Abstract

We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_{\infty }$-output feedback controllers that stabilize the infinite-dimensional system exponentially in closed loop. The method is applied to control torsional vibrations in drilling systems with the goal to avoid slip-stick.

中文翻译：

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反稳定波动方程的边界反馈控制

摘要

我们讨论具有非线性反阻尼边界条件的波动方程的边界控制。我们设计结构化的有限维$ H _ {\ infty} $输出反馈控制器，该控制器在闭环中使指数系统无限稳定。该方法用于控制钻井系统中的扭转振动，目的是避免打滑。