An official website of the United States government
State estimation is key to both analysing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When desired, the full state can be recovered via the ROM.) Current methods in this category nearly always use a linear model to relate the sensor data to the reduced state, which often leads to restrictions on sensor locations and has inherent limitations in representing the generally nonlinear relationship between the measurements and reduced state. We propose an alternative methodology whereby a neural network architecture is used to learn this nonlinear relationship. A neural network is a natural choice for this estimation problem, as a physical interpretation of the reduced state–sensor measurement relationship is rarely obvious. The proposed estimation framework is agnostic to the ROM employed, and can be incorporated into any choice of ROMs derived on a linear subspace (e.g. proper orthogonal decomposition) or a nonlinear manifold. The proposed approach is demonstrated on a two-dimensional model problem of separated flow around a flat plate, and is found to outperform common linear estimation alternatives.
more »
« less
Sliding mode estimation and closed‐loop active flow control under actuator uncertainty
Summary 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.
more »
« less
- Award ID(s):
- 1809790
- PAR ID:
- 10456561
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal of Robust and Nonlinear Control
- Volume:
- 30
- Issue:
- 16
- ISSN:
- 1049-8923
- Page Range / eLocation ID:
- p. 6645-6660
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Tear film plays a key role in protecting the cornea surface against contaminations and dry eye syndrome which can lead to symptoms of discomfort, visual trouble, and tear film instability with the potential to damage the ocular surface. In this paper, coupled nonlinear partial differential equations of the fourth order proposed by Aydemir et al. to describe the evolution of tear film dynamics are considered. These equations are of Benney type and known to suffer from unbounded behavior and lack of a global attractor. The objective here is to identify a reduced order modeling framework with the potential to be used as a basis for control in future work using smart tears with a surfactant that can modify the surface tension to prevent tear film breakup. Since the dynamics are infinite dimensional and nonlinear, a reduced order model based on the proper orthogonal decomposition (POD) is developed, analyzed, and compared to the full order model. Numerical simulations illustrate that only a small number of POD modes are required to accurately capture the tear film dynamics allowing for the full partial differential model to be represented as a low-dimensional set of coupled ordinary differential equations.more » « less
-
This paper presents an integrated structure of artificial neural networks, named state integrated matrix estimation (SIME), for linear parameter-varying (LPV) model identification. The proposed method simultaneously estimates states and explores structural dependency of matrix functions of a representative LPV model only using inputs/outputs data. The case with unknown (unmeasurable) states is circumvented by SIME using two estimators of the same state: one estimator represented by an ANN and the other obtained by LPV model equations. Minimizing the difference between these two estimators, as part of the cost function, is used to guarantee their consistency. The results from a complex nonlinear system, namely a reactivity controlled compression ignition (RCCI) engine, show high accuracy of the state-space LPV models obtained using the proposed SIME while requiring minimal hyperparameters tuning.more » « less
-
This paper presents an integrated structure of arti cial neural networks, named state integrated matrix estimation (SIME), for linear parameter-varying (LPV) model identi cation. The proposed method simultaneously estimates states and explores structural dependency of matrix functions of a representative LPV model only using inputs/outputs data. The case with unknown (unmeasurable) states is circumvented by SIME using two estimators of the same state: one estimator represented by an ANN and the other obtained by LPV model equations. Minimizing the difference between these two estimators, as part of the cost function, is used to guarantee their consistency. The results from a complex nonlinear system, namely a reactivity controlled compression ignition (RCCI) engine, show high accuracy of the state-space LPV models obtained using the proposed SIME while requiring minimal hyperparameters tuning.more » « less
-
Tobias Ekholm (Ed.)We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $$\mathbb{T}\times[0,1]$$. More precisely, we consider shear flows $(b(y),0)$ given by a function $$b$$ which is Gevrey smooth, strictly increasing, and linear outside a compact subset of the interval $(0,1)$ (to avoid boundary contributions which are incompatible with inviscid damping). We also assume that the associated linearized operator satisfies a suitable spectral condition, which is needed to prove linear inviscid damping. Under these assumptions, we show that if $$u$$ is a solution which is a small and Gevrey smooth perturbation of such a shear flow $(b(y),0)$ at time $t=0$, then the velocity field $$u$$ converges strongly to a nearby shear flow as the time goes to infinity. This is the first nonlinear asymptotic stability result for Euler equations around general steady solutions for which the linearized flow cannot be explicitly solved.more » « less
