Sliding mode estimation and closed‐loop active flow control under actuator uncertainty
Sliding mode estimation and closed‐loop active flow control under actuator uncertainty
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DOI：
10.1002/rnc.5129
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发表时间：
2020-08
影响因子：
3.9
通讯作者：
Krishna Bhavithavya Kidambi;W. MacKunis;S. Drakunov;V. Golubev
中科院分区：
文献类型：
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作者：
Krishna Bhavithavya Kidambi;W. MacKunis;S. Drakunov;V. Golubev
本文提出了一种非线性闭环主动流量控制(AFC)方法，在存在执行器不确定性和传感器测量限制的情况下，实现了对流体速度场的渐近调节。为了得到这一结果，建立了一个流动动力学的降阶模型，该模型利用本征正交分解(POD)将Navier-Stokes方程表示为一组非线性常微分方程组。降阶模型形式上考虑了合成射流致动器(SJA)的驱动效应。由此得到的基于POD的降阶模型所固有的挑战包括(1)状态不可直接测量，(2)测量方程是非标准的数学形式，以及(3)SJA模型包含参数不确定性。为了应对这些挑战，设计了一种滑模观测器(SMO)来估计驱动流场动力学降维模型中的不可测状态。拟议的SMO的一个显著特征是，它正式补偿了SJA模型中固有的参数不确定性。严格证明了在SJA中存在参数不确定性的情况下，SMO能够实现对不可测状态的局部有限时间估计。然后将状态估计用于非线性控制律，该控制律将流场速度调节到期望的状态。给出了基于Lyapunov的稳定性分析，证明了流场速度的局部渐近规律性。为了说明所提出的估计方法和AFC方法的性能，给出了比较的数值仿真结果，证明了加入不确定补偿器后所获得的性能改善。
This article presents a nonlinear closed‐loop active flow control (AFC) method, which achieves asymptotic regulation of a fluid flow velocity field in the presence of actuator uncertainty and sensor measurement limitations. To achieve the result, a reduced‐order model of the flow dynamics is derived, which utilizes proper orthogonal decomposition (POD) to express the Navier‐Stokes equations as a set of nonlinear ordinary differential equations. The reduced‐order model formally incorporates the actuation effects of synthetic jet actuators (SJA). Challenges inherent in the resulting POD‐based reduced‐order model include (1) the states are not directly measurable, (2) the measurement equation is in a nonstandard mathematical form, and (3) the SJA model contains parametric uncertainty. To address these challenges, a sliding mode observer (SMO) is designed to estimate the unmeasurable states in the reduced‐order model of the actuated flow field dynamics. A salient feature of the proposed SMO is that it formally compensates for the parametric uncertainty inherent in the SJA model. The SMO is rigorously proven to achieve local finite‐time estimation of the unmeasurable state in the presence of the parametric uncertainty in the SJA. The state estimates are then utilized in a nonlinear control law, which regulates the flow field velocity to a desired state. A Lyapunov‐based stability analysis is provided to prove local asymptotic regulation of the flow field velocity. To illustrate the performance of the proposed estimation and AFC method, comparative numerical simulation results are provided, which demonstrate the improved performance that is achieved by incorporating the uncertainty compensator.