Tuning PI controllers based on ℋ∞ Weighted Sensitivity

H_∞ control theory is usually associated with high order controllers. In this paper, simple tuning rules (extending the well-known SIMC) for the Proportional-Integral (PI) algorithm are derived analytically based on H_∞ Weighted Sensitivity. The presented approach deals with stable, integrating and unstable plants in a unified way, avoiding any notion of coprime factorization. The final tuning involves two adjustable parameters, λ and γ, with clear engineering meaning: λ selects the Robustness/Performance compromise, whereas γ allows to balance the Servo/Regulator performance. Based on this, several application scenarios are considered. First, a One-Degree-Of Freedom (1-DOF) PI controller is assumed. Second, 2-DOF and switched implementations are investigated.