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Related Experiment Videos

Robust and nominal stability conditions for a simplified model predictive controller.

Jonathan R Webber1, Yash P Gupta

  • 1Department of Chemical Engineering, Dalhousie University, Halifax, Nova Scotia, Canada.

ISA Transactions
|February 17, 2006
PubMed
Summary
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A new robust stability condition ensures reliable control for linear systems using simplified model predictive control (SMPC). This method uses a bounding function to manage uncertainty in discrete control systems.

Area of Science:

  • Control Systems Engineering
  • Robust Control Theory
  • Linear System Analysis

Background:

  • Linear time-invariant (LTI) systems are fundamental in control engineering.
  • Model Predictive Control (MPC) offers advanced control strategies but can be sensitive to model uncertainty.
  • Simplified Model Predictive Control (SMPC) aims to reduce computational complexity while maintaining performance.

Purpose of the Study:

  • To derive a novel condition for guaranteeing robust stability in discrete SISO LTI plants under SMPC.
  • To address time-domain uncertainty by stabilizing sets of pulse response functions.
  • To develop a method applicable to stabilizing unrelated plant sets.

Main Methods:

  • Development of a bounding function dependent on model and controller parameters.

Related Experiment Videos

  • Ensuring the bounding function's magnitude exceeds all plant pulse response functions.
  • Analysis of the bounding function's behavior, particularly its monotonic decrease for first-order plus dead-time models.
  • Utilizing the coincidence point in SMPC as a robustness tuning parameter.

    • Main Results:

    • A new condition for robust stability of SMPC-controlled LTI plants is established.
    • The bounding function approach effectively handles time-domain uncertainty.
    • The monotonic decrease of the bounding function simplifies robustness analysis and tuning, especially for dead-time uncertainty.
    • A comparison between two nominal stability conditions is presented.

    Conclusions:

    • The derived condition provides a robust stability guarantee for SMPC of discrete LTI systems.
    • The bounding function method offers a practical approach to managing plant uncertainty.
    • The findings simplify robustness tuning and analysis in SMPC, particularly for systems with dead time.