A New Approach to Mixed H2/H∞ Optimal PI/PID Controller Design

Abstract

This paper proposes a new approach to the problem of designing optimal proportional−integral−derivative (PID) controllers that minimize an H2 norm associated with the set-point response subjected to a constraint on the H∞ norm of disturbance rejection. The proposed design approach consists of constructing the feasible domain in the controller gain space and searching over the domain for the optimal gain values of minimizing the H2-norm objective function. The construction of the feasible domain that satisfies the requirements of closed-loop stability and H∞-norm constraint is achieved through analytic characterization of the domain boundary with the notion of principal points associated with the value set of a differentiable mapping. The constructed feasible domain saves greatly on the computational effort requied to search for the H2-optimal controller gain values that satisfy both the stability and disturbance rejection requirements.