Hybrid Modelling and Simulation Approaches for a Class of Mechatronic Systems

Abstract

Starting from a generic model of a magnetically actuated mass spring damper with linear continuous dynamics and nonlinear input constraints, this paper proposes a hybrid approximating model, based on a partitioning of the evolution interval of the mass position variable. A piecewise-constant control law is deduced from the state space partition and the behaviours of the resulting hybrid control system and of the initial nonlinear constrained control are comparatively analysed within MATLAB simulation experiments. A Zeno path avoidance scheme, based on fixed-step discrete time conversion of the local differential equations is applied, and a second hybrid model of the generic mechatronic system is built. Simulation experiments show an adequate dynamic behaviour of this second hybrid model, compared to the hybrid model with continuous state equations.