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Related Concept Videos

State Space to Transfer Function01:21

State Space to Transfer Function

451
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:
451
Transfer Function to State Space01:23

Transfer Function to State Space

623
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 RLC...
623
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

291
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
291
Multimachine Stability01:25

Multimachine Stability

382
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:
382
State Space Representation01:27

State Space Representation

414
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...
414
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.5K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.5K

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Related Experiment Video

Updated: Dec 3, 2025

Rodent Brain Microinjection to Study Molecular Substrates of Motivated Behavior
10:05

Rodent Brain Microinjection to Study Molecular Substrates of Motivated Behavior

Published on: September 16, 2015

14.8K

Learning Fuzzy Automaton's Event Transition Matrix When Post-Event State Is Unknown.

Hao Ying, Feng Lin

    IEEE Transactions on Cybernetics
    |October 29, 2020
    PubMed
    Summary

    This study introduces new algorithms for fuzzy discrete event systems (FDESs) to learn system transitions when post-event states are unknown. This advances fuzzy automata modeling for event-driven systems.

    Related Experiment Videos

    Last Updated: Dec 3, 2025

    Rodent Brain Microinjection to Study Molecular Substrates of Motivated Behavior
    10:05

    Rodent Brain Microinjection to Study Molecular Substrates of Motivated Behavior

    Published on: September 16, 2015

    14.8K

    Area of Science:

    • Control Engineering
    • Artificial Intelligence
    • Fuzzy Logic Systems

    Background:

    • Fuzzy discrete event systems (FDESs) model event-driven systems using fuzzy automata.
    • Previous work focused on learning transition matrices with available post-event states.
    • This study addresses learning when only pre-event states are known.

    Purpose of the Study:

    • Develop algorithms for learning fuzzy automaton transition matrices when the post-event state is unavailable.
    • Extend FDESs methodology to scenarios with ambiguous post-event states.
    • Enable learning of transition matrices and fuzzy set parameters.

    Main Methods:

    • Developed stochastic-gradient-descent-based algorithms.
    • Assumed post-event states are described by fuzzy sets linked to available physical variables.
    • Focused on Gaussian-type fuzzy sets for parameter learning.

    Main Results:

    • Algorithms successfully learn the transition matrix and fuzzy set parameters.
    • Computer simulations validate the theoretical developments.
    • Demonstrated effective learning in FDESs with unobserved post-event states.

    Conclusions:

    • The developed algorithms effectively handle learning in FDESs with unobserved post-event states.
    • This research expands the applicability of fuzzy automata for modeling complex event-driven systems.
    • The findings contribute to advancements in supervised learning for fuzzy systems.