ABSTRACT In this paper, a soft computing based scheme is proposed for the model order reduction of single input-single output commensurate fractional-order (FO) systems. The fractional-order system is first converted into an integer order (IO) system. The reduced order model of the corresponding integer order system is then determined via big bang – big crunch (BBBC) optimization algorithm. Finally, the reduced IO transfer function is transferred back to its FO form through an inverse substitution. The proposed approach is substantiated by two numerical examples of different orders. The effectiveness of the technique is demonstrated by the comparison of two performance indices, i.e. integral square error (ISE) and error and the response characteristics in time and frequency domain with the existing techniques from the literature. It is revealed that the response of the proposed BBBC based reduced order model is much closer to that of the original higher-order system.

中文翻译：

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使用 Big Bang – Big Crunch 算法的公称分数阶系统的模型降阶

摘要 在本文中，提出了一种基于软计算的方案，用于单输入单输出相称分数阶 (FO) 系统的模型降阶。分数阶系统首先转换为整数阶（IO）系统。然后通过 big bang – big crunch (BBBC) 优化算法确定相应整数阶系统的降阶模型。最后，简化的 IO 传递函数通过逆替换被传递回其 FO 形式。所提出的方法得到了两个不同阶数的数值例子的证实。该技术的有效性通过两个性能指标，即积分平方误差（ISE）和误差以及时域和频域响应特性与文献中现有技术的比较来证明。