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首页> 外文期刊>IEEE Transactions on Automatic Control >Performance Output Tracking for Multidimensional Heat Equation Subject to Unmatched Disturbance and Noncollocated Control
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Performance Output Tracking for Multidimensional Heat Equation Subject to Unmatched Disturbance and Noncollocated Control

机译：多维热方程的性能输出跟踪，对无与伦比的干扰和非旋能控制

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摘要

This paper investigates performance output tracking for a boundary controlled multidimensional heat equation. It is assumed that the so-called total disturbance (which is composed of internal possibly nonlinear uncertainty and external disturbance) the equation is subject to is on one part of the boundary, and that the control is applied on the rest of the boundary. Using only partial boundary measurement, we first propose an extended state observer to estimate both system state and the total disturbance. This allows us to design a servomechanism and then an output feedback controller. Under the condition that both the reference signal and the disturbance vanish or belong to spaces $H<^>1(0,infty ;L<^>1(Gamma _1))$ and $L<^>2(0,infty ;L<^>2(Gamma _0))$, respectively. We show that the over-all control strategy achieves three objectives on the system performance: first, exponentially output tracking for arbitrary given reference signal; second, uniformly boundedness of all internal signals; and, third, the internal asymptotic stability of the closed-loop system. In addition, the control strategy turns out to be robust to the measurement noise. We provide numerical experiments to illustrate the effectiveness of the proposed control strategy.
机译：本文研究了边界控制多维热方程的性能输出跟踪。假设等式的所谓的总干扰（由内部可能非线性不确定性和外部干扰组成）在边界的一部分上，并且控制在边界的其余部分上施加控制。仅使用部分边界测量，我们首先提出了一个扩展的状态观察者来估计系统状态和完全干扰。这使我们能够设计伺服机构，然后是输出反馈控制器。在参考信号和干扰消失或属于空间的条件下，H <^> 1（0， idty; l <^> 1（ gamma _1））$和$ l <^> 2（0， idty; l <^> 2（ gamma _0））分别为$。我们表明，全部控制策略在系统性能上实现了三个目标：首先，任意给定参考信号的指数输出跟踪;第二，所有内部信号的均匀界限;并且第三，闭环系统的内部渐近稳定性。此外，控制策略结果向测量噪声变为强大。我们提供数值实验，以说明所提出的控制策略的有效性。

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