Control strategies and performance analysis of doubly approximation and large-scale system control using hybrid model reduction approach

A hybrid approach has been proposed in this paper, for simplification of a high-dimensional system. In the proposed hybrid technique, benefits of two distinct strategies are being leveraged which make the simplification of higher-dimensional systems more effective and easier. Here, the denominator polynomial is obtained by using Routh stability criteria, while improved Padé approximation scheme is used to derive the numerator polynomial coefficients for the estimated plant. The proposed method ensures the stability of reduced model and preserves the initial few time moments and Markov parameters of the stable original systems. Some of the well-known standard higher-dimensional systems found in the literature are simplified to validate the proposed hybrid approach. Different performance indices such as integral square error (ISE), integral time absolute error (ITAE), integral absolute error (IAE), and relative integral square error (RISE) are examined to confirm the effectiveness and efficiency of the proposed approach by contrasting it with other state-of-the-art cutting-edge model reduction strategies. The outcomes of the simulation demonstrate the efficacies of the proposed approach, in terms of stability and time response. Additionally, a novel approach to design PID controllers for higher-dimensional systems is also discussed in this article. The moment matching algorithm is utilized to develop the PID controller for effective control of the large-scale systems. The suggested design method of controller is validated using a typical real-time mechanical system obtained from the literature.