Singular-perturbation-based estimation of nominal input gain in lightly damped systems with multiple modes

Abstract

Active disturbance rejection controllers have been widely employed for governing a class of high-dimensional lightly damped systems with multiple eigenmodes. Nevertheless, previous studies rarely focused on the impact of neglected fast resonant mode dynamics on the nominal input gain, especially if high-frequency unmodeled resonant dynamics gradually approach the target control bandwidth. Here, we have quantitatively analyzed the effect of fast resonant mode dynamics on the nominal input gain using the singular perturbation method. A practical method for estimating the nominal input gain is provided for various control bandwidths. The stability bound associated with the fast resonant mode and coupling dynamics between the slow and fast resonant modes is also investigated. Finally, the validity and superiority of the proposed method are demonstrated through simulations.