CAREER: Control Design using Data-Driven Models: Exploiting Model Structure

摘要：罗伯特·S.帕克研究所：剑桥大学提案编号：0134129工业对工艺性能的要求越来越高，而用于改造或增加传感器的资本投资很少。 因此，过程必须在高度非线性状态下运行，可能在线性控制算法下运行。 该职业奖致力于研究和教育的整合，目标是开发能够解决非线性模型识别和控制问题的工具和学生。具体来说，研究将集中在基于非线性模型的最优控制器设计中与控制相关的过程模型的使用。 建模研究使用三阶沃尔泰拉和Volterra-Laguerre表示，一个子类的非线性多项式移动平均模型。 这些模型结构的选择的动机是（i）能够定制输入序列以激发（或取消）特定的模型动态;（ii）减少系数空间和噪声破坏而几乎不降低模型精度的机会;（iii）这些模型结构可以近似的广泛系统类别（例如聚合器、蒸馏塔、生物反应器）;和（iv）这些结构在控制器合成中的效用。 基于聚合反应器的案例研究，三阶沃尔泰拉模型将被识别使用定制的输入序列，设计激发线性，非线性对角，或非线性非对角项。 然后将得到的模型投影到正交拉盖尔基上，以减少系数维数和噪声对输出估计的影响。 这些模型将被用来合成一个非线性模型预测控制算法。 该项目的最终目标是将识别和控制结果整合到一个单一的算法中，以实现同时识别和控制。 第一个是帮助学生从一堂课到另一堂课保留材料，并且能够在应用示例中使用给定课程的材料。 符合ABET 2000标准，这些跨课程的问题将探讨学生的数学技能。 所研究的问题类型有助于将课程与借鉴早期课程的反复出现的案例研究垂直整合，因此加强了跨课程材料的保留。 研究和教育的整合是通过使用研究成果开发两个新的单元的过程控制模块，案例研究，研究数据驱动的模型识别和非线性模型预测控制在一个水平访问的本科生。

ABSTRACTPI: Robert S. Parker Institution: University of PittsburghProposal Number: 0134129Industry is demanding higher and higher levels of performance from their processes and little capital investment is available for retrofitting or additional sensors. Thus processes must operate in highly nonlinear regimes, likely under linear control algorithms. This CAREER award addresses the integration of research and education with the goal of developing tools and students capable of solving problems in nonlinear model identification and control.Specifically, the research will focus on the use of control-relevant process models in nonlinear model-based optimal controller design. The modeling studies use third-order Volterra and Volterra-Laguerre representations, a subclass of nonlinear polynomial moving-average models. The selection of these model structures is motivated by (i) the ability to tailor input sequences to excite (or cancel) particular model dynamics; (ii) the opportunity to reduce the coefficient space and noise corruption with little to no decrease in model accuracy; (iii) the wide class of systems these model structures can approximate (e.g. polymerizers, distillation columns, bioreactors); and (iv) the utility of these structures in controller synthesis. Based on a polymerization reactor case study, third-order Volterra models will be identified using tailored input sequences, design to excite the linear, nonliear diagonal, or nonlinear off-diagonal terms. The resulting model will then be projected onto the orthonormal Laguerre basis to reduce coefficient dimension and noise effects on the output estimate. These models will then be used to synthesize a nonlinear model predictive control algorithm. The culmination of the project will be the integration of the identification and control results into a single algorithm for simultaneous identification and control.The educational component has two primary aims. The first is to help the student retain material from class to class, and to be able to employ material from a given class on an application example. Consistent with ABET 2000 criteria, these cross-curriculum problems will probe the students' mathematical skills. The type of problems examined serve to vertically integrate the curriculum with a recurring case study which draws on earlier courses, and therefore reinforces retention of material across classes. The integration of research and education is accomplished through the use of research results in the development of two new units for the Process Control Modules, case studies that examine data-driven model identification and nonlinear model predictive control at a level accessible to the undergraduate.