Informative Order-Reduction of Underdamped Third-Order Systems

Model order reduction simplifies the understanding of a given system and minimizes the simulation studies computational burden. A new order reduction method that depends on a predetermined normalized error of the transient performance indices is introduced. Ten percent and five percent error criteria in modeling and analyzing the transient performance of the third-order system are considered to have an accurate study. All sufficient special conditions and general rules required to achieve precise order reduction are determined. This work focuses on underdamped third-order systems without zeros. Third-order systems with three real poles are also analyzed for the study completeness. The relationships between the characteristic equation parameters are identified and the range in which the reduction is accurately valid is clearly specified. Each approximation or order reduction is studied separately in terms of the transient response characteristics: rise time, settling time and percentage overshoot. The comparison shows the effectiveness of the proposed method.