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