8.2. COOLING SCHEME FOR LASER MATERIALS 253
fuzzy logic-based system. This feature is the most significant benefit derived
from the proposed methodology.
Table 8.1 illustrates the fuzzy associative memory for the inputs and outputs
of the fuzzy controller.
Table 8.1. Fuzzy associative memory
←− Temperature Error −→
↑ LNE MNE SNE ZE SPE MPE LPE
Rate of LNR LA LA LA LA LA SIC SIC
Change SNR LA LA LA LA SIC MIC MIC
in Temp- ZR LA LA LA LA SIC MIC LIC
erature SPR LA LA LA SIC MIC LIC LIC
↓ LPR LA LA LA MIC LIC LIC LICThefuzzysetsforthetemperatureerror,therateofchangeintemperature,and
the incremental change in current are defined in Table 8.2.
Table 8.2. Fuzzy set definitions
Temperature Error Rate of Change in Temperature
LNE = Large Negative Error LNR = Large Negative Rate
MNE = Medium Negative Error SNR = Small Negative Rate
SNE = Small Negative Error ZR = Zero Rate
ZE=ZeroError SPR=SmallPositiveRate
SPE = Small Positive Error LPR = Large Positive Rate
MPE = Medium Positive Error
LPE = Large Positive ErrorIncremental Change in TEC Current
LA = Leave Alone
SIC = Small Incremental Change
MIC = Medium Incremental Change
LIC = Large Incremental ChangeThese subsets are implemented by a set of triangular membership functions,
and the centroid method of defuzzification is used. Figure 8.2 illustrates the
resulting fuzzy control surface.
Simulation results AMatlabSimulink model is developed to simulate the
TEC heat transfer dynamics and to examine the effectiveness of a fuzzy con-
troller to control a nonlinear process. These simulations are carried out for a
lithium niobate crystal of dimensions1cm◊1cm◊3cmwhose thermal con-
ductivity is 5 .6W/mK. A heat deposition of 5 .6W/m^3 per unit time interval,
a desired surface temperature of 300 ◦K, and initial cold junction temperature
of 500 ◦K, are assumed. The time interval chosen depends on the repetition
rate of the pumping source and the time constants associated with the cooler
and the crystal dynamics. To compute an incremental change in current, an