A simple approach for on-line PI controller tuning using closed-loop setpoint responses

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A simple and new procedure has been developed for the PI controller tuning of an unidentified process using closed-loop responses. The method requires only one step test in the closed-loop system to obtain the proportional gain and integral time. The step test is a setpoint change performed with a proportional only controller while disabling any integral and derivative action. From the setpoint response one observes the overshoot and the corresponding time to reach the peak. In addition one observes the proportional gain (k c0 ) and the steady-state offset. Based on a range of first-order with delay test processes, a simple analytical correlation has been developed for the controller gain (k c /k c0 ) as a function of the overshoot. The integral time setting is mainly a function of the time to reach the peak. The settings were derived to match the SIMC tuning rule (with τ c =θ) which gives good robustness with a gain margin of about 3 and sensitivity peak (M s -value) of about 1.6. The proposed tuning method, originally derived for first-order with delay processes, has been tested on a broad range of other stable and integrating processes. The results using the closed-loop data are comparable with the SIMC tuning rule using the open-loop model.