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相关概念视频

State Space Representation01:27

State Space Representation

157
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...
157
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

59
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,...
59
Transfer Function to State Space01:23

Transfer Function to State Space

181
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...
181
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

81
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....
81
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

37
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
37
Multimachine Stability01:25

Multimachine Stability

127
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
127

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    科学领域:

    • 控制系统工程 控制系统工程
    • 信号处理 信号处理
    • 机器学习 机器学习

    背景情况:

    • 网络控制系统 (NCS) 面临着未知的非线性和数据传输可靠性的挑战.
    • 二进制编码机制 (BEM) 用于减少数据大小,但在噪音频道的传输过程中引入潜在的比特错误.
    • 准确的状态估计对于NCS的稳定性和性能至关重要.

    研究的目的:

    • 为未知非线性和BEMs的NCS开发一个强大的递归状态估计策略.
    • 为了解决通过杂的通信通道传输的二进制位字符串 (BBS) 中随机位错误的影响.
    • 为了近似未知的非线性,使用具有自适应调的神经网络 (NN).

    主要方法:

    • 提出了一个基于神经网络 (NN) 的递归估计策略.
    • 具有时间变化的调标的NN用于近似未知非线性.
    • 系统状态估计错误和NN重量 (NNW) 估计错误痕迹的上限得到推导.
    • 估计器增益矩阵和NNW调标量是递归设计的,以最大限度地减少衍生的误差界限.

    主要成果:

    • 拟议的战略有效地估计了非线性NCS的状态,尽管存在未知的非线性和位错误.
    • 估计错误的上限已成功推导出并将其最小化.
    • 估计器增益和NN调标的递归设计提高了估计准确度.

    结论:

    • 开发的基于NN的递归估计策略为在具有挑战性的NCS环境中进行状态估计提供了可行的解决方案.
    • 该方法在处理BEM,未知的非线性和通道噪声方面表现出有效性.
    • 数字示例验证了拟议的估计策略的性能和稳定性.