Optimal Industrial Controller Tuning Algorithms in View of Constraints for Stability Margins

This paper presents a technique for optimal H2 tuning of a fixed-order and fixed-structure controller for SISO plant represented by a state-space realization. The proposed technique is based on minimization of some H2 proximity criterion for transfer functions of closed-loop control system and its implicit reference model (internal model control) subject to restrictions onto H∞ norm of transfer function of closed-loop system guaranteeing its stability. Proposed tuning algorithm for the controller parameters uses estimates of the plant parameters obtained via parametric identification. It is shown that necessary conditions for minimum of H2 norms of open and closed-loop systems coincide with necessary conditions for minimum of Frobenius norm of a matrix tuning polynomial linearly depending on the controller parameters. The proposed technique is illustrated by a numerical example.