Performance-Index-Driven Model Order Reduction of LTI Systems using Artificial Bee Colony (ABC) Algorithm

Next Generation Engineering: Smart Solutions and Applications

Editors: Sabri KOÇER, Özgür DÜNDAR


Next Generation Engineering: Smart Solutions and Applications

16

Performance-Index-Driven Model Order Reduction of LTI Systems using Artificial Bee Colony (ABC) Algorithm

Chapter Authors: Mehmet SAVAN, Hasan Huseyin BILGIC

Pages: 141-154

 This study addresses the challenges of modeling and analyzing highorder Linear Time-Invariant (LTI) systems, where classical Model Order Reduction (MOR) techniques often fail to simultaneously achieve optimal transient and steadystate responses. To overcome these limitations, a metaheuristic optimization approach utilizing the Artificial Bee Colony (ABC) algorithm is introduced to derive accurate, low-order representations. The primary novelty lies in the systematic analysis of how different error-based performance indices—namely the Integral of Squared Error (ISE), Integral of Absolute Error (IAE), Integral of Time-weighted Absolute Error (ITAE), and Mean Squared Error (MSE)—influence the dynamic characteristics of the resulting reduced model. The ABC algorithm was employed to optimize the parameters of a second-order model  to match the step response of a ninth-order benchmark system, minimizing a cost function defined by a weighted sum of these indices. The experimental evaluations conclusively demonstrated that the ABC-based reduction method not only achieved rapid convergence and computational efficiency but also produced models with superior fidelity and dynamic flexibility compared to prominent benchmark techniques. Specifically, IAE achieved a critically damped response with minimal overshoot, ITAE resulted in the fastest settling time (approx. 1.5 seconds) and superior error attenuation, and MSE provided a highly balanced dynamic response.These findings establish the ABC algorithm as a reliable, robust, and versatile parameter-tuning tool for real-time control applications, allowing engineers to tailor the reduction process based on specific dynamic requirements such as speed, stability, or overshoot minimization.

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