Active Disturbance Rejection Control: Application to the temperature stabilization of ultra-stable cavities

The examples of controls in a high-precision scientific laboratory are countless and most scientific applications rely on controls of the powerful proportional-integral-derivative (PID), first introduced by Minorsky in 1922. In recent years a novel Active Disturbance Rejection Control (ADRC) has been proposed. The ADRC is a linear, simple, intuitive, and inherently robust form of control. It is based on a linear extended state observer (LESO) that estimates and compensates the disturbance of the system in real time with a certain bandwidth. The bandwidths of the control and of the observer are the only parameters needed for tuning. The design of the ADRC is model independent and requires only some approximate knowledge of the fast frequency response of the system. We applied the ADRC to the stabilization of the temperature of optical ultra-stable cavities. Such cavities are used for laser frequency stabilization for high-resolution spectroscopy and in optical clocks. In our case a 578 nm yellow laser is locked to the cavities and it will be used for the spectroscopy of ytterbium atoms. The temperature of the cavities has to be stabilized to prevent drift in their length and thus in the frequency of the laser. We will present the details of the ADRC and show the performance of the temperature stabilization. The ADRC shows attractive features that motivates our choice: it is easy to design and to implement digitally, insensitive to environmental changes, and avoids typical problems encountered with PID like overshoots and integral windup.