An optimal iterative learning control （ILC） strategy of improving endpoint products in semi-batch processes is presented by combining a neural network model. Control affine feed-forward neural network （CAFNN） is proposed to build a model of semi-batch process. The main advantage of CAFNN is to obtain analytically its gradient of endpoint products with respect to input. Therefore, an optimal ILC law with direct error feedback is obtained explicitly, and the convergence of tracking error can be analyzed theoretically. It has been proved that the tracking errors may converge to small values. The proposed modeling and control strategy is illustrated on a simulated isothermal semi-batch reactor, and the results show that the endpoint products can be improved gradually from batch to batch.
概率符号有向图(probabilistic signed digraph,PSDG)模型通过在传统定性符号有向图(signed digraph,SDG)的模型结构中引入节点和支路的概率信息,改善了传统定性SDG故障诊断的性能,提高了故障诊断的分辨率。然而,在PSDG模型中,节点的概率分布通常是在给定其父节点条件下的条件概率分布,建模时所需要的先验条件概率参数的个数与其父节点的个数成指数关系,定义如此数量巨大的先验条件概率参数无疑会极大地增加对大规模系统建模的难度。为了解决对象先验知识不完备的情况下PSDG建模过程中先验条件概率参数的设置问题,本文提出了一系列获取未知条件概率参数的估计方法:针对父节点影响状态相同的情况,提出了扩展Noisy-OR门理论的估计方法;针对父节点影响状态相异的情况,提出了近似估计方法和极值估计方法。文中对这些估计方法进行了理论分析,证明了采用这些方法的可行性。应用这些估计法方法使得建模需要确定的先验条件概率参数的数量从节点个数的指数关系降为线性关系,极大地降低了建立大规模PSDG模型的复杂性和工作量。通过对某石化公司气体分馏装置建立PSDG模型进行故障诊断实例研究,在使用本文提出的估计方法后,建模所需事先确定的先验概率参数数量急剧降低,诊断结果与实际发生的故障相符,进一步证明了该估计方法的有效性。
