The theory of a new analytical-solution-based algorithm for calculating the optimal solution in model-predictive control applications with hexagonal constraints is discussed in this article. Three-phase voltage-source inverters for power electronic and electric motor drive applications are the target of the proposed method. The indirect model-predictive control requires a constrained quadratic programming (QP) solver to calculate the optimal solution. Most of the QP solvers use numerical algorithms, which may result in unbearable computational burdens. However, the optimal constrained solution can be calculated in an analytical way when the control horizon is limited to the first step. A computationally efficient algorithm with a certain maximum number of operations is proposed in this article. A thorough mathematical description of the solver in both the stationary and rotating reference frames is provided. Experimental results on real test rigs featuring either an electric motor or a resistive–inductive load are reported to demonstrate the feasibility of the proposed solver, thus smoothing the way for its implementation in industrial applications. The name of the proposed solver is aVsIs, which is released under Apache License 2.0 in GitHub, and a free example is available in Code Ocean.

中文翻译：

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aVsIs：基于分析解的求解器，用于电压源逆变器应用中具有六边形约束的模型预测控制


本文讨论了一种基于解析解的新算法的理论，用于计算具有六边形约束的模型预测控制应用中的最优解。用于电力电子和电动机驱动应用的三相电压源逆变器是该方法的目标。间接模型预测控制需要约束二次规划 (QP) 求解器来计算最优解。大多数QP求解器使用数值算法，这可能会导致难以承受的计算负担。然而，当控制范围仅限于第一步时，可以通过解析的方式计算最优约束解。本文提出了一种具有一定最大操作数的计算高效算法。提供了求解器在静止和旋转参考系中的全面数学描述。在具有电动机或阻感负载的实际测试台上的实验结果证明了所提出的求解器的可行性，从而为其在工业应用中的实施铺平了道路。所提出的求解器的名称是 aVsIs，它在 GitHub 中根据 Apache License 2.0 发布，并且在 Code Ocean 中提供了免费示例。