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.

因为它们表示具有传播延迟的物理系统，所以双曲系统非常适合于前馈控制。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，我们解决了通用类别的前馈控制器的设计$2\times 2$双曲系统，其单个扰动输入位于一个边界，而单个控制致动位于另一边界。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。我们证明，对于此类系统，存在因果关系且稳定的高效理想前馈控制器。首先针对简单的线性系统在频域中陈述并研究了该问题。然后，我们的主要贡献是说明如何在时域中将该理论扩展到一般的非线性双曲系统。该方法在应用到以圣维南方程表示的明渠控制的应用中进行了说明，其目的是使输出水位对输入流量的变化不敏感。最后，我们针对级联池解决了更复杂的应用，其中盲目应用完美的前馈控制会导致有害的振荡。提出了一种实用的修改控制律以解决该问题的方法，并通过仿真实验进行了验证。