An optimization-based method for tuning PI controllers for systems subject to control and output constraints

. This article presents an optimization-based method to tuning Proportional-Integral (PI) controllers for systems subject to actuator saturation and constraints on the controlled variable. The theory of invariant sets is used to treat constraints and a polytopic model is adopted to account for actuator saturation. For the numerical validation of the method, four examples are presented. The results show that the method can establish a tuning that does not violate any constraint.