Robustness-based tuning of two-degree-of-freedom proportional integral controllers for unstable processes

The aim of this paper is to present a robustness-based (M_S) tuning method of two-degree-of-freedom (2DoF) proportional integral (PI) controllers for unstable controlled processes. The design procedure uses a model reference optimization procedure with servo and regulatory closed-loop transfer functions targets. The unstable processes control system robustness with proportional integral (PI) controllers is analyzed. It is confirmed that the dead-time of the unstable processes imposes a constraint to the closed-loop control system achievable robustness. High robustness control systems may be obtained only for a reduced range of controlled process models. Using the proposed tuning method the designer is allowed to deal with the performance/robustness trade-off of the closed-loop control system by specifying the desired robustness level by selecting a maximum sensitivity in the range from 2.0 to 6.0. Controller tuning equations that guarantee the designed robustness level are provided for unstable first-order plus dead-time (UFOPDT) models with normalized dead-times in the range from 0.10 to 0.55. Comparative examples show the effectiveness of the proposed tuning method.