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相关概念视频

State Space to Transfer Function01:21

State Space to Transfer Function

143
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
143
Transfer Function to State Space01:23

Transfer Function to State Space

158
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
158
State Space Representation01:27

State Space Representation

145
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
145
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

207
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
207
Definition of z-Transform01:26

Definition of z-Transform

227
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
227
Properties of the z-Transform II01:16

Properties of the z-Transform II

89
The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
89

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相关实验视频

Updated: May 9, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
00:10

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一种新的方法来计算状态过渡矩阵,因为无香转换.

Rahil Makadia1, Davide Farnocchia2, Steven R Chesley2

  • 1Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 104 S. Wright St., Urbana, IL 61801 USA.

Celestial mechanics and dynamical astronomy
|May 1, 2025
PubMed
概括

我们为非线性动态系统开发了一种新的无气质转换方法. 这种方法通过避免衍生和任意步骤来简化计算,与传统的性能相匹配.

关键词:
天体力学是一门天体力学.动态系统理论 动态系统理论进入飞行机械师的入境飞行机械师没有香味的转化转化.

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Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
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Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

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相关实验视频

Last Updated: May 9, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
00:10

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科学领域:

  • 动态系统和控制理论.
  • 天体动力学和太空飞行机械学
  • 计算数学 计算数学 计算数学

背景情况:

  • 状态过渡矩阵对于分析非线性动态系统至关重要.
  • 像有限差异这样的传统方法涉及复杂的导数或任意的步骤大小.
  • 在许多科学和工程应用中,准确地传播不确定性是必不可少的.

研究的目的:

  • 引入一种新的,简化的方法来计算非线性动态系统的状态过渡矩阵.
  • 消除了复杂的部分导数和任意扰动步骤的需要.
  • 在各种应用中评估拟议方法的性能和准确性.

主要方法:

  • 拟议的方法利用无味变换来计算状态过渡矩阵.
  • 它避免了雅可比矩阵和自动区分的明确计算.
  • 该方法在两体问题,火星大气入口和小行星近距离碰撞上进行了测试.

主要成果:

  • 没有香味的转换状态过渡矩阵被证明可以保持简单性.
  • 性能与经典的无气味转换方法相提并论.
  • 这种新方法准确地复制了蒙特卡洛模拟的后面分布,即使具有刚性动态.

结论:

  • 提出的无香转换方法为计算非线性系统中的状态过渡矩阵提供了一个强大的和简化的替代方案.
  • 它保持了准确性和理想的特性,如简易性.
  • 该方法在天体动力学,飞行力学和其他涉及复杂动力学的领域具有广泛的适用性.