Nonmodel-based explicit design relations for PID controllers

Explicit design relations are proposed for tuning PID controllers with a view to nearly constant controller output after a step in the set point. First relations are derived from weighted moments of the deviation of the controller output from its steady-state value. Adaptations are introduced for systems with long dead time or large inverse response. From simulation results simple relations using the static gain, average residence time and apparent dead time of a self-regulating process, provide closed-loop responses nearly identical to the process reaction curve. Frequency response analysis shows gain and phase margins better than 2 and 60 degrees with a maximum closed-loop sensitivity less than 2.