Limitations of linear control of thermal convection in a porous medium
Limitations of linear control of thermal convection in a porous medium
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多孔介质中热对流线性控制的局限性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
H. Bau
中科院分区：
文献类型：
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作者：
Hui Zhao;H. Bau
从理论上研究了线性控制器稳定饱和多孔层从下加热到上冷却的传导（不运动）状态的能力。考虑了比例、次优鲁棒（H∞）和线性二次高斯（H2）控制器。比例控制器将对流开始的临界瑞利数增加了2倍之多。H2和H∞控制器都使线性化系统在所有瑞利数处保持稳定。尽管所有这些控制器都成功地使线性化系统的特征值的实部为负，但被控系统的线性算子是非正态的，并且干扰在其最终的渐近衰减之前经历了实质性的增长。当系统受到“最危险的干扰”时，将非线性系统的动力学作为扰动幅度的函数进行检验。这些计算提供了初始条件的临界幅值，超过这个初始条件，系统就不能再…
The ability of linear controllers to stabilize the conduction (no-motion) state of a saturated porous layer heated from below and cooled from above is studied theoretically. Proportional, suboptimal robust (H∞) and linear quadratic Gaussian (H2) controllers are considered. The proportional controller increases the critical Rayleigh number for the onset of convection by as much as a factor of 2. Both the H2 and H∞ controllers stabilize the linearized system at all Rayleigh numbers. Although all these controllers successfully render negative the real part of the linearized system’s eigenvalues, the linear operator of the controlled system is non-normal and disturbances undergo substantial growth prior to their eventual, asymptotic decay. The dynamics of the nonlinear system are examined as a function of the disturbance’s amplitude when the system is subjected to the “most dangerous disturbances.” These computations provide the critical amplitude of the initial conditions above which the system can no longer...