Optimal design of a predictive PI controller for integrating processes with time delay using the fata morgana algorithm

Integrating-plus-dead-time (IPTD) processes are difficult to control because they are non-self-regulating and sensitive to parameter uncertainty. This simulation study presents a constraint-aware tuning framework for a Predictive PI (PPI) controller. The Fata Morgana Algorithm (FATA) minimizes a penalty-augmented objective that combines ITAE with quadratic penalties on maximum overshoot ( M _p ) and settling time ( t _s ). Two IPTD benchmark systems are used to compare the proposed controller with published PI–PD and I–PD designs. Within these comparisons, the settling time decreases by up to 47.5%, while the objective value J decreases by up to 71.3%. Twenty independent FATA runs are performed for each benchmark to characterize the repeatability of the tuning results. Under the tested simultaneous ± 25% gain-and-delay perturbations, both the proposed controller and the corresponding published comparator exhibit bounded responses approaching the reference in each benchmark. In Benchmark II, the I–PD response under the +25% perturbation exhibits more pronounced, slowly decaying oscillations than the PPI response, rather than instability. These simulation results indicate improved nominal transient performance within the selected comparisons, but do not establish formal robustness margins.