Here we consider optimal PI control of a first-order plus delay process. Comparing the performance of the SIMC-rule with the optimal for a given robustness (Ms value) shows that the SIMC-rule give settings close to the Pareto-optimal. This means that the room for improving the SIMC PI-rule is limited, at least for the first-order plus delay processes considered in this paper, and with a good trade-off between rejecting input and output (setpoint) disturbances. 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.

The paper also has some interesting results for the robustness margins (GM, PM, DM, Ms) of the SIMC-rule. See equations (7) and (8) and Figure 10.