改进的基于PSE和Tustin变换的分数阶系统求解递推算法

以分数阶算子近似方法的分析研究为基础，基于Tustin变换理论及其用于分数阶算子的离散生成函数公式特点，利用二项式幂函数的Maclaurin展开能够保证收敛的特性，考虑常用算法的局限性，提出了一种改进的基于幂级数展开和Tustin变换的分数阶运算方法，并应用于线性分数阶系统的求解，给出了递推算法的详细推导。算例仿真及其分析表明，该算法有效且具有良好的运算速度和精度。

Improved recursive algorithm for fractional-order system solution based on PSE and Tustin transform

As an important and foundational work of fractional-order control which is a new study field of control science and engineering, the solution method of fractional-order calculus (FOC) and fractional-order system (FOS) receives great attention. Based on the analysis of some aspects, such as the approximative algorithm of FOC, the Tustin transform theory and its generating function formula's character, the convergence guarantee of binomial power function by Maclaurin expanding, and the consideration of the limitation of conventional methods, an improved method is proposed to compute the numerical evalution of FOC using PSE and Tustin transform and is further applied to solving the linear FOS. The recursive algorithm is deduced in detail, its effectiveness and advantage are verified by some illustrative simulation examples.