Lyapunov-stable control of mechatronic systems

Abstract

In this paper, a method for controlling mechatronic systems using inverse dynamics is proposed. The starting point is a unified mathematical approach to modelling electromechanical systems based on Lagrange formalism. This mathematical theory is used to represent such systems taking into account all interactions between their substructures. The concept of Lagrange formalism for electromechanical systems is given and the complete governing equations are presented. The Voronetz equations of a partially kinematically controlled electromechanical system (EMS) are derived. The corresponding reaction forces and voltages following from the Voronetz equations are determined. Using these reactions with small modifications, a so-called ‘augmented proportional-derivative (PD) dynamic control law’ is generated. This controller consists of a non-linear feedforward - based on inverse dynamics - and a linear feedback. The stability of the controller is proved using a Lyapunov function. The controller can also be applied to pure multibody systems or a sheer electrical system, both of which are borderline cases of mechatronic systems.