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関連する概念動画

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

124
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
124
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

511
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
511
Linear time-invariant Systems01:23

Linear time-invariant Systems

403
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
403
Stability01:28

Stability

186
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
186
Pole and System Stability01:24

Pole and System Stability

419
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
419
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

131
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
131

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量子化下の線形システムのデータ駆動超安定化

Jared Miller1,2, Jian Zheng2, Mario Sznaier2

  • 1J. Miller is with the Automatic Control Laboratory (IfA), Department of Information Technology and Electrical Engineering (D-ITET), ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland.

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PubMed
まとめ
この要約は機械生成です。

この研究は,定量化されたデータによる線形システムの安定化に取り組んでいます. 新しい線形プログラミングアプローチは,センサーと入力量子化にもかかわらず,システムの安定性を確保し,実例システムでの有効性を実証しています.

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科学分野:

  • 制御システム工学
  • 情報理論
  • 応用数学

背景:

  • 線形システムはデータの量子化により性能が低下する可能性があります.
  • 状態移行データと制御入力における定量化は,システムの安定化に重大な課題をもたらします.
  • 既存の方法は,定量化下で非保守的な安定化に苦戦する.

研究 の 目的:

  • 定量化状態移行データと制御入力で線形システムを安定させるための堅牢な方法を開発する.
  • センサーの定量化と入力制限を考慮する非保守的なアプローチを策定する.
  • 観測された量子データと一致する全てのシステムの 超安定性を確保する.

主な方法:

  • セクター限定の不確実性に対する強度に基づく入力対数定量化安定化の特徴を用いる.
  • 非保守的な無限次元の線形プログラムを作成します.
  • この問題を2つの指数式スケーリングの 線形プログラムで解く.

主要な成果:

  • 提案された方法は,量子化された線形システムに対する超安定化を成功裏に実行します.
  • 無限次元の線形プログラムは 非保守的な解を提供します.
  • 様々な例の量子化システムで有効性を証明した.

結論:

  • 開発された線形プログラミング技術は,量子化されたシステムを安定させる強力なツールを提供します.
  • このアプローチは,データの不確実性がある場合に制御システムの信頼性を高めます.
  • この方法は,デジタルコンポーネントを持つシステムの堅牢な制御の分野を前進させます.