A New Control Design Strategy Based on Dominant Pole Concept and System Reduction
摘要
Most existing dominant pole retention reduction algorithms consider poles near the origin as dominant, which may lead to poor approximations for systems whose dynamics are dominated by large-magnitude poles. This study proposes a conventional order reduction technique that utilizes the model dominance index (MDI) to determine the significance of each pole and select the dominant poles, regardless of their location in the complex plane. The denominator of the reduced model is then retrieved using a modified generalized pole clustering approach, which estimates the relative distance from the first dominant pole in each cluster. This approach avoids bias toward poles near the origin and enhances adherence in both steady-state and transient dynamics. To compute the numerator parameters, a factor division approach is utilized to retain the required time moments and Markov parameters of the actual system without explicitly computing them. The novelty of the proposed work lies in integrating the MDI-based pole selection within a customizable clustering mechanism and incorporating the resulting reduced model into a resilient control design procedure. The technique ensures stability and preserves the dominant poles, as well as other essential attributes of higher-order systems. Subsequently, it reinforces a simple procedure for designing PID controllers analytically, whose closed-loop responses are approximately following the selected second-order closed-loop model. The proposed algorithm is substantiated using SISO and MIMO baseline systems through time and frequency responses, time-response data, various performance measures, and a Monte Carlo robustness analysis under parametric uncertainty. The outcomes indicate noteworthy enhancements over existing approaches and demonstrate that the controllers designed via the reduced models attain closed-loop responses similar to those designed using actual order plants.