A Novel Order Abatement Technique for Linear Dynamic Systems and Design of PID Controller

This article proposes a novel hybrid technique of order abatement for large-scale models that combines the Mihailov stability method (MSM) and the stability equation method (SEM). In this approach, the denominator coefficients of the higher-order system (HOS) are estimated using the MSM, while the numerator coefficients are computed using the SEM. The suggested approach is based on the MSM, which guarantees the stability of the estimated model if the actual model is stable. The MSM also makes sure that important factors of the original plant, such as dominant poles and stability, are retained in the reduced order system (ROS). The suggested approach is compared to several current conventional reduction methods using error indicators, and the smallest performance error indices values reflect the supremacy of the method. The transfer function (TF) of the ROS is then used to design controllers by employing the moment matching technique. When the controller designed with the approximated model is applied to the real HOS, it indicates that the response of the closed-loop system of the real model entirely overlaps with the response of the reference plant. To further demonstrate the efficiency of the proposed schemes, time-domain specifications are produced and time responses are plotted.