Analogous Non-Smooth Models of Mechanical and Electrical Systems

Summary

The non-smooth modeling of mechanical and electrical systems allows for ideal unilateral contacts, sprag clutches and dry friction in mechanical systems and for ideal diodes and switches in electrical systems. The formulation of nonsmooth electrical models is demonstrated by the example of the DC-DC buck converter using the flux approach. The non-smooth electrical elements are described with set-valued branch relations in analogy with set-valued force laws in mechanics. With the set-valued branch relations, the dynamics of the circuit are described as measure differential inclusions. The measure differential inclusions obtained for the DC-DC buck converter are related to an analogous mechanical system. For the numerical solution, the measure differential inclusions are formulated as a measure complementarity system and discretised with a difference scheme, known in mechanics as time-stepping. For every time-step a linear complementarity problem is obtained.