论文标题
feedforward边界控制$ 2 \ times 2 $非线性双曲线系统，并应用于圣人方程
Feedforward boundary control of $2 \times 2$ nonlinear hyperbolic systems with application to Saint-Venant equations
论文作者
论文摘要
由于它们代表了具有传播延迟的物理系统，因此双曲线系统非常适合馈电控制。当干扰和输出之间的延迟大于控制延迟时，尤其如此。在本文中，我们针对$ 2 \ times 2 $双曲系统的通用类别的前馈控制器的设计，其单个干扰输入位于一个边界，另一个边界的一个控制驱动。目的是设计一个前馈控制，使系统输出对测得的干扰输入不敏感。我们表明，对于这类系统，存在有效的理想进发液控制器，该控制器是因果关系且稳定的。该问题首先在频域中为简单的线性系统进行了研究和研究。然后，我们的主要贡献是向一般的非线性双曲线系统展示如何将理论扩展到时域。该方法用应用于控制的开放通道的应用，该通道代表了圣经方程，其中目的是使输出水位对输入流量的变化不敏感。最后，我们将更复杂的应用程序介绍到一系列池塘中，其中盲目的完美馈送控制可能会导致有害的振荡。通过模拟实验提出并验证了修改控制法以解决此问题的务实方法。
Because they represent physical systems with propagation delays, hyperbolic systems are well suited for feedforward control. This is especially true when the delay between a disturbance and the output is larger than the control delay. In this paper, we address the design of feedforward controllers for a general class of $2 \times 2$ hyperbolic systems with a single disturbance input located at one boundary and a single control actuation at the other boundary. The goal is to design a feedforward control that makes the system output insensitive to the measured disturbance input. We show that, for this class of systems, there exists an efficient ideal feedforward controller which is causal and stable. The problem is first stated and studied in the frequency domain for a simple linear system. Then, our main contribution is to show how the theory can be extended, in the time domain, to general nonlinear hyperbolic systems. The method is illustrated with an application to the control of an open channel represented by Saint- Venant equations where the objective is to make the output water level insensitive to the variations of the input flow rate. Finally, we address a more complex application to a cascade of pools where a blind application of perfect feedforward control can lead to detrimental oscillations. A pragmatic way of modifying the control law to solve this problem is proposed and validated with a simulation experiment.
