Review Active Disturbance Rejection Control Using a Phase Optimized Extended State Observer for a Nanopositioner Wei Wei 1, * , Pengfei Xia 2, and Min Zuo 3 1 School of Intelligent Engineering and Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China 2 School of Automation, Beihang University, Beijing 100191, China 3 School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China * Correspondence: weiweizdh@126.com Received: 5 April 2024; Revised: 9 June 2024; Accepted: 12 June 2024; Published: 28 June 2024 Abstract: A piezoelectric actuator is commonly utilized in nanopositioning for its stiffness, fast response, and ultrahigh precision. However, hysteresis in piezoelectric materials dramatically degrades system performance. By introducing a straightforward and effective modification to a classical extended state observer, a phase-optimized extended state observer is proposed to provide a phase-leading estimation of the generalized disturbance. Accordingly, a phase-optimized active disturbance rejection control is designed, and much more satisfied performance can be guaranteed. Convergence of the phase-optimized extended state observer and closed-loop stability of the phase-optimized active disturbance rejection control have been analyzed. Moreover, steady-state estimation error and phase-leading property have been proved. Advantages of the phase optimized active disturbance rejection control over the PI and the active disturbance rejection control are confirmed. Experimental results show that the phase-optimized active disturbance rejection control can achieve more desired disturbance rejection and motion tracking.