Abstract Hydrogen production systems supplied by photovoltaic solar energy have nonlinear dynamics and discontinuities which must be taken into account when a control system is applied. The main purpose of the control system is to maintain the electrolyzer current at the desired operating point and, at the same time, to optimize the grid energy consumption despite the solar energy variability. Classic controllers, like PID ones, are not able to obtain good performance over the whole operation range of these kinds of plants because of the aforementioned characteristics. To overcome these limitations, an optimal control strategy and a linear hybrid model predictive controller (HMPC) are applied to a hydrogen production system in this work. Regarding the optimal control design, a systematic framework is presented in order to obtain the optimal (in the sense of minimal grid energy consumption) trajectory of the states by converting the control problem into a boundary value problem by means of the Pontryagin’s Maximum Principle. Interestingly, the resulting control law is explicit and piecewise continuous. Regarding the linear HMPC strategy, a mixed logical dynamical description of the linearized equations of the system is considered in order to obtain the control law by solving an optimization problem in the form of a mixed integer quadratic programming. For this control strategy three cost functions associating the grid energy consumption and the electrolyzer efficiency are presented. The proposed controllers are tested through numerical simulations for both the nominal and uncertain cases and different performance indexes are considered. Finally, a discussion of the main advantages and disadvantages of each controller in real-life applications is presented.

中文翻译：

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电网辅助 PV-H2 生产系统的控制：最优控制和混合 MPC 的比较研究

摘要 由光伏太阳能提供的制氢系统具有非线性动力学和不连续性，在应用控制系统时必须考虑到这一点。控制系统的主要目的是将电解槽电流保持在所需的工作点，同时优化电网能源消耗，尽管太阳能变化很大。由于上述特性，传统控制器，如 PID 控制器，无法在此类设备的整个运行范围内获得良好的性能。为了克服这些限制，本文将最优控制策略和线性混合模型预测控制器 (HMPC) 应用于制氢系统。关于优化控制设计，提出了一个系统框架，以便通过庞特里亚金最大原理将控制问题转换为边值问题来获得状态的最优（在最小电网能量消耗的意义上）轨迹。有趣的是，由此产生的控制律是明确的和分段连续的。关于线性HMPC策略，考虑系统线性化方程的混合逻辑动力学描述，以通过以混合整数二次规划的形式求解优化问题来获得控制律。对于这种控制策略，提出了与电网能耗和电解槽效率相关的三个成本函数。所提出的控制器通过数值模拟对标称和不确定情况进行了测试，并考虑了不同的性能指标。最后，讨论了每个控制器在实际应用中的主要优点和缺点。