Abstract
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.
Highlights
Mathematical models are essential in the development, design, and control processes of the systems
The OS of the underdamped third-order system is less than or equal to 10% and 5% if the conditions summarized in Table 7 is satisfied
This gives the underdamped third-order system the highest priority without losing the effectiveness of the proposed work in overdamped systems
Summary
Mathematical models are essential in the development, design, and control processes of the systems. Many systems are modeled as first and second-order models for simplicity and existing mathematical design, analysis, and direct formulations. This is valid based on some acceptable assumptions. A reduced-order and enhanced observer-based control strategy for dc tot dc converter is presented in [17] to have better performance in terms of disturbance rejection and sensitivity to parameter variation. As this paper is the first step toward this goal, the proposed work shows the necessary conditions to accurately reduce the order to first or second-order systems. The possibility of acceptable reduction to a first or second-order system is checked for all possible values based on the essential time-domain performance indices error.
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