Analytical PI Controller Tuning Using Closed-loop Setpoint Response

Recently Shamsuzzoha and Skogestad proposed a proportional-integral (PI) tuning rule for a wide range of unidentified processes. The rule relies on a closed-loop setpoint response (CSR) of a process and was developed from extensive numerical experiments. This work analytically derives a similar PI tuning rule using the CSR method. Simulations indicate that the two rules perform similarly if the tuning parameter is selected properly for the analytical rule. Meanwhile, a guideline is proposed for choosing the P controller gain for the CSR experiment to result in a proper overshoot for obtaining good PI settings. Numerical examples are used to demonstrate the usefulness of the theoretical results.