Frequency response analysis on modified plant of extended state observer

The active disturbance rejection control (ADRC) framework gives birth to a new concept, the modified plant (MP), describing the dynamics after the total disturbance is estimated and cancelled approximately. Ideally the modified plant is in integral form, to greatly simplify and fix the controller design, even though actual plant contains higher-order dynamics or dead time. This paper investigates that when such processes are modified into the integral, how the parameters of the extended state observer (ESO) impact on the dynamic characteristics and stability of the MP. Frequency-domain analyses show that the MP can gradually approach the integral form through parameters tuning. However, it should be cautious that an aggressive set of parameters may lead to an unstable modified plant in the presence of order mismatch.