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Frequency characteristics of a phase optimised active disturbance rejection control

A linear extended state observer (LESO) can just estimate constant disturbances with no steady-state error. To estimate time-varying disturbances more actively and accurately, a phase optimisation law (POL) is proposed. Based on the POL, both a phase optimised extended state observer (POESO) and a phase optimised active disturbance rejection control (POADRC) are proposed. Estimation errors, estimation phases, and frequency response have been analysed and compared. The estimation phase of a POESO always leads the one of a LESO, and a POESO estimates slope disturbances with no steady-state error. Transfer functions of tracking, total disturbance and noise are also obtained. Ability of the POADRC and the linear active disturbance rejection control (LADRC) to cancel out the total disturbance or suppress noise, and their stable regions are also analysed and compared. Both frequency analyses and numerical results show that the POADRC estimates the time-varying disturbances and improve the closed-loop performance more effectively.