A New Look at the Target Feedback Loop Parameterization for $$\mathcal {H}_{\infty }$$ H ∞ /LTR Control

Abstract

In this paper, a new approach on the target feedback loop (TFL) parameterization for the \(\mathcal {H}_{\infty }\)/loop transfer recovery (LTR) control is presented. The proposed procedure, which is based on a similarity transformation, allows to obtain a first-order system behavior through a particular shaping of the TFL sensitivity in terms of singular values. Furthermore, the proposed methodology makes possible to augment the design plant model with any stable real-finite pole, and not only a pole at the origin, as classical TFL parameterization procedures suggest. Thus, the proposed methodology should gather great attention by LTR-based control applications in which the use of integrators in the open-loop is undesirable or even prohibitive. Additional properties are derived if the design plant model does not have poles at the open right-half plane. Since \(\mathcal {H}_{\infty }\)/LTR control can be viewed as a generalization of well-known LQG/LTR control, the proposed methodology in this paper to shape the TFL can be properly extended to the LQG/LTR control.