nonlinear systems

Abstract. Goal of the work is to apply periodic Ateb-functions to investigate dynamic processes of strongly nonlinear systems with a finite number of degrees of freedom. Significance. Practically all problems in mechanics and engineering related to system oscillations, when strictly formulated, are nonlinear, as they are mathematically described by nonlinear differential equations. This often poses significant challenges in studying their behaviour, as finding a solution in exact form can be difficult.

Among the promising non-classical control systems electromechanical systems, it can be distinguished the system of energy-based control, where the object is taken as port-controlled Hamiltonian system. The energy shaping control essence consists in forming the shape of energy based on formed task. The article raises the problem of the synthesis of energy-based control systems with nonlinearities. As example, it was selected DC motor with two-zones speed control and model, that takes into account the nonlinearity of the magnetization curve and variable time constant of the field loop.

Main energy-based methods for synthesis of control systems of port-controlled Hamiltonian systems were considered, in particular: passivity-based control, energy-balance approach, interconnection and damping assignment and their combination with elements from linear and nonlinear control system theory. There are shown examples of using such methods for nonlinear object — permanent magnet synchronous machine. Result of their computer research and detail analyzes are presented as well.