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Related Concept Videos

State Space Representation01:27

State Space Representation

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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...
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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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Transfer Function to State Space01:23

Transfer Function to State Space

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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...
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Linear Approximation in Frequency Domain01:26

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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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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...
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Multimachine Stability01:25

Multimachine Stability

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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:
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    This study introduces a novel neural network-based recursive estimation strategy for networked control systems. It effectively handles unknown nonlinearities and bit errors from binary encoding mechanisms (BEMs) for reliable state estimation.

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    Area of Science:

    • Control Systems Engineering
    • Signal Processing
    • Machine Learning

    Background:

    • Networked control systems (NCS) face challenges with unknown nonlinearities and data transmission reliability.
    • Binary-encoding mechanisms (BEMs) are used to reduce data size but introduce potential bit errors during transmission over noisy channels.
    • Accurate state estimation is crucial for the stability and performance of NCS.

    Purpose of the Study:

    • To develop a robust recursive state estimation strategy for NCS with unknown nonlinearities and BEMs.
    • To address the impact of random bit errors in binary bit strings (BBSs) transmitted through noisy communication channels.
    • To approximate unknown nonlinearities using a neural network (NN) with adaptive tuning.

    Main Methods:

    • A neural network (NN)-based recursive estimation strategy is proposed.
    • An NN with a time-varying tuning scalar is employed to approximate unknown nonlinearities.
    • Upper bounds for system state estimation error and NN weight (NNW) estimation error trace are derived.
    • Estimator gain matrix and NNW tuning scalar are recursively designed to minimize derived error bounds.

    Main Results:

    • The proposed strategy effectively estimates the state of nonlinear NCS despite unknown nonlinearities and bit errors.
    • Upper bounds on estimation errors were successfully derived and minimized.
    • The recursive design of the estimator gain and NN tuning scalar improved estimation accuracy.

    Conclusions:

    • The developed NN-based recursive estimation strategy provides a viable solution for state estimation in challenging NCS environments.
    • The method demonstrates effectiveness in handling BEMs, unknown nonlinearities, and channel noise.
    • Numerical examples validate the performance and robustness of the proposed estimation strategy.