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Chapter 5 in:

**
Abstract. ** The SIMC method for PID controller tuning (Skogestad 2003) has
already found widespread industrial usage. This chapter gives an updated
overview of the method, mainly from a user’s point of view. The basis for the SIMC
method is a first-order plus time delay model, and we present a new effective method
to obtain the model from a simple closed-loop experiment. An important advantage
of the SIMC rule is that there is a single tuning parameter (tc) that gives a good
balance between the PID parameters (Kc; tI ; tD), and which can be adjusted to get
a desired trade-off between performance (tight control) and robustness (smooth
control). Compared to the original paper of Skogestad (2003), the choice of the
tuning parameter tc is discussed in more detail, and lower and upper limits are
presented for tight and smooth tuning, respectively. Finally, the optimality of the
SIMC PI rules is studied by comparing the performance (IAE) versus robustness
(Ms) trade-off with the Pareto-optimal curve. The difference is small which leads to
the conclusion that the SIMC 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 may be implemented by adding 1/3 of the delay to tau1, and then use the original rule. For a pure delay process, this gives a PI-controller rather than a pure I-controller for the original SIMC-rule.

A related paper is the following:

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 in more detail optimal PI control of a first-oder 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 original SIMC paper (JPC, 2003)