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首页> 外文期刊>IMA Journal of Mathematical Control and Information >Stabilization of an Orr–Sommerfeld equation cascaded by both the Squire equation and ODE subject to boundary control matched disturbance via active disturbance rejection control
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Stabilization of an Orr–Sommerfeld equation cascaded by both the Squire equation and ODE subject to boundary control matched disturbance via active disturbance rejection control

机译：由Squire方程和ODE级联的Orr–Sommerfeld方程的稳定受边界控制，通过主动干扰抑制控制匹配干扰

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摘要

In this paper, we consider boundary feedback stabilization for an Orr-Sommerfeld equation cascaded by both the Squire equation and ordinary differential equations (ODE). In the system under consideration, there are two boundary control inputs subject to matched disturbance. By the active disturbance rejection control approach, two boundary disturbances are estimated by means of two disturbance estimators with time-varying high gain and constant high gain, respectively, and the disturbances are cancelled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.
机译：在本文中，我们考虑了由Squire方程和常微分方程（ODE）级联的Orr-Sommerfeld方程的边界反馈镇定。在所考虑的系统中，有两个边界控制输入受到匹配的干扰。通过主动干扰抑制控制方法，分别通过两个具有时变高增益和恒定高增益的干扰估计器来估计两个边界干扰，并在反馈回路中在线消除干扰。结果表明，所得的具有随时间变化的高增益的闭环系统是渐近稳定的，并且在恒定的高增益下实际上是稳定的。进行了数值实验，以说明所提出的控制律的有效性。

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