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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.
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Nonlinear observer design for two‐time‐scale systems
Abstract A two‐time‐scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two‐time‐scale systems and presents two alternative nonlinear observer design approaches, one full‐order and one reduced‐order. The full‐order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced‐order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow‐motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced‐order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.
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- Award ID(s):
- 1706201
- PAR ID:
- 10456962
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- AIChE Journal
- Volume:
- 66
- Issue:
- 6
- ISSN:
- 0001-1541
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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