A BMI-Based Design of Switched PID Controllers

Abstract

This paper provides a design method for two-degrees-of-freedom PID controllers including switched PD compensator based on bilinear matrix inequalities (BMIs). Two design specifications based on H 2 norm are formulated in BMIs, and PID parameters can be exactly obtained by solving the BMI problems via branch and bound algorithms. A set of PD compensators can be obtained simultaneously by using proposed design method. The most effective parameter is selected out of the set of PD compensator based on the switching criterion which obtained from estimated system conditions using recursive least square algorithms. Numerical example is also shown.