Suppression of Rayleigh-Bénard convection with proportional-derivative controller

We study theoretically (linear stability) and experimentally the use of proportional and derivative controllers to postpone the transition from the no-motion state to the convective state in a circular cylinder heated from below and cooled from above. The heating is provided with an array of individually controlled actuators whose power is adjusted in proportion to temperatures measured in the cylinder’s interior. As the proportional controller’s gain increases, so does the critical Rayleigh number for the onset of convection. Relatively large proportional controller gains lead to oscillatory convection. The oscillatory convection can be suppressed with the application of a derivative controller, allowing further increases in the critical Rayleigh number. The experimental observations are compared with theoretical predictions.