基于MPC-AUKF的多加热器阵列温控研究

Research on Temperature Control of Multi-Heater Array Based on MPC-AUKF

摘要: 多加热器阵列系统因包含对流散热、非线性辐射换热及节点间热耦合效应而呈现强非线性、强耦合特征。本文针对包含10个加热节点的非线性多加热器阵列系统，提出了一种融合自适应无迹卡尔曼滤波器(AUKF)与模型预测控制(MPC)的协同控制框架。AUKF通过新息滑窗协方差估计、指数移动平均突变检测及协方差膨胀限幅机制实现噪声统计特性的在线自适应更新，MPC控制器则采用实时线性化策略以适应系统强非线性。基于50组独立随机种子的蒙特卡洛仿真实验表明，MPC + AUKF方案实现了全程RMSE为3.96 ± 0.05 K、调节时间12步及稳态误差0.247 ± 0.011 K，较PID + EKF基准方案RMSE降低69.0%，较MPC + EKF稳态后RMSE由5.94 K降至0.31 K (降低94.8%)。消融实验验证了实时线性化使调节时间改善22.5倍，PID替代MPC导致系统全程无法收敛。

Abstract: Multi-heater array systems exhibit strongly nonlinear and highly coupled characteristics due to convective heat dissipation, nonlinear radiative heat transfer, and inter-node thermal coupling effects. Targeting an on linear multi-heater array system with 10 heating nodes, this paper proposes a synergistic control framework integrating an Adaptive Unscented Kalman Filter (AUKF) and Model Predictive Control (MPC). The AUKF realizes the online adaptive updating of noise statistical characteristics through innovation sliding window covariance estimation, exponential moving average abrupt change detection, and covariance inflation clipping mechanisms, while the MPC controller employs a real-time linearization strategy to accommodate the strong nonlinearity of the system. Monte Carlo simulation experiments based on 50 independent random seeds demonstrate that the MPC + AUKF scheme achieves an overall RMSE of 3.96 ± 0.05 K, a settling time of 12 steps, and a steady-state error of 0.247 ± 0.011 K. Compared with the PID + EKF baseline scheme, the overall RMSE is reduced by 69.0%, and compared with the MPC + EKF approach, the post-steady-state RMSE is reduced from 5.94 K to 0.31 K (a reduction of 94.8%). Ablation studies confirm that real-time linearization improves the settling time by 22.5 times, whereas replacing MPC with PID results in a complete failure of system convergence through out the entire process.