only 1.5V dropout voltage on high temperature at full load etc.

The minimum input voltage should be 17V 3A to get 15V 3A from output, the maximum input voltage can be any from 18V to 29V DC. The input voltage source can be a battery, 3A plug pack or 3A transformer, the input voltage is filtered by the 10uF electrolytic capacitor and the output voltage is also filtered by the 100uF electrolytic capacitor, the output voltage can be adjusted with the 5K variable resistor or a 5K potentiometer can also be used instead. The input and output voltage difference will be converted into heat thus a heatsink will be required with the IC.
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Here is another great regulated power supply adjustable from 1.2V to 15V DC with maximum 3A output current built with LM1085. LM1085 is a positive voltage regulator IC, there are many built in features of this IC some of them are over heat protection, current limiting, 3A output current,
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1.2V To 15V Adjustable Regulated Power Supply Using LM1085-ADJ