H∞ Guaranteed Cost Temperature Tracking Control for Microwave Heating Debye Media Process
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摘要: 德拜媒质微波加热过程中，由于介电常数具有随温度变化的特性，导致电磁场的空间分布将会产生巨大的变化.若缺乏合理的功率调控策略，将导致燃烧、爆炸等一系列热失控现象.针对上述问题，本文提出一种滚动时域H∞保性能温度跟踪控制策略，以实现对监测位置的最高温度进行控制.基于微波加热德拜媒质的机理模型，同时考虑跟踪系统稳定性、动态性能和输入约束，以H∞增益和保性能函数作为性能指标，本文将温度跟踪问题转化为线性矩阵不等式（Linear matrix inequality，LMI）多目标优化问题，使得系统动态性能达到最优.最后以德拜媒质微波加热短波导模型为例，对所提出方法的有效性进行仿真验证.Abstract: For the microwave heating Debye media process, the spatial distribution of electromagnetic field may be changed greatly with the temperature-dependent permittivity. Without any reasonable power regulation strategy, the phenomenon of thermal runaway, such as burning and explosion, may occur. Therefore, this paper proposes a receding horizon H∞ guaranteed cost control strategy. Specifically, the proposed controller has an explicit expression and involves the stability of system, dynamic performance and constrained input. Thereby, the temperature tracking problem can be cast into the linear matrix inequality (LMI) multi-objective optimization problem. The closed-loop control system can not only constrain the intensity of incident electric field, but also satisfy the H∞ norm and guaranteed cost function. The proposed control strategy is implemented on a one-dimensional waveguide heating model and its effectiveness can be evaluated through the simulation.
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Key words:
- Microwave heating /
- Debye media /
- constrained input /
- H∞ guaranteed cost /
- temperature tracking
1) 本文责任编委 张化光 -
图 1 微波加热德拜媒质的详细原理图
Fig. 1 Detailed schematic diagram for microwave heating Debye medium
图 2 相对介电常数$\epsilon '( T )$和相对介电损耗$\epsilon ''( T )$
Fig. 2 Relative dielectric constant $\epsilon '( T )$ and relative dielectric loss $\epsilon ''( T )$
图 3 监测点最高温度与期望温升曲线
Fig. 3 Maximum temperature rise curve in monitoring positions and reference temperature rise curve
表 1 热力学参数和非齐次Neumann边界条件
Table 1 Thermodynamic parameters and nonhomogeneous Neumann boundary condition
$\rho C_p$ $\kappa $ $ a $ $ b $ $ \rm{ J / \left( cm^3 \cdot {}^\circ C \right)}$ $ \rm{ W / \left( cm \cdot {}^\circ C \right)}$ $ \rm{W / cm} $ $ \rm{W / cm} $ 4.156 0.0068 1 $-1$ 
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