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Related Concept Videos

Stability01:28

Stability

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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Linear Approximation in Time Domain01:21

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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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Pole and System Stability01:24

Pole and System Stability

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The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
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Second Order systems II01:18

Second Order systems II

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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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Control System Problem01:21

Control System Problem

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In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
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Stabilization of non-smooth variable order switched nonlinear systems.

Xiao Peng1, Yijing Wang1, Zhiqiang Zuo1

  • 1Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, PR China.

ISA Transactions
|October 23, 2020
PubMed
Summary

This study presents a novel switching strategy to achieve global asymptotic stabilization for complex nonlinear switched systems, even with unstable modes. The findings offer robust control methods for real-world applications.

Keywords:
Filippov differential inclusionNon-smooth functionUnstable modeVariable order switched system

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Switched Systems

Background:

  • Non-smooth variable order nonlinear switched systems present significant control challenges, particularly those with partial unstable modes.
  • Ensuring the existence and uniqueness of solutions is a prerequisite for developing effective stabilization strategies.

Purpose of the Study:

  • To develop and verify sufficient criteria for global asymptotic stabilization of non-smooth variable order nonlinear switched systems.
  • To address systems with both stable and unstable modes through a hybrid switching approach.

Main Methods:

  • Utilized Gronwall-Bellman inequality and inductive methods to prove the existence and uniqueness of solutions.
  • Implemented a hybrid switching strategy: slow switching for stable modes and fast switching for unstable modes.
  • Applied Filippov differential inclusion, mode-dependent average dwell time, and dwell time schemes to derive stabilization criteria.

Main Results:

  • Established sufficient conditions for global asymptotic stabilization.
  • Demonstrated the effectiveness of the proposed switching strategy.
  • Validated the theoretical results through numerical simulations.

Conclusions:

  • The developed hybrid switching strategy effectively stabilizes non-smooth variable order nonlinear switched systems with partial unstable modes.
  • The derived criteria provide a robust framework for designing controllers for such complex systems.
  • The study offers practical implications for real-world systems requiring advanced control techniques.