Model-based discrete-time output regulator design is proposed for fluid flow systems using a geometric approach. More specifically, a class of vortex shedding and falling thin film phenomena modelled by complex Ginzburg–Landau equation (CGLE) and Kuramoto–Sivashinsky equation (KSE) are considered. Differently from a traditional continuous-time controller design, a novel discrete-time modelling technique is proposed in a general infinite-dimensional state-space setting, which does not pertain any spatial approximation or model reduction, and preserves model intrinsic properties (such as stability, controllability and observability). Based on the time discretized plant model (CGLE and KSE systems) by the Cayley–Tustin method, discrete regulator regulation equations are established and facilitated for an output regulator design to achieve fluid flow control and manipulation. To address model instability, a spectrum analysis is utilized in stabilizing continuous-time CGLE and KSE systems, and a link between discrete- and continuous-time closed-loop system stabilizing gains is established. Finally, the proposed methodology is demonstrated through a set of simulation cases, by which the output tracking, disturbance rejection, and model stabilization are achieved for the considered CGLE and KSE systems.

提出了一种基于模型的离散时间输出调节器设计，用于采用几何方法的流体流动系统。更具体地说，考虑了一类由复杂的Ginzburg-Landau方程（CGLE）和Kuramoto-Sivashinsky方程（KSE）建模的涡旋脱落和掉落的薄膜现象。与传统的连续时间控制器设计不同，在一般的无穷维状态空间设置中提出了一种新颖的离散时间建模技术，该技术不涉及任何空间逼近或模型归约，并且保留了模型的固有属性（例如稳定性） ，可控性和可观察性）。根据采用Cayley-Tustin方法的时间离散植物模型（CGLE和KSE系统），建立离散调节器调节方程式，并简化输出调节器设计，以实现流体流量控制和操纵。为了解决模型的不稳定性，利用频谱分析来稳定连续时间CGLE和KSE系统，并在离散和连续时间闭环系统之间稳定增益。最后，通过一组仿真案例演示了所提出的方法，通过这些仿真案例，可以为所考虑的CGLE和KSE系统实现输出跟踪，干扰抑制和模型稳定。