<p>This paper proposes an improved generalized pole clustering technique for model order reduction of higher-order LTI systems. The method has been modified from the traditional generalized pole clustering by incorporating a quantitative measure of model dominance criteria to sort the poles of the higher-order systems (HOSs), enabling clusters to be formed based on pole dominance. The improved cluster centers derived from the proposed algorithm provide a better approximation and a more accurate representation of the original system’s performance than other clustering and truncation methods. The reduced model numerator coefficients are obtained using a simple mathematical process that matches Markov parameters and time moments. It sidesteps the standard phases of computing the time moments and Markov parameters, solving the Pade equations, and constructing Routh-type tables. The paper also highlights the limitations of existing traditional and generalized pole clustering approaches. These methods may result in reduced models with improper transfer functions, making simulation more challenging. Various case studies from the literature were considered to evaluate the efficacy of the suggested approach. The proposed method preserves the dominant dynamics, stability, time moments, Markov parameters, and other essential aspects of HOS in the reduced model. Further, the proposed method is applied to design a PID controller. The simulation results, performance measure values, and time-domain features illustrate the efficacy and superiority of the suggested strategy. All simulations were carried out using MATLAB.</p>

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Model Dominance Index Assisted Enhanced Generalized Pole Clustering Technique for Order Reduction and Application to PID Controller Design

  • Bala Bhaskar Duddeti,
  • Asim Kumar Naskar

摘要

This paper proposes an improved generalized pole clustering technique for model order reduction of higher-order LTI systems. The method has been modified from the traditional generalized pole clustering by incorporating a quantitative measure of model dominance criteria to sort the poles of the higher-order systems (HOSs), enabling clusters to be formed based on pole dominance. The improved cluster centers derived from the proposed algorithm provide a better approximation and a more accurate representation of the original system’s performance than other clustering and truncation methods. The reduced model numerator coefficients are obtained using a simple mathematical process that matches Markov parameters and time moments. It sidesteps the standard phases of computing the time moments and Markov parameters, solving the Pade equations, and constructing Routh-type tables. The paper also highlights the limitations of existing traditional and generalized pole clustering approaches. These methods may result in reduced models with improper transfer functions, making simulation more challenging. Various case studies from the literature were considered to evaluate the efficacy of the suggested approach. The proposed method preserves the dominant dynamics, stability, time moments, Markov parameters, and other essential aspects of HOS in the reduced model. Further, the proposed method is applied to design a PID controller. The simulation results, performance measure values, and time-domain features illustrate the efficacy and superiority of the suggested strategy. All simulations were carried out using MATLAB.