Self-tuning bistable parametric feedback oscillator: Near-optimal amplitude maximization without model information

Area of Science:

• Nonlinear dynamics
• Control theory
• Physics

Background:

• Parametrically excited oscillators can achieve large-amplitude oscillations for applications like signal amplification.
• Traditional methods face limitations like amplitude saturation, lack of robustness to model uncertainty, and limited sensitivity.

Purpose of the Study:

• To present a principle of self-tuning parametric feedback excitation to overcome limitations of traditional parametric excitation.
• To achieve robust large-amplitude oscillations with minimal control implementation.

Main Methods:

• A minimalistic control implementation combining self-tuning (slow parameter adaptation) and feedback pumping (fast parameter modulation).
• Experimental implementation without sophisticated signal processing or model-based control computation.

Main Results:

• The oscillator self-tunes near dynamic bifurcation, achieving extreme sensitivity to small resonant parametric perturbations.
• Large-amplitude oscillations are achieved by leveraging nonlinearity, despite model uncertainties and external perturbations.

Conclusions:

• The proposed self-tuning parametric feedback excitation offers an effective and robust approach for real-world applications.
• This method alleviates amplitude saturation and enhances robustness and sensitivity in parametric oscillators.