Should model-based inverse inputs be used as feedforward under plant uncertainty?

Bounds on the size of the plant uncertainties are found such that the use of the inversion-based feedforward input improves the output-tracking performance when compared to the use of feedback alone. The output-tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance. The worst-case performance is compared for two cases: (1) with the use of feedback alone and (2) with the addition of the feedforward input. It is shown that inversion-based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty Δ (jw) in the nominal plant is smaller than the size of the nominal plant G₀(jw) divided by its condition number K_G0 (jw), i.e., ||Δ(jw)||₂ < ||G₀(jw) ||₂/k_G0 (jw). A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small. The use of this modified inverse with (any) feedback results in improvement of the output tracking performance, when compared to the use of the feedback alone.