Divergence Method to Stability Study of Andronov-Vyshnegradsky Problem. Hidden Oscillations

TL;DR

This paper applies a divergence method to analyze the stability and hidden oscillations in the classical Andronov-Vyshnegradsky control problem with Watt regulators, identifying the hidden boundary of global stability.

Contribution

It introduces a divergence-based approach to precisely determine the hidden stability boundary and stability criteria for systems with Watt regulators, including effects of self-regulation.

Findings

Hidden oscillations occur with and without self-regulation.

Exact hidden boundary of global stability is obtained.

Stability conditions depend on three parameters of the Watt regulator.

Abstract

The classical Andronov-Vyshnegradsky problem, which deals with locating regions of stability and oscillations in control systems with a Watt regulator, is solved using a divergence method for studying the stability of dynamic systems. This system is studied both with and without the self-regulation effect. The exact value of the hidden boundary of the global stability region is obtained. The stability criteria for a system with a Watt regulator are also presented in the context of the solvability of a linear matrix inequality. Computer modelling shows that the system exhibits hidden oscillations when the self-regulation effect is present and when it is not. The conditions for computing the hidden boundary of global stability are determined by three parameters in the Watt regulator model.