Determination of the Admissible Parameter Set in Designing PID Controllers with Guaranteed Robust Performance

This paper presents a method to determine the admissible set of controller parameters when the H-infinite norm of the mixed sensitivity is taken as the objective function for the PID controller design. First the mixed sensitivity requirement can be translated into the stabilization problem of a family of complex polynomials as well as the close-loop characteristic polynomial. Then by stabilizing these polynomials with PID controller parameters in their coefficients, we can get the admissible parameter set. The Hermite-Biehler theorem is applied to solve the polynomial stabilizing problem.