Kalman-Predictive-Proportional-Integral-Derivative (KPPID) Temperature Control

Abstract

With third generation synchrotron X‐ray sources, it is possible to acquire detailed structural information about the system under study with time resolution orders of magnitude faster than was possible a few years ago. These advances have generated many new challenges for changing and controlling the state of the system on very short time scales, in a uniform and controlled manner. For our particular X‐ray experiments [1] on crystallization or order‐disorder phase transitions in metallic alloys, we need to change the sample temperature by hundreds of degrees as fast as possible while avoiding over or under shooting. To achieve this, we designed and implemented a computer‐controlled temperature tracking system which combines standard Proportional‐Integral‐Derivative (PID) feedback, thermal modeling and finite difference thermal calculations (feedforward), and Kalman filtering of the temperature readings in order to reduce the noise. The resulting Kalman‐Predictive‐Proportional‐Integral‐Derivative (KPPID) algorithm allows us to obtain accurate control, to minimize the response time and to avoid over/under shooting, even in systems with inherently noisy temperature readings and time delays. The KPPID temperature controller was successfully implemented at the Advanced Photon Source at Argonne National Laboratories and was used to perform coherent and time‐resolved X‐ray diffraction experiments.