Constrained model predictive control (MPC) usually requires the computation of a quadratic programming problem (QP) at each sampling instant. This is computationally expensive and becomes a limitation to embed and use MPC in plants with fast sampling rates. Several special solvers for MPC problems have been proposed in the last years, but most of them focus on state-space formulations, which are very popular in academia. This paper proposes a solution based on alternated direction method of multipliers, tailored for embedded systems and applied to generalized predictive control (GPC), which is a very popular formulation in industry. Implementations issues of parallel computation are discussed in order to accelerate the time required for the operations. The implementation in an FPGA proved to be quite fast, with the observed worst case execution time of 11,54 µs for the presented example. These results contribute to embed GPC applications in processes that are typically controlled by classical controllers because of their fast dynamics.

中文翻译：

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ADMM 嵌入在 FPGA 中的快速约束广义预测控制

约束模型预测控制 (MPC) 通常需要在每个采样时刻计算二次规划问题 (QP)。这在计算上是昂贵的，并且成为在具有快速采样率的工厂中嵌入和使用 MPC 的限制。过去几年已经提出了几种针对 MPC 问题的特殊求解器，但其中大部分都集中在状态空间公式上，这在学术界非常流行。本文提出了一种基于乘法器交替方向法的解决方案，为嵌入式系统量身定制并应用于广义预测控制（GPC），这是一种在工业上非常流行的公式。讨论了并行计算的实现问题，以加快操作所需的时间。事实证明，在 FPGA 中的实现非常快，对于本示例，观察到的最坏情况执行时间为 11.54 µs。这些结果有助于将 GPC 应用程序嵌入到通常由经典控制器控制的过程中，因为它们具有快速动态性。