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C. Grimholt and S. Skogestad, ''Optimal PID-Control for First Order Plus Time Delay Systems & Verification of the SIMC Rules'',
Paper at: 10th IFAC International Symposium on Dynamics and Control of Process Systems (DYCOPS). December 18-20, 2013. Mumbai, India

The SIMC method for PID controller tuning (Skogestad 2003) has already found widespread industrial usage. The optimality of the SIMC PI rules has been studied by Skogestad and Grimholt (2012) by comparing the performance (J=IAE) versus robustness (Ms) trade-off with the Pareto-optimal curve. The difference is small which leads to the conclusion that the SIMC PI-rules are close to optimal. The only exception is for pure time delay processes, so we introduce the improved SIMC rule to improve the performance for this case.

For PI-control, the improvement is to add theta/3 to tau1, and then use the original rule. This resulting PI-controller is close to the optimal one ( Skogestad and Grimholt (2012)).
For PID-control, the improvement suggested in this paper is to add theta/3 to taud (cascade PID form). We show in this presentation that this is close to the optimal PID-controller, but to take advantage of the derivative action one should choose tauc=theta/2, rather than the standard value tauc=theta.

For a pure delay process, the two "improved" controllers (PI and PID) are identical and give a PI-controller (rather than a pure I-controller which results from the original SIMC-rule).

The reason for putting "improved" in quotes, is because it can be argued that the improved performance by the D-action may not be worth the increased complexity of the controller and the increased sensitivity to noise.

The original SIMC paper (JPC, 2003)