An approach to linear active disturbance rejection controller design with a linear quadratic regulator for a non-minimum phase system

Abstract

This study proposes an approach to determining the controller gain based on the linear quadratic regulator (LQR) method for a non-minimum phase plant. The extended state observer is designed based on the conventional pole placement method to prevent the observer from being unstable. The control law is determined based on the LQR method in terms of fast responses of the plant outputs and the magnitude of its inputs. The stability of the whole closed-loop control system is evaluated using the Routh-Hurwitz stability criterion. The effectiveness of the proposed method is confirmed by performing numerical simulations and comparing their results with those of the conventional I–PD control. In addition, a superior robustness of the plant with a modeling error is achieved compared with that of the fundamental I–PD control system. Finally, the proposed LADRC with an LQR is confirmed to demonstrate a performance that is approximately the same as that of the conventional LADRC.