We consider backstepping control for ODE/wave PDE cascaded systems with dynamic boundary conditions. The ODE state is driven by the uncontrolled boundary of the wave PDE. A backstepping compensator is designed such that the closed-loop system is globally asymptotically stable. The controller design and stability analysis are based on coordinate and backstepping transformations. Changes of coordinate recast the original system into a coupled $2\times 2$ first-order hyperbolic system with spatially-varying coefficients cascading into an ODE. Backstepping transformations are exploited to design a compensator for the resulting coupled system. The validity of the proposed design is illustrated by controlling a bit of the oil well drilling system to operate at a constant uniform rotary speed.

我们考虑具有动态边界条件的 ODE/波 PDE 级联系统的反步控制。ODE 状态由波 PDE 的不受控制的边界驱动。设计了一个反步补偿器，使得闭环系统是全局渐近稳定的。控制器设计和稳定性分析基于坐标和反推变换。坐标变化将原系统重铸成耦合$2\times 2$空间变化系数级联到 ODE 的一阶双曲系统。利用反步转换来为产生的耦合系统设计补偿器。通过控制油井钻井系统的一部分以恒定的均匀旋转速度运行来说明所提出设计的有效性。