IEEE Systems, Man and Cybernetics Magazine - January 2023 - 65

heat absorbed by the Peltier element from (12) is shown
in Figure 9. The average value of uc
between 2,000 and
3,000 s is 15.43 W, which is close to the heater's heating
value of 15 W. The measurement error is 2.87% from (30).
Figure 10 shows the robust stability analysis results,
which are fewer than one for all
experimental times, indicating that
the proposed control system is
robustly stable.
Next, the experimental results
for a DUT (heater only) heat capacity
of 10 J/K are shown in Figures
11-15. From Figure 11, it can
be seen that the internal temperature
follows the target ambient
temperature in about 750 s. Figure
12 shows the temperatures of the
radiation side and the endothermic
side of the Peltier element, and Figure
13 shows the input current. The
result of the quantity of the heat
absorbed by the Peltier element
from (12) is shown in Figure 14. The
average value of uc
The results of the
robust stability
analysis confirm that
the robust stability
of the designed
nonlinear feedback
control system is
guaranteed.
Conclusions
In this article, a nonlinear control system was designed
based on operator theory and isomorphism to solve the
problem that the calorimetric power loss measurement
system using the Peltier element in the previous study [8],
[9] could not adapt to changes in
the heat capacity of the measurement
target. The design of the nonlinear
control system was based
on operator theory and isomorphism
to guarantee the BIBO stability
and passivity of the feedback
control system. From the results
of experiments, it was confirmed
that when the thermal capacity of
the DUT is 10 J/K, the internal temperature
of the chamber follows
the temperature outside the chamber
in approximately 750 s, with a
measurement error of 4.07%. When
the thermal capacity of the DUT is
300 J/K, the internal temperature
of the chamber follows the temperbetween
1,000 and 1,500 s is 15.61 W,
which is close to the heater's heating value of 15 W. The
measurement error is 4.07% from (30). Figure 15 shows the
robust stability analysis results, which are lower than one
for all experimental times, indicating that the proposed
control system is robustly stable.
The results of the two experiments confirm that good
tracking performance was obtained. Compared to the
previous study [9], the error rate of uc
7.2% to 4.07%, and the time for Tin
decreased from
to follow Tamb
decreased by about 50 s when the heat capacity of the
DUT was 10 J/K. This confirms the effectiveness of the
proposed control system.
ature outside the chamber in approximately 1,700 s, with a
measurement error of 2.87%. Even when the thermal
capacity of the DUT was varied using a heat sink, good
control performance could be obtained without changing
the design parameters.
The control system was designed based on operator
theory, adaptive control theory, and isomorphism, and the
error of the uc
IEEE Systems, Man and Cybernetics Magazine - January 2023

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