We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

我们用粘性圣维南 PDE 系统建模的液体解决了储罐的输出反馈稳定问题。控制输入​​是坦克的加速度，并使用控制李亚普诺夫函数方法。测量值是储罐位置和储罐壁处的液位。控制方案是状态反馈法则与罐速度和液体动量的功能观测器的组合。提出了四种不同类型的输出反馈稳定器。使用全阶观察器和降阶观察器来估计罐速度，而未测量的液体动量要么通过使用适当的标量滤波器进行估计，要么被忽略。降阶观测器不同于全阶观测器，因为它省略了对测量罐位置的估计。在每种情况下都实现了闭环系统到所需平衡点的指数收敛。提供了一种算法，保证无论玻璃杯有多满，机械臂都可以将一杯水移动到预先指定的位置，不会将水从玻璃杯中溢出，不会出现剩余端点晃动，也不会测量水动量和玻璃速度。最后，通过使用简单的有限差分数值方案获得的数值示例验证了所提出的输出反馈定律的效率。确定所提出的显式有限差分格式的属性。提供了一种算法，保证无论玻璃杯有多满，机械臂都可以将一杯水移动到预先指定的位置，不会将水从玻璃杯中溢出，不会出现剩余端点晃动，也不会测量水动量和玻璃速度。最后，通过使用简单的有限差分数值方案获得的数值示例验证了所提出的输出反馈定律的效率。确定所提出的显式有限差分格式的属性。提供了一种算法，保证无论玻璃杯有多满，机械臂都可以将一杯水移动到预先指定的位置，不会将水从玻璃杯中溢出，不会出现剩余端点晃动，也不会测量水动量和玻璃速度。最后，通过使用简单的有限差分数值方案获得的数值示例验证了所提出的输出反馈定律的效率。确定所提出的显式有限差分格式的属性。