基于控制理论的数据驱动延迟旁路过渡方法
A realizable data-driven approach to delay bypass transition with control theory
摘要：
本文提出了一种控制边界层流动中的条纹扰动并通过主动流动控制延迟向湍流转捩的可行方法。对Blasius边界层中的非线性转捩区进行了数值模拟，其中通过高水平的自由流湍流（FST）在边界层中激发条纹。发生的扰动通过局部壁传感器测量，并通过类似等离子体致动器的近壁致动器阻尼。通过处理来自传感器的信号来计算每个致动器的信号的时变幅度。这个过程是两个控制律的结果：线性二次高斯调节器（LQG）和逆前馈控制技术（IFFC）。使用第一，LQG，需要一个状态空间表示的系统动态，所以流是通过一个运营商，只捕捉最相关的动态信息，并在一个降阶模型（ROM）的结果。ROM是通过特征系统实现算法计算的，基于实际系统的脉冲响应。当考虑FST时，收集这样的脉冲响应可能是不可行的，因为精确描述这种现象所需的输入强迫的高维性。在这里，提出了一种新的方法来识别相关的系统动力学和生成所需的脉冲响应，在数据驱动的方法，将在实验中实现。最后，该技术在延迟旁路过渡的有效性。这项工作（i）提出了一个系统的方法来处理高维扰动，建立ROM的控制技术，（ii）表明，即使考虑到约束条件，如类型和大小的致动器和传感器，它是可能的，以实现至少大的旁路过渡延迟，在更理想的情况下，在文献中找到。
英文摘要：
The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence via active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer via a high level of free-stream turbulence (FST). The occurring disturbances are measured via localized wall sensors and damped via near-wall actuators resembling plasma actuators. The time-varying amplitude of the signal of each actuator is computed by processing signals from the sensors. This processing is the result of two control laws: the Linear Quadratic Gaussian regulator (LQG) and the Inverse Feed-Forward Control technique (IFFC). The use of the first, LQG, requires a state-space representation of the system dynamics, so the flow is described via an operator that captures only the most relevant information of the dynamics and results in a reduced order model (ROM). The ROM is computed via the eigensystem realization algorithm, based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering FST because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, in a data-driven approach that would be realizable in experiments. Finally, the effectiveness of the technique in delaying bypass transition is shown. The work (i) presents a systematic way to deal with high dimensional disturbances to build ROMs for a control technique, and (ii) shows that even when considering constraints such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in literature.
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