The model predictive controller (MPC) design is developed for a tubular chemical reactor, considering a second-order hyperbolic partial differential equation as the model of the transport-reaction process with boundary actuation. Without loss of generality, closed–closed boundary conditions and relaxed total flux are assumed. At the same time, the model is discretized in time by the Cayley–Tustin method, and, under the assumption that only the reactor's output is measurable, the observer design for the state reconstruction is addressed and integrated with the MPC design. The Luenberger observer gain is obtained by solving the operator Ricatti equation in the discrete-time setting, while the MPC accounts for constrained and optimal control. The simulations show that the output-based MPC design stabilizes the system under the input and output constraints satisfaction. In addition, to address the models' disparities, the results for both parabolic and hyperbolic equations are presented and discussed.

中文翻译：

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二阶双曲线转运反应过程的模型预测控制

模型预测控制器 (MPC) 设计是为管式化学反应器开发的，考虑到二阶双曲偏微分方程作为具有边界驱动的传输反应过程的模型。不失一般性，假设闭-闭边界条件和松弛的总通量。同时，模型通过 Cayley-Tustin 方法在时间上离散化，并且在只有反应堆输出可测量的假设下，状态重建的观测器设计被解决并与 MPC 设计集成。Luenberger 观测器增益是通过在离散时间设置中求解算子 Ricatti 方程获得的，而 MPC 则考虑了约束和最优控制。仿真表明，基于输出的 MPC 设计在满足输入和输出约束条件下稳定了系统。此外，为了解决模型的差异，对抛物线和双曲线方程的结果进行了介绍和讨论。