Advanced order diminution technique for linear time-invariant systems with applications in lag/lead compensators and PID controller design

This paper presents a new order diminution method for large-scale model simplification. The suggested strategy relies on the Mihailov stability method, which promises the stability of the approximated model under the condition that the intricate model is stable. In this approach, the Mihailov stability approach is applied to estimate the denominator coefficients of the original system, while the numerator coefficients are obtained using the Routh stability method. The proposed methodology is both straightforward and designed to guarantee the stability of the reduced-order system (ROS), provided that the higher-order system itself is stable. To ascertain the efficacy of the proposed methodology, a comparison is conducted between the step responses of the actual plant and those of the simplified ROS. The proposed approach undergoes a comparative analysis with various contemporary conventional reduced-order modelling methods, utilizing error indicators such as relative integral square error, integral square error, integral time absolute error, and integral absolute error. The abated system is then used to design controllers for the actual complex model using a Padé-type algorithm. The simulation findings demonstrate that the proposed methodology outperforms the most recent model diminution strategies reported in the literature.