Tamb
Tr
Rp
Rin
Rh
Rc
Rw
Rd
Cin
Ch
Cc
Cd
Qin
QFc
Description
Thermopower
Resistance of the Peltier element
Temperature on the radiation side
Temperature on the endothermic side
Temperature inside the chamber
Temperature outside the container
Temperature of the DUT
(12)
In this article,
adaptive control
theory is used to
respond to changes
in the measurement
object's heat
capacity.
The Control System Design
In this section, based on operator
theory, adaptive control theory,
and passivity, the control
system design of the calorimeter
using the Pelt ier element is
described. The section " A Nonlinear
Feedback Control System
Design Based on Operator Theory "
describes the control system
design, considering the stability
guarantee based on operator
theory, and the section " Passivity "
explains the passivity of the
Unit
[V/K]
[Ω]
[K]
[K]
[K]
[K]
[K]
Thermal resistance of the Peltier element [K/W]
Thermal resistance of the internal air
Thermal resistance of the radiation side
cooler
Thermal resistance of the endothermic
side cooler
[K/W]
[K/W]
[K/W]
Thermal resistance of the chamber wall [K/W]
Thermal resistance of the DUT
Heat capacity of the internal air
Heat capacity of the radiation side
cooler
Heat capacity of the endothermic side
cooler
Heat capacity of the DUT
Power dissipation of the DUT
Power dissipation of the endothermic
side cooler
[K/W]
[J/K]
[J/K]
[J/K]
[J/K]
[W]
[W]
designed control system. The section " Adaptive Control
System Design " describes the design of the tracking
compensator based on adaptive control theory,
and the section " The Design of a Feedback Control
System Based on Isomorphism " describes the control
system design based on operator theory and isomorphism.
See Table 3 for a list of the equipment used for
the calorimeter.
A Nonlinear Feedback Control System
Design Based on Operator Theory
Figure 3 illustrates the configuration of the feedback
control system based on operator theory [10], [11]. In
previous studies, a robust control system was based on
operator theory [12], [13], [14], [15], [16], [17], [18]. In
Figure 3, C1
is the tracking compensator, and D ,1and
R 1are
the operators.
If the current flowing through the Peltier element Ip
is the input signal u(t) to the plant and the temperature
Table 3. The equipment used for the
calorimeter.
Peltier
element
Sensors
Chamber
DUT
Power meter
TEC1-12706: Cooling capacity 50 W
Size: 40 × 40 × 3.9 mm
Temperature
Current
Pt100: Accuracy ±0.01 °C
CASR 6-NP: Accuracy 0.8%
Material: Styrofoam
Size: 300 × 300 × 300 mm
Wall thickness: 30 mm
Aluminum resistor: Resistance 3.3 Ω
Size: 148 × 210 × 0.5 mm
PPA4520: Accuracy 0.04%
Radiation side
Coolers
Endothermic side
CC-Siberian-01
Size:
120 × 96 × 66 mm
62 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE January 2023
TY-140
Size:
152 × 140 × 26.5 mm
N, S,
IEEE Systems, Man and Cybernetics Magazine - January 2023

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