Guaranteed State Estimation Using a Bundle of Interval Observers with Adaptive Gains Applied to the Induction Machine

Area of Science:

• Electrical Engineering
• Control Systems Theory
• Applied Mathematics

Background:

• Interval observers are vital for guaranteed state estimation in uncertain systems, especially safety-critical ones.
• Traditional interval observers can yield impractically large estimation intervals.
• Existing methods struggle with maintaining accuracy and practicality for time-varying dynamics.

Purpose of the Study:

• To design an interval observer bundle for guaranteed state estimation of uncertain induction machines with linear, time-varying dynamics.
• To improve the usability of interval observers by reducing interval widths for practical applications.
• To develop an adaptive observer gain for optimal state observation and minimal interval width.

Main Methods:

• Design of a reduced-order hybrid interval observer bundle.
• Reinitialization strategy for interval observers during runtime to decrease interval widths.
• Inclusion of unstable observer dynamics to leverage transient behavior while maintaining overall stability.
• Algorithm for determining the parametrization of reduced-order interval observers.
• Introduction of an adaptive observer gain for optimal state observation.

Main Results:

• Demonstrated improved guaranteed enclosure within intervals for magnetizing current estimates.
• Achieved decreasing interval widths through reinitialization strategies.
• Validated real-time capability and effectiveness of the proposed methods.
• Showcased optimal state observation with minimal interval width at variable operating points.

Conclusions:

• The interval observer bundle effectively enhances state estimation accuracy and practicality for uncertain induction machines.
• The adaptive observer gain and reinitialization techniques are key to achieving minimal interval widths and real-time performance.
• The proposed approach offers a robust solution for safety-critical systems requiring guaranteed state estimation.