Compensating the Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems
Compensating the Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems
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DOI：
10.1109/tac.2010.2091187
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发表时间：
2011-03
影响因子：
6.8
通讯作者：
N. Bekiaris-Liberis;M. Krstić
中科院分区：
文献类型：
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作者：
N. Bekiaris-Liberis;M. Krstić
利用反推方法实现了SISO、LTI系统中无穷维输入或传感器动态的补偿。对于MIMO，LTI系统与分布式输入或传感器动态，由扩散与对流，我们开发了一种方法来构建控制律和观测器，补偿无限维执行器或传感器动态。补偿器的显式构造基于新颖的变换，该变换可以被认为是“backstepping-forwarding”类型的、工厂的有限维状态的和无限维致动器或传感器状态的。基于这些转换，我们构造显式的李雅普诺夫泛函证明指数稳定的闭环系统，或收敛的估计误差的情况下，观察器的设计。最后，我们用一个数值例子来说明我们的控制器的有效性。
Compensation of infinite-dimensional input or sensor dynamics in SISO, LTI systems is achieved using the backstepping method. For MIMO, LTI systems with distributed input or sensor dynamics, governed by diffusion with counter-convection, we develop a methodology for constructing control laws and observers that compensate the infinite-dimensional actuator or sensor dynamics. The explicit construction of the compensators are based on novel transformations, which can be considered of “backstepping-forwarding” type, of the finite-dimensional state of the plant and of the infinite-dimensional actuator or sensor states. Based on these transformations we construct explicit Lyapunov functionals which prove exponential stability of the closed-loop system, or convergence of the estimation error in the case of observer design. Finally, we illustrate the effectiveness of our controller with a numerical example.