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Decentralized stabilization of large-scale linear parameter varying systems.

Maryam Dehghani1

  • 1School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran.

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|March 19, 2024
PubMed
Summary

This study introduces a new decentralized controller design for large-scale systems (LSS) using Linear Parameter Varying (LPV) models. The method ensures system stability and performance improvement with limited information exchange, validated on a power system.

Keywords:
Decentralized controlLarge-Scale System (LSS)Linear Matrix Inequality (LMI)Linear Parameter Varying (LPV) system

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Systems Analysis
  • Large-Scale System Stabilization

Background:

  • Centralized controllers are impractical for large-scale systems (LSS) due to implementation challenges.
  • Decentralized controller design must ensure overall LSS stability with restricted information exchange.
  • Linear Parameter Varying (LPV) models represent complex nonlinear LSS.

Purpose of the Study:

  • To design a decentralized controller for nonlinear LSS modeled by LPV.
  • To ensure overall LSS stability while allowing only local information exchange.
  • To improve H∞ and H2 performance of LSS under disturbances.

Main Methods:

  • Controller design formulated as a convex feasibility problem solvable via Linear Matrix Inequalities (LMIs).
  • Lyapunov function of the LSS is the sum of individual subsystem Lyapunov functions.
  • Stability conditions derived based on the sum of Lyapunov functions.

Main Results:

  • A fully decentralized controller is designed, forbidding inter-controller communication.
  • Only data transfer between controllers and their subsystems is permitted.
  • The approach is successfully applied to a large-scale power system, demonstrating controller efficacy.

Conclusions:

  • The proposed LMI-based approach effectively designs decentralized controllers for LPV systems.
  • The method guarantees stability and enhances performance (H∞, H2) in large-scale systems.
  • Simulation results on a power system confirm the practical applicability and appropriateness of the designed local controllers.