Chriss Grimholt and Sigurd Skogestad.
"Optimal PI-Control and Verification of the SIMC Tuning Rule".
Proceedings IFAC conference on Advances in PID control (PID'12), Brescia, Italy, 28-30 March 2012.

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.


A related paper, but with more emphasis on the SIMC method and its derivation, is the following:
Sigurd Skogestad and Chriss Grimholt, ''The SIMC Method for Smooth PID Controller Tuning'',
Chapter 5 in: R. Vilanova, A. Visioli (eds.), PID Control in the Third Millennium, Advances in Industrial Control, DOI 10.1007/978-1-4471-2425-2_5, © Springer-Verlag London Limited 2012


The original SIMC paper (JPC, 2003)