1. Dynamics in Mechatronic Systems

Section 1.1 is devoted to the study of dynamical processes in electric circuits. It includes derivations of the constitutive relations of elements of electric circuits (capacitors, inductors) and describes current and voltage sources and Kirchhoff’s law. Section 1.2 deals with dynamical processes in mechatronic systems (transducers) and the electromagnetomechanical circuit. In Sect. 1.3, the dynamics and control of a mass levitating in magnetic and gravitational fields is discussed. Two cases of numerical control are considered and verified experimentally. In Sect. 1.4, combined analytical and numerical analyses of vibrations in string-type generators is carried out. The vibrations of a string are governed by a PDE, whereas the dynamics of an amplifier is governed by an ODE with a time delay. The voltage generated on the string ends depends on both electromagnetic induction and string vibration speed. An averaged set of equations is derived and numerically studied. Finally, in Sect.1.5, a 2-DOF nonlinear dynamics of a rotor supported by a magnetohydrodynamic bearing is investigated using perturbation analysis. Two modes corresponding to the vertical and horizontal vibrations of the rotor are coupled. The non-resonant case and the various resonant cases (with and without an internal resonance) are considered. Frequency-response curves are obtained. When the amplitude of the external harmonic excitation is near one of the natural frequencies of the vibrations and the system experiencing internal resonance, a saturation phenomenon occurs.