Research articleA PI tuning rule for integrating plus dead time processes with parametric uncertainty

•An approach to tune a PI for an IPDT process with parametric uncertainty is provided.•The analysis is performed on the controller parameter space.•A tuning rule, that is given as function of the parametric uncertainty, is obtained.•Several examples, in which the results are applied, are studied.

A novel method to tune a Proportional-Integral (PI) compensator for an integrating plus dead time (IPDT) process, in presence of interval parametric uncertainty, is presented. The design is based on optimization of load disturbance rejection with constraints on the magnitude of the sensitivity and complementary sensitivity functions, that must be satisfied for any element belonging to a set of plants. Instead of solving this problem with a brute force approach (grid the uncertainty set), we prove that this problem can be solved by considering only two plants. That lets us to obtain a tuning rule, after using some approximations. To conclude, some examples will be given in order to elucidate the usefulness of the proposed tuning rule.