一类连续发酵的分数阶建模及参数辨识
Fractional Order Modeling and Parameter Identification for a Class of Continuous Fermentation
针对一类连续发酵生产~1, 3-丙二醇~(1, 3-PD)~问题,~引入了 分数阶微积分的相关概念,~建立了分数阶微生物发酵模型,~并以模型中 的阶数和系统参数为辨识对象,~以终端时刻状态变量的计算值与实验值 的相对误差为性能指标,~建立了相应的分数阶参数辨识模型.~应用梯形 方法与预估校正方法求解分数阶微分方程,~讨论了分数阶情况下性能指 标与状态约束关于参数的梯度计算公式.~为辨识阶数和系统参数,~ 构造 了基于粒子群和序列二次规划方法的数值优化算法.~ 通过大规模优 化计算,~ 对模型进行了数值求解.~ 数值结果表明,~用分数阶方程描 述连续发酵过程,~优于已有的整数阶模型.
For a class of continuous fermentation production of 1, 3-propanediol, the concept of fractional calculus is introduced. The fractional-order microbial fermentation model is established. Taken the orders and system parameters of model as objects to be identified and taken the average relative error between the calculated values and the experimental values at terminal time as performance index, the corresponding fractional-order identification model is formulated. Trapezoidal method and predictive correction method are applied to solve fractional differential equation. The gradient formulas of performance index and state constraints with respect to parameters are discussed under fractional order condition. In order to identify the orders and system parameters, a numerical optimization algorithm is constructed combining particle swarm optimization and sequential quadratic programming method. Through large-scale optimization calculations, the model is solved numerically. The results show that the model for continuous fermentation process described by fractional differential equation is better than the previous integer order models.
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