Model predictive PDE control for energy efficient building operation:Economic model predictive control and time varying systems

节能建筑运行的模型预测 PDE 控制：经济模型预测控制和时变系统

• 批准号: 274853298
• 负责人: Professor Dr. Lars Grüne
• 金额: --
• 依托单位: Lehrstuhl für Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/274853298?language=en
• 关键词: Model; predictive; PDE; control; energy

Heating, Ventilation and Air Conditioning (HVAC) facilities form a class of control systems which have a huge potential for energy savings. In order to realize these savings, we propose to use Model Predictive Control (MPC) as an optimization based control technique. In order to obtain the accurate models needed for MPC, we intend to explicitly take into account the spatio-temporal distribution of the state veriable, i.e., to use dynamic models based on Partial Differential Equations (PDEs). This proposal, which shall be carried out in close cooperation with the partner proposals by Thomas Meurer and Stefan Volkwein, aims at analyzing and designing MPC schemes for spatially distributed and time varying models, at implementing the respective algorithms, and at applying it to a joint benchmark problem. In light of the intended energy efficiency, economic MPC formulations will be in the focus of the proposal. Here "economic MPC" stands for a class of MPC algorithms in which the control objective is not the stabilization of an equilibrium or the tracking of a time varying reference trajectory. Instead, the goal is to follow an energy optimal path which is not given a priori but implicitly defined by the objective of the MPC optimization, itself. The key question in economic MPC is how to design the objective and constraints such that the iterative optimization on moving horizons yields an approximately optimal closed loop trajectory on a long, possibly infinite time horizon. To this end, in the first work package economic MPC for PDEs will be investigated in detail. Key difficult is the fact that the system dynamics evolve in an infinite dimensional state space. Our goal is to develop new methods exploiting the special stuctures of HVAC control problems. In the second work package, problems with time varying system dynamics or depending on time varying data are considered. Here, in particular, an appropriate generalization of the concept of an optimal equilibrium must be found and appropriate terminal constraints in the time varying setting shall be developed. The third work package concerns the implementation. Beyond the coding of the newly developed routines, which will be carried out in close collaboration with the partner projects, the a posteriori performance measure for stabilizing MPC shall be extended to economic MPC, as a device to measure the errors introduced by using reduced order models in the optimization. The results from all work packages will be applied and particularly focused to a benchmark problem for HVAC control. These activities are detailed in the fourth work package and will be carried out in parallel with the other work packages.

采暖、通风和空调(HVAC)设施构成了一类具有巨大节能潜力的控制系统。为了实现这些节省，我们建议使用模型预测控制(MPC)作为一种基于优化的控制技术。为了得到预测控制所需的精确模型，我们打算显式地考虑状态变量的时空分布，即使用基于偏微分方程(PDE)的动态模型。这项提案将与Thomas Meurer和Stefan Volkwein的合作伙伴提案密切合作，旨在分析和设计空间分布和时变模型的预测预测方案，实施各自的算法，并将其应用于联合基准问题。鉴于预期的能源效率，经济的MPC配方将是提案的重点。这里的“经济预测控制”指的是一类预测控制算法，其控制目标不是平衡点的稳定，也不是对时变参考轨迹的跟踪。相反，目标是遵循一条能量最优路径，该路径不是先验的，而是由MPC优化的目标本身隐含地定义的。经济预测控制中的关键问题是如何设计目标和约束条件，使得在移动水平上的迭代优化在一个长的、可能是无限的时间范围内产生一个近似最优的闭环系统轨迹。为此，在第一个工作包中，将详细研究PDE的经济MPC。关键的困难是系统动力学在无限维的状态空间中演化。我们的目标是开发利用暖通空调控制问题的特殊结构的新方法。在第二个工作包中，考虑了具有时变系统动力学或依赖于时变数据的问题。在这里，尤其是，必须找到最优均衡概念的适当推广，并在时变环境中开发适当的终端约束。第三个工作方案涉及执行。除了将与伙伴项目密切合作对新开发的程序进行编码外，稳定预测预测的后验业绩衡量应扩展到经济预测预测，作为衡量在优化中使用降阶模型引入的误差的一种手段。所有工作包的结果将被应用，并特别侧重于暖通空调控制的基准问题。第四个工作方案详细说明了这些活动，并将与其他工作方案同时开展。