非线性间歇过程的容错控制和满意性能优化研究

In recent years, the fault-tolerant control for complex multivariable and time-varying batch processes with multiple operations and uncertain running time is a new research area, which is different from the well-developed fault-tolerant control problem in continuous process. Based on the three basic requirements with high reliability, high quality and high effect in batch production target, this project is constructed on the iterative learning control, periodic adaptive control and robust control method under the nonlinear mathematical models and uncertain 2D periodic systems. On the restriction of the batch time, convergence and other criterion of fault-tolerant system, the integrated fault-tolerant control strategy will be studied when the unknown fault occur, and the robust optimization algorithms are applied to ensure the systems have satisfied performances. Firstly, it will solve the passive fault-tolerant control problem for arbitrarily relative degree batch process by using iterative learning algorithms based on λ norm theory; Secondly, the integrity iterative learning controller will be designed by equivalent error definition and spectral theory of operators when simultaneous multiple faults occur in batch process; Furthermore, the compatibility analysis and optimization problem of satisfactory fault-tolerant control will be researched together for uncertain batch process;At last, the synthetical active fault-tolerant control strategy for batch systems by using iterative learning observer and adaptive fault accommodation controller will be proposed.On the basis of promoting the further development of the fault-tolerant control theory, this project will be applied to the basic simulation research on batch process of biological fermentation and so on, so that the batch process will be reliable, and the product quality and efficiency will be raised simultaneously.

区别于较为成熟的连续过程的容错控制问题，复杂的多变量、多工序和运行时间不确定的时变间歇过程的容错控制是近年来新的研究方向。针对间歇过程操作目标的生产安全、产品质量和生产效率三大基本要求，本项目拟分别基于非线性机理模型和不确定2D周期系统，依据迭代学习、周期自适应和鲁棒控制策略，在间歇过程批次时间和收敛性等容错标准的指导下，研究未知故障发生情形下的集成容错控制方法，并通过鲁棒优化算法保证系统性能的满意评价。基于λ范数理论解决任意相对阶迭代学习间歇过程的批次被动容错控制问题；基于等效偏差和算子谱理论解决故障并发间歇过程的完整性迭代学习控制问题；解决不确定批次过程的满意容错性能的综合相容性分析和优化问题；基于迭代学习观测器和周期自适应故障调节，解决批次间歇过程的主动容错控制集成；目的在推动容错控制理论纵深发展的基础上，应用到生物发酵等间歇过程的基础仿真研究，实现批量生产的可靠安全和满意质量。

针对多工序和运行时间周期重复的多变量非线性间歇过程的容错控制问题，本项目主要以执行器和传感器故障的重复系统为研究对象，在讨论系统故障诊断问题的基础上研究了系统的鲁棒容错控制器设计和性能优化方法，并进一步得到满意容错性能的相容性条件。首先，针对一类存在执行器和传感器故障的非线性重复系统，提出基于扩展滤波器的故障检测和重构方法，并采用迭代学习调节算法更新虚拟故障使之逼近实际故障；然后，考虑离散重复混杂系统的非均匀输出采样特点，运用积分中值定理得到其等效故障模型，再用输出时滞方法对系统输出采样保持，进而利用迭代学习滤波器实现故障检测和估计；其次，利用线性矩阵不等式技术研究鲁棒迭代学习容错控制方法，控制器增益通过凸优化技术保证闭环间歇过程满足时间和批次两个方向的多性能指标约束；同时针对多率采样间歇过程，设计迭代学习容错控制的多率算法确保多率采样间歇过程在正常和故障条件下的耗散性能；进而通过KYP引理，给出分频容错控制器的设计以进一步降低算法求解的保守性；另外，针对时变非线性重复系统，基于算子理论和λ范数分析给出容错控制器存在的充分条件，使故障系统输出能够单调收敛于给定输出轨迹的有界邻域内；最后，针对一类不确定非线性系统提出一种连续二阶滑模自适应迭代学习控制方法，在保证不确定系统的稳定性同时提高系统的收敛速度；同时考虑系统的输入饱和时滞问题，针对不确定Brunovsky型非线性周期系统设计自适应学习补偿算法，通过构造Lyapunov-Krasovskii 复合能量函数差分证明了系统跟踪误差的收敛性，并可用于解决间歇性周期系统的故障自适应补偿容错控制问题。注塑成型过程与机械臂等间歇重复系统的模拟实验和仿真结果验证了本项目算法的有效性。本项目所取得的理论研究成果具有一定的创新性，且研究思路可以进一步推广到连续过程的容错控制研究中。