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1. A Time-Delayed Lur’e Model with Biased Self-Excited Oscillations

   https://doi.org/10.23919/ACC45564.2020.9147761  

   Paredes, Juan ; Ul Islam, Syed Aseem ; Bernstein, Dennis S. ( July 2020 , Proc. American Control Conference)

   Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluidstructure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur’e model that exhibits biased oscillations under constant inputs. The model involves arbitrary asymptotically stable linear dynamics, time delay, a washout filter, and a saturation nonlinearity. For all sufficiently large scalings of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an oscillatory response. A bias-generation mechanism is used to specify the mean of the oscillation. The main contribution of the paper is the presentation and analysis of a discrete-time version of this model. 

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2. Output-only identification of self-excited systems using discrete-time Lur'e models with application to a gas-turbine combustor

   https://doi.org/10.1080/00207179.2022.2137702  

   Paredes, Juan A. ; Yang, Yulong ; Bernstein, Dennis S. ( November 2022 , International Journal of Control)

   A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimization to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimization to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor. 

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3. NARMAX Identification Based Closed-Loop Control of Flow Separation over NACA 0015 Airfoil

   https://doi.org/10.3390/fluids5030100  

   Obeid, Sohaib ; Ahmadi, Goodarz ; Jha, Ratneshwar ( September 2020 , Fluids)

   null (Ed.)

   A closed-loop control algorithm for the reduction of turbulent flow separation over NACA 0015 airfoil equipped with leading-edge synthetic jet actuators (SJAs) is presented. A system identification approach based on Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) technique was used to predict nonlinear dynamics of the fluid flow and for the design of the controller system. Numerical simulations based on URANS equations are performed at Reynolds number of 106 for various airfoil incidences with and without closed-loop control. The NARMAX model for flow over an airfoil is based on the static pressure data, and the synthetic jet actuator is developed using an incompressible flow model. The corresponding NARMAX identification model developed for the pressure data is nonlinear; therefore, the describing function technique is used to linearize the system within its frequency range. Low-pass filtering is used to obtain quasi-linear state values, which assist in the application of linear control techniques. The reference signal signifies the condition of a fully re-attached flow, and it is determined based on the linearization of the original signal during open-loop control. The controller design follows the standard proportional-integral (PI) technique for the single-input single-output system. The resulting closed-loop response tracks the reference value and leads to significant improvements in the transient response over the open-loop system. The NARMAX controller enhances the lift coefficient from 0.787 for the uncontrolled case to 1.315 for the controlled case with an increase of 67.1%. 

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4. Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics

   Kazuyoshi Tsutsumi, Ernst Niebur ( November 2022 , arXivorg)

   We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are connected with a layered internetwork that consists of a pair of forward and backward subnets composed of static neurons (with an instantaneous time-course). Dynamical neurons with large time constants in the internal space determine the overall time-course. The model offers a framework in which state variables in the network relax in a warped space, due to the cooperation between dynamic and static neurons. We assume that the system operates in either a learning or an association mode, depending on the presence or absence of feedback paths and input ports. In the learning mode, synaptic weights in the internetwork are modified by strong inputs corresponding to repetitive neuronal bursting, which represents sinusoidal or quasi-sinusoidal waves in the short-term average density of nerve impulses or in the membrane potential. A two-dimensional mapping relationship can be formed by employing signals with different frequencies based on the same mechanism as Lissajous curves. In the association mode, the speed of convergence to a goal point greatly varies with the mapping relationship of the previously trained internetwork, and owing to this property, the convergence trajectory in the two-dimensional model with the non-linear mapping internetwork cannot go straight but instead must curve. We further introduce a constrained association mode with a given target trajectory and elucidate that in the internal space, an output trajectory is generated, which is mapped from the external space according to the inverse of the mapping relationship of the forward subnet. 

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5. Linear Time-Invariant Models of a Large Cumulus Ensemble

   https://doi.org/10.1175/JAS-D-23-0194.1  

   Kuang, Zhiming ( March 2024 , Journal of the Atmospheric Sciences)

   Methods in system identification are used to obtain linear time-invariant state-space models that describe how horizontal averages of temperature and humidity of a large cumulus ensemble evolve with time under small forcing. The cumulus ensemble studied here is simulated with cloud-system-resolving models in radiative–convective equilibrium. The identified models extend steady-state linear response functions used in past studies and provide accurate descriptions of the transfer function, the noise model, and the behavior of cumulus convection when coupled with two-dimensional gravity waves. A novel procedure is developed to convert the state-space models into an interpretable form, which is used to elucidate and quantify memory in cumulus convection. The linear problem studied here serves as a useful reference point for more general efforts to obtain data-driven and interpretable parameterizations of cumulus convection.

    

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