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Distributed preview control for large-scale systems with time-varying delay.

Li Li1, Yaofeng Zhang1

  • 1School of Information Management and Statistics, Hubei University of Economics, Wuhan, 430205, China; Collaborative Innovation Center of China Pilot Reform Exploration and Assessment-Hubei Sub-Center, Hubei University of Economics, Wuhan, 430205, China.

ISA Transactions
|October 5, 2020
PubMed
Summary
This summary is machine-generated.

This study presents a distributed preview controller (DPC) for large-scale systems with time-varying delays and uncertainty. The proposed method ensures system stability and demonstrates effectiveness through examples.

Keywords:
AESDistributed preview control designLarge-scale systemsSSGState feedback

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Large-scale systems often face challenges with time-varying delays and uncertainties, complicating controller design.
  • Distributed preview control (DPC) is crucial for managing these complex systems effectively.

Purpose of the Study:

  • To design a robust distributed preview controller (DPC) for discrete-time large-scale systems.
  • To address challenges posed by time-varying delays and polytopic uncertainty.
  • To ensure the stability and performance of the controlled systems.

Main Methods:

  • Reformulation of time-varying delay systems into constant delay systems using model transformation.
  • Extension of the difference operator method to create an augmented error system (AES).
  • Application of state augmentation and scaled small-gain theorem (SSG) for stabilization and condition derivation.
  • Utilization of linear matrix inequality (LMI) techniques for DPC design.

Main Results:

  • Sufficient conditions for stability derived using the scaled small-gain theorem (SSG).
  • A novel distributed preview controller (DPC) designed using linear matrix inequality (LMI) techniques.
  • Validation of the controller's effectiveness through two illustrative examples for large-scale systems.

Conclusions:

  • The proposed DPC design effectively handles time-varying delays and polytopic uncertainty in discrete-time large-scale systems.
  • The methodology provides a robust framework for stabilizing complex systems.
  • The presented examples confirm the practical applicability and performance of the developed controller.