On the Control of the 2D Navier–Stokes Equations with Kolmogorov Forcing

This paper is devoted to the control problem of a nonlinear dynamical system obtained by a truncation of the two-dimensional (2D) Navier–Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction. This special case of the 2D N-S equations is known as the 2D Kolmogorov flow. Firstly, the dynamics of the 2D Kolmogorov flow which is represented by a nonlinear dynamical system of seven ordinary differential equations (ODEs) of a laminar steady state flow regime and a periodic flow regime are analyzed; numerical simulations are given to illustrate the analysis. Secondly, an adaptive controller is designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime; the value of the Reynolds number is determined using an update law. Then, a static sliding mode controller and a dynamic sliding mode controller are designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime. Numerical simulations are presented to show the effectiveness of the proposed three control schemes. The simulation results clearly show that the proposed controllers work well.

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A Novel Control Scheme for PWM Boost Converter based on Sliding Mode Control using Particle Swarm Optimization

Recent Patents on Engineering ◽

10.2174/1872212114999200824110203 ◽

2020 ◽

Vol 14 ◽

Author(s):

Gang Liu ◽

Dong Qiu ◽

Xiuru Wang ◽

Ke Zhang ◽

Huafeng Huang ◽

...

Keyword(s):

Particle Swarm Optimization ◽

Steady State ◽

Sliding Mode ◽

Particle Swarm ◽

Mathematic Model ◽

Absolute Error ◽

Boost Converter ◽

Sliding Mode Controller ◽

Swarm Optimization ◽

Steady State Performance

Background: The PWM Boost converter is a strongly nonlinear discrete system, especially when the input voltage or load varies widely, therefore, tuning the control parameters of which is a challenge work. Objective: In order to overcome the issues, particle swarm optimization (PSO) is employed for tuning the parameters of a sliding mode controller of a boost converter. Methods: Based on the analysis of the Boost converter model and its non-linear characteristics, a mathematic model of a boost converter with a sliding mode controller is built firstly. Then, the parameters of the Boost controller are adjusted based on the integrated time and absolute error (ITAE), integral square error (ISE) and integrated absolute error (IAE) indexes by PSO. Results: Simulation verification was performed, and the results show that the controllers tuned by the three indexes all have excellent robust stability. Conclusion: The controllers tuned by ITAE and ISE indexes have excellent steady-state performance, but the overshoot is large during the startup. The controller tuned by IAE index has better startup performance and slightly worse steady-state performance.

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Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

Electronics ◽

10.3390/electronics10151794 ◽

2021 ◽

Vol 10 (15) ◽

pp. 1794

Author(s):

Hilmy Awad ◽

Ehab H. E. Bayoumi ◽

Hisham M. Soliman ◽

Michele De Santis

Keyword(s):

Sliding Mode ◽

Tracking Error ◽

Nonlinear Dynamical System ◽

Sufficient Conditions ◽

Linear Matrix ◽

Nonlinear Dynamical ◽

Load Variations ◽

Invariant Ellipsoid ◽

Steady State Responses ◽

Linearized Model

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

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Comparison of dynamic programming policies for long-term hydrothermal scheduling of single-reservoir systems in steady-state regime

Electric Power Systems Research ◽

10.1016/j.epsr.2021.107275 ◽

2021 ◽

Vol 196 ◽

pp. 107275

Author(s):

Thayze D’Martin Costa ◽

Secundino Soares

Keyword(s):

Dynamic Programming ◽

Steady State ◽

Steady State Regime ◽

Hydrothermal Scheduling ◽

Reservoir Systems ◽

State Regime

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Local quantum criticality out of equilibrium: Effective temperatures and scaling in the steady-state regime

EPL (Europhysics Letters) ◽

10.1209/0295-5075/102/50001 ◽

2013 ◽

Vol 102 (5) ◽

pp. 50001 ◽

Cited By ~ 13

Author(s):

Pedro Ribeiro ◽

Qimiao Si ◽

Stefan Kirchner

Keyword(s):

Steady State ◽

Quantum Criticality ◽

Steady State Regime ◽

Local Quantum ◽

State Regime ◽

Effective Temperatures

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Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime

Physical Review B ◽

10.1103/physrevb.80.115107 ◽

2009 ◽

Vol 80 (11) ◽

Cited By ~ 161

Author(s):

Petri Myöhänen ◽

Adrian Stan ◽

Gianluca Stefanucci ◽

Robert van Leeuwen

Keyword(s):

Steady State ◽

Quantum Transport ◽

Steady State Regime ◽

Nanoscale Systems ◽

State Regime

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Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

10.21203/rs.3.rs-332858/v1 ◽

2021 ◽

Author(s):

Kristian Haška ◽

Stevan Cvetićanin ◽

Dušan Zorica

Keyword(s):

Asymptotic Behavior ◽

Steady State ◽

Constitutive Equation ◽

Magnetic Flux ◽

Electromotive Force ◽

Constitutive Models ◽

Steady State Regime ◽

Power Type ◽

State Regime ◽

Transient And Steady State

Abstract Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

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A New Control Strategy for Bi-directional DC/DC Converter in DC Microgrid

E3S Web of Conferences ◽

10.1051/e3sconf/202123301051 ◽

2021 ◽

Vol 233 ◽

pp. 01051

Author(s):

Tianze Miao ◽

Xiaona Liu ◽

Siyuan Liu ◽

Lihua Wang

Keyword(s):

Steady State ◽

Control Strategy ◽

Feedback Linearization ◽

Sliding Mode ◽

Response Speed ◽

Fast Response ◽

Sliding Mode Controller ◽

Exponential Approximation ◽

Dc Microgrid ◽

Simulation Results

The bi-directional DC / DC converter in DC microgrid is a typical nonlinear system which has large voltage disturbance during lead accumulator charging and discharging. In order to solve the problem of voltage disturbance, the linearization of the converter is realized by exact feedback linearization, and the sliding mode controller is designed by using exponential approximation law. The simulation results show that the method has fast response speed, strong anti-interference ability and good steady-state characteristics.

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