IMC-like analytical H∞ design with S/SP mixed sensitivity consideration: Utility in PID tuning guidance

This article presents an H∞ design that alleviates some difficulties with standard Internal Model Control (IMC), while still obeying the same spirit of simplicity. The controller derivation is carried out analytically based on a weighted sensitivity formulation. The corresponding frequency weight, chosen systematically, involves two tuning parameters with clear meaning in terms of common design specifications: one adjusts the robustness/performance trade-off as in the IMC procedure; the other one balances the servo and regulatory performance. For illustration purposes, the method is applied to analytical tuning of PI compensators. Due to its simplicity and effectiveness, the presented methodology is also suitable for teaching purposes.