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.
翻译:我们解决了一个液态的罐体以Saint-Venant PDE 系统为模型的液态液态稳定化问题。 控制输入是加速罐体, 使用控制 Lyapunov 功能方法。 测量是罐体壁上的储罐位置和液体水平。 控制方案是州反馈法与储罐速度和液体动力的功能观察者相结合的组合。 提出了四种不同类型的产出反馈稳定器。 使用一个全级观察器和一个缩放观察器来估计罐体速度, 而无法测量的液态动力要么使用适当的压压滤过滤器估计, 要么被忽略。 降序观察器与全顺序观察器不同, 因为它忽略了测量储罐体位置的估测。 每一次都实现了闭环系统与理想平衡点的指数趋同。 提供了一种算法, 保证机器人手臂能够将玻璃移到一个预定的位置, 不论玻璃是否满, 不将水溢出, 也不使用适当的玻璃端端端端过滤器或被忽略。 降级观察者与全序观察器不同, 因为它忽略了完全的顺序观察者与全顺序,, 建议的定了测量了测量了测量了水量, 。 。 定定的定的定的定值 。 。