A BMI based design for robust PID controllers with two-degrees-of-freedom structure

This paper provides a design method for two-degrees-of-freedom I-PD (2DOF-I-PD) controllers including a switched PD compensator based on bilinear matrix inequalities (BMIs). Two design specifications based on the H2 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 using the proposed design method. The most effective parameter is selected from the set of the PD compensator based on the switching criterion obtained from estimated system conditions using statistical algorithms. Numerical examples are also shown.