252 CHAPTER 8. APPLICATIONS
optimum heat extraction can be achieved. For this purpose, a fuzzy logic-based
scheme is proposed. Figure 8.1 illustrates an overview of the control process.
Figure 8.1. Control scheme for thermoelectric cooling of laser materialsThe thermal gradients generated by the pumping process in the laser medium
are detected by a temperature measurement scheme to provide an input to the
fuzzy controller. This temperature normally refers to the peak temperature of
the crystal. A temperature error signal is generated by comparing the actual
crystal temperature with a reference temperature. This is one of the inputs to
the fuzzy controller. For the effective performance of the controller, an addi-
tional input, namely, the rate of change in temperature is also required. The
output of the controller is the incremental change in current required to regulate
the operation of a TEC in order to extract an incremental amount of heat from
the surface of the crystal. This process is continued until a quiescent point is
achieved where the surface temperature of the crystal is at the desired tempera-
ture. For our analysis, a thin slab geometry for an LiNbO 3 crystal was assumed.
In an ideal case, the one-dimensional temperature profile across the thickness
of the slab is parabolic in nature according to the relationship
∆T=
b^2
8 KcQ
where,bis the crystal thickness,Qis the heat deposition in watts per cubic
meter,Kcis the thermal conductivity of the slab in watts per meter Kelvin,
and∆Tis the maximum temperature difference that occurs between the surface
and the center of the slab. Without any loss of generality, we assume∆T is
equivalent to the difference in the temperature between the hot and cold junc-
tions of a TEC. Note that these assumptions simplify the model development in
order to demonstrate the feasibility of a fuzzy controller implementation. Nev-
ertheless, deviations from ideal conditions are implicitly accounted for in the