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Adaptive step size numerical algorithm for fractional order control systems

机译：分数阶控制系统的自适应步长数值算法

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For fractional order control systems, fast and accurate numerical algorithm is the key step in real-time control and simulation. Although the short memory method (SMM) and the constant weight memory method (CWMM) accelerate the computation speed through the choice and approximation of the historical information of the fractional differential operator, the computation precision decreases with the increase of time. The CWMM is affected by input function and the error range is large. Considering the limitation of fixed step size discretization (FSSD) of fractional differential operator, a variable step size discretization (VSSD) scheme is utilized. According to the local error obtained by the step-doubling technique, the iterative step size is adjusted adaptively. The algorithm not only can achieve good accuracy, uniform error, but also fast calculation speed, which provides a feasible way for the numerical calculation of state space description of fractional order control system. Finally, the reliability of the algorithm is verified by an example.
机译：对于分数阶控制系统，快速准确的数值算法是实时控制和仿真的关键步骤。尽管短存储方法（SMM）和恒权存储方法（CWMM）通过选择和逼近分数微分算子的历史信息来加快计算速度，但计算精度会随着时间的增加而降低。 CWMM受输入功能的影响，并且误差范围较大。考虑到分数阶微分算子的固定步长离散化（FSSD）的局限性，采用了可变步长离散化（VSSD）方案。根据通过分步技术获得的局部误差，可以自适应地调整迭代步长。该算法不仅精度高，误差均匀，而且计算速度快，为分数阶控制系统状态空间描述的数值计算提供了一种可行的方法。最后，通过实例验证了算法的可靠性。

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