H₂-H∞ Composite Control for Singularly Perturbed Systems With Finite-Frequency Performances.

Area of Science:

• Control Theory
• Systems Engineering
• Electrical Engineering

Background:

• Singularly perturbed systems present challenges due to distinct slow and fast dynamics.
• Traditional control methods may not adequately address performance requirements across different frequency ranges.
• Finite-frequency (FF) control offers a way to tailor performance to specific frequency bands.

Purpose of the Study:

• To develop a finite-frequency (FF) H2-H-infinity composite control strategy for continuous singularly perturbed systems.
• To address performance requirements in both low-frequency (slow subsystem) and high-frequency (fast subsystem) ranges.
• To design a controller that integrates FF H2 and FF H-infinity control principles.

Main Methods:

• Utilizing FF H2 and FF H-infinity norms to specify performance for slow and fast subsystems, respectively.
• Employing the FF Gramian matrix method for analyzing FF H2 control of the slow subsystem.
• Applying the Generalized Kalman-Yakubovič-Popov (GYKP) Lemma for studying FF H-infinity control of the fast subsystem.
• Developing a composite controller by combining the designed controllers for the subsystems.

Main Results:

• A novel FF H2-H-infinity composite controller was successfully developed for continuous singularly perturbed systems.
• The proposed control scheme effectively imposes performance requirements on both slow and fast dynamics within specified frequency ranges.
• Simulation examples demonstrated the effectiveness and superiority of the developed control strategy compared to existing methods.

Conclusions:

• The finite-frequency H2-H-infinity composite control approach is effective for singularly perturbed systems.
• This method provides a robust framework for achieving desired performance in both low and high-frequency domains.
• The proposed control scheme offers superior performance, validated through simulation on a DC motor system.