Quantitative feedback–feedforward control for model matching and disturbance rejection

This study addresses two major single-input single-output control problems involving both feedback and feedforward actions: (i) the model matching in reference tracking and (ii) the rejection of measurable disturbances. Its aim is to overcome the limitations of inversion-based feedforward design methods when system uncertainty is considered, and to find a control engineering solution based on the quantitative feedback theory (QFT). The proposed methodology leads to minimum cost of feedback by limiting the feedback action to the strictly necessary amount that enables the use of a feedforward controller. Although the model matching problem had drawn some attention of the QFT community in the last few years, the measurable disturbance rejection problem remained unaddressed. This study provides a novel solution for both of them in which the need for feedback is linked to the existence of a common feedforward solution for all plants within the model uncertainty. This work also deals with the generation of the corresponding quadratic inequalities and new QFT bounds for the mentioned feedback demand. A practical and well-known benchmark example illustrates the main details and advantages of the new methodology.