<p>Higher-order transfer functions (HOTFs) adequately depict real-world system dynamics, but they are difficult and expensive to study and regulate. As a result, reduced-order transfer functions (ROTFs) are preferable. Conventional dominant pole retention (DPR) and clustering approaches frequently fail for systems with large-magnitude poles, resulting in inaccurate approximations. This paper presents a unique ROTF derivation method that determines pole dominance independent of its position in the complex plane and optimizes the reduced model order. The logarithmic pole clustering approach has been adapted to emphasize pole dominance and relative pole distances, which improves cluster center precision and system simulation. The factor division method (FDM) obtains the ROTF numerator by retaining time moments (TiMs) and Markov parameters (MaPs). Through case studies, including those of a boiler system and a Cuk converter, MATLAB simulations confirm this approach and demonstrate its enhanced performance compared to current methods. The precision of the approach is further demonstrated by a PID controller design, which qualifies it for real-time applications and large-scale systems. The proposed approach generates stable ROTFs for stable HOTF and retains dominant dynamics, TiMs, MaPs, and other attributes. Various performance analysis measures like integral square error (ISE), integral absolute error (IAE), integral time absolute error (ITAE), root mean square error (RMSE), and time-domain features like rise time, overshoot, and settling time are used to illustrate the efficacy and superiority of the suggested strategy. The proposed reduced models' step and frequency reactions are similar to the original system, in contrast to existing DPR and pole clustering-based techniques. There is a substantial enhancement in various system performance analysis measures of the proposed results. In addition, for better comprehension and understanding, the bar charts are provided to support the results.</p>