Abstract Temperature control in solar collectors is a nonlinear problem: the dynamics of temperature rise vary according to the fluid flowing through the collector and to the temperature gradient along the collector area. In this way, this work investigates the formulation of a Model Predictive Control (MPC) application developed within a Linear Parameter Varying (LPV) formalism, which serves as a model of the solar collector process. The proposed system is an adaptive MPC, developed with terminal set constraints and considering the scheduling polytope of the model. At each instant, two Quadratic Programming (QPs) programs are solved: the first considers a backward horizon of N steps to find a virtual model-process tuning variable that defines the best LTI prediction model, considering the vertices of the polytopic system; then, the second QP uses this LTI model to optimize performances along a forward horizon of N steps. The paper ends with a realistic solar collector simulation results, comparing the proposed MPC to other techniques from the literature (linear MPC and robust tube-MPC). Discussions regarding the results, the design procedure and the computational effort for the three methods are presented. It is shown how the proposed MPC design is able to outrank these other standard methods in terms of reference tracking and disturbance rejection.

中文翻译：

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具有快速自适应多面体 LPV MPC 公式的太阳能集热器的非线性温度调节

摘要 太阳能集热器中的温度控制是一个非线性问题：温升的动力学根据流过集热器的流体和沿集热器区域的温度梯度而变化。通过这种方式，这项工作研究了在线性参数变化 (LPV) 形式主义中开发的模型预测控制 (MPC) 应用程序的公式，该应用程序用作太阳能收集器过程的模型。所提出的系统是一个自适应 MPC，在终端集约束下开发并考虑了模型的调度多面体。在每个时刻，求解两个二次规划 (QP) 程序：第一个考虑 N 步的后向范围，以找到定义最佳 LTI 预测模型的虚拟模型过程调整变量，考虑多面体系统的顶点；然后，第二个 QP 使用此 LTI 模型沿 N 步的前向范围优化性能。该论文以真实的太阳能集热器模拟结果结束，将提出的 MPC 与文献中的其他技术（线性 MPC 和稳健管 MPC）进行了比较。讨论了这三种方法的结果、设计程序和计算工作量。显示了所提出的 MPC 设计如何能够在参考跟踪和干扰抑制方面优于这些其他标准方法。介绍了这三种方法的设计过程和计算工作。显示了所提出的 MPC 设计如何能够在参考跟踪和干扰抑制方面优于这些其他标准方法。介绍了这三种方法的设计过程和计算工作。显示了所提出的 MPC 设计如何能够在参考跟踪和干扰抑制方面优于这些其他标准方法。