Nominal Input Gain Estimation of ADRC for Lightly Damped System with Multiple Eigenmodes

Active disturbance rejection control (ADRC) has been widely employed for governing a class of lightly damped systems with multiple eigenmodes. However, it has so far not investigated in detail how to estimate their nominal input gains, associated with the relative order, especially under different desirable control bandwidths for the same controlled object. This paper proposes an estimation rule regarding the nominal input gain of ADRC. The modal decomposition for a class of lightly damped systems with multiple eigenmodes is deduced in detail. Then, the frequency response for an elementary example of a system with two eigenmodes is analyzed, and the ADRC design with the corresponding tuning guideline is developed. The validity and superiority of the proposed method are demonstrated through simulations.