stabilization of LTI time-delayed processes using analytical PID controllers

The analytical proportional-integral-derivative (PID) controllers, the tuning of which depend on simple formulas with one adjustable parameter, have been developed for processes with time delay. In this paper, using a simple method called dual-locus diagram, the solutions to the problems of stabilizing stable, integrating and unstable processes with time delay using analytical PID controllers are presented, respectively. For the stable and integrating process, the stabilizing range of the adjustable parameter is only related to the delay of the plant, while, for the unstable process, it depends on both the time constant of the plant and the ratio of the delay to the time constant. With the available stabilizing solution, it can avoid the time-consuming stability check in the controller application.