A magnitude optimum approach for tuning Reduced-order ADRC with FOPDT models

In this paper, the Reduced-order Active Disturbance Rejection Control (RADRC) is tuned with a new set of tuning rules based on the First Order Plus Dead-time plant models. The tuning rules are developed to achieve the desired robustness $(M_{s})$ level. The tuning process is carried out in two stages. In the first stage, a set of non-linear equations is formulated using the magnitude optimum method and are solved with the desired settling time requirement resulting in controller bandwidth $(\omega_{c})$, observer bandwidth $(\omega_{0})$ and high-frequency gain $(b_{0})$. The parameter $b_{0}$ is further adjusted to meet the robustness $(M_{s})$ and stability requirements. The data collected from stage-I is used as input to the next stage. In stage-II, tuning rules for $\omega_{0}$ and $b_{0}$ are formulated in the form of a polynomial model. Finally, the proposed tuning rules are tested on standard benchmark systems and experimentally verified to control a DC motor.