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Updated: Sep 12, 2025

Experimental Methods to Study Human Postural Control
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Published on: September 11, 2019

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确定刺激-响应数据的控制方程,用于运行和动力学

Shicong Lei1,2, Yu'an Li2,3,4, Zheng Ma1,2

  • 1School of Mathematics, Shanghai Jiao Tong University, Shanghai, China.

PLoS computational biology
|August 5, 2025
PubMed
概括

这项研究引入了一个神经网络模型,揭示了控制微生物跑动运动的数学规则. 该模型成功地预测了细胞行为,并揭示了隐藏的生化途径,进步了我们对微生物导航的理解.

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Second Order systems II01:18

Second Order systems II

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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Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
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Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
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Linear Approximation in Time Domain

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.
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