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Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

I Salgado1, S Kamal2, B Bandyopadhyay3

  • 1Centro de Innovación y Desarrollo Tecnológico en Cómputo (CIDETEC), Instituto Politécnico Nacional, Mexico City, Mexico.

ISA Transactions
|August 2, 2016
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Summary
This summary is machine-generated.

Researchers developed a discrete time super-twisting-like algorithm (DSTA) for control and state estimation, overcoming limitations in discrete-time sliding mode theory. The DSTA ensures system stability and bounded trajectories, validated through simulations and applications.

Keywords:
Discrete-time super twisting algorithmElectro-mechanical systemsSliding mode controlSliding mode differentiator

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Control Theory
  • Discrete-Time Systems

Background:

  • Sliding mode theory primarily focuses on continuous-time systems for control and estimation.
  • High-order sliding mode algorithms are less developed in the discrete-time domain.
  • Existing discrete-time methods often lack robust stability guarantees.

Purpose of the Study:

  • To propose a novel discrete-time super-twisting-like algorithm (DSTA).
  • To address control and state estimation challenges in discrete-time systems.
  • To provide rigorous stability analysis for the proposed algorithm.

Main Methods:

  • Development of a discrete-time super-twisting-like algorithm (DSTA).
  • Stability analysis using discrete-time Lyapunov methods.
  • Verification through linear matrix inequalities (LMIs).
  • Simulation-based testing on benchmark systems.

Main Results:

  • The DSTA ensures ultimate boundedness of system trajectories within a sampling-period-dependent region.
  • Stability of the proposed algorithm is proven using discrete-time Lyapunov theory and LMIs.
  • Successful application as a controller for a Furuta pendulum.
  • Effective use in a DC motor control scenario with a DSTA differentiator.

Conclusions:

  • The DSTA offers a viable solution for discrete-time control and state estimation problems.
  • The algorithm demonstrates robust stability and performance in practical applications.
  • This work advances the field of high-order sliding modes in discrete-time systems.