Analog cross coupled controller for oscillations: modeling and design via dominant system theory

TL;DR

This paper introduces a novel analog feedback controller for inducing oscillations in passive plants, using dominance theory and a graphical inverse circle criterion, with practical applications to RLC, RC, and motor models.

Contribution

It develops a new modeling and design framework for oscillation controllers based on dominance theory and inverse circle criterion, applied to simple circuit architectures.

Findings

Derived a graphical condition for certifying oscillations in Lur'e systems.

Specialized the conditions to minimal RLC and RC networks.

Validated the approach with an example involving a DC motor model.

Abstract

We propose a new analog feedback controller based on the classical cross coupled electronic oscillator. The goal is to drive a linear passive plant into oscillations. We model the circuit as Lur'e system and we derive a new graphical condition to certify oscillations (inverse circle criterion for dominance theory). These conditions are then specialized to minimal control architectures like RLC and RC networks, and are illustrated with an example based on a DC motor model.