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Finite time control for MIMO nonlinear system based on higher-order sliding mode.

Xiangjie Liu1, Yaozhen Han2

  • 1State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China.

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|October 4, 2014
PubMed
Summary

A new control algorithm ensures finite-time stability for uncertain nonlinear systems using higher-order sliding mode. This method effectively handles uncertainties and reduces chattering for robust system control.

Keywords:
Finite time stabilityHigher-order sliding modeMIMO nonlinearSuper-twisting algorithm

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Robotics

Background:

  • MIMO (Multiple-Input Multiple-Output) uncertain nonlinear systems present significant control challenges.
  • Existing control methods may struggle with uncertainties and chattering, impacting performance.
  • Finite-time stability is crucial for applications requiring rapid response and convergence.

Purpose of the Study:

  • To propose a novel finite-time stable control algorithm for MIMO uncertain nonlinear systems.
  • To leverage the higher-order sliding mode concept for enhanced control performance.
  • To address system uncertainties and mitigate the chattering phenomenon.

Main Methods:

  • The control problem is reformulated as a finite-time stability problem for a multivariable system.
  • A continuous control law is designed for nominal integral chain systems.
  • Second-order sliding mode is implemented to manage system uncertainties.
  • Quadratic form Lyapunov functions are used to prove finite-time stability.

Main Results:

  • The proposed algorithm guarantees finite-time stabilization for the nominal system.
  • System uncertainties are effectively overcome by the second-order sliding mode.
  • High-frequency chattering is significantly weakened, enabling arbitrarily fast convergence.
  • Simulations demonstrate effectiveness and robustness in complex systems.

Conclusions:

  • The developed higher-order sliding mode control algorithm provides robust finite-time stability for MIMO uncertain nonlinear systems.
  • The approach successfully mitigates chattering and achieves fast convergence, outperforming traditional methods.
  • Validated through simulations, the algorithm shows promise for practical applications like hovercraft trajectory tracking.