Robust feedforward design from data via approximate inverse SM identification

In this paper the design of the feedforward block of a two degree of freedom controller for reference tracking in SISO systems in the presence of model uncertainty is addressed. From previous works, it is known that given a set of noisy input-output measurements, an uncertainty model set for the plant can be obtained through set membership H_∞ identification techniques and, on the basis of such a model set, a robust design of the feedback compensator can be performed. In this work the design of the feedforward filter is formulated as a robust model matching problem. An optimal solution is provided in closed form on a finite set of frequencies obtained from a suitable frequency gridding. Then a FIR model, approximation of the optimal solution, is obtained solving a linear programming problem. The efficiency of the method is tested on two examples, related to two typical patterns of uncertainty, the first one arising in the case of unmodeled dynamics, the second one in the case of parametric uncertainty.