ローナー・フレームワークにおける低注文システムの識別
Arya Honarpisheh1, Rajiv Singh2, Jared Miller3
1ECE Dept., Northeastern University, Boston, MA 02115 USA.
IFAC-PapersOnLine
|August 20, 2025
まとめ
この研究では,実験データから低次元のシステムモデルを特定するための新しい方法が導入されています. ローナーベースのアプローチは,より速い単数値の崩壊を提供し,従来のハンケル行列方法と比較してより効率的なモデルを生成します.
科学分野:
- システムエンジニアリング
- 制御理論
- 数値分析
背景:
- 正確なシステム識別は,制御と分析に不可欠です.
- ハンケルマトリックスベースの識別のような伝統的な方法は,計算が集約され,高次元のモデルを生成します.
- タイム・ドメインデータによる非パラメトリックの識別は,ユニークな課題を提示します.
研究 の 目的:
- タイムドメインデータから低次元のシステムモデルを識別するための新しい非パラメトリックの方法を開発する.
- ローナーベースのインターポレーションと還元の効率を伝統的なハンケル行列法と比較する.
- 提案されたアプローチの有効性を数値的な例で示す.
主な方法:
- カラテオドリー・フェジャーとローナーによるインターポレーションを用いてシステムの実現.
- モデル・オーダー・削減のためのローナー・マトリックス・バランス・リダクション (LBR) ステップを適用する.
- 単数値の衰退率を分析するためにゾロタレフ数を使用します.
主要な成果:
- ローナー行列は,システムの痕量基準の有効な推定値として機能する.
- ロウナー行列の単数値は,ハンケル行列のそれよりも著しく速い衰退率を示しています.
- Loewnerベースの方法は,比較可能な誤差の限界を持つ低次元のシステムモデルを達成します.
結論:
- 提案されたローナーベースの方法は,非パラメトリックシステムの識別により効率的なアプローチを提供します.
- この技術により,精度や計算効率が向上した 縮小型モデルが得られます.
- この発見は,様々なエンジニアリングのアプリケーションにおけるシステム識別のための貴重な代替案を提供します.
さらに関連する動画
13:44Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
43.0K
05:57Long-term Video Tracking of Cohoused Aquatic Animals: A Case Study of the Daily Locomotor Activity of the Norway Lobster Nephrops norvegicus
Published on: April 8, 2019
6.9K
関連する概念動画
01:20Second Order systems I
231
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
231
01:21First Order Systems
162
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
162
01:18Second Order systems II
169
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
169
01:26Classification of Systems-I
293
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
293
01:23Linear time-invariant Systems
398
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...
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...
398
01:26Linear 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....
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