In this paper, a new method is proposed for the reduced-order model approximation of commensurate/incommensurate fractional order (FO) systems. For integer order approximation, the model order is determined via Hankel singular values of the original system; while the order of FO approximations is determined via optimization. Unknown parameters of the reduced model are obtained by minimizing a fitness function via the genetic algorithm (GA). This fitness function is the weighted sum of differences of Integral Square Error (ISE), steady-state errors, maximum overshoots, and ISE of the magnitude of the frequency response of the FO system and the reduced-order model. Therefore, both time and frequency domain characteristics of the system considered in obtaining the reduced-order model. The stability criteria of the reduced-order systems were obtained in various cases and added to the cost function as constraints. Three fractional order systems were approximated by the proposed method and their properties were compared with famous approximation methods to show the out-performance of the proposed method.

本文提出了一种新的方法，用于对等价/不等价分数阶（FO）系统的降阶模型逼近。对于整数阶近似，模型阶是通过原始系统的Hankel奇异值确定的；而FO近似的阶数是通过优化确定的。简化模型的未知参数是通过遗传算法（GA）最小化适应度函数获得的。该适应度函数是积分平方误差（ISE），稳态误差，最大过冲以及FO系统和降阶模型的频率响应幅度的ISE的加权和。因此，在获得降阶模型时要考虑系统的时域和频域特性。在各种情况下都获得了降阶系统的稳定性标准，并将其作为约束添加到成本函数中。该方法对三个分数阶系统进行了近似，并将它们的性质与著名的近似方法进行了比较，以证明该方法的性能。