Selection of weighting matrices in H∞ controller by error model

In this paper, it is proposed to estimate the robustness of a closed loop system by a error model which is obtained calculating the difference between the transfer matrix of the closed loop system with nominal and uncertain plant. For the estimation it is assumed an approximated model of the uncertainty in frequency domain. An advantage of this error model is its generality since it allows to consider additive, multiplicative or feedback uncertainty Δ. Additionally, here it is introduced a procedure based on this estimation to select the signals spectrum which must be weighted in the objective function used to synthesize linear controller. This procedure simplifies the task to weight signals in the frequency domain cost to be minimized, which could become a difficult job, specially for MIMO systems. Specifically, considering the standard H_∞ optimal control problem, the approach is validated with two design problems.