Path following control for a class of electro-mechanical systems and its application

This paper is devoted to path following control for electro-mechanical systems described by the port-Hamiltonian form. Path following control is investigated mainly for mechanical systems since the desired path is characterized by its 'position'. Therefore, most of the existing results use the nature of second order differential equations since mechanical systems are described by them. The present paper proposes a new path following controller for 3rd order differential equations described by the port-Hamiltonian form. This is done by generalizing the authors' former result on passive velocity field control for mechanical systems. 1 Introduction Path following control, whose objective is to make the state of the system track the desired path, is an important task for control of mechanical systems. This control task is investigated mainly for mechanical systems for which 'position' plays an important role since the desired path is characterized by its 'position.' Therefore, most of the existing results use the nature of second order differential equations since mechanical systems are described by them. The purpose of the present paper is to provide a new class of path following controllers for electro-mechanical systems which are described by 3rd (or higher) order differential equations. Most of the existing results for this problem use the distance between the current state (position) and its desired path. See, e.g., [1, 2]. However, it is difficult to measure the smallest distance between the current state and the desired path for complicated desired paths. Therefore several methods not using the distance are proposed to overcome this problem. See e.g. [3, 4, 5, 6] and the references therein. The authors proposed path following controllers in [7, 8] by generalizing the result in [6]. We re-formulated the existing results to cope with port-Hamiltonian systems and derive a path following control method applicable to a wider class of systems. Most of the existing path following control methods are only applicable to mechanical systems. The authors' former result in [7] solves the path following control problem by adopting a virtual potential function which takes its minimum value on the desired path. The vector field of the feedback system with respect to the generalized momentum is designed in such a way that the virtual potential function decreases smoothly. The generalized momentum is decomposed into two elements. One is the direction tangent to the desired path (i.e. it is perpendicular to the gradient of the potential function), and the other is …