Boundary control of coupled reaction-diffusion processes with constant parameters
Boundary control of coupled reaction-diffusion processes with constant parameters
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DOI：
10.1016/j.automatica.2015.01.032
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
A. Baccoli;A. Pisano;Y. Orlov
中科院分区：
文献类型：
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作者：
A. Baccoli;A. Pisano;Y. Orlov
研究了几类耦合抛物线性反应扩散型偏微分方程的边界稳定问题。参考n个耦合方程，每个方程都配备有一个标量边界控制输入，状态反馈律的设计与驱动只有一端的域，并证明了闭环系统的指数稳定性。处理是单独解决的情况下，所有的过程都具有相同的扩散性和更具挑战性的情况下，每个过程都有自己的扩散性和不同的解决方案的方法必须采取。控制器的设计采用反推方法，特别是通过逐次逼近法求解相应的偏微分方程，将变换的核矩阵以类贝塞尔矩阵函数级数的显式形式导出。因此，所提出的控制律成为可用的明确形式。此外，在边界输入为标量的限制下，研究了两个耦合反应扩散过程的欠驱动系统的镇定问题。所提出的合成能力及其有效性的支持与不同的扩散参数和欠驱动线性化无量纲的温度-浓度动态的管式化学反应器，通过边界控制在低流体表观速度时对流项变得可以忽略不计的三个耦合系统的数值研究。
The problem of boundary stabilization is considered for some classes of coupled parabolic linear PDEs of the reaction–diffusion type. With reference to n coupled equations, each one equipped with a scalar boundary control input, a state feedback law is designed with actuation at only one end of the domain, and exponential stability of the closed-loop system is proven. The treatment is addressed separately for the case in which all processes have the same diffusivity and for the more challenging scenario where each process has its own diffusivity and a different solution approach has to be taken. The backstepping method is used for controller design, and, particularly, the kernel matrix of the transformation is derived in explicit form of series of Bessel-like matrix functions by using the method of successive approximations to solve the corresponding PDE. Thus, the proposed control laws become available in explicit form. Additionally, the stabilization of an underactuated system of two coupled reaction–diffusion processes is tackled under the restriction that only a scalar boundary input is available. Capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature-concentration dynamics of a tubular chemical reactor, controlled through a boundary at low fluid superficial velocities when convection terms become negligible.