Weighted Clustering-Based Approach for Reduced Order Modeling of SISO and MIMO Systems

With the increasing complexity of high-order dynamical systems (HOS), significant challenges arise in its analysis and controller design. Classical pole-zero clustering has been investigated for several decades, yet its conventional form provides only limited approximation accuracy on the reduced order (RO) approximant. This work extends the clustering approach by introducing a novel weighting vector concept coupled with an optimization stage. The problem of finding the optimal values of elements of the vector is framed in an optimization framework where the objective function represents the integral square error (ISE) between the response of the original HOS and that of the final reduced order system (ROS). Comparative analysis of the proposed algorithm has been carried out using performance indicators namely ISE, integral absolute error (IAE), integral time-weighted absolute error (ITAE), and relative integral square error (RISE) for stable / unstable / non minimum phase (NMP) SISO / MIMO benchmark systems. The comparative analysis results validate the efficacy of the proposed algorithm, and the resultant reduced order model (ROM) shows an improved approximation accuracy over that given in the existing literature, making it a viable process for obtaining a RO approximant for HOS SISO / MIMO systems preserving its original characteristics in the ROS. The results confirm that even though the pole clustering concept is classical, the integration of a pole / zero weighting scheme in an optimization framework provides a meaningful and modern enhancement that makes the method competitive with the recent state-of-the-art approaches.