Quantitative relationship in terms of time-delay tolerance of two kinds of extended state observers

Active Disturbance Rejection Control (ADRC), an innovative control method, has been applied successfully in dealing with internal uncertainties and external disturbances. However, ADRC for time-delay plants is still a challenge due to the restriction on the bandwidth of the extended state observer (ESO). When designing the ESO for time-delay plants, both full-order and reduced-order extended state observers can be utilized and the selection of the proper order and the bandwidth of the ESO is necessary. Therefore we seek to compare the two kinds of observers in terms of the time-delay tolerance of the closed-loop stability and find an appropriate bandwidth to ensure the robustness to the time-delay uncertainty. First, the quantitative bandwidth relationship between the two kinds of observers is established with the equivalent effective bandwidth, and then the time-delay tolerance of the closed-loop stability are calculated for the first- and second-order plants to conduct the comparison, whilst the effects of the bandwidth and other parameters on the time-delay tolerance is analyzed. Furthermore, simulation results for a second-order plant are provided to verify the meaning of this investigation.