Optimal PI-Control and Verification of the SIMC Tuning Rule

Optimal PI-settings are derived for first-order with delay processes for specified levels of robustness (Ms-value) and compared with the simple SIMC-rule. Optimality (performance) is defined in terms of the integrated absolute error (IAE) of the output for combined step changes in setpoints and input disturbances. With SIMC, the robustness level is adjusted by changing the tuning parameter τc, and the SIMC-rule was found to give surprisingly good setting with almost Pareto-optimal performance. The exception is a pure time delay processes where the SIMC-rule gives a pure integral controller with somewhat sluggish response. A simple modification to improve on this, is to increase the time constant in the rule by one third of the time delay.