分数阶控制器离散方法的评估策略研究

针对分数阶控制器数值计算和应用难的问题，提出了分数阶微积分算予数字实现方法的评估策略，分析了分数阶微积分算予的多种数值计算法的机理和实现步骤．引入一个位置控制系统作为分数阶控制对象，将Mittag-Leffler函数的全记忆长度分数阶控制系统作为评估基准，提出了一种离散算法的近似性能函数，通过时域误差分析以及近似性能分析，对比研究了分数阶微积分算子的数字实现方法．研究结果表明，幂级数直接离散法得到近似离散模型需要记忆长度为100方可获得较好的近似，而连分式直接离散法近似离散模型为10阶时就可以获得较好的近似，因此连分式直接离散法比较适合于分数阶控制算法的实际工程应用．

Evaluation Strategies of Fractional Order Controllers Discretization Methods

To solve the difficulties of the discretization and application of fractional order controllers(FOC),evaluation strategies of digital realization of FOC are investigated.The realization principle and process of various discretization methods are discussed.One position control system is introduced as the objective controlled by FOC.Based on Mittag-Leffler function,the fractional order control system with full memory length is adopted as evaluation criterion,and an approximation performance function of discretization methods is proposed.Analyzing the time domain error and approximation performance,the investigation to various discretization methods is carried out comparatively in detail.The result verifies that the discrete model with power series direct discretization method requires 100 memory length to obtain the better approximation,while one with continued fraction direct discretization method requires only 10 order.Thus the continued fraction direct discretization method is preferable to digital realization of fractional order control algorithms in engineering applications.