Optimal damping stabilisation based on LQR synthesis

Abstract

Significant attention is currently being paid to the synthesis of stabilising controllers for nonlinear and non-autonomous plants. We aimed to present a new method for nonlinear time-dependent control law design based on the application of Zubov’s optimal damping concept. This theory is used to reduce significant computational costs in solving optimal stabilisation problems. The main contribution is the proposition of a new methodology for selecting the functional to be damped. The central idea is to perform parameterisation of a set of admissible items for the mentioned functional. As a particular case, a new method of this parameterisation has been developed, which can be used for constructing an approximate solution of the classical optimisation problem. The emphasis is on the specific choice of the functional to be damped using LQR control to provide the desirable stability and performance features of the closed-loop connection. The applicability and effectiveness of the proposed approach are confirmed using a practical numerical example of the convey-crane control.