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Cooking sous vide requires a constant temperature water bath. Controlling temperature with a simple thermostat (on-off control or bang-bang control) usually leads to temperature oscillations that considerably exceed the desirable ±0.25°C or better, depending on the thermal inertia of the heating system. To avoid temperature overshoot resulting from heating at full power until set point (i.e. the desired temperature) is reached, heating power must be gradually reduced while temperature approaches set point; this is called proportional control. Due to heat loss of the water bath, a simple proportional controller will never reach the set point but stabilize at a temperature below set point (negative offset). To correct negative offset, an integral term is introduced: it integrates (sums up) the deviation from set point over time and increases heating power accordingly; this is PI control. When cold food is placed in the water bath, temperature may drop faster than PI control can cope with. To correct this temperature drop faster, a derivative term is introduced which increases heating power according to the temperature change over time (Δtemp/Δtime); this is PID control.
A guide to PID control for sous vide cookery can be downloaded from an eGullet forums post of 20 August 2011. This guide is copyright protected by FreshMealsSolutions; Frank Hsu of FreshMealsSolutions explicitly gave permission to make the guide available for download in the eGullet forum, but not for publication on other websites (except his own of course) or otherwise.