发表机构
Institute of Robotics and Automatic Information System, Nankai University; Beijing ENN Fusion Energy Science and Technology Co., Ltd.（南开大学机器人与自动化信息研究所; 北京新奥聚变能源科技有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对EXL-50U球形托卡马克，提出基于观测器的约束模型预测控制，通过模型降维和高效计算实现电流与等磁通联合调节，误差低于PID和LQR，计算时间小于1毫秒。
AI 中文摘要
球形托卡马克中的等磁通控制需要在线圈电压和计算约束下协调等离子体电流和边界调节。本研究为EXL-50U开发了基于观测器的约束模型预测控制（MPC）。真空室空间粗化将538状态线性化模型缩减至40个状态，同时保留控制相关响应。卡尔曼观测器提供全状态估计，MPC联合优化电流和边界磁通跟踪，并带有显式电压约束。矩阵预计算、专用求解器代码生成和结构化线性系统求解减少了在线计算。非线性自由边界Grad-Shafranov演化模拟评估了标称运行、测量噪声、配置失配、一步延迟以及噪声与延迟组合情况，并与比例-积分-微分（PID）控制和线性二次调节器（LQR）进行比较。标称MPC的均方根误差为：等离子体电流1.126 kA，最外闭合磁面几何0.0164 m，最差磁通通道2.463 mWb，均低于两种基线。有噪声时，在共同评估窗口内边界误差为0.0199 m，且整个测试期间调节持续维持。MPC无需重新线性化或重新调参即可完成限制器到偏滤器的过渡，并在延迟和组合扰动下保持调节。在所有五种情况下，MPC平均计算时间为0.413–0.441 ms，所有第99百分位数均低于1 ms。这些结果支持联合电流和等磁通调节以及毫秒级计算可行性，为未来EXL-50U实验提供了基础。
英文摘要
Isoflux control in spherical tokamaks requires coordinated plasma-current and boundary regulation under coil-voltage and computational constraints. This study develops observer-based constrained model predictive control (MPC) for EXL-50U. Vacuum-vessel spatial coarsening reduces a 538-state linearized model to 40 states while retaining control-relevant responses. A Kalman observer provides full-state estimates, and MPC jointly optimizes current and boundary-flux tracking with explicit voltage bounds. Matrix precomputation, specialized solver code generation, and structured linear-system solution reduce online computation. Nonlinear free-boundary Grad--Shafranov evolutive simulations evaluate nominal operation, measurement noise, configuration mismatch, a one-step delay, and combined noise and delay against proportional--integral--derivative (PID) control and a linear--quadratic regulator (LQR). Nominal MPC root-mean-square errors are 1.126 kA for plasma current, 0.0164 m for last-closed-flux-surface geometry, and 2.463 mWb for the worst flux channel, all below both baselines. With noise, the boundary error is 0.0199 m over the common evaluation window, and regulation is sustained throughout the test. MPC completes a limiter-to-divertor transition without relinearization or retuning and maintains regulation under delay and combined disturbances. Across all five cases, mean MPC computation times are 0.413--0.441 ms, with all 99th percentiles below 1 ms. These results support joint current and isoflux regulation and millisecond-scale computational feasibility, providing a basis for future EXL-50U experiments.
