中文摘要：

针对分数阶系统在进行有理函数近似时，往往会存在得到的有理函数阶次较高、近似精度低或优化速度慢等问题，本文基于频域误差极小化原理，提出了一种利用低阶有理传递函数逼近分数阶系统的方法．该方法将分数阶系统和其有理逼近函数之间的误差极小化运算转化为一个线性规划问题进行求解，避免了求解方程组和非线性问题的复杂运算。仿真验证结果表明，与Charef近似法及Ousta—loup近似法相比，在整个需要逼近的频段内，利用该方法得到的有理逼近函数能够以较低的阶次达到较好的近似效果．该方法不仅适用于具有分数次幂极点的系统，也适用于由分数阶微分算子组成的一般形式的分数阶系统，且降低了计算复杂度，提高了优化速度。

英文摘要：

The rational approximation of a fractional order system usually has some disadvantages ： the order of the rational transfer function is high, the approximating precision is low, and the optimization speed is too slow. We propose a method of approximating the fractional order system using a lower order rational transfer function based on error minimum theory in the frequency domain. The method transforms the calculation of the mini- mum error between the fractional order system and its rational approximation function into a linear program- ming problem, thus avoiding having to solve a system of equations and nonlinear problems. Simulation results show that the rational approximation function constructed by the proposed method can achieve a better approx- imation effect with lower order in the whole frequency range of interest compared with the Charef and Ousta- loup methods. The proposed method can apply to systems with fractional power poles and general fractional or- der systems composed of fractional order differential operators. The proposed method reduces the computation complexity and improves the optimization speed.