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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Optimal Control of Uniformly Heated Granular Fluids in Linear Response.

Natalia Ruiz-Pino1, Antonio Prados1

  • 1Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain.

Entropy (Basel, Switzerland)
|January 21, 2022
PubMed
Summary

This study optimizes control for granular gases by minimizing connection time between steady states. Optimal control strategies are proven to be bang-bang, with a single switch in the linear regime.

Keywords:
Sonine approximationbang-bang controlsgranular fluidslinear responseoptimal control

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Area of Science:

  • Statistical mechanics
  • Non-equilibrium systems
  • Granular materials

Background:

  • Granular gases exhibit complex non-equilibrium steady states (NESSs).
  • Controlling transitions between NESSs is crucial for understanding granular dynamics.
  • Previous studies often lack rigorous analytical control strategies.

Purpose of the Study:

  • To analytically investigate optimal control of uniformly heated granular gases.
  • To minimize the connection time between two NESSs with different granular temperatures.
  • To determine the nature of optimal control strategies in the linear regime.

Main Methods:

  • Linearization of evolution equations around NESSs.
  • Mathematical analysis of control strategies.
  • Application of the first Sonine approximation.
  • Investigation of bang-bang control properties.

Main Results:

  • Optimal control strategies are rigorously proven to be of bang-bang type.
  • A single switch in control is identified within the first Sonine approximation.
  • The dependence of optimal connection time on driving intensity bounds is analyzed.
  • The validity limits of the linear regime are explored.

Conclusions:

  • Bang-bang control is an effective strategy for rapid state transitions in granular gases.
  • The study provides a rigorous mathematical framework for optimal control in granular systems.
  • Understanding control limits is essential for practical applications of granular gas dynamics.