Dynamics and Control of Discrete Electromechanical Systems

Abstract

Dynamics and control of complex mechatronic systems can be investigated efficiently by using a suitable mathematical standard model. Based on such a mathematical standard model, well-known approaches to dynamics and control can be used in different application fields. Some of the most important mechatronic systems are electromechanical systems which can be regarded as physical structures characterized by interaction of electromagnetic fields with inertial bodies. The equations governing discrete electromechanical systems are obtained by combining Kirchhoff’s theory with the appropriate constitutive equations. The motion of an electromechanical system will be understood as the motion of its representing point in its configuration space. Based on the principle of virtual work, the equations of motion are Lagrange’s equations of the second kind (Maiser and Steigenberger, 1979). The analytical mechanics and its application to multibody dynamics can be regarded as a suitable starting point (Maiser, 1991). Lagrange’s equations of mixed type for constrained mechanical systems constitute a mathematical standard model which is often used in dynamics as well as in force and position control of robot manipulators (Arimoto et al. 1993). Often the so called disturbed equations of motion obtained by linearization of Lagrange’s equations near a nominal trajectory q(t) are used to design optimal controllers in mechatronics