Improved PID method of temperature control for adiabatic demagnetization refrigerators

We report a new method of precise temperature control for an adiabatic demagnetization refrigerator (ADR). Temperature of the experimental stage of ADRs is usually controlled with the standard PID (Proportional, Integral, and Derivative control) method by decreasing the magnet current of the superconducting solenoid surrounding the paramagnetic salt inside the ADR. In controlling the temperature of our portable ADR system, we found a small residual between the aimed and measured temperatures, which gradually increased in time as the magnet current decreases. This phenomenon is explained by the magnetic cooling theory, and we have introduced a new functional parameter to improve the standard PID method. Applying this improvement to our system, highly stabilized temperature of 10 μ K rms at 100 mK up to the period of ∼ 15 ks is presented. It is demonstrated that the temperature controlled time was increased by ∼ 30 % in our experiment. Our improved PID method is useful to maintain the long-term temperature stability down to almost zero magnet current with a relatively small ADR.