分数阶控制系统微积分数值实现——分析与比较

Analysis and comparison of numerical algorithms for fractional calculus

介绍并对比了两种分数阶微积分的直接离散化数值实现方法:连分式展开(CFE)方法和递归Tustin方法。这两种方法都是采用直接离散方法得到近似模型,且都是得到具有最小相位的稳定系统。在频域里对这两种分数阶离散方法对比结果表明:CFE求解方法要优于递归Tustin方法。论文最后通过实例给出了仿真验证。

Two direct discretization methods for fractional order differentiation and integration are introduced,namely direct recursive discretization of the Tustin operator and direct discretization by continued fraction expansion of the Tustin transformation.Both approximate discretization methods afford stable minimum phase systems.Comparison of frequency domains demonstrates that the continued fraction expansion method is better than the recursive Tustin method and the reasons for this are discussed.