Tuning PID controllers for disturbance rejection based on Linear Quadratic Optimal methods

Structural stability and sensitivity properties of a PID regulator tuned as a linear quadratic optimal controller (LQOC) are presented. The solution of the LQOC control problem gives as a result a PID structure, but only when a resticted class of models for the disturbance and the plant is considered. The concept of robustness is introduced for those models which can not be included in the class of models leading to PID structures. This method gives as a result, a set of simple tuning rules for PID regulators, which can be applied to a wide range of processes and disturbances.