粘性贮液系统的输出反馈控制及其数值逼近
Output-Feedback Control of Viscous Liquid-Tank System and its Numerical Approximation
摘要：
我们解决了输出反馈稳定问题的坦克与液体的粘性圣维南PDE系统建模。控制输入是坦克的加速度和控制李雅普诺夫函数的方法。测量值为罐位置和罐壁处的液位。该控制方案是一个组合的状态反馈法与功能观察员的坦克速度和液体动量。提出了四种不同类型的输出反馈稳定器。一个全阶观测器和一个降阶观测器被用来估计坦克的速度，而未测量的液体动量是通过使用一个适当的标量滤波器估计或被忽略。降阶观测器与全阶观测器不同，因为它省略了对被测坦克位置的估计。在每种情况下，实现闭环系统到期望的平衡点的指数收敛。提供了一种算法，该算法保证机器人臂可以将一杯水移动到预先指定的位置，无论杯子有多满，而不会将水溢出杯子，没有残留的终点晃动，并且不测量水的动量和玻璃速度。最后，通过数值算例验证了所提出的输出反馈律的有效性。所提出的，明确的，有限差分格式的属性被确定。
英文摘要：
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.
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