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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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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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Event-triggered observer-based H∞ sliding mode control of nonlinear systems.

Zhengtian Wu1, Baoping Jiang1, Mingyang Xie2

  • 1School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, China.

ISA Transactions
|October 13, 2020
PubMed
Summary

This study introduces a novel sliding mode control strategy for nonlinear systems using fuzzy models. The method ensures finite-time stability despite unavailable states and communication delays, verified by H-infinity performance analysis.

Keywords:
Event-triggered mechanismNonlinear systemsObserver designSliding mode controlT–S fuzzy systems

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Area of Science:

  • Control Systems Engineering
  • Fuzzy Logic Systems
  • Nonlinear System Analysis

Background:

  • Takagi-Sugeno fuzzy models are widely used for nonlinear systems.
  • State observers are crucial for systems with unmeasured states.
  • Event-triggering mechanisms and signal delays pose significant control challenges.

Purpose of the Study:

  • To develop a sliding mode control (SMC) strategy for nonlinear one-sided Lipschitz systems based on Takagi-Sugeno fuzzy models.
  • To address challenges of unavailable states and signal delays in control design.
  • To guarantee finite-time reachability and stability with H-infinity performance.

Main Methods:

  • Design of a state observer utilizing an event-triggering mechanism.
  • Proposal of an integral sliding surface based on estimated states.
  • Application of the equivalent control principle to derive sliding mode dynamics.
  • Construction of a sliding mode controller ensuring finite-time convergence.
  • Stability analysis using Lyapunov functions and H-infinity performance criteria, formulated via Linear Matrix Inequalities (LMIs).

Main Results:

  • Finite-time reachability of the predefined sliding surface is guaranteed.
  • The stability of the sliding mode dynamics is confirmed with H-infinity performance.
  • LMIs are established for controller synthesis and performance verification.
  • Numerical examples demonstrate the efficacy of the proposed control method.

Conclusions:

  • The proposed event-triggered sliding mode control strategy effectively handles nonlinear Takagi-Sugeno fuzzy systems with state estimation and communication delays.
  • The method ensures finite-time stability and H-infinity performance, validated through theoretical analysis and simulations.