Demonstration of the improved PID method for the accurate temperature control of ADRs

Microcalorimeters require extreme stability ( ≲ 10 μ K ) of thermal bath at low temperature ( ∼ 100 mK ) . We have developed a portable adiabatic demagnetization refrigerator (ADR) system for ground experiments with TES microcalorimeters, in which we observed residual temperature between aimed and measured values when magnet current was controlled with the standard Proportional, Integral, and Derivative control (PID) method. The difference increases in time as the magnet current decreases. This phenomenon can be explained by the theory of the magnetic cooling, and we have introduced a new functional parameter to improve the PID method. With this improvement, long-term stability of the ADR temperature about 10 μ K rms is obtained up to the period of ∼ 15 ks down to almost zero magnet current. We briefly describe our ADR system and principle of the improved PID method, showing the temperature control result. It is demonstrated that the controlled time of the aimed temperature can be extended by about 30% longer than the standard PID method in our system. The improved PID method is considered to be of great advantage especially in the range of small magnet current.