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相关概念视频

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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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,...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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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....
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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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...
229
Classification of Systems-I01:26

Classification of Systems-I

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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:
177
Feedback control systems01:26

Feedback control systems

296
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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Second Order systems II01:18

Second Order systems II

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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.
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Updated: Jun 14, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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动态系统的数据驱动的线性化.

George Haller1, Bálint Kaszás1

  • 1Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092 Zurich, Switzerland.

Nonlinear dynamics
|September 2, 2024
PubMed
概括
此摘要是机器生成的。

动态模式分解 (DMD) 通过其适用性的新理由得到了改进. 数据驱动线性化 (DDL) 为分析动态系统提供了一种更强大的方法,其性能优于现有的技术.

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科学领域:

  • 动态系统理论 动态系统理论
  • 数据驱动建模数据驱动建模
  • 应用数学 应用数学 应用数学

背景情况:

  • 动态模式分解 (DMD) 和其变体广泛用于从数据中对动态系统进行线性建模.
  • 现有的DMD解释,特别是那些基于库普曼运算符的解释,具有局限性,并基于限制性假设.
  • 需要澄清DMD适用的条件,并开发更强大的方法.

研究的目的:

  • 为动态模式分解 (DMD) 提供严格的理由,作为主导系统动态的本地领先阶段模型.
  • 开发一个新的,更高阶的线性化算法,数据驱动线性化 (DDL),用于分析可观测的动态.
  • 与DMD和扩展DMD (EDMD) 相比,为了证明DDL的优越性能.

主要方法:

  • 开发了一个理论框架,根据一般可观测的概率为1的条件来证明DMD的合理性.
  • 在吸引缓慢光谱子多元体 (SSM) 中构建了主导动态的线性化转换.
  • 介绍了数据驱动线性化 (DDL) 算法,这是一个系统的,高阶线性化技术.

主要成果:

  • 已确定的条件,在这些条件下,DMD提供了系统动态的有效的本地领先顺序近似值.
  • 新的DDL算法系统地线性化了缓慢的SSM内可观察到的动态.
  • 在数值和实验数据集上,DDL表现优于DMD和EDMD.

结论:

  • 该研究为DMD提供了坚实的理论基础,并介绍了一种更先进的方法,DDL.
  • DDL为动态系统分析提供了更准确,更系统的线性化方法.
  • 这些发现促进了数据驱动方法的适用性和可靠性,以了解复杂的系统.